U.S. patent number RE34,663 [Application Number 07/319,340] was granted by the patent office on 1994-07-19 for non-invasive determination of mechanical characteristics in the body.
Invention is credited to Joseph B. Seale.
United States Patent |
RE34,663 |
Seale |
July 19, 1994 |
Non-invasive determination of mechanical characteristics in the
body
Abstract
A non-invasive system and method for inducing vibrations in a
selected element of the human body and detecting the nature of
responses for determining mechanical characteristics of the element
are provided. The method comprises the steps of: inducing
multiple-frequency vibrations, including below 20 KHz, in a
selected element of the body by use of a driver; determining
parameters of the vibration exerted on the body by the driver;
sensing variations of a dimension of the element of the body over
time, including in response to the driver; correlating the
variations with frequency components of operation of the driver
below 20 KHz to determine corresponding frequency components of the
variations; resolving the frequency components into components of
vibration mode shape; and determining the mechanical
characteristics of the element on the basis of the parameters of
vibration exerted by the driver and of the components of vibration
mode shape.
Inventors: |
Seale; Joseph B. (Buzzards Bay,
MA) |
Family
ID: |
24822789 |
Appl.
No.: |
07/319,340 |
Filed: |
March 3, 1989 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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Reissue of: |
702833 |
Feb 19, 1985 |
04646754 |
Mar 3, 1987 |
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Current U.S.
Class: |
600/587; 600/402;
600/490; 702/56 |
Current CPC
Class: |
A61B
3/16 (20130101); A61B 5/02133 (20130101); A61B
5/02216 (20130101); A61B 5/02233 (20130101); A61B
5/205 (20130101); A61B 8/04 (20130101) |
Current International
Class: |
A61B
3/16 (20060101); A61B 5/03 (20060101); A61B
5/022 (20060101); A61B 8/04 (20060101); A61B
005/10 () |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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0001127 |
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Sep 1978 |
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EP |
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0721678 |
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Mar 1980 |
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SU |
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Other References
Thompson, G. A. et al., "In Vivo Determination of Mechanical
Properties of the Human Ulna", MBE, vol. 14, No. 3, pp. 253-262,
May 1976. .
Devine, IBM Technical Disclosure Bulletin, vol. 20 No. 8 1978 pp.
3330-3331. .
Lang, Acta Gerontologic..
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Primary Examiner: Jaworski; Francis
Attorney, Agent or Firm: Fish & Richardson
Claims
I claim:
1. An non-invasive system for inducing vibrations in a selected
element of the human body and detecting the nature of responses for
determining mechanical characteristics of said element,
said system comprising:
a drive means for inducing multiple-frequency vibrations, including
below 20 KHz, in .[.a.]. .Iadd.the .Iaddend.selected element of the
body,
means for determining parameters of the vibration exerted on the
body by the driver means,
.Iadd.means for determining the frequency components of mechanical
impedance of the body based on said parameters of vibration exerted
by said driver means, .Iaddend.
means for sensing variations of a dimension of said element of the
body over time, including in response to said driver means,
means for correlating said variations with frequency components of
.[.operation.]. .Iadd.at least one .Iaddend.of .Iadd.said
parameters of vibration exerted by .Iaddend.said driver means below
20 KHz, in order to determine corresponding frequency components of
said variations.
means for resolving said frequency components .Iadd.of said
variations .Iaddend.into components of vibration mode shape,
and
computer means for interpreting said parameters of vibration
exerted by the driver means.Iadd., said frequency components of
mechanical impedance, .Iaddend.and said components of vibration
mode shape in a manner to determine said mechanical
characteristics.
2. The system of claim 1 wherein said parameters of vibration
exerted by the driver means include force.
3. The system of claim 1 wherein said parameters of vibration
exerted by the driver means include velocity.
4. The system of claim 1 wherein one said mechanical characteristic
determined is pressure.
5. The system of claim 1 wherein said system further comprises
means for detecting change in said components of vibration mode
shape due to pressure change of said element, said change being
included by said computer indetermination of said mechanical
characteristics of said element.
6. The system of claim 1 wherein said driver means is adapted to
induce a vibration frequency that changes over time.
7. The system of claim 1 wherein said driver means is adapted to
induce multiple vibration frequencies simultaneously.
8. The system of claim 1, 4 or 5 wherein said body element includes
a wall, and further comprising:
means for resolving said components of vibration mode shape for at
least two modes, and
means for comparing said determined mechanical characteristics of
said elements respectively determined on the basis of said
components of vibration mode shape for at least two modes in a
manner to provide an indication of element wall stiffness.
9. The system of claim 1, 4 or 5 wherein said means for sensing
variations of a dimension of said element of the body comprises
means for emitting and receiving ultrasound signals.
10. The system of claim 4 or 5 wherein a said mechanical
characteristic determined is systemic arterial blood pressure and
said body element is a segment of the arterial system.
11. The system of claim 1 or 5 wherein a said mechanical
characteristic determined is the mechanical impedance of a body
element and said body element is an entire organ.
12. The system of claim 4 or 5 wherein a said mechanical
characteristic determined is intraocular pressure and said body
element is an eyeball.
13. The system of claim 12 wherein said means for sensing
variations of a dimension of said eyeball comprises a time-varying
display adjustable for creating visual impressions representative
of the response of the eyeball to the vibrational forces exerted by
the driver means.
14. The system of claim 4 or 5 wherein a said mechanical
characteristic determined is pulmonary blood pressure and said body
element is a segment of the pulmonary arterial system.
15. The system of claim 1 comprising a further means for sensing a
dimension of said element, said sensed dimension being included by
said computer means in determination of said mechanical
characteristics of said element.
16. The system of claim 15 wherein said means for sensing a
dimension of said element comprises optical measuring
equipment.
17. The system of claim 4 or 5 further comprising means for
applying a known pressure to said element in a manner to permit
calibration of the system.
18. The system of claim 17 wherein the pressure application means
is a pressure cuff.
19. The system of claim 1 wherein said means for sensing variations
of a dimension is further adapted for sensing a dimension of said
element, said sensed dimension being included by said computer
means in determination of said mechanical characteristics of said
element.
20. The system of claim 19 wherein said means for sensing a
dimension of said element comprises equipment for emitting and
receiving ultrasound signals.
21. A method for inducing vibrations in a selected element of the
human body and detecting the nature of responses for determining
mechanical characteristics of said element non-invasively,
said method comprising the steps of:
inducing multiple-frequency vibrations, including below 20 KHz, in
.[.a.]. .Iadd.the .Iaddend.selected element of the body by use of a
driver means,
determining parameters of the vibration exerted on the body by the
driver means,
.Iadd.determining freuqency components of mechanical impedance of
the body based on said parameters of vibration exerted by said
driver means, .Iaddend.
sensing variations of a dimension of said element of the body over
time, including in response to said driver means,
correlating said variations with frequency components of
.[.operation.]. .Iadd.at least one .Iaddend.of .Iadd.said
parameters of vibration exerted by .Iaddend.said driver means below
20 KHz to determine corresponding frequency components of said
variations,
resolving said frequency components .Iadd.of said variations
.Iaddend.into components of vibration mode shape, and
interpreting said parameters of vibration exerted by the driver
means.Iadd., said frequency components of mechanical impedance,
.Iaddend.and said components of vibration mode shape in a manner to
determine said mechanical characteristics of said element.
22. The method of claim 21 wherein said determination of parameters
of vibration exerted by the driver means includes determining
force.
23. The method of claim 21 wherein said determination of parameters
of vibration exerted by the driver means includes determining
velocity.
24. The method of claim 21 wherein a mechanical characteristic
determined is pressure.
25. The method of claim 21 further comprising the step of detecting
change in components of vibration mode shape due to pressure change
of said element, said change being included in determination of
said mechanical characteristics of said element.
26. The method of claim 21 wherein said multiple-frequency
vibrations are generated by changing the operation frequency of the
driver means over time.
27. The method of claim 21 wherein said multiple-frequency
vibrations are generated by operation of the driver means at
multiple frequencies simultaneously.
28. The method of claim 21, 24 or 25 wherein said body element
includes a wall, and further comprising the steps of:
resolving said components of vibration mode shape for at least two
modes, and
comparing said determined mechanical characteristics of said
elements respectively determined on the basis of said components of
vibration mode shape for at least two modes in a manner to provide
an indication of element wall stiffness.
29. The method of claim 21, 24 or 25 comprising sensing said
variations of a dimension of said element of the body by means of
ultrasound echo signals.
30. The method of claim 24 or 25 wherein a said mechanical
characteristic determined is systemic arterial blood pressure and
said body element is a segment of the arterial system.
31. The method of claim 21 or 25 wherein a said mechanical
characteristic determined is the mechanical impedance of a body
element and said body element is an entire organ.
32. The method of claim 24 or 25 wherein a said mechanical
characteristic determined is intraocular pressure and said body
element is an eyeball.
33. The method of claim 32 wherein said step of sensing variations
of dimension comprises sensing variations of a dimension of said
eyeball, and said method further comprises incorporating user
feedback in response to visual impressions of a time-varying
display, said visual impressions being representative of the
response of the eyeball induced by the driver means.
34. The method of claim 24 or 25 wherein a said mechanical
characteristic determined is pulmonary blood pressure and said body
element is a segment of the pulmonary arterial system.
35. The method of claim 21, in addition to the step of sensing
variations of a dimension of said element, said method further
comprises sensing a dimension of said element, said sensed
dimension being included in determination of said mechanical
characteristics of said element.
36. The method of claim 35 wherein said dimension of said element
is sensed by interpreting ultrasound echo signals.
37. The method of claim 35 wherein said dimension of said element
is sensed optically.
38. The method of claim 24 or 25 further comprising applying a
known pressure to said element in a manner to permit
calibration.
39. The method of claim 38 further comprising applying said known
pressure by means of a pressure cuff. .Iadd.
40. A non-invasive system for inducing vibrations in a selected
element of the human body and detecting the nature of responses for
determining mechanical characteristics of said element,
said system comprising:
a driver means for inducing multiple-frequency vibrations,
including below 20 KHz, in the selected element of the body,
means for determining parameters of the vibration exerted on the
body by the driver means,
means for determining frequency components of mechanical impedance
of the body based on said parameters of vibration exerted by said
driver means,
means for determining a dimension of the selected element of the
body, and
computer means for interpreting said frequency components of
mechanical impedance and said determined dimension in a manner to
determine said mechanical characteristics. .Iaddend. .Iadd.
41. A method for inducing vibrations in a selected element of the
human body and detecting the nature of responses for determining
mechanical characteristics of said element non-invasively,
said method comprising the steps of:
inducing multiple-frequency vibrations, including below 20 KHz, in
the selected element of the body by use of a driver means,
determining parameters of the vibration exerted on the body by the
driver means,
determining frequency components of mechanical impedance of the
body based on said parameters of vibration exerted by said driver
means,
determining a dimension of the selected element of the body,
and
interpreting said frequency components of mechanical impedance and
said determined dimension in a manner to determine said mechanical
characteristics of said element. .Iaddend. .Iadd.
42. In a non-invasive system for determining characteristics of an
entire organ in a human body using an ultrasound beam,
apparatus for aligning said beam with respect to said entire organ
in two axes, comprising
means for generating at least one magnetic field in response to a
control signal,
an assembly adapted to rotate about said two axes in response to
said at least one magnetic field, said assembly comprising an
ultrasound component for steering said beam with respect to said
two axes as said assembly rotates, and
means for producing said control signal as a function of the
relative alignment of said beam with said entire organ to cause
said beam to be steered with respect to said two axes and into
alignment with said entire organ. .Iaddend. .Iadd.
43. The system of claim 42 wherein said assembly further comprises
a permanent magnet. .Iaddend. .Iadd.44. The system of claim 43
wherein said means for generating said at least one magnetic field
comprises circuitry for generating a pair of magnetic fields to
cause said permanent magnet to rotate independently with respect to
each of said two axes. .Iaddend. .Iadd.45. The system of claim 42
wherein said ultrasound component
includes an electroacoustic ultrasound transducer. .Iaddend.
.Iadd.46. The system of claim 42 wherein said apparatus for
aligning further comprises means for coupling said ultrasound beam
between said ultrasound
component and said entire organ. .Iaddend. .Iadd.47. The system of
claim 42 wherein said control signal is produced as a function of a
measure of rotational response of said assembly in response to said
at least one magnetic field. .Iaddend. .Iadd.48. The system of
claim 47 wherein said rotational response is based at least in part
on a model of response characteristics of said assembly to said at
least one magnetic field. .Iaddend. .Iadd.49. The system of claim
48 wherein said model of response characteristics operates based on
said control signal and does not require direct measurement of the
rotational response of said assembly. .Iaddend. .Iadd.50. The
system of claim 47 wherein said measure of rotational response is
based on echo signals of said ultrasound beam. .Iaddend. .Iadd.51.
The system of claim 42 wherein said control signal is
servo-controlled based on echo signals of said ultrasound beam.
.Iaddend. .Iadd.52. The system of claim 42 further comprising means
for varying said alignment to scan said ultrasound beam over an
angular sector. .Iaddend.
.Iadd.53. The systtem of claim 52 wherein said angular sector is
two-dimensional and said beam has a predetermined depth range,
whereby said scanning permits features in a volume of said entire
organ to be
mapped. .Iaddend. .Iadd.54. The system of claim 1 wherein said body
element is an entire organ and said means for emitting and
receiving ultrasound signals includes apparatus for aligning said
beam with said entire organ. .Iaddend.
Description
BACKGROUND OF THE INVENTION
This invention relates to non-invasive, small-perturbation
measurements of macroscopic mechanical properties of organs and
blood vessels to evaluate tissue pathology and body function.
Pathological changes in tissues are often correlated with changes
in the mechanical properties of density, elasticity and damping.
While microscopic mechanical changes have sometimes been correlated
with ultrasound wavelengths and frequencies, many important
mechanical changes are manifested most clearly on a large scale at
low frequencies down to zero. For these, manual palpation remains
almost the sole diagnostic tool. A great deal of effort has been
expended in the area of blood pressure measurement, but not by
analyzing small-perturbation mechanical properties of the
pressurized vessel.
Arterial blood pressure measurement methods are commonly either
invasive (catheterization or cannulation) or else disruptive
mechanical perturbations, typically causing temporary occlusion of
blood flow, e.g. by a sphygmomanometer cuff. Pulmonary arterial
pressure is so inaccessible that it is seldom measured. The trauma
of entering any artery is an obvious disadvantage. Most occlusive
methods are only capable of sampling the systolic and diastolic
extremes of the blood pressure waveform. Occlusive methods cannot
be used for extended monitoring because of the interruption of
circulation.
Recent less occlusive pressure monitoring methods include those
described by Aaslid and Brubkak, Circulation, Vol. 4, No. 4
(ultrasound doppler monitors brachial artery flow while a servoed
cuff maintains fixed, reduced flow) and Yamakoshi et al, "Indirect
Measurement of Instantaneous Arterial Blood Pressure in the Human
Finger by the Vascular Unloading Technique", IEEE Trans. on
Biomedical Eng., Vol. BME-27, No. 3, March 1980 (a similar system
optically monitors capillary blood volume in the finger while a
servoed cuff maintains a constant optical reading).
Non-invasive blood pressure monitoring approaches suggested in
prior art are described by Jeff Raines, Diagnosis and Analysis of
Arteriosclerosis in the Lower Limbs, Ph.D. Thesis, M.I.T., Sept.
1972 (using a low-pressure cuff surrounding a limb to monitor the
changing cross-section as enclosed arteries pulsate in diameter)
and by D. K. Shelton and R. M. Olson, "A Nondestructive Technique
To Measure Pulmonary Artery Diameter And Its Pulsatile Variations",
J. Appl. Physiol., Vol. 33, No. 4, Oct. 1972 (using an ultrasound
transducer in the esophagus to track canine pulmonary artery
diameter). The latter investigators reported approximate short-term
pressure/diameter correlation, while Itzchak et al, "Relationship
of Pressure and Flow to Arterial Diameter", Investigative
Radiology, May-June, 1982, using ultrasound to track canine
arterial diameter, found no useful longterm pressure/diameter
correlation.
In other areas of the human body, Kahn, U.S. Pat. No. 3,598,111,
describes a mechanically and acoustically tuned pneumatic system,
useful at a single frequency, for measuring the impedance of the
air passages and tissues of human lungs to obtain a two-component
trace (representing resistive and reactive impedance) as a function
of time.
SUMMARY OF THE INVENTION
The system uses a driver to induce vibrations below 20 KHz into
underlying body structures, including organs, fluid-filled organs
and segments of blood vessels. The driver includes apparatus for
determining parameters of the vibrational excitation applied to the
patient, e.g. applied forces or velocities, usually both. Means are
provided for sensing structure vibrational motions, e.g.
ultrasound, or visual impressions of a stroboscopic display for an
ocular approach. Structure dimensions may also be sensed. A
computer-controller includes signal-processing equipment and signal
interfaces with the sensors. The system obtains sufficient response
data related to differing frequencies and, in some cases, to
differing pressures, to infer data about the mechanical impedance
of the body structure in its local surroundings, and utilizing that
impedance data, to infer mechanical parameters of the structure.
These parameters may include such intensive tissue or fluid
parameters as density, shear modulus, rate of decay of shear
modulus due to creep, shear viscosity, and internal pressure; and
may also include such extensive or whole-structure parameters as
effective vibrating mass or the stiffness of an artery wall.
The computer-controller includes algorithms to infer physical
parameters of the structure from the performance and data of the
driver and sensing apparatus. These algorithms include at least one
of the following:
(1) Network Algorithm, derived from linear network theorems,
particularly the Theorem of Reciprocity, which proves there is a
useful symmetry for vibration transfer from driver to structure and
structure to driver. This algorithm can be applied where
time-variation in internal pressure generates at least two
distinguishable vibration response patterns at a single
frequency.
(2) Simulation Algorithm, including a mathematical simulation model
of a structure and its surrounding environment, and sometimes also
of the coupling between the driver/sensor assembly and the
structure. Parameters of the model are adjusted to optimize the fit
between simulated and measured responses. The spectrum of data used
for a simultation algorithm is derived at least in part from
differing frequencies of driver excitation.
(3) Analytic Function Fit Algorithm, an abstracted simulation
approach ignoring structural detail, uses frequency variation data
to deduce mass per-unit-length and pressure in a cylindrical
vessel, or total mass and the product of pressure times radius in a
spherical organ.
Where a network algorithm can be applied, simulation is simplified.
Network analysis provides an accurate model for the transfer of
vibration energy between driver and structure, substantially
independent of the detailed structure of the organ, the driver and
intervening tissues. The network analysis reveals the mechanical
vibrational impedance of the structure in its local surroundings.
Impedance determinations at several frequencies are then
incorporated into a simulation analysis without need to model the
complicated coupling between the driver and structure. Network
results are frequently applied to the analytic function fit
algorithm, avoiding the more difficult generalized simulation
algorithm.
Where vessel wall stiffness mimics internal pressure, analysis of
two different vibration modes distinguishes the separate effects of
stiffness and fluid pressure.
Four embodiments of the system illustrate combinations of
measurements that determine the mechanical impedance of an organ or
vessel in its local surroundings, permitting determinations of
pressure and/or tissue properties. Simplified systems taking fewer
measurements sometimes yield useful data, while added measurement
capabilities often yield better data.
In one aspect of the invention for measuring systemic arterial
blood pressure, an elongated vibration driver is disposed in
contact with the skin, the long axis parallel to the artery. The
vibrational velocity of the driver surface is measured, as is the
applied vibrational force over a central segment of the driver. A
pulsed ultrasound system measures the time-varying depths of the
near and far walls of the artery segment under test, along three
cross-arterial axes in the same plane. Circuits correlate
ultrasound depth variations with the audio driver vibration
signals, to determine the amplitudes and phases of vibrational
velocities associated with the three changing diameters and
center-depths. These multi-axis vibration correlations are resolved
into components of vibration mode shapes. Blood pressure variation
over time alters the response phases and amplitudes of these modes.
These vibration response alterations in turn affect the surface
vibration force and velocity measurements. This
blood-pressure-induced change data enables the computer, via a
network algorithm, to deduce arterial impedance for one or more
mode shapes. The network algorithm is applied repeatedly at
different frequencies, to determine the frequency-dependence of an
arterial mode impedance at a single pressure. The impedance versus
frequency data enter the analytic function fit algorithm, which
infers absolute pressure. For an individual patient, the system
establishes a table of pressures and vibration parameters, all
expressed as functions of arterial radius. For rapid computation of
a pressure waveform point, the system interpolates from the table
the reference pressure and vibration parameters for the
currently-measured radius. The difference between tabulated and
current vibration parameters reveal, via the network algorithm, the
difference between tabulated pressure and actual current pressure.
In this way, a graph of pressure is plotted as a function of
time.
If the artery can be excited at close range, it is possible to
resolve both two- and three-lobed arterial vibration mode
amplitudes and phases from the ultrasound data. The dual-mode data
are analyzed to yield two pressure values, one for the two-lobe
mode and one for the three-lobe mode. The three-lobe pressure is
more sensitive than the two-lobe pressure to wall stiffness
artifacts. The difference between the two computed pressures is
therefore used to discern true fluid pressure and a wall stiffness
parameter.
In another aspect, the invention is configured primarily to
determine the impedance of whole vibrating organs. (In the
artery-pressure aspect just described, only a segment of a
cylindrical vessel was excited. Analysis was based on force at the
driver center and a substantially two-dimensional cross-sectional
response.) According to this aspect, the driver induces vibrations
while its velocity and total applied force are inferred from driver
electrical responses. An ultrasound system whose beam is aimed in
two dimensions measures vibrational velocities of the near and far
walls of an organ. For fluid-filled organs, e.g. a urinary bladder,
the system determines internal pressure. The system also discerns
pressure gradients in organ tissues, e.g. from edema. If pressure
changes significantly over time, e.g. from urine accumulation or
changing tonus of the muscular wall of the bladder, the system uses
a network algorithm to compute an especially accurate organ
vibrational impedance, leading to a correspondingly accurate
internal pressure.
In the absence of pressure-change data, the system infers organ
vibrational impedance through detailed simulations. Parameters of
the simulated structure are adjusted until mathematical performance
substantially matches actual measured data at several frequencies.
Adjusted simulation parameters indicate corresponding properties of
the underlying organ. Where internal pressure is present, it can be
inferred from simulation results. For organs that are not hollow,
some simulation parameters correspond to average intensive tissue
parameters of the organ: density, shear modulus, viscosity, and
sometimes even frequency-variations of modulus and viscosity. Where
changes of clinical interest affect these tissue parameters, this
aspect has applications as a diagnostic tool, e.g. in instances of
cirrhosis of the liver or cystic kidney disease.
Still another aspect of the invention, useful for measuring
intraocular pressure, is similar to the last-described aspect of
the invention, except that visual impressions and user feedback
replace ultrasound as a means of sensing vibrational motions in the
eye. In one preferred embodiment, vibrations are induced from the
driver through the lower eyelid, avoiding uncomfortable direct
contact with the eye surface. Eyelid surface forces and velocities
are inferred from driver electrical responses over a wide frequency
range. Resonance of the eyeball is measured by a combination of
eyelid surface responses and user feedback. The user watches a
time-varying display, e.g. on which a horizontal line on a black
background strobes, alternately, red and blue-green, at points
180.degree. out-of-phase on the vibrator applied-force sinusoid.
For a computer-determined phase setting, the user adjusts frequency
until the strobing lines appear to converge into a single white
line, indicating synchronization of the strobe with eyeball
vibrations. If the lines pulsate perceptably in and out of
convergence with each heartbeat, the user is instructed to adjust
the frequency to the two outer limits where convergence is just
barely achieved at the maximum fluctuations. These settings tell
the system the frequency at which a specified vibrational phase is
achieved, and how much that frequency varies with intraocular
pressure pulsations. The system also strobes a dot whose perceived
image is split maximally when the lines are converged. The user
adjusts driver amplitude to match the perceived dot spacing to a
pair of reference dots, strobed at the zero-displacement times of
the line flashes. This amplitude adjustment tells the system the
excitation level needed to achieve a reference response. A final
spacing adjustment of the reference dot pair gives convergence of
these dots at the moment of maximum pulsatile separation from
convergence of the strobed lines, telling the system the change in
amplitude response due to pulsations in intraopthalmic
pressure.
Analysis of these data follows similar lines to the last described
aspect, the content of the visual data being comparable to the
content of the ultrasound data. The system infers the product of
pressure times average ocular radius. For more accuracy and if a
separate pressure determination is desired, the user measures
eyeball radius, e.g. by looking into a mirror, observing
reflections of two lights on the sclera (white of the eye), and
matching two cursors to the reflections. It is noted that the
radius-pressure product is perhaps a better indicator of glaucoma
danger than pressure alone.
Another aspect of the invention is suited for measuring pressure in
the pulmonary artery. In preferred embodiments, the patient
swallows a cylindrical probe, which is held by a cable partway down
the esophagus to rest behind the the right pulmonary artery.
The ends of the probe vibrate axially, driven by transducers that
move against a gas volume inside the probe, like
acoustic-suspension speaker drivers. Driver expansion/contraction
and output pressure vibrations are inferred from changes in driver
electrical response. Acceleration sensors detect lateral vibrations
at the center and ends of the probe. The lateral movement is caused
by asymmetry of the probe surroundings, which include the spinal
column just behind the probe. Driver response motion, pressure and
lateral movement data are combined to simulate the excitatory field
geometry. Ultrasound transducers just above and below the
artery-crossing level measure three angularly-displaced diameters.
Time variations in the diameter data are analyzed to determine the
amplitudes and phases of arterial vibration modes next to the
probe. A pressure sensor facing the artery samples the local
vibrational pressure field, as well as low-frequency pressure
pulsations caused by the artery. This pressure sensing permits
refinement of the excitatory vibration field model, which is used
to extrapolate mode-excitation strength over the strongly-affected
length of artery. Vibration-energy integrals over that length lead
to a total energy model, permitting network algorithm solution and
subsequent analytic function fit algorithm solution for pressure.
By interpreting the decay ot he diastolic pressure curve, the
system infers pulmonary capillary pressure.
According to another aspect of the invention, a method for inducing
vibrations in a selected element of the human body and detecting
the nature of responses for determining mechanical characteristics
of the element non-invasively, comprises the steps of: inducing
multiple-frequency vibrations, including below 20 KHz, in a
selected element of the body by use of a driver means, determining
parameters of the vibration exerted on the body by the driver
means, sensing variations of a dimension of the element of the body
over time, including in response to the driver means, correlating
the variations with frequency components of operation of the driver
means below 20 KHz to determine corresponding frequency components
of the variations, resolving the frequency components into
components of vibration mode shape, and interpreting the parameters
of vibration exerted by the driver means and the components of
vibration mode shape in a manner to determine the mechanical
characteristics of the element.
In preferred embodiments determination of parameters of vibration
exerted by the driver means includes determining force, or
determining velocity; a mechanical characteristic determined is
pressure; the method further comprises the step of detecting change
in components of vibration mode shape due to pressure change of the
element, change being included in determination of the mechanical
characteristics of the element; the multiple-frequency vibrations
are generated by changing the operation frequency of the driver
means over time; the multiple-frequency vibrations are generated by
operation of the driver means at multiple frequencies
simultaneously; the body element includes a wall, and the method
further comprises the steps of: resolving the components of
vibration mode shape for at least two modes, and comparing the
determined mechanical characteristics of the elements respectively
determined on the basis of the components of vibration mode shape
for at least two modes in a manner to provide an indication of
element wall stiffness; the method comprises sensing the variations
of a dimension of the element of the body by means of ultrasound
echo signals; a mechanical characteristic determined is systemic
arterial blood pressure and the body element is a segment of the
arterial system; a mechanical characteristic determined is the
mechanical impedance of a body element and the body element is an
entire organ; a mechanical characteristic determined is intraocular
pressure and the body element is an eyeball, preferably the step of
sensing variations of dimension comprises sensing variations of a
dimension of the eyeball wherein the method comprises incorporating
user feedback in response to visual impressions of a time-varying
display, the visual impressions being representative of the
response of the eyeball induced by the driver means; a mechanical
characteristic determined is pulmonary blood pressure and the body
element is a segment of the pulmonary arterial system; in addition
to the step of sensing variations of a dimension of the element,
the method further comprises sensing a dimension of the element,
the sensed dimension being included in determination of the
mechanical characteristics of the element, preferably the dimension
of the element is sensed by interpreting ultrasound echo signals,
and preferably the dimension of the element is sensed optically;
and the method further comprises applying a known pressure to the
element in a manner to permit calibration, preferably the method
further comprises applying the known pressure by means of a
pressure cuff.
Other features and advantages of the invention will be understood
from the following description of the presently preferred
embodiments, and from the claims.
PREFERRED EMBODIMENTS
FIG. 1 is a diagrammatic perspective view of the system according
to a preferred embodiment of the invention for measuring systemic
arterial pressure;
FIG. 2 is an enlarged perspective view of the vibration driver and
sensors of FIG. 1;
FIG. 3 is a sectional view of the vibration driver and sensor
assembly of FIG. 2 taken along the line 3--3, while FIG. 3a is an
enlarged side section view of one of the ultrasound transducer
assemblies shown in FIG. 3;
FIG. 4 is a sectional view of a vibration driver assembly;
FIG. 5 is a diagrammatic representation of arterial vibration
modes;
FIG. 6 is a block flow diagram of the demodulation function;
FIG. 7 is a block flow diagram of ultrasound data acquisition;
FIG. 8 is a representation of electronic waveform traces of FIG.
7;
FIG. 9 is a block flow diagram of interfacing of computer input and
output data;
FIG. 10a is a representation of the vibration drivers and sensors
in a whole-organ measurement aspect of the invention viewed from
above, while FIG. 10b is a side section view;
FIG. 11a is an enlarged view of the ultrasound-transducer aiming
system of FIG. 10 from above, while FIG. 11b represents magnetic
fields of FIG. 11a and FIG. 11c is a side section view;
FIG. 12 is a block flow diagram of vibration-driver velocity
measurement for the drivers of FIG. 10;
FIG. 13 is a diagrammatic representation of an intraocular
pressure-measuring aspect of the invention; and
FIG. 14 is a diagrammatic cutaway view of the vibration driver and
sensors in a pulmonary arterial pressure-measuring aspect of the
invention.
HARDWARE AND OPERATION OF THE INVENTION
Essential Hardware
The principal subassemblies of the invention in an aspect for
measuring systemic arterial pressure are illustrated in FIG. 1.
Vibration driver and sensor assembly 1 is adapted to be affixed to
the skin of the patient, e.g. above left common carotid artery 40
shown in dashed outline. Cable 2 connects assembly 1 to
computer-controller 3, which includes oscilloscope display 4 for
observing ultrasound depth signals. Cable 5 couples
computer-controller 3 to video display terminal 6, including
keyboard 7. Cable 8 couples computer-controller 3 to
pressure-regulating air pump 9, which is coupled in turn by tube 10
to inflatable pressure cuff 11. This cuff includes inset 12 on its
inner surface, allowing it to fit over assembly 1, around the neck.
The cuff is for optional calibration, to verify or improve system
accuracy by applying a known time-varying pressure perturbation,
typically much less than diastolic pressure. The correlation slope
relating cuff pressure change and vibration-determined pressure
change indicates scaling accuracy. Oscilloscope traces 13 and 14
show ultrasound echoes taken from two angles across artery 40.
Intensified segments 15 and 16 show echo regions being tracked,
corresponding to near- and far-wall artery depths, for one
ultrasound angle. Segments 17 and 18 show the corresponding tracked
depths for the other ultrasound angle. On the display of terminal
6, the decimal number indicated by 19, e.g. the value 0.987 as
shown, is an indication of the average of the squares of the signal
trace slopes for echo segments 15, 16, 17 and 18. This signal
strength indication is referenced to unity for the strongest signal
previously encountered, so that it can be used to compare current
alignment of assembly 1 with the "best" previous ultrasound
alignment. The number indicated by 20, e.g. the value 77 as shown,
is heart rate per minute, derived from blood pressure pulsations
and averaged e.g. over the ten most recent pulses. The numbers
indicated by 21 and 22 and separated by a slash mark, e.g. 135/88
as shown, indicate systolic and diastolic blood pressure in mm Hg,
averaged e.g. over the ten most recent cycles. Optionally, the
system can display arrhythmia count over a specified time period
ending at the present time, again derived from blood pressure data.
Finally, trace 23, which moves from right to left as the trace is
extended on the right, displays the blood pressure waveform
determined by the system.
Assembly 1 is illustrated in greater detail in FIG. 2. Vibrator
plate 50 extends the full length of the assembly and includes a
central elevated bridge section 51. Plate 50 is configured to
contact the skin surface except over the elevated central section.
Plate segment 52 fills the gap under segment 51, except for small
decoupling gaps at the left and right ends, to contact the skin and
provide continuity to the contact area of plate 50. Segment 52 is
held substantially rigidly with respect to bridge section 51 of
plate 50 by axial post 54 from load cell 53. Using a fairly stiff
semiconductor strain gauge bridge, e.g. as sold by Entran Devices,
Inc., 10 Washington Ave., Fairfield, NJ 07006, load cell 53
measures the axial force along post 54. Load cell 55 is similar to
cell 53 and measures axial force exerted by electronic assembly 56
on post 57. Assembly 56 serves as a countermass, so that the
combination of parts 55, 56 and 57 acts as a transducer for
accelerations along the vertical axis common to posts 54 and
57.
Positive and negative DC supply voltages arriving through cable 2
into junction box 67 drive the strain gauge bridge circuits in load
cells 53 and 55. The two differential signals developed in the
bridge circuits of cells 53 and 55 are coupled to two balanced
twisted wire pairs in cable 2, via junction box 67. These signals
are received and amplified by differential amplifiers in
computer/controller 3, resulting in signals representing axial
acceleration and force. A small fraction of the acceleration signal
is summed with the force signal, to compensate for the acceleration
of the inertial mass of plate segment 52 and post 54. This
compensation is set so that the force reading from the vibrating
assembly is negligible when plate 52 is in air, not contacting a
load. Thus, the corrected reading represents force actually
delivered to tissue in the patient over the left-to-right length of
segment 52. The acceleration signal in computer/controller 3 is
integrated over the frequency band of vibration driver excitation,
resulting in a signal that closely approximates velocity over that
frequency band. Highpass filtering to cut off frequencies below
about 20 Hz results in a zero-average velocity signal.
The vibration driver consists of open-ended cylindrical housings 58
and 60, containing respective internal driver and reaction mass
assemblies 59 and 61, the housings being affixed to the ends of
plate 50. A twisted lead pair in cable 2 provides balanced AC
excitation for parallel-wired assemblies 59 and 61. The excitation
signal originates from a digitally-controlled sine-wave oscillator
in computer/controller 3. In response to this excitation,
assemblies 59 and 61 vibrate up and down together, exerting a
reaction force via housings 58 and 60 on plate 50. Plate 50 and
instrumented segment 52 vibrate together, substantially as a rigid
body, transmitting force through the contacting skin area and
inducing vibrations in the shape of underlying artery 40, as
illustrated in the cross-section of FIG. 3.
Matched ultrasound transducer assemblies 62 and 65 lie on either
side of segment 52. They are partially decoupled, vibrationally,
from the remaining assembly by flexible flat attachments, e.g. thin
spring-metal strips. For transducer 62 these attachments are
numbered 63 and 64. For transducer 65, attachment 66 is opposite
63, while the remaining attachment opposite 64 is obscured. Cable
2, via junction box 67, provides coupling of ultrasound electrical
signals to and from assembly 1. Assembly 56, besides serving as an
accelerometer countermass, contains two small torroidal ultrasound
impedance-matching transformers (not shown), whose higher-impedance
windings (typically) are coupled to transducers 62 and 65. Assembly
56 also contains a field effect transistor switching circuit (not
shown) that selects one of the two transformer lower-impedance
windings (typically) for coupling to a coaxial cable in cable 2. A
binary select signal to control the switching circuit arrives via
an independent coaxial cable included in cable 2. The received
ultrasound voltage signal from the selected disk is thus
transformed to match the coaxial cable impedance for transmission
to computer/controller 3. Conversely, electrical drive pulses from
computer/controller 3 are transformed in the other direction for
efficient energy coupling to the selected disk.
The DC power supply voltages used for strain gauge bridge
excitation are also used to power the selector switching circuit.
High frequency decoupling capacitors and resistors (not shown) are
included in assembly 56, to avoid cross-coupling interference.
Finally, Cable 2 provides grounding and shielding between wire
groups, as needed to prevent signal interference.
Vibration plate 50 is oriented with its long axis parallel to
artery 40. Ultrasound assemblies 62 and 65 detect arterial diameter
at two angles, as shown in FIG. 2 and in the cross-sectional
perspective of FIG. 3, top. The sectional plane is parallel to the
ultrasound plane defined by the axes of transducers 62 and 65,
which includes the vertical axis common to load cells 53 and 55.
The section in FIG. 3 is taken just to the right of load cells 53
and 55, along line 3--3 and dashed line 30 of FIG. 2, so that it
cuts through segment 52 and bridge section 51 of plate 50. In FIG.
3, an ellipse-mode vibration in artery 40 is indicated by the solid
and dashed elliptical coutours. FIG. 3a shows a cross-section of
ultrasound transducer assembly 65. The internal details of
transducers 62 and 65, discussed later, are the same, since the two
assemblies are matched.
Basic Operation
A preliminary description of system operation follows. In a typical
application, the patient's neck is lubricated with an ultrasound
transmission gel and assembly 1 applied above a common carotid
artery. Oscilloscope display 4 initially shows the operator two
ultrasound echo traces, displayed one above the other,
corresponding to the alternating transmit-receive cycles of
assemblies 62 and 65. Horizontal displacement across screen 4
represents echo delay time or, equivalently, depth, while the
vertical deflections represent reflected acoustic pressure. The
ultrasound signal has been subjected to phase and amplitude
correction to maximize depth resolution, by achieving a
phase-linear response pulse with smooth band limiting of
amplitude.
The transducer assembly is manually centered over the artery by
matching the depths of the two echo traces. The operator adjusts
rotational alignment so that the artery axis lies, as nearly as
possible, perpendicular to the ultrasound plane defined by the two
ultrasound beam axes. (If the artery axis does not lie parallel to
the skin surface, this causes an irreducible angle error.) This
alignment is achieved by maximizing the amplitudes of the two pairs
of wall echo traces while maintaining matched depths.
As the operator approaches correct transducer position and
alignment, pattern recognition programs in the computer/controller
identify the echo complexes of the near and far artery walls for
the two displayed ultrasound signals. The machine-recognizable
artery echo identification patterns are: (1) approximate depth
matching of the two pairs of well echoes, assured by operator
adjustments; (2) expected ranges of average depth and spacing for
each near-far wall echo pair, based on typical human anatomy; and
(3) pulsating echo spacing, resulting from pulsating artery
diameter. When the wall echo complexes are machine-identified, the
vibration driver is activated and the computer fine-tunes the
depths sampled. Specifically, the controller includes phase-lock
loop circuitry capable of tracking the depth (i.e., the ultrasound
signal delay) of a rapidly-repeated echo signal zero-crossing in a
wall echo complex. The computer intervenes in the phase-lock
circuit operation to select the zero-crossing to be tracked. A
zero-crossing is sought that has a relatively steep slope and whose
vibrational motion is large, such that the product of slope times
vibration response amplitude is maximized. More specifically, the
vibration amplitude to maximize is amplitude relative to the
opposite artery wall, so that ultimately the zero-crossing
selection is for a pair of zero crossings with large relative
motion. The vicinities of the selected zero-crossings are
highlighted by oscilloscope beam intensity modulation, as
illustrated at 15, 16, 17 and 18.
A digital readout of average wall echo signal strength appears on
the screen of terminal 6, to assist the operator in fine-tuning the
alignment. The decimal fraction displayed (at 19) becomes 1.000
whenever response amplitude matches or exceeds all previous values.
As amplitude declines, the reading indicates response strength as a
fraction of the largest achieved. The operator thus learns the best
alignment by crossing it, and then returns to the position of
maximum signal strength.
Ultimately, the system locks onto three pairs of wall-depth
signals, representing three angles across the artery: one for
assembly 62, one for assembly 65, and the final pair for a
transverse signal where assembly 62 sends the pulse and assembly 65
receives the echo (or vice versa). Trigonometric computer
operations give a scaling correction factor for the transverse
echo, so that the depth sensitivities of the three depth pairs are
computationally matched.
If extended monitoring is contemplated, assembly 1 is now affixed
more permanently to the skin. The position is marked with ink dots
on the skin, the assembly is removed, and the ultrasound gel is
wiped off. A specially cut and marked piece of double-stick
surgical adhesive tape is placed on the skin, aligned to the marks.
Assembly 1 is applied to the upper adhesive surface of the tape, in
the original position and alignment. The tape makes an efficient
ultrasound and audio vibration interface.
If extended monitoring is not contemplated, the transducer assembly
may be held in place manually.
Once in place and operating, assembly 1 induces vibrations through
the skin into the underlying artery. The surface vibration velocity
is derived, over the driver frequency band, from the acceleration
signal of load cell 55, as described above, while the corresponding
force, sampled over the known length of segment 52, is derived from
the output of load cell 53, with the acceleration correction
described. Plate 50, including the gap-filling segment 52, is of
constant width in the middle and widens at both ends to minimize
vibrational "end effects", so that the vibration field under
segment 52 extending down through the artery depth shows minimal
axial variation. Thus, all vibrational motions below segment 52 lie
nearly parallel to the ultrasound plane (defined by the axes of
transducers 62 and 65). The ultrasound plane should lie
substantially perpendicular to the artery axis. Hence, for an
arterial segment directly below driver segment 52, and whose length
equals the length of segment 52, the vibrational energy coupled to
and from that artery segment should correspond closely to the
energy coupled to and from driver segment 52. This symmetry permits
a proper scaling of sensed parameters to infer blood pressure. The
measured force and velocity for driver segment 52 define the
instant-by-instant energy flow through the segment. The ultrasound
measurements through the three angularly-displaced diameters of
artery 40 suffice to define the significant vibration mode
responses induced in the artery. Blood pressure variations alter
the vibrational properties of the artery. The resulting changes in
the signal measurements reveal coupling coefficients characterizing
the dissipative and reactive components of force and energy
transfer between driver segment 52 and the corresponding artery
segment. Further analysis reveals the mechanical impedance of the
artery and nearby coupled tissues. Frequency analysis of this
arterial mechanical impedance reveals blood pressure, as perturbed
by artery wall stiffness. Analysis of two separate vibration modes
for apparent pressure reveals separated wall stiffness pressure
artifacts and true fluid pressure.
Ultrasound Transducer Details
Referring to FIG. 3a, housing 66 includes air space 67 behind
piezoelectric ceramic transducer disk 68, fabricated e.g. of lead
titanate zirconate, metallized on the flat surfaces and axially
poled, e.g. as manufactured by Edo Corp., Western Division, 2645
South 300 West, Salt Lake City, Utah 84115. The metallizations on
the front and back of the disk are typically coupled to the
higher-impedance winding of one of the torroidal transformers in
assembly 56. Bonded to the front surface of disk 68 are two
acoustic interface layers, 69 and 70, which present a graduated
change in acoustic impedance from the high impedance of the disk to
the low impedance human tissues. The thickness of each layer is
approximately 1/4 wavelength at the design center frequency of the
transducer. Layer 69 may consist of quartz, and layer 70 of acrylic
plastic. The ultrasound transducer acoustic interface layers and
electrical matching circuitry are constructed in a manner familiar
to engineers in the medical ultrasound field, e.g. as in "The
Design of Broad-Band Fluid-Loaded Ultrasonic Transducers", IEEE
Trans. on Sonics and Ultrasonics, Vol. SU-26, No. 6, November
1979.
Adjoining the front surface of interface layer 70 is an astigmatic,
divergent acoustic lens. It consists of material layers 71 and 72,
with an interface between them that curves relatively strongly in
the "ultrasound plane" mentioned above, i.e. the plane of the
cross-sectional diagram being examined, and curves weakly in the
other direction. Both layers have approximately the acoustic
impedance of human tissue (close to the impedance of water), and
are made of a polymer of lower acoustic impedance than water, e.g.
room temperature vulcanizing (RTV) silicone rubber, loaded with a
fine powder of high acoustic impedance. The powder concentration is
chosen to raise the low impedance of the polymer up to the desired
tissue impedance value. Layer 71 is loaded with high-density
powder, e.g. tungsten carbide, while layer 72 is loaded with
low-density powder, e.g. graphite. The light powder raises the
acoustic impedance of the polymer largely by raising the modulus,
while a lesser volume concentration of the heavy powder achieves
the same impedance largely by raising the density. As a result of
the differing ratios of modulus to density, the speed of sound is
higher in the relatively high-modulus, low density layer 72 than in
the relatively low-modulus, high density layer 71. The curvature of
the interface between the layers, convex away from layer 72 towards
layer 71, creates the desired divergent acoustic lens. While the
modulus/density ratios are caused to differ, giving differing sound
speeds, the modulus-density products of the layers are matched,
resulting in matched acoustic impedances and minimal interface
reflections. The matched impedances are made close to that of human
tissue, to minimize reflections at the lower sloping interface of
layer 72 to the patient.
Powder loading of uncured silicon in layers 71 and 72 is achieved
without introducing bubbles by mixing powder and uncured silicone
and molding in a vacuum. Brief centrifuging settles the mixture
into the mold and collapses large voids, but is not extended long
enough to settle the fine particles. Upon restoration of
atmospheric pressure, remaining vacuum-filled voids collapse,
leaving a bubble-free mixture. Housing 66 is part of the mold, and
is porous to allow air curing of the contents. After layers 71 and
72 are fabricated and cured, the surface of housing 66 is sealed by
impregnation with a polymer resin.
The divergent lenses in the transducers allow the ultrasound system
to tolerate differing depths of arteries in various patients. Due
to the astigmatic design and low divergence outside the ultrasound
plane, the system is relatively sensitive to misalignment whereby
the ultrasound plane fails to cut perpandicular to the artery
axis.
The ultrasound system is not intended for point-by-point imaging.
Instead, the system primarily "sees" surfaces of discontinuity in
acoustic impedance in the regions where those surfaces lies
approximately tangent to the spreading wavefronts from the
ultrasound assembly. Thus, the ultrasound system "sees" near and
far artery wall depths, averaged over a significant wall surface
area. This spatial averaging minimizes sensitivity to roughness and
irregularity of the artery walls. The design also avoids ultrasound
"hot spots" where the beam might otherwise expose a small area of
tissue for prolonged periods at relatively high intensity. Apparent
ultrasound-measured diameters are slightly distorted by arterial
wall curvature, since effective echo averaging extends over a
finite angle of curvature. Computer algorithms correct for this
distortion as necessary.
Vibration Driver Details
FIG. 4 illustrates the internal construction of housing 60 and
driver/mass assembly 61. Housing 58 and driver/mass assembly 59 are
the same. The circular surface 61, visible in FIG. 2, in FIG. 4 is
seen as the top surface of an inverted cup-shaped magnetic pole
piece, viewed now in cross-section. This cup consists of annealed
transformer-grade silicon steel. Inside cup 61 is permanent magnet
82, which may be a rare-earth cobalt magnet consisting, e.g. of
material Crucore 18 from Colt Industries, Crucible Magnetics
Division, Route #2, Elizabethtown, KY 42701. The polarization of
magnet 82 is axial. An electric current in winding 83 will either
reinforce or oppose the permanent field, depending on polarities. A
similar electrically-variable magnetic field source is set up by
silicon steel cup 84, permanent magnet 85 and winding 86. These two
magnetic sources are spaced by rigid post 87, of non-ferromagnetic
material. Silicon steel washer 88 sits in the gap between the two
magnetic field sources. The north-south polarizations of magnets 82
and 85 are parallel and matched, so that the magnetic flux
primarily follows a donut-shaped path. The dominant flux path can
be traced from magnet 82 down, through an air gap, into the inner
area of washer 88, through a second air gap into magnet 85, down
into cup 84, up from the "rim" of cup 84, across an air gap to the
outer area of washer 88, up through an air gap to the "rim" of cup
61, and finally full circuit back into the top of magnet 82.
When washer 88 is centered and no current flows through the
windings, the magnetic forces on washer 88 substantially balance.
Coils 83 and 86 are wound and connected so that an electrical
signal that strengthens the fields crossing the upper air gap will
correspondingly weaken the fields crossing the lower air gap. This
will unbalance the attractive forces, creating a net axial force
between washer 88 and the driver/mass assembly.
The axial position of washer 88 relative to the driver/mass
assembly is restored by silicone rubber o-rings 89 and 90. The
o-rings rest in grooves in windings 83 and 86, with the outer walls
of the grooves being the inner surfaces of cups 61 and 84. The
windings are resin-impregnated and cured for dimensional stability.
The o-rings contact washer 88 only at a circularly-arrayed set of
teeth or ridges, illustrated landing in the cross-section of the
diagram at 91 and 92. The contact areas of the teeth are curved to
follow the round surface of the o-ring, to provide a radial
centering force for the washer. The tooth area is chosen to provide
the desired restoring force on the washer, enough to overcome the
destabilizing influence of the magnetic field and achieve resonance
with the inertial load at a desired frequency. When shocked, the
washer can contact the entire circumference of an o-ring, which
cushions impact force.
Open cylindrical housing 60, as seen in this detailed drawing, is
split and includes separable lower and upper sections 93 and 93'.
The sections are bonded together to capture washer 88, and the
lower end of section 93 is bonded to plate 50. Housing sections 93
and 93' are non-ferromagnetic to avoid diverting flux from the
axial gaps. The dashed line at 94 indicates an optional flexible
diaphragm to bridge the top of the gap between 60 and 61 and keep
dust and especially ferrous particles away from the magnetic
gaps.
The leakage flux from the driver/mass assembly will be a steady
dipole field and, primarily, a quadrupole AC signal field. The AC
component of the field travels radially in the washer and splits
roughly symmetrically to travel up and down to cups 61 and 84.
Since quadrupole fields lose strength rapidly with distance,
unwanted AC magnetic signal couplings are minimized. Washer 88 can
be made relatively thin, within minimum stiffness constraints,
without causing magnetic saturation, since only signal fields and
not the large permanent polarizing field pass radially through the
flat plane of the washer disk. For small motions,
electro-mechanical efficiency is very high, with a high ratio of
response force to input wattage determined by the relatively large
available winding volume and the strong polarizing fields in the
gaps. The symmetry of the structure minimizes second-order
distortion responses. Most of the mass of the assembly is
concentrated in the moving element, which includes the permanent
magnet, most of the silicon steel and the windings. This transducer
is useful for driving high mechanical impedances and for minimizing
the mass of one moving part by concentrating the mass in the
oppositely-moving part.
OPERATING PRINCIPLES OF A SYSTEMIC ARTERIAL PRESSURE EMBODIMENT
The Fundamental Pressure-Determining Steps
Briefly, a preferred set of procedural steps for determining
time-varying absolute systemic arterial blood pressure follows:
(1) Vibrate the skin surface to excite the underlying artery.
(2) Assure, by design and operational adjustment, that vibrational
symmetry is maintained for a length of the arterial axis, so that
energy relations along a given surface length correlate with energy
relations along a corresponding parallel length of underlying
artery.
(3) Measure the phase and amplitude of the vibrational force
applied along that given surface length paralleling the artery.
(4) Measure the velocity whose product with the force measured in
step (3) equals the instant-by-instant power transfer into the
given surface length paralleling the artery.
(5) By correlating ultrasound wall echo phase variations with the
surface vibrational velocity signal, determine the amplitudes and
phases of all significantly-excited arterial vibration modes that
are pressure-sensitive.
(6) For each pressure-sensitive vibration mode, by measuring the
observable effects of undetermined pressure change at constant
frequency, determine the vibrational force/velocity transfer factor
that symmetrically relates surface velocity to artery-mode force,
and artery-mode velocity to surface force.
(7) Using the result from (6), compute the arterial vibrational
impedance for each pressure-sensitive mode. For a given mode,
impedance variation is a strong indicator of blood pressure
variation.
(8) Through repetitions of the above steps for different
frequencies, establish arterial vibrational impedance as a function
of frequency for a reference value of blood pressure. Each time
that pulsating blood pressure crosses this reference, the crossing
is recognized by a vibration signature.
(9) Using known general characteristics of arterial impedance as a
function of frequency, use a function-fit to the above
impedance-versus-frequency data at constant pressure to establish
the dominant low-frequency limit term of the impedance function.
This limit term establishes an absolute blood pressure, with
possible additive wall-stiffness artifacts.
(10) (Optional) Repeat step (9) for the same reference pressure and
a different vibration mode, establishing a second value for
absolute blood pressure. This value will differ from the value of
step (9) in direct proportion to wall stiffness. A proportion of
the difference between these two results is substracted from the
reference pressure of step (9) to give baseline fluid pressure, now
independent of wall stiffness.
(11) Repeating steps (1) through (9), establish a table of
pressures and associated vibration parameters as functions of
radius, for a fixed frequency. With this table calibrated to the
sensor/patient linkage, real-time pressure tracking is accomplished
by table lookup and network algorithm correction to current
pressure, using current vibration parameters. The network algorithm
correction is needed because pressure is typically not a repeatable
function of artery radius.
In deriving detailed operating algorithms, we first concentrate on
a common situation in which only one pressure-sensitive vibration
mode is measurably excited, specifically the ellipse-mode vibration
illustrated in FIG. 3. Where modes of higher order than the
ellipse-mode cannot be resolved, it is impossible to complete step
10, and consequently there is no direct way to measure wall
stiffness artifacts. Real-time pressure may then be computed with
an undetermined additive wall-stiffness error. Except in patients
with advanced arteriosclerosis, this wall-stiffness error is
small.
Pressure and Frequency Baselines
By analogy to vision, the system gains "parallax" on the measured
quatities, to gain "perspective" into the underlying mechanics,
through "movement" along either of two separate baselines.
The first baseline movement is change in blood pressure. Internal
pressure tends to force the artery towards a circular
cross-section. When pressure changes, this alters the effective
restoration of the artery towards circularity, which changes the
amplitude and phase of the vibrational velocity detected in the
artery. The effect of this vibrational change is detected, in turn,
by the surface sensors.
Since the change in vibrational motion of the artery arises from
internal pressure variation, this change of motion may be treated
as if it were a new vibration signal, generated within the artery
and propagating outward to the surface sensors. We might call this
incremental signal the "parallax" signal, since it is revealed by a
movement along the pressure baseline. By combining data about this
parallax signal with the original data about driver excitation and
arterial response, the system can compute a force/velocity transfer
factor that describes the symmetric coupling of force from the
driver to the artery and from the artery to the driver. The
symmetry of this transfer factor in both directions is proved by
the Theorem of Reciprocity. The system can measure both vibrator
and artery-mode velocities, plus vibrator force. That leaves only
artery-mode force as an unknown in the force-coupling problem. When
blood pressure changes, the resulting parallax signal, combined
with the original signal, provides enough data to solve for the
unknown force. The force/velocity transfer factor falls out,
followed by the actual vibrational impedance of the artery in its
local environment. Thus, the combined measurements of the invention
constitute a powerful remote impedance-measuring probe. Blood
pressure and vibrational impedance are related by a simple
equation. The impedance and pressure-change data gathered by this
pressure-baseline probe are used in the next, frequency-baseline
step, to solve for absolute blood pressure.
The second baseline "movement" is change in frequency of the
vibrator output. Frequency change strongly alters the relative
influences of inertia and stiffness, making it possible to
discriminate between the two. Inertial impedance is attributed to
the effect of vibrating tissue and blood mass, while stiffness, or
restoring impedance, is attributed primarily to blood pressure
restoring the arterial cross-section to circularity.
A baseline not needed for pressure determination is organ radius.
The dynamics of arterial radius-change with blood pressure-change
reveal artery-wall elastic and creep properties, as well as
changing tonus of arterial sphincter muscles. For pressure
determination alone, however, radius variation tends to complicate
matters. All vibration-parameter data need accompanying radius
values. Ideally, a time-varying relationship between radius and
pressure makes it possible to scan the data and extract both
pressure and frequency baseline variations at a constant radius. In
cases where radius varies substantially repeatably as a function of
pressure, without creep or muscle-tone effects, self-calibrating
vibrational determinations of pressure are actually more
difficult.
One may define inertial velocity impedance as having a phase angle
of +90.degree., which leads approximately, but not exactly, to a
linear frequency dependence. Because of the frequency-dependent
influence of viscous shear forces on vibration field geometry, the
effective moving mass of a vibration mode is frequency-dependent.
Extra mass is entrained by shear forces at low frequencies. Hence,
inertial velocity impedance does not decline as fast as the first
power of frequency at low frequencies.
Restoring velocity impedance has a phase angle of -90.degree. and
varies almost exactly as the reciprocal of frequency. The
reciprocal relationship is substantially exact for blood pressure
and less exact for stiffness pressure, which may decline slightly
at low frequencies due to visco-elastic creep. Since stiffness
pressure is usually a small correction term, its gradual frequency
dependence can usually be ignored. Because of its
reciprocal-frequency dependence, restoring impedance dominates
overall impedance in the low-frequency limit. Determination of a
mode-shape restoring force coefficient (per unit length) to match
arterial impedance in a low-frequency limit constitutes
determination of blood pressure plus a possible additive
wall-stiffness term. Since inertial and restoring impedances
together determine net 90.degree. impedance, determination of blood
pressure amounts to determining and subtracting out the inertial
impedance term from the 90.degree. impedance data, revealing the
pressure term.
We define damping velocity impedance as zero-phase impedance.
Because of the phase, this impedance is measured independent of
inertial and stiffness impedances. This does not make damping
impedance irrelevant to separating inertial and stiffness
impedances. Rather, changes in damping impedance are correlated
with changes in inertial impedance, since both relate to common
underlying changes in vibration-mode geometry with changing
frequency. Damping impedance tends to increase weakly with
frequency as shear boundary layers become thinner and
shear-gradients correspondingly steeper, leveling off at high audio
frequencies as boundary layer thicknesses approach the
pressure-containing arterial wall thickness. For the purposes of
this analysis, mode-shape coefficients for restoring-constant,
velocity-damping and mass (all per-unit-length) may be approximated
to approach definite high- and low-frequency limits. Though this is
not rigorously true (e.g. compressibility effects invalidate this
model above the audio frequency range), the approximation leads to
an analytic model that is useful over a wide frequency range and
reveals parameters of effective moving mass and total elastic
restoration (from blood pressure plus tissue elasticity).
The connection between damping and inertial impedances transcends
particular models of vibration geometry and can be described in
terms of the fundamental properties of complex analytic functions.
(A complex function is defined to be analytic if it has a unique
complex derivative.) The 0.degree. component of a real-world
impedance function correlates with the real part of an analytic
function. The 90.degree. component similarly correlates with the
imaginary part. Frequency corresponds to an imaginary argument of
the analytic function. The real and imaginary parts of analytic
transfer functions are interdependent, and the same interdependence
is observed between the 0.degree. and 90.degree. components of
real-world impedances. Consequently, in attempting to extrapolate
real impedance data to discover the limiting behavior of the
90.degree. component, it is effective to fit both phase components
of impedance to a complex analytic function. Such a function fit
utilizes more good data than a real-valued function fitted solely
to the 90.degree. component of arterial impedance.
Inertial and restoring impedances cancel at a resonant frequency,
leaving a pure damping impedance. Artery vibration mode
measurements are typically only accurate in the broad vicinity of
this resonant frequency. Very far from resonance, excitation of an
arterial vibration mode becomes vanishingly small. It is not
feasible to measure arterial impedance so far below resonance that
the measurement is totally dominated by the pressure-revealing
restoring impedance term. Hence, the goal of the frequency-baseline
determination is to observe the behavior of arterial impedance at a
fixed pressure, over the usable range of measurement frequencies,
and to establish a rational analytic function fit to these data.
The correct general form of the transfer function has already been
defined, to a great extent, by the physical arguments given above
concerning the high- and low-frequency limits of effective
restoring constant, damping and inertia terms. Using an approximate
fit based on a finite number of measurements and a finite number of
analytic function coefficients, the low-frequency limit of the
curve is established. The accuracy of this fit depends not so much
on the numbers of measurements and function-fit terms as on the
linearity of the measurements, on the signal-to-noise ratio of
measurements (which can be improved by averaging of many
measurements), and on the accurate fulfillment of the symmetry
conditions demanded in step (2) and described earlier, in relation
to the shape and alignment of assembly 1 in FIGS. 1, 2 and 3. It is
noted here that substantial parallelism of tissues along the
arterial symmetry axis is needed for high accuracy. If arterial
vibrations are monitored where a bone or tendon crosses very near
the artery at a sharp angle, symmetry will be compromised. Even
with total tissue parallelism along the arterial axis, a sharp
departure from radial symmetry very near the artery wall (e.g.,
from a tendon lying very close alongside the artery) will couple
significant energy into high-order vibration modes, causing errors
in a system of measurements and analysis based on insignificant
energy beyond three-lobed mode shapes.
We now examine how to collect data in a way that permits us to
distinguish pressure and frequency dependencies. We designate the
two perspective baselines for analysis as:
(1) pressure-change effects at constant frequency, and
(2) frequency-change effects at constant presssure.
The two effects are distinguished in this embodiment by monitoring
at a fixed frequency through two or three cardiac cycles (for
pressure change effects), shifting to a new frequency for
subsequent cycles, then returning to the original frequency, and so
on. Although pressure waveforms do not repeat exactly, similar
pressure cycles measured at different vibration frequencies are
paired as follows: two waveform data segments, sampled and stored
close together in time and monitored at different vibration
frequencies, are paired if the non-vibratory diameter traces match
closely over at least two consecutive cardiac cycles. This ongoing
match is a strong indication of matched pressure waveforms,
unaffected by progressive trends in arterial sphincter-muscle tone
or inelastic creep of the wall tissue. Starting with a frequency
analysis based on pairs of matched-pressure cardiac cycles
monitored at different fixed frequencies, improved results are
obtained by repeating the pair analysis for many matched pairs and
averaging the inferred pressure calibration parameters, i.e. those
numbers that are subsequently used for determining an absolute
baseline pressure. By this averaging, effects of
imprecisely-matched pressure cycles tend to cancel, revealing
accurately the fixed parameters of the coupled sensor-artery
system.
(It is possible to analyze responses while the driver emits more
than one frequency essentially simultaneously, for example, by
rapid frequency modulation, by frequency splitting using amplitude
modulation, by emitting superimposed sinusoids at different
frequencies, or pulses with multiple-frequency harmonic content, or
a random signal. In some instances, transform analysis is needed to
unscramble the data. In the embodiments presented here, excitation
and vibration decoding at only one frequency at a time is chosen
for economy.)
Arterial Vibration Modes
The vibration mode shapes illustrated in FIG. 5 are the lowest
terms in an infinite series of shapes that can be used to analyze
any arbitrary vibrational perturbation in a medium that is radially
symmetric and unchanging along the third axis, i.e. the axis
perpendicular to the cross-sectional plane of the diagram. Mode
shape analysis can be applied, with added complexity, where radial
symmetry is broken severly, e.g. where a tendon parallels an artery
in close proximity. Since the analysis is two-dimensional, it is
valid only where the vibrational perturbation is unchanging along
the third axis. In the absence of severe violations of radial
symmetry, these vibration modes are substantially orthogonal,
meaning that there are amplitude-squared terms for
power-dissipation and energy of individual modes, but negligible
power or energy associated with products of amplitudes of differing
modes. Thus the different modes do not interact significantly, but
simply coexist superimposed on each other. Modes can therefore be
analyzed separately.
The terms in the cylinder mode shape analysis correspond directly
to the terms in a Fourier series for a periodic function. The
lowest term in a Fourier series is the zero-frequency term, a
constant, corresponding to Mode 0 of FIG. 5. We see that radius is
changed by a constant amount, independent of angle, from solid
contour 100 to dashed contour 101 (FIG. 5a). Since we are
discussing vibrations whose acoustic wavelengths typically exceed
arterial dimensions by a factor greater than 100, compressibility
effects are negligible. Since Mode 0 represents a net change in
cross-section, it can only be observed in the present context of
incompressible motions if there is axial vibrational movement, so
that cross-section areas change differently at other axial
locations. This property is reflected by contours 102 and 103 (FIG.
5b), corresponding to contours 100 and 101 and illustrating the
same cylinder viewed from the side. The dotted line indicates where
the upper cross-sections are taken. To the extent that the desired
vibrational symmetry is maintained, Mode 0 excitation should be
negligible. Thus, Mode 0 is not a significant vibration mode in the
context of the measurements and computations of the systemic
arterial pressure-measuring embodiment of this invention.
Mode 1 is a rigid-body vibration of the cylinder between coutours
104 and 105 (FIG. 5c). An energetically orthogonal component of
Mode 1 is illustrated in contours 106 and 107 (FIG. 5d), where the
motion is at right angles to the upper illustration. Mode 1
vibrations are not sensitive to blood pressure. The vibrations can
be affected by pulsating arterial cross-sectional area, but the
effect is very weak since it depends primarily on the small
difference between blood density and artery-surround density.
Mode 2 and all higher modes are "shape" modes, sensitive both to
blood pressure and arterial wall stiffness. They may be influenced
to a lesser extent by stiffness in tissues outside the arterial
wall, although this effect is very small. Contours 108 and 109
(FIG. 5e) illustrate one axis of excitation of Mode 2, while
contours 110 and 111 (FIG. 5f) illustrate a second axis, displaced
by a 45.degree. angle. The modes for the two axes are energetically
orthogonal.
Mode 3 has a three-lobed symmetry, with one excitation axis
illustrated by contours 112 and 113 (FIG. 5g) and a second axis
illustrated by contours 114 and 115 (FIG. 5h). This second,
energetically orthogonal vibration axis is displaced from the first
axis by 30.degree..
If the vibration driver is directly above the artery and if tissues
are symmetric on the left and right sides of the artery, then the
excited vibration axes will be vertical, as in the top-row figures
for Modes 1, 2 and 3. This left-right symmetry will be violated,
for example, if a vein or tendon parallels the artery nearby and to
the left or right of the central vertical axis down from
driver/sensor assembly 1 (recalling FIGS. 1-3). The differing axis
excitations may not be in the same vibration phase, since the
symmetry-perturbing object will have its own vibrational phase
response to the applied excitation. Circularly-polarized vibrations
are possible, in which the shape perturbation appears to rotate
rather than vibrate. This arises from the superposition of
excitations along energy-orthogonal mode axes and differing in
phase by 90.degree..
High-order vibration mode shapes are excited only by high-order
geometric derivatives of pressure and stress in the medium. If the
medium is relatively homogeneous, high-order derivatives attenuate
very rapidly with depth below the vibration driver. Hence, for deep
arteries in relatively homogeneous surroundings, vibration mode
excitations above Mode 2 are negligible. Measurable Mode 3
excitation is achieved in shallow arteries or arteries lying next
to an impedance discontinuity. Excitation of Mode 3 in shallow
arteries can be reduced by using a relatively wide vibration
driver, which generates a "smoother" vibration field. Even with a
wide driver, however, Mode 3 excitation in the common carotids
arises from the proximity of stiff tendons and larynx cartilage and
the soft jugular vein. Carotid vibration mode axes may not line up
with the vibration driver, and excitation phases may depend
significantly on local surroundings.
Significant excitation of arterial vibrations above Mode 3 is
difficult to achieve without direct contact between the vibration
driver and the artery. For blood pressure determination, high-order
mode excitation is undesirable, since it complicates the analysis
and since more than three ultrasound angles across the artery are
required to separately distinguish higher modes.
Vibrations as Complex Numbers
Throughout, we discuss vibrational quantities characterized by both
amplitude and phase relative to a specified reference sinusoid. It
is convenient to represent such two-dimensional phase-vector, or
"phaser" quantities as complex numbers. In complex notation, the
real part of a complex number represents the component of the
amplitude-phase vector that is in-phase with a reference sinusoid,
while the imaginary part represents the component leading the
reference phase by 90.degree..
Since vibrations induced by the driver are related consistently to
the driver velocity phase and proportioned to driver velocity
amplitude, the vibrational components are often expressed as
complex-valued ratios, with driver velocity in the denominator. In
such complex ratios, the phase angle of the quotient is the phase
angle of the numerator minus the phase angle of the denominator,
and the amplitude of the quotient is the amplitude of the numerator
divided by the amplitude of the denominator. Thus, even though the
mechanical phase and amplitude response of the driver may change
relative to the electrical excitation signal e.g. in response to
changing mechanical loading, responses are expressed in a way that
is unaffected by "absolute" driver amplitude and phase. The
measured vibrator force, when expressed as a complex ratio with
velocity in the denominator, is called "surface mechanical
impedance". Likewise, velocity measured in an artery by ultrasound
is expressed as a transfer ratio, relative to the driver velocity.
(Had admittance notation been chosen instead of impedance notation
to express mechanical relationships, it would have been more
convenient to express all vibrational quantities as ratios to
vibrator force, rather than vibrator velocity. The choice of a
reference is arbitrary.)
AC Signal Demodulation
The functions of a demodulator circuit module are illustrated in
FIG. 6. Each repetition of this circuit module in FIG. 7 is
designated by the abbreviated schematic symbol box 145, shown at
the top of FIG. 6, a box with an "X" for multiplication, the
process central to demodulation. The terminals of box 145 are
designated "S" for analog Signal input, ".phi." for PHase reference
input (after the Greek "PHI"), and "O" for Output.
The original, or unconditioned input signals S and .phi. are
designated by a subscript-o and enter the circuit via wires 140 and
141. These signals are conditioned by matched bandpass filters,
shown at 152 and 153. Only one bandpass filter is required per
original signal, since a filter output may drive many demodulators.
The conditioned signals are designated by unsubscripted "S" and
".phi.", shown at 143 and 144 and in the input labels of box 145.
Since the demodulated output is sensitive only to the relative
phases of S and .phi., matched bandpass filtering causes no
phase-related errors. Demodulated output amplitude is insensitive
to the magnitude of the .phi. input, but varies linearly with the
magnitude of the S input. The effect of bandpass filtering on S
magnitude is canceled by using the magnitude of the filtered .phi.
signal as a reference magnitude, as was discussed above.
Specifically, when the reference vibration driver velocity signal
is demodulated against itself, i.e., when this signal is
bandpass-filtered and applied to both the S and .phi. inputs of a
demodulator, the amplitude-versus-frequency dependence of the
bandpass filter appears in the resulting reference amplitude, just
as it appears in other demodulated amplitudes. When the computer
divides demodulated signals by the demodulated reference velocity
amplitude, the amplitude error caused by the bandpass filters
cancels.
Conditioned analog signal S, at 143 in the expanded diagram, enters
a differential-output amplifier shown generally at 145. This
amplifier is represented schematically as a pair of amplifiers,
non-inverting and inverting, at 146 and 147, respectively. Above
148, a transistor current-switching network is represented
symbolically as a simple double-pole, double-throw switch. The
switch typically involves two switching transistor pairs.
Differential-output amplifer 145 and switch 148 are found embodied
functionally in a widely-manufactured integrated circuit,
designated by a manufacturer prefix followed by "1496", e.g. LM1496
for the National Semiconductor version. The differential output of
switch 148 (or the 1496 integrated circuit) is applied to a
differential-input amplifier 149, and the single-ended output 150
is applied to lowpass filter 151 to give output "O" at 142. In the
actual circuit, part of the filtering function of 151 is
incorporated directly into the inputs of amplifier 149, to avoid
generating large high-frequency amplitudes.
The polarity of phase reference .phi. determines whether the switch
poles are up or down. They are up when .phi. is positive and down
when .phi. is negative, with a very fast transition between states.
It is easy to see that the signal at 150 represents +S or -S, where
the sign is + if .phi. is positive and - if .phi. is negative.
Hence, the central portion of the demodulator is a four-quadrant
multiplier circuit which is linear only with respect to the S
input. Such a multiplier is simpler, faster and less prone to noise
and drift than a comparable fully-linearized multiplier.
A demodulator circuit correlates its signal input with the phase of
the reference input. In this invention, each vibration signal to be
decoded into complex real and imaginary parts is applied to the
analog inputs of two identical demodulator circuits. The phase
reference input for one of the demodulators typically represents
the driver velocity signal, while the phase reference input for the
other is phase-locked 90.degree. ahead of the first phase
reference. The outputs from the pair of demodulators thus represent
the desired real and imaginary vibration components of the analog
input, with respect to the reference phase. The phase reference
signal (e.g. driver velocity) is expressed by a single demodulator
output voltage representing a single real component, since this
reference signal is in-phase with itself and thus has no
out-of-phase imaginary component.
The filtered output from each demodulator represents a correlation
averaged over many vibration cycles. The averaging time-constant is
set to the longest value that does not interfere with the needed
time resolution of the system. Almost all time-varying
blood-pressure data can be encompassed by a bandwidth of 20 Hz,
while vibrator frequencies for carotid measurements are typically
above 150 Hz. Hence, a margin for signal averaging by the
demodulator filters yields good output data from noisy input data.
The filtered demodulator output is finally sampled and digitized
for computer input. Without preconditioning by demodulation and
filtering, the digital input data rate and processing load would
typically be increased tenfold, though digital signal processing
incorporating the analog demodulation function described here is a
feasible design alternative.
The demodulator outputs are typically sampled and digitized at 40
samples/second, sufficient to capture the roughly 20 Hz bandwidth
of blood pressure events. Quantities typically sampled at this rate
are: 0.degree. driver vibrational velocity (the phase reference);
0.degree. and 90.degree. driver vibrational force; three near-wall
and three far-wall arterial ultrasound depths (for the three
ultrasound axes, filtered to represent non-vibrational averaged
position); and 0.degree. plus 90.degree. phase components, for each
of the three ultrasound axes, of differential-mode and common-mode
vibrational velocity of the artery walls. That gives a total of 21
parameters at 40 samples/second each, or 840 samples/second, peak.
In addition, six ultrasound signal-strength values are typically
sampled infrequently, primarily to establish initial phase-lock to
the desired ultrasound echoes. Sampling at the peak rate occurs
only during short bursts. Data from these bursts is stored and
analyzed to define the vibrational characteristics of the measured
system. After selection of data for pairing of matched cardiac
pressure cycles, a large fraction of the gathered data is
discarded. Once baseline reference pressure calculations are
complete, subsequent real-time blood pressure computation involves
less data sampling and much less data processing.
The Single-Mode Network Algorithm
The network algorithm for pure Mode 2 vibration relates
pressure-induced changes in vibration measurements at constant
frequency to the coupling between vibrator and artery and to
mechanical impedance of the artery itself. The algorithm is based
on generalized linear network theorems, particularly the Theorem of
Reciprocity, which states in effect that energy must be able to
pass through a passive linear network or medium between two objects
with equal efficiency in either direction. Here, the medium is the
tissue between the vibration driver surface and the artery. Because
the energy flow takes the form of vibrations of very small
amplitude, non-linear fluid and elastic behaviors of the medium are
not elicited. In effect, any smooth function (in this case a
mechanical stress as a function of the excitatory vibrational
velocity field) appears to be linear if only a very short segment
of the function is viewed, e.g. here, a very small vibrational
velocity and amplitude.
We have seen how vibration-mode analysis is simplified where there
is two-dimensional field symmetry in the arterial cross-section
plane over the axial length under study, here the length of
driver/sensor segment 52 (FIGS. 2 and 3). Symmetry should cause the
measured force for segment 52 to correspond to the transmitted
force driving an equal length of the artery below. For a
constant-width vibration driver, end-effects cause the
artery-driving vibration field to weaken moving off-center. To
offset this, the ends of the driver are broadened.
We seek to define a two-dimensional force, i.e. force per unit of
axial length, exerted on the artery, simplifying the effects of
distributed pressure and shear stress into a single number. We use
the approach of generalized coordinate analysis, e.g. as explained
in Symon, Mechanics, ch.9, Addison Wesley, 1960. The sought-after
definition is possible only for a specified vibration mode
undergoing a specified motion when force is evaluated. With a
defined mode shape, we can use a single length-coordinate to
describe motion. For mode shapes like those illustrated in FIG. 5,
we describe mode shape changes in terms of changes in length of the
radius vector to the cylinder surface along an axis of maximum
length-change. If during the vibration cycle we perturb this radius
by a very small increment, this perturbation (and the simultaneous
radius perturbations at other angles to preserve the mode shape)
requires a net increment in work on the vibrating cylinder. The
resulting ratio of work increment to length increment defines an
effective force for the specified mode shape, according to Eq.
1:
We understand that "F" and "work increment" in Eq. 1 are both
quantities per-unit-length in the direction perpendicular to the
cross-section of analysis. We can use an analogous force definition
in three-dimensional contexts by omitting the implicit
"per-unit-length" qualification. Given a principal vibrational axis
for a single mode, we use the term "semi-axis length" to describe
the radius along that axis, i.e., the length used to define force.
For a Mode 2 vibration, assuming that the ultrasound depth
measurements are parallel to the principal vibrational axis, the
increment in semi-axis length amounts to half the change in
ultrasound-measured diameter. For a Mode 1 or a Mode 3 vibration,
ultrasound measurements resolved parallel to a principal vibration
axis show a constant diameter but a changing average depth of the
near and far artery walls (correcting for ultrasound transducer
motion). This changing average depth, or common-mode depth signal,
is the change in semi-axis length used in the force definition.
If we consider an entire vibrational cycle, we find that the
"work-slope" force defined by Eq. 1 describes a sinusoid having an
amplitude and phase. Extending from the definition of incremental,
instantaneous force, we define vibrational force Fn, for Mode n at
a specified angular frequency f, as a complex phaser quantity
having the amplitude and phase of the instantaneous force signal
just defined:
For a multi-mode vibration, we describe force as a
multi-dimensional quantity extending along as many complex axes as
there are excited modes.
Mechanical vibrational impedance (per-unit-length) is defined
according to normal engineering practice, as complex vibrational
force divided by complex vibrational velocity. This definition is
readily extended to mode shapes using definitions 1 and 2, above.
(Recall that the amplitude of a complex quotient is the numerator
amplitude divided by the denominator amplitude, and the quotient
phase is the numerator phase minus the denominator phase.
Similarly, the amplitude of a complex product is the product of the
amplitudes of the terms, and the product phase is the sum of the
phases of the terms.)
These definitions can be used to apply results of discrete network
theory to the continuum measurements of this system. With the
symmetries, measurements and definitions outlined here, the passive
tissue "network" in question can be modeled in the same fashion as
a two-port electrical network, such as is described in electrical
engineering and physics texts, e.g. Scott, The Physics of
Electricity and Magnetism, 2nd ed., 1966, John Wiley & Sons,
Inc., New York, p. 500. We consider a black box with two connection
terminals, 1 and 2. We know only that the box is passive,
containing no internal energy sources, and that its responses are
linear. Though this box is usually described as an electrical
network, the physical principles apply equally to mechanical
systems. The electrical-to-mechanical analogy is as follows. There
is a known input electrical current analog, here a vibrational
velocity V1 (terminal 1, Mode not applicable); a known input
voltage analog, here a vibrational force F1 (terminal 1, Mode not
applicable); a known output current analog, here velocity-of-change
of the arterial semi-axis length, V22 (terminal 2, Mode 2); and an
unknown output voltage analog, here the force F22 (terminal 2, Mode
2) driving the vibration mode. These forces and velocities are
related by simultaneous equations 3 and 4, with four
velocity-impedance coefficients. (In electrical networks, these are
usually stated as admittance coefficients, although the equations
are easily rewritten in equivalent form using impedance
coefficients.)
The Theorem of Reciprocity proves that two of these Z-coefficients
are equal. They are both designated Zt2, for transfer impedance,
Mode 2. Zt2 and the input and output impedances Z1 and Z22 are
unknowns to be determined. Observe that the total "surface
mechanical impedance" experienced by the vibration driver is the
complex ratio F1/V1, not to be confused with Z1 of Eq. 3. The
measured surface mechanical impedance is influenced by arterial
velocity V22 via transfer impedance Zt2.
We designate a further arterial impedance, Za2, attributed to the
vibrating pressurized blood inside the artery. The force F22 is
exerted entirely to overcome impedance Za2 and excite velocity V22
in the cylinder of blood. There is no active source of vibration in
the artery to affect the measurements. (Noise from blood flow is
present, but is uncorrelated with the vibration driver sinusoid,
and thus causes no average error in the demodulated vibration
signals.) Hence, we may represent F22 as -V22.multidot.Za2. The
minus sign arises from the defined direction of F22 relative to
V22. We may thus rewrite Eq. 4 as Eq. 5, in terms of the combined
tissue-plus-artery impedance, (Z22+Za2), reducing by one the number
of complex unknowns.
If blood pressure changes, this alters the sum (Z22+Za2).
Designating the altered values at the new blood pressure with an
apostrophe ('), for prime, then we obtain a second set of
measurements represented in Eqs. 6 and 7, were V1', F1', and V22'
are measured and the Z-coefficients are presumed to be
unchanged.
Eqs. 3 and 6 can now be solved simultaneously, yielding Z1 and Zt2.
Substitution into Eq. 5 yields (Z22+Za2), and into Eq. 7 yields
(Z22+Za2)'. In Eq. 4, the force F22, representing
-V22.multidot.Za2, is still unknown, as is Z22.
This solution relies on a change in pressure that alters the
vibration measurements to an extent resolvable to useful accuracy.
The pressure change need not be known. The system reveals its
properties when blood pressure varies, because the phase and
amplitude of arterial vibrational motion are altered, and because
the effect of this alteration on driver velocity and on driver
force is measured, revealing the precise effects of the coupling
between the vibration driver and the artery.
To illustrate the parallax increment argument given above,
subtraction of Eq. 3 from Eq. 6 yields an equation with the
increment terms V1'-V1, V22'-V22, and F1'-F1. Solving
simultaneously with Eq. 3 yields the same result as solution of
Eqs. 3 and 6 directly. The vibrational change induced by blood
pressure can be regarded as an independent vibration signal,
generated within the artery, measured by the ultrasound system, and
felt as the effects propagate to the surface sensors. Combining the
data on this parallax signal with the Eq. 3 data on the baseline
signal yields the critical transfer-impedance coefficient, Zt2,
permitting subsequent solution for the inaccessible impedances
(Z22+Za2) and (Z22+Za2)'.
For simplicity, the geometry of the system has been implicitly
presumed constant through the change in blood pressure. Arterial
radius is different at different pressures most of the time, but
not at every instant. The most accurate analysis relies on
extracting data sets for which equal radii are observed at
differing pressures, as evidenced by differing vibration
measurements. Pulmonary artery radius waveforms have been observed
to lag behind corresponding internal pressure waveforms, apparently
because of visco-elastic behavior of the arterial wall. In
peripheral arteries, averaging over several heartbeats, radius has
been observed to correlate better with average flow rate than with
average pressure, apparently because of active regulation of the
smooth sphincter muscles in the artery walls. Whatever the cause of
poor pressure/radius correlation, the phenomenon is useful for the
current invention because it allows the system to obtain
matched-radius data pairs with pressure separation. The network
algorithm can then be applied without correction for differing
geometry.
In situations where the data fail to yield useful pressure
separation for equal-radius data points, the network algorithm
becomes more complicated. The single-mode solution just illustrated
is based on unchanging values for driver self-impedance, Z1, and
driver-artery transfer-impedance, Zt2. The combined
artery-plus-surround self-impedance, Z22+Za2, is affected by
changes in both pressure and radius, but for the moment, the two
sources of change need not be distinguished. Z1 is substantially
unaffected by arterial radius change. This leaves Zt2, which is
significantly altered by radius change. Where the data for Eqs. 6
and 7 are for a different radius than for Eqs. 3 and 5, it is
necessary to rewrite Zt2 to analyze radius-change sensitivity.
An expression is derived for the complex ratio Zt2'/Zt2, where Zt2
applies to Eqs. 3 and 5, and Zt2' applies to radius-altered Eqs. 6
and 7. This expression permits solution of the network algorithm
where there is radius change. This ratio is determined iteratively,
proceeding from an estimated Zt2'/Zt2 ratio to solve the network
algorithm, then using the approximate network results to improve
the estimate of Zt2'/Zt2, then using this ratio to re-solve the
network algorithm, etc. Zt2=2.multidot.Vt2.multidot.Z22,
approximately. Here, "Vt2" represents the velocity transfer
coefficient for Mode 2. To understand the physical significance of
Vt2, imagine that the artery has been removed and replaced by a
uniform tissue whose mechanical properties match the average
properties of tissues immediately surrounding the artery. Under
these conditions, Za2=Z22, and Vt2=V22/V1. In the section
"Simulation Algorithms", it is argued that the vibration field in
the vicinity of an organ or artery can usually be approximated as a
potential field under this hypothetical condition of tissue
uniformity. For a two-dimensional potential field, it is easily
shown that Vt2 varies linearly with radius, r (or more generally,
Vtn varies as r.sup.n-1). Assuming that the effects of tissue
elastic modulus are small (a good approximation at the frequencies
used to probe a systemic artery), the phase angle of Vt2 is a
simple function of the phase angle of Z1, and the magnitude of Vt2
equals radius multiplied by a function of artery center-depth. The
specifics of the approach are the effective vibrator method
described (in the context of a circular driver) under "Regions
Dominated by Potential Flow" in the "Simulation Algorithms"
section. The real part of Z22 varies in proportion to r.sup.2,
while the imaginary part varies as a power law of r that is a
function of the phase angle of Z22. A Z22 phase angle approaching
zero implies a zero-power law, r.sup.0, while a phase angle
approaching +90.degree. implies a first-power law, r.sup.1. The two
functions of phase angle just described are derivable using
simulation algorithm techniques. With the information given here
and in the "Simulation Algorithms" section, it is possible to solve
the network algorithm for measurements at different radii. Solution
at a number of frequencies reveals the frequency dependence of Z1,
Zt2 and (Z22+Za2). This information can be used in more
sophisticated corrections for arterial radius, in a procedure where
network solutions are improved iteratively, based on simulation
algorithm evaluation of the frequency dependences of network
parameters.
It can be shown that the mechanical impedance associated with blood
pressure as it restores an artery to roundness in a particular
vibration mode shape is directly proportional to blood pressure,
inversely proportional to frequency, and indepenent of arterial
diameter, tissue properties, etc. As shown in Eq. 8, pressure
impedance Zpn for vibration Mode n is imaginary, containing the
imaginary unit "j" in the denominator, multiplied by angular
frequency "f" in radians/second.
The Mode n=2 and n=3 cases are especially important:
Where a relatively pure Mode n=2 vibration is obtained and analyzed
by the network algorithm for constant radius r and frequency f,
then changes in impedance (Z22+Za2) are simply the changes in Zp2.
Hence, we can solve for changes in pressure P.
If artery radius differs for different pressures, then it is more
difficult to determine pressure change. The change in radius alters
the entire geometry of the vibration field, changing effective
vibrating mass and damping. It becomes necessary to obtain a
complete solution for absolute pressure. Two rapid methods for
real-time pressure tracking are described briefly. Subsequent
sections provide details to implement these methods.
As an extension of the network algorithm with simulation-algorithm
corrections for radius change as described above, we have seen how
to estimate the transfer ratio Vt2, and how to use the phase angle
and radius-dependence of Vt2 to determine Zt2. Once this is
accomplished, we can determine artery-surround impedance Z22. The
network algorithm gives the sum, Z22+Za2. Hence, we can subtract
Z22 and solve for Za2. Using methods to be described under
"Absolute Pressure from a Simplified Simulation", we learn how to
estimate the component of Za2 attributed to inertial
impedance--half of Zm of Eq. 15. This estimate can be refined,
based on the real-valued damping component of Za2. Subtracting the
imaginary inertial impedance term from the imaginary part of Za2
yields pressure-impedance Zp2. Solution of Eq. 9 subsequently
yields absolute pressure, P.
The second method is to take measurements and compute values for a
patient-calibration function, tabulating reference pressures and
corresponding vibration parameters as functions of radius. When
vibration parameters are subsequently sampled, they are inserted
into Eqs. 6 and 7 while radius-interpolated tabular reference
parameters are inserted into Eqs. 3 and 5. Network algorithm
solution yields a change in the arterial impedance (Z22+Za2), which
is related to a change in blood pressure via Eq. 9. The resulting
pressure increment is added to the interpolated reference pressure
for current radius, yielding current blood pressure.
Of the two rapid methods for pressure determination, the latter
requires more lead time to develop a calibration table, but the
subsequent computations are probably both quicker and more
accurate.
Wall Stiffness Impedance
Arterial wall stiffness causes a velocity impedance having a
similar form to Eq. 8, but independent of pressure and having a
fourth-power dependence on Mode number n. If arterial wall
thickness is approximated as constant during the course of a
vibration cycle, then Eq. 11 describes the mechanical impedance Zwn
due to wall stiffness.
For the important Mode n=2 and n=3 cases, we write:
Eq. 14 expresses the important difference in proportions between
wall stiffness impedance and pressure impedance for Modes 2 and 3.
When net effective pressure is computed, separately, for the two
modes, the difference in results will represent 0.8984 times the
Mode 2 wall stiffness pressure.
The approximation that artery wall thickness does not vary at the
vibration frequency, as needed for Eqs. 11-14, is valid if the
thickness of the arterial wall is not too large a fraction of
radius and if the wall material is much stiffer than adjacent
tissue. Under these conditions, the "thin" wall can be bent
significantly, but the relatively weak tangential shear forces from
adjacent tissues will not cause significant tangential stretch
displacements. If the wall is healthy and compliant, there may be
significant tangential stretch displacements, but in that case,
stiffness impedance Zw is small and unimportant.
Where geometry corrections for changing radius must be
incorporated, the dependence of Zwn on radius must specified. A
stiffness correction is based on the principle that arterial wall
thickness varies roughly as the reciprocal of mean radius, to
maintain constant tissue volume under incompressible deformation.
Stiffness of a beam or sheet is known to vary as the cube of
thickness and inversely as the cube of length. Since the
circumferential length of the arterial wall sheet varies in
proportion to radius, it follows that arterial stiffness impedance
varies roughly as the inverse sixth power of radius. Actually,
non-linear changes of tissue elastic modulus with radius-change
cause stiffness impedance to vary somewhat more gradually than the
inverse sixth-power law.
Absolute Pressure From A Simplified Simulation
To solve mathematically for absolute blood pressure, we must
determine the detailed makeup of the term (Z22+Za2). To a first
approximation, the imaginary part of (Z22+Za2)is composed partly of
the restoring impedance (Zp2+Zw2), and partly of an inertial
impedance dependent on the mode shape, the arterial diameter and
the average density of blood and surrounding tissues.
There are several ways to evaluate the inertial impedance and
extract approximations of blood pressure. The most precise way, as
previewed earlier, is to fit a rational analytic function to the
measured data and extract the coefficient corresponding to
pressure. This approach is quite abstract. What is needed are
simple models that indicate the kind of signal to expect and how to
design equipment to receive such a signal. This and more
sophisticated models tied to the details of arterial structure
become valuable in the broadened context where we wish not only to
find blood pressure, but to interpret measured impedance data and
gain information on the behavior or the artery itself. This kind of
question becomes central in the whole-organ embodiment, where
evaluation of tissue responses is a primary goal.
From potential flow theory, applying the force definitions of Eqs.
1 and 2, it can be shown that Eq. 15 gives non-viscous inertial
mass impedance Zm, as a function of frequency f (multiplied by the
imaginary unit j), average density .rho., artery radius a, and Mode
number n:
Zm is an impedance per-unit-length. Half of Zm is attributed to
exterior moving mass (e.g. a part of Z22 in the Mode 2 case), and
the remaining half is attributed to interior moving mass (e.g. a
part of Za2 in the Mode 2 case). Notice the special n=1 case of
rigid cylinder motion. In this case, halving Zm, we recognize the
formula for mass per-unit-length of a cylinder, multiplied by the
ratio of acceleration to velocity, j.multidot.f. The other half of
Zm is attributed to surrounding fluid. For higher n, the inertia
decreases as the field of motion becomes increasingly localized to
the immediate vicinity of the vibrating cylinder surface.
Combining Eq. 15 with Eq. 8 gives the Mode n resonant frequency,
frn, where pressure and inertial impedances cancel, leaving only a
damping impedance. We can expect the imaginary part of the network
impedance term (Z2n+Zan) to pass through zero in the vicinity of
frn:
The Mode n=2 and n=3 cases are the most useful:
To correlate these formulas with a real artery, set r to the
estimated radius in the artery wall where pressure has fallen
halfway from internal blood pressure to ambient pressure. To obtain
an effective weighted-average density, .rho., weight estimated
arterial wall density by n multiplied by (wall-thickness/radius),
and for the remainder of the average give equal weightings to
estimated blood density and surrounding tissue density. Thus, if
wall thickness is 9% of r, then effective average density for n=2
is 2.times.9%=18% of wall tissue density, plus 41%, each, of blood
density and surrounding tissue density, to give a 100% total
weighting. For n=3, the weighting factors become 27%, 36.5% and
36.5%. Note that the three densities entering the weighted average
will not differ greatly unless calcification has increased wall
density, or unless the material around the artery is very fatty and
therefore less dense. A better corrected-density estimate, still
based on the simplifying assumption of non-viscous fluid flow,
takes into account the effective thickness over which blood
pressure drop takes place.
The vicinity of fr2 provides the greatest sensitivity of vibration
measurements to pressure change. For normal blood pressure and
typical carotid artery dimensions, the radian-frequency fr2
translates to about 300 Hz. Because the resonant quality factor, or
Q-factor, of arterial vibrations is typically less than 1.0, the
usable Mode 2 measurement frequency region typically extends from
150 to 600 Hz. Since resonant frequency varies only as the square
root of blood pressure, good signals can be obtained continuously
at around 300 Hz without varying frequency over time to track
changing frequency fr2.
The most sensitive data on Mode 3 vibrations are obtained at fr3,
which is twice as high as fr2 in Eq. 17, and possibly more than
twice as high when the large Mode 3 contribution to P from wall
stiffness is considered. Consequently, the system uses a
higher-frequency measurement range for correlating Mode 2 and Mode
3.
Analytic Function Fit Algorithm
The most recent analysis provides a sense of the nature and
magnitudes of the significant terms in arterial vibration dynamics.
A general equation for the impedance associated with vibration Mode
n expresses this understanding:
For n=2, Z2 corresponds to (Z22+Za2) of network algorithm Eq. 5, or
to the corresponding primed quantity of Eq. 7. Where an artery is
shallow enough to obtain good Mode 3 excitation, and where the
three-angle ultrasound system resolves the modes, Z3 may also be
determined by a network algorithm. Hence, we analyze the
frequency-dependence of Zn, normally for n=2 or 3, deriving data on
Zn from multiple applications of a network algorithm using both
pressure-baseline and frequency-baseline data. From this analysis,
we distinguish the effect of pressure from other overlapping
effects.
It is realized that a wall stiffness error may reside in the term,
P. The damping and mass terms, D and M, are functions of frequency
f. From Eq. 15, we know that M(f) approaches
(.rho..multidot.2.multidot.pi.multidot.a.sup.2 /n) in the
high-frequency limit, where viscous shear ceases to entrain extra
mass. M is greater than this high-frequency value as f approaches
0. D(f) goes in the opposite direction, from a low-frequency
minimum where viscous and shear forces control the flow pattern and
prevent steep shear velocity gradients, up to a high-frequency
maximum where shear gradients are quite steep, being confined to
the arterial wall thickness over which pressure drops from blood
pressure to ambient pressure. Define Mode n resonant frequency,
frn, as the frequency where complex impedance Zn is real-valued.
The relationship of frn to P is shown in Eq. 20:
Pressure P is nearly computable from known data, given the tools of
network analysis. Where Mode n=2 is dominant, we can easily measure
zero-phase frequency frn, here fr2. In the vicinity of fr2, we can
evaluate the imaginary part, IM, of the frequency slope of
impedance Zn. Relatively simple simulation models tell us how the
log-log slope, d(ln(M))/d(ln(f)), typically varies as a function of
the non-dimensional quality factor, Q, defined by Eq. 21:
At resonant frequency fr2, denominator Z2 is real by definition. If
D and M were constants, defining a simple second-order system, then
Eq. 21 would give the actual resonant quality factor Q, and the
log-log slope of Eq. 20 would be zero. For the more complex viscous
flow problem being considered here, absolute pressure can be
computed from Eqs. 20 and 21 plus an empirical expression for the
log-log slope of Eq. 20 as a function of Q. This empirical function
is derivable from computer simulation studies, with possible
refinement based on animal studies and clinical studies of patients
who require arterial catheterization.
Eqs. 22-24 provide a basis for a function-fit approach to determine
pressure P, using more computation time but achieving better
accuracy: ##EQU1##
As Eq. 24 suggests, the measured complex function Zn of the
imaginary argument j.multidot.f can be expressed as a part of the
encompassing complex function Zn of the arbitrary complex variable
s, i.e., as part of Zn(s). As long as Zn arises from a causal
linear network ("causal" networks are mathematically defined as
responsive only to past and present input, and not to inputs that
have not yet arrived), this extension to a complex function is
valid and, for most applications of importance to this invention,
uniquely defined. Furthermore, Zn(s) is an analytic function, i.e.
it has a unique complex derivative and desirable extrapolation
properties. Both the real and imaginary parts of the measured
responses bear on the extrapolation of the imaginary part of the
function towards zero frequency, to determine pressure-dominated
response in a frequency range where measurement accuracy
deteriorates. For insight into the connection between imaginary
parts and real parts of measured, causal response functions, both
in the time and frequency domains, see "The Hilbert Transform", by
N. Thrane, Ph.D., in Technical Review No. 3--1984 by Bruel and
Kjaer Instruments, Inc., 185 Forest Street, Marlborough, Mass.
01752.
A useful form for an analytic function that can be fitted to a
finite number of empirical data points is the ratio of two complex
polynomials. The polynomial coefficients must be real numbers,
since non-zero imaginary parts of the coefficients would lead to
assymmetry of Zn for positive and negative frequencies, unlike
real-world impedances. Finally, the expression should fit the
behavior of Eq. 19, where the real-valued functions D(f) and M(f)
approach finite limits as frequency f goes to zero and to infinity.
This is accomplished by starting the denominator polynomial with a
first-order term in s and terminating it at order m, while
extending the order of the numerator by one at either end, from a
zero order starting term to an m+1 order final term. These criteria
are all incorporated into Eq. 22. The first-order denominator
coefficient "B1" can always be simplified to "1" by dividing the
value of B1 through both the numerator and denominator
coefficients.
Clearly, coefficients A0, A1 and A2 of Eq. 22 correspond to the
low-frequency limit values (n.sup.2 -1).multidot.pi.multidot.P,
D(0) and F(0). In the high-frequency limit, where the highest-order
terms dominate, the pressure-related, damping and mass terms of Eq.
19 correspond to Am-1/Bm, Am/Bm and Am+1/Bm, respectively. The
Am-1/Bm ratio is not reliably correlated with real pressure or
stiffness, however, since pressure and stiffness effects are
swamped in the high-frequency data by damping and inertial effects.
Physical significance may be attributed to the high-frequency
damping and mass terms of the polynomial expression. By comparing
the empirical mass term, Am+1/Bm, with the value derived for Eq. 15
using the effective radius and density procedures described, it is
possible to seek density anomalies due, for example, to artery wall
calcification. Recall that Eq. 15 is valid in a high-frequency
limit, where damping forces cease to perturb vibrational geometry.
The high-frequency damping coefficient, Am/Bm, may carry physical
significance, although it may not accurately reflect the
infinite-frequency limit behavior of the artery, depending on the
quality and frequency range of the data.
The Ai and Bi coefficients are real values to be determined from
data. Multiplying through by the denominator of Eq. 22 and
collecting terms gives: ##EQU2##
Eq. 25 splits into two real-number equations if the real and
imaginary parts are equated separately. Both equations are linear
in Ai and Bi and are defined completely by one impedance Zn at one
frequency, i.e., one s. Determinations of Zn at m+1 separate
frequencies and a fixed pressure give 2m+2 equations to solve for
the combined total of 2m+1 Ai and Bi coefficients. One excess
equation may be dropped. The separate impedance determinations are
obtained using pressure-matched pairs of cardiac cycles, one
monitored at a reference frequency to recognize the reference
pressure point in the cycle, and the second cycle monitored at a
new frequency for each pair, as described above.
Additional frequency determinations of Zn permit a least-squares
regression to obtain a statistically better fit for a given order,
m. Once we have solved for coefficient A0, we can solve for
pressure P using Eq. 23.
Setting m too high in Eqs. 22 and 25 is likely to cause increased
function-fit errors, because the fitted function follows noise in
the data. Using a given set of Zn versus s data and least-squares
regressions, we start with a small m and determine pressure for
successively higher m. Computed pressure will first settle with
decreasing steps toward an apparent limit, but will then show
increasing fluctuations as m becomes too high. A value of m is
found for routine machine computations such that computed pressure
is minimally sensitive to m.
Pressure could also be determined from a data fit by using a
generalized simulation model for an artery, with undetermined
physical parameters for stiffnesses, viscosities, densities, radii
and even possible coupling terms for nearby disturbing influences,
e.g. tendons. The more abstract approach just shown is
computationally simpler and probably at least as good in its final
result. A detailed simulation model would provide information
besides blood pressure, and may be needed in more complex
situations, for example, to probe the mechanical properties of
organ tissues. More extensive uses of detailed simulation
algorithms are described below.
A Simplified Version of the Systemic Arterial Pressure
Embodiment
The concepts so far discussed are easily applied to a simplified
version of the systemic arterial pressure embodiment, using only a
single ultrasound beam. Referring to FIGS. 2 and 3, we see that the
reference segment 52 of assembly 2 could be thickened and an
ultrasound transducer set in its center, beamed straight down. The
ultrasound assembly is then similar to assembly 65 of FIG. 3,
except that the long, slightly tapered conical section of housing
originally cut obliquely for angling skin contact is cut short and
straight across in the simplified version. The divergent acoustic
lens remains, but with reduced defocusing in the plane that cuts
across the artery. The operator centers the transducer assembly
over an artery by maximizing ultrasound echo signal strength, and
aligns the assembly based on anatomical knowledge of the artery
below.
When an artery receives negligible Mode 3 excitation and when Mode
2 excitation aligns with the transducer symmetry axis and the
ultrasound beam, the single-mode network algorithm and analytic
function fit algorithm suffice to solve for blood pressure.
Left-right tissue asymmetries can cause misalignment between the
ultrasound and vibration mode axes, leading to pressure errors. For
many anatomical sites, such asymmertries are negligible. This
single-mode determination does not resolve ambiguities of wall
stiffness.
In the next section, we consider a single-axis ultrasound vibration
measurement that includes resolvable Mode 3 excitation. Assuming
left-right tissue symmetry, we show that the measured data is not
quite sufficient to allow a "pure" two-mode network solution. One
can complete the solution using a few fairly reliable simulation
assumptions. Hence, with an artery segment in the right depth range
and in fairly symmetric tissue surroundings, the simplified version
of the systemic arterial pressure embodiment can provide an
estimate of blood pressure corrected for arterial wall stiffness.
Undetectable errors may arise due to assymmetric tissue
surroundings, however, giving the two-transducers, three-axis
ultrasound approach an advantage in accuracy and confidence,
mitigated by increased hardware cost.
The Two-Mode Network Algorithm
If the ultrasound system measures depths of near and far walls of
an artery along a single axis, and if that axis is presumed to be a
major vibration axis for Modes 1, 2 and 3, then the equivalent of
one real parameter of the network solution remains undetermined.
The ambiguity is approximately resolved by a simple correction
based on the relative sensitivities of different modes to arterial
radius change. More sophisticated simulation analysis can improve
the approximation. We call this overall approach the two-mode
network algorithm, since there are two pressure-sensitive modes
involved, 2 and 3. The presence of pressure-insensitive Mode 1 adds
some difficulty.
For convenience, vibrator velocity V1 is defined as a constant
reference quantity, and all other variables are expressed relative
to this reference, as was discussed under "Vibrations as Complex
Numbers". Arterial wall velocity V2 splits into measured
common-mode and differential velocity components, V2c and V2d. The
measured common-mode velocity, V2c, has two superimposed Mode
contributions: V2c=V21+V23, for Mode 1 and Mode 3. We avoid
subsequent use of the unknown amplitude V23 by substituting
V23=V2c-V21. Since only Mode 2 contributes significantly to the
measured differential velocity, we set V2d=V22. The measured driver
force, F1, consists of Mode 2 and Mode 3 transfer impedance
contributions, plus a pressure-insensitive contribution, Fpi. The
force driving Modes 2 and 3 is then the total driver force minus
the pressure-insensitive contribution: F1-Fpi. Mode 2 and Mode 3
transfer impedances, Zt2 and Zt3, complete the variable list. With
these, we may write Eqs. 26-28:
Eq. 26 states that the pressure-sensitive component of the driver
force, obtained by subtracting the unknown Fpi from measured F1,
arises from the two pressure-sensitive transfer impedances Zt2 and
Zt3, multiplied by the corresponding mode velocities V22 (=V2d) and
V23 (=V2c-V21). Eq. 27 states that there is zero internal active
force driving V22 (=V2d), so 0 is equated to the sum of the
transfer-force V1.multidot.Zt2, plus the passive internal impedance
force V2d.multidot.Z2. Eq. 28 expresses the same thing as Eq. 27,
except for Mode 3.
If there is a delta-pressure, Pd, altering vibration conditions at
constant diameter, we obtain a second set of of equations. Scaled
V1 is held constant at its reference value, which is simply (1+0j)
if all other measurements are scaled using complex division by the
unscaled V1. Changed quantities are designated by an apostrophe
('), for "primed" values in Eqs. 29, 30 and 31:
V1 is not primed since by adjusting other variables to this
reference, V1 remains unchanged. V21 is not primed, since this Mode
1 excitation is unaffected by the pressure change at constant
arterial diameter, and so remains constant relative to V1. The
factors 3K and 8K come from Eqs. 9 and 10, with K defined by Eq.
32, expressing the sensitivity of Z2 and Z3 to delta-pressure Pd.
For the six equations 26-31, there are six complex unknowns plus
one real unknown: Z2, Zt2, Z3, Zt3, V21, Fpi, and the real
variable, Pd. All other quantities are defined by measurements. For
solution, it is convenient to rewrite Eqs. 29-31 as differences
with corresponding Eqs. 26-28 subtracted out (i.e., as "parallax
equations" for pressure baseline "movement", recalling the earlier
heuristic explanation of the meaning of these measurements):
Beginning with a tentative value for Pd, to be subject to
iteration, the remaining equations can be solved, recalling that
most of the varibles are measured knowns. Beginning with Pd and Eq.
34, we solve for Z2; then with Eq. 27 for Zt2; then with Eq. 33 for
Zt3. We must then solve Eqs. 28 and 35 simultaneously for Z3 and
V21. The solution is quadratic in V21, leading to two values for
V21 and, upon substitution, two values for Z3. The extraneous
quadratic root for V21, and the corresponding Z3, must be
recognized and discarded. The correct quadratic root is used to
solve Eq. 26 for Fpi. In most situations, the extraneous quadratic
root can be recognized as "unreasonable" in terms of anatomy and
physics.
The above analysis presumes no corrections for changing arterial
radius at different pressures. In situations where
differing-pressure data can be resolved only at differing radii, it
is necessary to account for radius-sensitive changes in transfer
impedances. The basic approach to this has been described for the
single-mode network algorithm. The same principles apply here.
To determine Pd, more information is needed than the network
algorithm can provide directly. The analytic function fit algorithm
is therefore applied. To obtain equal-pressure data extended along
a frequency baseline, using matched pressure-cycle pairs, data
quadruples (f, F1, V2c, V2d) are required, each referenced to a
fixed V1. The quadruples are required for a set of frequencies,
f=f1, f2, f3, etc., with enough frequencies to obtain analytic
function fit solutions. At each frequency, the data quadruples must
be measured at two distinct pressures, P1 and P2, to be determined,
but recognized as differing pressures by differences in vibration
data. The same two pressures are required for each frequency. This
is accomplished by the pressure-cycle matching process (described
previously). If a pressure differential Pd=P2-P1 is assumed, then
the network algorithm can be solved for arterial impedances at P1
and P2 for each of the measured frequencies. This impedance data
plugs into the analytic function fit algorithm, which yields values
for P1 and P2. The difference, P2-P1, is used to establish a
revised estimate of Pd, which feeds back into the network and
analytic function fit solutions in an iterative manner, to
convergence. The network and analytic function fit algorithms are
thus solved simultaneously.
Given dual-mode pressure solutions, detectable arterial wall
stiffness will cause a positive apparent pressure difference,
(P3-P2), for Mode 3 and Mode 2 pressures. Recalling Eq. 14, this
pressure difference represents the Mode 2 wall stiffness "pressure"
multiplied by 0.8984. The value P2-((P3-P2)/0.8984) therefore
represents absolute fluid pressure, corrected for wall
stiffness.
Three-Axis Ultrasound Interpretation
The analysis shown so far is valid only to the extent that
vibration-mode principal axes all lie parallel to an ultrasound
axis, as with the single-axis variation of this systemic arterial
pressure embodiment. If this symmetry criterion is met, then
three-axis ultrasound measurements suffice to determine the
separate Mode 1, Mode 2 and Mode 3 vibrational excitations. With
these data, the two-mode network algorithm can be solved
separately. Then, the analytic function fit algorithm need only be
solved once for an absolute pressure.
If single-axis vibration symmetry is not assumed (the assumption is
often inaccurate), then the network and analytic function fit
algorithms must be solved simultaneously, iteratively, even with
three-axis ultrasound data.
To understand the data requirements for resolving
simultaneously-excited vibration modes, consider Mode 1 for
single-frequency excitation. Mode 1 is a simple translational
motion in two dimensions. Whenever single-frequency sinusoidal
motions along different axes in a plane are superimposed, the
resulting trace is an ellipse (including the special cases of a
circle and a line segment, which is a degenerate ellipse). To
specify all the parameters of the trace, begin by specifying the
two components of the major axis vector. Resolving the component of
sinusoidal trace motion along this major axis, the third parameter
is the phase of this major-axis sinusoid relative to a specified
reference phase (e.g., vibration driver velocity V1). Rotating in
space +90.degree. from the major-axis vector, the minor-axis
amplitude is described as the fourth parameter. This amplitude is
positive for counter-clockwise rotation, or otherwise negative. By
choosing to measure along the major and minor axes, the phase of
trace motion resolved along the minor axis is constrained to differ
from the major-axis phase by 90.degree.. Hence, four parameters
completely specify the vibrational motion.
For single-frequency excitation of a higher-order shape mode, four
parameters are again sufficient. Recalling the descriptions of
Modes 2 and 3 in conjunction with FIG. 5, it is seen that two
energetically-orthogonal shapes are separated by principal axis
rotations of 45.degree. for Mode 2 and 30.degree. for Mode 3.
The three-axis ultrasound system resolves three common-mode and
three differential-mode vibrational velocities. Each resolved
velocity has 0.degree. and 90.degree. phase components. The
resulting six differential-mode components are more than sufficient
to determine the four parameters of the differential Mode 2
vibration. The six common-mode components are insufficient to
determine the eight parameters needed to determine both Modes 1 and
3. To help resolve the uncertainty, Mode 1 excitation is not
significantly affected by either pressure or radius changes in the
artery, while pressure and radius sensitivities of higher modes
have been described. This is useful for determining the Mode 3
velocity transfer ratio parameter, Vt3, which in this context is a
four-parameter quantity, like the vibration modes, involving two
energetically-orthogonal versions of the Mode 3 shape. Common-mode
vibration changes directly reveal the major-axis direction and
major/minor axis amplitude ratio for Vt3. Final resolution of the
network algorithm uncertainty uses simultaneous solution of the
network algorithm with the analytic function fit algorithm. The
detailed solution process follows directly from the principles and
procedures already described.
Electronic Signal Acquisition
The functions of vibration driver and sensor assembly 1 (FIGS. 1-3)
have been described. We now described what happens to the
electronic signals that pass via cable 2 (FIGS. 1, 2) between
assembly 1 and computer/controller 3.
The signal processing is illustrated in FIGS. 7, 8 and 9. The
"Ultrasound Data Acquisition" assemblies of FIG. 7 generate and
receive broadband ultrasound signals (typically exceeding 500 KHz
bandwidth) and process them into low audio-band (typically below 1
KHz) analog voltages representing arterial wall depths and echo
signal strengths. FIG. 8, "Ultrasound Sequencing", illustrates
timing waveforms from FIG. 7. FIG. 9, "Computer Input Interface",
illustrates how all low audio-band data is demodulated and/or
filtered to yield depth and vibration phaser signals with typical
bandwidths of 20 Hz. These narrow-band signals are predigested
vibration data that is sampled and digitized for computer
input.
In FIG. 7, modules across the top perform pulse-generating,
shaping, amplification and switching. Modules across the middle of
the figure perform gain controlled amplification, further
pulse-shaping, 90.degree. phase-shift filtering, and digital
sequencing, including the control of oscilloscope display
functions. Modules across the bottom of FIG. 7 cause the time
window of highlighted segment 15 on the oscilloscope trace to track
a positive-sloping waveform zero-crossing. In the 90.degree.
phase-shifted counterpart of the tracked signal, a peak amplitude
appears in the tracking time window. A lowpass filter circuit
averages this 90.degree. signal over select-time windows, yielding
a narrow-band output representing signal strength in the vicinity
of the tracked zero-crossing. Computer selection of the phase
signal to be tracked allows the tracking circuitry to move forward
and backward in delay time through 90.degree. phase increments.
Thus, the computer can access and track almost any peak or
zero-crossing in the ultrasound waveform. This tracking circuitry
in the lower portion of the diagram is repeated six times
(including the one repetition drawn), to track near- and far-wall
depths for the three ultrasound angles generated by transmissions
and receptions of the two ultrasound assemblies, 62 and 65 (FIGS. 2
and 3).
The echo depth signals generated by repetitions of the lower
circuitry in FIG. 7 are designated N1 through N6. The signal
strength voltages are designated M1 through M6. These signals all
enter the "Computer Input Interface" assemblies illustrated in FIG.
9. Here, the "N" signal voltages are filtered, and these plus the
already-filtered "M" signals are sampled and digitized for input to
the computer as non-vibrational ultrasound dimension and signal
strength data. In addition, the "N" signals are processed for
audio-band vibration content, yielding narrow-band demodulated
phaser signals representing 0.degree.-phase and 90.degree.-phase
components of common-mode and differential-mode depth
vibrations.
In the circuit diagrams, all input-only connections are marked by
arrows pointing into circuit modules. The absence of an arrow means
that a connection is an output or is bi-directional. All contiguous
branches of a wire within a diagram are designated by a single
number. Interconnection points for jumps between regions within a
diagram or between diagrams are designated by labeled circles,
whose numbering is kept the same at all repetitions of the circle
symbol. Wire numbers change for non-contiguous regions joined by
circles. In FIG. 8, waveform traces are labeled with the number or
numbers of all wires or interconnects of FIG. 7 that carry the
illustrated signal voltage. The horizontal axis in FIG. 8 is
time.
Examining FIG. 7 in detail, we begin with clock input 200,
designated CK, from the computer. This input travels via wire 201
into sequencing circuit 202, labeled SEQ. This digital circuit
contains a counter that starts at zero and counts upward on clock
pulses, timing all the processes of a complete ultrasound data
acquisition cycle. Upon reaching a full count, the counter resets
to zero and starts a new cycle. To generate the output waveforms,
multiple-input gating circuits monitor the counter and recognize
specific counts where waveform transitions are to take place. The
outputs of these count-recognition gates trip appropriate flip-flop
circuits, whose outputs are the timing waveforms. Sequencer circuit
details, not shown, are easily provided by digital circuit
designers.
In FIG. 8, the beginning of a full acquisition cycle is marked by
arrow 400 and the associated dashed line extending below, while the
termination of that cycle and the beginning of the subsequent cycle
is indicated by arrow 401 and the associated dashed line below. The
FIG. 8 waveforms include: sequencer outputs 211, 203, 276-277-315,
278-279, 280-281, and 265; timing ramp 225-264-310 triggered by the
sequencer; pulses 268-269-330, 270-271, 272-273, 274-275, 402, and
403, associated with the times of ultrasound waveform
zero-crossings being tracked; and display intensity control
waveform 267. The sequencer cycle consists of three sub-cycles,
corresponding to ultrasound pulse generation and reception for the
three ultrasound paths. A binary select signal on wire 203 (FIG. 7)
and trace 203 (FIG. 8) enters coaxial cable 204, which is part of
cable assembly 2. This signal controls the switching circuits in
sub-assembly 56 of assembly 1 (FIGS. 2 and 3, only the physical
location of the sub-assembly shown) that select one of two
impedance-matching transformer secondary windings (as designated)
for coupling via coaxial cable 205 (FIG. 7) of cable assembly 2,
thus determining which of ultrasound transducer assemblies 62 and
65 (FIGS. 2 and 3) is accessed. A low logic level on wire 203
selects transducer assembly 62 and its matching transformer for
coupling to cable 205 and wire 209. A high logic level selects
assembly 65 and its matching transformer instead. The high logic
levels on trace 211 (FIG. 8) mark pulse transmit times, while the
low logic levels mark echo receive times.
Following traces 203 and 211 together from arrow and dashed line
400, ultrasound assembly 62 is initially selected (203 low) to
transmit a pulse (211 high), and remains selected (203 low) to
receive the echo (211 low). At the end of the first sub-cycle,
transducer assembly 65 is selected (203 high) to transmit a pulse
(211 high) and receive the return echo (211 low). This time,
assembly 65 remains selected (203 high) to transmit another pulse
(211 high), but assembly 62 is immediately coupled (203 low) to
receive the echo (211 low). Thus, the third timing sub-cycle is for
a transverse echo signal from assembly 65 down to the artery and
back to assembly 62. The cycle concludes at dashed line 401, and a
repetition begins.
Wires 206 and 207 connect the shields of cables 204 and 205
together and to ground 208, completing the FIG. 7 connections
associated with cable assembly 2. Wire 209 carries bi-directional
ultrasound signals to terminal B of solid state switch 210. Drive
pulses traveling toward the transducer assembly are channeled from
switch terminal A1 to terminal B, while echo signal voltages are
channeled from terminal B to terminal A0. Only one of the two
signal paths is activated at a given time, depending on a binary
switch-control input designated S, whose signal arrives via wire
211 from sequencer 202. When the logic signal on wire 211 (see also
FIG. 8) is driven high by sequencer 202, terminal A1 of switch 210
to be connected to terminal B. The positive transition of the
signal on wire 211 initiates the generation of a pulse from "PULSE
GEN" 212, which travels via wire 213 to "SHAPE FILT" 214, which
modifies the shape of the pulse. This modification pre-compensates
for linear phase and amplitude "distortions" (commonly so-called,
although rigorously they are linear transformation phenomena) of
the ultrasound transducer assembly, resulting in a substantially
phase-linear ultrasound pressure waveform with smooth
band-limiting. This substantially minimizes acoustic output pulse
duration within the constraints of transducer bandwidth and
amplifier power bandwidth. The pre-compensated electronic waveform
is somewhat spread out in time, largely because of phase and
amplitude distortions that anticipate offsetting transducer
effects. Thus the acoustic pulse duration from the transducer is
effectively shorter than the pre-compensated pulse duration
emerging from filter 214 via wire 215. The shaped pulse travels via
wire 215 to the input of amplifier 216, labeled "PWR" for power
amplification. The output signal of amplifier 216 passes via wire
217, through termination resistor 218, and from the far side of the
resistor via wire 219 into terminal A1 of switch 210. The
termination resistor provides impedance matching to cable 205 to
minimize signal reflections. (To save amplifier power, output
series resistor 218 can be reduced, while feedback modifications
result in an unchanged effective output impedance at wire 219. The
voltage differential across the reduced series resistor is applied
as negative feedback to the amplifier input. The detailed circuit
involves a differential-input amplifier plus several input and
feedback components. Triangle symbol 216, like other labeled
triangle symbols in FIG. 7, designates both a voltage amplifier and
associated input and feedback components. By contrast, triangles
336 and 355, labeled only with "+" and "-" signs to designate
inverting and non-inverting inputs, are simple operational
amplifiers whose input and feedback components are shown
explicitly.)
When a pulse output period is complete, the sequencer output on
wire 211 goes to a low logic level, causing terminal B of switch
210 to connect to terminal A0, thereby connecting wire 209 through
the switch to wire 220. Wire 220 connects to termination resistor
221, whose far side is connected via wire 222 to ground 223. The
reflection-minimizing function of resistor 221 during signal
reception is analogous to the function of resistor 218 during pulse
transmission. Wire 220 also couples the received signal to the
signal input terminal of amplifier 224, labeled "AGC" for Automatic
Gain Control. Typically, amplifier 224 will include more than one
gain stage, to amplify very low-level input signals. (To minimize
signal power loss and improve signal-to-noise ratio, it is possible
to increase the value of resistor 221 and re-establish the original
effective termination resistance using negative feedback. After
increasing resistor 221, wire 222 is disconnected from ground 223
and reconnected to the output of an inverting, fixed-gain input
amplifier stage in 224. A small capacitor paralleling reconnected
resistor 221 may be provided to compensate for the effect of
first-stage amplifier frequency response rolloff, to maintain a
resistive termination impedance to wire 220. Gain control and
frequency response compensation must be performed in one or more
separate amplification stages following this
impedance-synthesizing, low-noise input stage. The details will be
apparent to those skilled in the art.)
The signal amplification to the output of amplifier 224 varies as a
function of the voltage signal arriving at its gain control input
via wire 225. A linear voltage ramp on 225 (see trace, FIG. 8)
causes amplifier gain to increase progressively during an echo
reception period. This ramp, generated by module 226, labeled
"RAMP", is reset and held at zero by high logic levels arriving at
the input to 226 via wire 211, from sequencer 202. The downward
transistion of signal 211 initiates the ramp. The gain control
response in 224 to ramp voltage 225 is tailored to minimize the
signal-strength sensitivity at output wire 227 to ultrasound depth.
The signal on wire 227 is applied to the input of filter 228,
labeled "SHAPE FILT". This filter functions like filter 214, to
compensate for the linear phase and amplitude distortions of the
ultrasound transducer assembly operating in receive mode. Since
these "linear distortions" (i.e. amplitude-independent alterations
of amplitude and phase as a function of frequency) of signal
reception are substantially identical to the distortions of signal
transmission (because of the transmit-receive symmetry of
transducer characteristics), complete shape compensation requires
two repetitions of essentially the same compensating filter. Both
filters could be placed in series (or functionally combined) on
either the input or output side of the circuit, but splitting the
filter function between input and output circuits maintains a more
uniform signal energy spectrum in the transmit and receive paths.
(The functions of the shape filters could be time-shared using only
filter 214, coupled as shown only during output pulses, with filter
214 output connected to both wires 215 and 229. The input is
switched from wire 213 to wire 227 during echo reception periods,
using a switch e.g. of the type of switch 210, controlled by the
logic level on 211. This variation on the design shown in FIG. 7
functionally replaces precision filter 228 by a low-cost transistor
switch.)
The ultrasound echo signal, now fully compensated for optimum depth
resolution, travels via wire 229 into linear network 230, labeled
".phi.", the Greek "PHI", symbolizing phase angle. The network
produces two complementary output signals whose labeling,
"0.degree." and "90.degree.", indicates the relative phase-angle
responses approximated over the ultrasound passband. Over the
passband, the amplitude-versus-frequency responses of the two
outputs are approximately flat. To generate such complementary
phases with flat amplitude response requires a network having some
effective time delay from input to output. This time delay,
technically called group delay and defined as the derivative of
input-output phase shift with respect to frequency, is kept
substantially constant over the frequency passband, while amplitude
and relative-phase errors are simultaneously minimized.
There are several possible approaches to implementing network 230.
For example, an uncomplicated prototyping approach, effective at
frequencies where active filter circuits present problems, is
implemented using passive allpass filter stages consisting of
capacitors and tapped inductor coils. These stages are decoupled by
broadband amplifiers for tuning and adjustment with minimal
interactions. Amplifiers are also used to compensate for coil
resistances, allowing more precise allpass filter realizations.
Using this approach, with computer transfer function analysis and
optimization routines to specify filter design parameters, a pair
of matched delay filters is implemented, each giving flat amplitude
and matched, constant group delay response in the passband, but
with a fixed 90.degree. phase differential between the two outputs.
This approach is "traditional" and familiar to many designers.
Several alternative approaches show promise of reducing costs,
compared to the approach just described. They typically involve
electronic means for delaying the signal and achieving a weighted
average of the recent time-history of the signal--more technically,
a convolution integral. The 0.degree. output is derived from a
single delay line tap, at the midpoint. The 90.degree. output uses
a weighting function resembling a truncated rectangular hyperbola,
with the weighting becoming large near the center-tap delay. (The
weighting process is an approximation of the Hilbert Transform.)
The weighting can be positive for delays less than the center tap
delay, and symmetrically negative for delays exceeding the center
tap delay. This weighted average description sheds light on how the
filters behave. The 90.degree. signal output shows a positive peak
at about the time when the 0.degree. signal output shows a
positive-sloping zero crossing. This property is used to track a
zero crossing of one signal and use the simultaneous peak of the
quadrature signal as a measure of signal strength at that point.
This property also permits computer-controlled phase switching to
alter the waveform point being tracked.
Three examples of suitable implementations of a tapped signal delay
are given. One approach is a center-tapped electromagnetic delay
line, consisting of a long solenoid wound on a grounded cylinder,
creating a distributed inductance with a distributed capacitative
shunt to ground. The ground can be a foil, etched into two
complementary regions whose relative circumferential widths differ
as a function of length along the solenoid. The foil pattern shape
thus becomes a weighting function of the displaced charge.
Differential amplification and integration of the current from the
two foils results in a time-history-weighted average, or
convolution integral. A second approach uses a charge-coupled
analog delay device, or "bucket brigade" delay, with multiple taps.
Weighting resistors and summing amplifiers achieve the desired
weighted time history. Hardware for this purpose may perform poorly
above 1 to 3 MHz, limiting its usefulness for high ultrasound
frequencies. A third approach, the "crystal filter" approach, uses
piezoelectric transducers and acoustic delay through a solid or
along the surface of a solid. Once developed for a given
application, crystal filters can be inexpensive to manufacture.
The 0.degree. signal from filter 230 is interconnected to remote
diagram points via wire 239 and through interconnect circle 240,
labeled "U0" (for Ultrasound, 0.degree.-phase). The signal on wire
239 is inverted by amplifier 241, resulting in the signal carried
via wire 242 to interconnect circle 243, labeled "U180" for
"Ulrasound, 180.degree.-phase". The 90.degree. signal travels via
wire 244 to interconnect circle 246, labeled "U90 , designating the
90.degree. ultrasound signal. Wire 244 also provides input to
inverting amplifier 247, whose output travels via wire 248 to
interconnect circle 249, labeled "U270", designating the
270.degree. ultrasound signal. Both inverting amplifiers 241 and
247 are labeled "-1", indicating a configuration to achieve a gain
of -1 over the ultrasound bandwidth. The circuitry described
results in a symmetric group of four ultrasound signals, equally
spaced around a 360.degree. phase circle. Cyclic permutations of
these four signals can be used to move phase-lock circuitry in
controlled increments over the bumps, zero-crossings and dips of
the ultrasound signal, accessing virtually all resolvable
ultrasound data for computer pattern recognition and analysis, and
then tracking the most significant depth signals for continuous
vibration analysis.
For display purposes, the ultrasound signal on wire 239 is applied
to a positive-gain input, marked "+", of amplifier 261, labeled
"SUM". The select signal of wire 203 (see FIG. 8 for the waveform)
enters the negative-gain input, marked "-", of amplifier 261. The
resultant "sum" signal (actually a voltage difference), travels via
wire 262 to the vertical deflection input, "V", of oscilloscope
display assembly 263, labeled "SCOPE". The sequencing voltage on
wire 203 provides vertical separation of alternating traces 13 and
14 (shown also in FIG. 1), producing upper trace 13 when the
voltage on 203 is low, and lower trace 14 when the voltage on 203
is high. Ultrasound echoes on wire 239 appear as small sinusoidal
wave packets, typically resembling a sinusoid modulated on and off
by a Gaussian envelope whose standard deviation half-width is less
than one sinusoidal period. Multiple echoes may cause these wave
packets to overlap, producing more complex waveforms than those
illustrated. Horizontal deflection is provided by the ramp voltage
on wire 225 entering oscilloscope assembly 263 at "H". This voltage
on wire 225 also goes to interconnect circle 264, labeled "R", for
Ramp. A blanking signal is provided by sequencer 202 on wire 265.
This signal passes via a positive-gain input into SUMming amplifier
266, labeled "SUM", then from the amplifier output via wire 267 to
Intensity input "I" of oscilloscope module 263. When the signal on
265 is low (see trace, FIG. 8), the oscilloscope trace is blanked,
either for retrace during the drive pulse period, or for the
transverse echo period, since the transverse echo trace is not
displayed. The tracked portions of traces 13 and 14, namely
segments 15, 16, 17 and 18 on the display, are highlighted,
respectively, in response to pulses appearing at interconnect
circles 268, 270, 272 and 274, corresponding respectively to labels
"I1", "I2", "I3" and "I4". In the same order, interconnect wires
269, 271, 273 and 275 go to summing inputs of amplifier 266. Traces
for these signals are shown in FIG. 8. The summed output on wire
267, as shown in FIG. 8, causes blanking at the lowest level, a
normal trace at the intermediate level, and highlighting at the
upper level.
The sequencer generates Select signals which travel from the
sequencer via respective wire 276, 278 and 280 to respective
interconnect circles 277, 279 and 281, labeled "S1", "S2" and "S3".
As seen on the traces in FIG. 8, these signals are high during the
echo reception periods for the three ultrasound paths. The "blank
when low" signal on sequencer output wire 265 is seen to match the
Boolean logic expression "S1 OR S2", i.e. high when either or both
of S1 and S2 are high. Each of S1, S2 and S3 is used to gate two
separate phase-lock circuits like the one illustrated below the
dashed line in FIG. 7, giving a total of six such circuits. For one
group of three circuits associated with S1, S2 and S3, the signals
U0, U90, U180 and U270 are connected to multiplexer 290 as shown in
FIG. 7. For the other group of three, the "U" signals are
interchanged in polarity, which amounts to a cyclic permutation of
two steps around the group of four phase signals. Thus, U0 becomes
U180, U90 becomes U270, U180 becomes U0, and U270 becomes U90. The
six interconnection patterns just described are summarized in the
labeling just below the dashed line on the right in FIG. 7, stating
"REPEAT BELOW SIX TIMES FOR (+U or -U) and (S1 or S2 or S3)", i.e.
for any combination of normal +U, or polarity-interchanged -U,
signals, with any one of S1 or S2 or S3. The resultant tracked
time-window signals I1 through I6 are numbered, respectively, I1,
I3 and I5 for S1, S2 and S3 with +U, and I2, I4 and I6 for S1, S2
and S3 with -U. Of these six, only I1 through I4 are used for
oscilloscope trace intensification. Numberings for delay-time
signals N1 through N6, and for magnitude signals M1 through M6,
match the numbering just described for I1 through I6.
Following the particular circuit repetition shown below the dashed
line in FIG. 7, the four ultrasound signals labeled "U0", "U90",
"U180" and "U270", from respective interconnects 240, 246, 243 and
249, pass via respective wires 291, 292, 293 and 294 into
MUltipleXer 290, labeled "MUX". Multiwire computer bus 295, via
interconnect circle 296 from the ComPUter and labeled "CPU",
couples into multiplexer 290. Under computer control, the
multiplexer selects two of the four inputs for connection to output
wires 297 and 298, respectively labeled "U'0" and "U'90". (The
apostrophe designates "primed"). In a nominal setting, U0 connects
to U'0, and U90 to U'90. The computer can move the phase-lock point
along the ultrasound waveform in 90.degree. jumps by cyclic
permutation of the U0, U90, U180 and U270 connections to U'0 and
U'90. Thus, connecting "U90" to "U'0", and "U180" to "U'90", will
move the phase-lock point 90.degree. earlier in the waveform.
The selected ultrasound signals U'0 and U'90 are used in
conjunction with the following circuitry. Ramp interconnect circle
264, labeled R, is coupled to wire 310, leading to the inverting
"-" input of comparator 311 and to the non-inverting "+" input of
comparator 312. The respective comparator outputs, on wires 313 and
314, are coupled to inputs of AND-gate 316. The output of this AND
gate can go high only when both comparator outputs are high
simultaneously. As a further restriction, the select signal S1,
coupled via interconnect circle 277 and wire 315 to an input of AND
gate 316, must also be high to enable the AND output. For S1 high,
the AND condition is satisfied whenever voltage R on 310 is below
the voltage on 320 and above the voltage on 321, i.e. in a "window"
defined by these latter two voltages. The voltage on 320 couples to
the non-inverting "+" input of comparator 311, and when it exceeds
the voltage on 310, the output of 311 on 313 goes high. The voltage
on 321 couples to the inverting "-" input of comparator 312, and
when it falls below the voltage on 310, the output of 312 on 314
goes high. The voltage window below voltage 320 and above voltage
321 is centered about a voltage that is a fixed fraction of the
voltage on feedback wire 317 (which is seen looping over the top of
the entire circuit below the dashed line). This feedback voltage,
labeled "N1" at interconnect circle 338 (lower right corner of
diagram), is the ultrasound depth signal. The fixed large fraction
(typically exceeding 0.95) of voltage N1 that defines the window
center voltage is given by the resistor ratio R322/(R322+R318),
where the resistor R-numbers correspond to the diagram numbers. The
circuit design calls for R323=R322, and R319=R318. Bias voltages +V
and -V, being fixed positive and negative voltages of equal
magnitude, define the width of the voltage window, after scaling by
the four resistors just mentioned. Specifically, the voltage width
is 2.multidot.V.multidot.R318/(R322+R318). This voltage width, in
combination with the slope of ramp signal R from module 226,
defines a window time width. The time width is typically chosen to
correspond to a 90.degree. phase change at the ultrasound center
frequency. The ultrasound propagation delay time depends on the
fixed large fraction of voltage N1 mentioned above, and on the
slope of the ramp signal, R.
Specifically, the voltage window is defined by the series
connection from +V interconnect circle 326 to wire 324 to resistor
322 to wire 320 to resistor 318 to wire 317 to resistor 319 to wire
321 to resistor 323 to wire 325 to -V interconnect circle 327. The
center voltage on this string is driven by voltage 317 from
amplifier 336 (on the right). The connections to comparator inputs
from wires 320 and 321 complete the window implementation. When
voltage R passes through the window, a pulse may be generated,
centered at the time delay that is required for the ramp signal to
cross the window voltage. The pulse is only generated when select
signal S1 is high.
The time window caused by the passage of the ramp voltage through
the voltage window is the duration of the positive logic pulse
illustrated in FIG. 8, on the trace numbered 268, 269 and 330 for
the three appearances of this voltage in FIG. 7. This pulse
highlights segment 15 of the oscilloscope display. When select
signal S1 is high, the output pulse of AND-gate 316 is coupled via
wire 330 to transistor switches 331 and 332 at the inputs labeled
"S". For each switch, terminals A1 and B are connected during the
window duration. In switch 332, the effect of this connection is to
couple signal U'0 from wire 297 briefly to wire 333, the input wire
to an inverting integration circuit. The integrator is built around
operational amplifier 336, with input resistors 334 and 342, and
feedback capacitor 337. The non-inverting "+" input of amplifier
336 is grounded at 340 via wire 339, so that 336 acts like a very
high gain inverting amplifier. The output of 336, on feedback wire
317, is depth signal voltage N1. This output wire connects via
feedback capacitor 337 to input-junction wire 335, going to the
inverting "-" input of 336. Ends of input resistors 334 and 342
join to wire 335, while the opposite ends of the resistors are
respective input signal wires 333 and 341.
When no current is allowed to flow through integrator input wire
341, the integrator responds only to the U'0 input signals
connected from 297 to 333 during time windows determined by
AND-gate 316. If the windowed, highlighted segment 15 of the
ultrasound waveform (see oscilloscope display 4) is symmetric about
0 volts, the net increment in integral N1 over the duration of a
select window pulse on I1 will be zero. If the average value over
the window duration is non-zero, a net increment in integral N1 is
generated, negative if the average value is positive (since the
integration is inverting in polarity). Moving the window to the
right in trace 13 results in a positive average over the window
segment. The resulting accumulating negative increments in integral
voltage N1 move the voltage window to a lower point on ramp R,
resulting in an earlier appearance of the window on subsequent
pulses. Thus a self-correcting loop is established that tracks the
positive-going zero crossing. The same loop will avoid
negative-going zero crossings. Interchanging multiplexer 290 inputs
U0 with U180, and U90 with U270, will cause the circuit to track
negative-going zero crossings. The integration time constant
determined by input resistor 334 and feedback capacitor 337 is made
short enough to assure tracking of vibrational and pulsatile
arterial motions with minimal time lag, but not so short as to
compromise loop stability. Note that the speed of the tracking loop
varies with the slope of the tracked zero-crossing. The loop must
therefore operate over a range of signal strengths.
Cyclic permutations of the input-output connections in multiplexer
290 shift the phase-lock point by 90.degree. jumps. Permuting the
U-inputs "forward" by +90.degree. replaces a tracked
positive-sloping zero crossing of U'0 by a positive peak of U'0 in
the select time window. Sampling and integration of this positive
peak causes a negative change in inverting integral voltage N1.
This moves the select window earlier, to a positive-sloping zero
crossing of U'0. The effect is to reposition window 15 on trace 13,
which still displays signal U0, not re-selected signal U'0. The
highlighted segment 15 will now lie on a negative peak of U0.
Backward permutations of multiplexer interconnections will move the
tracking point to a later time in the U0 waveform.
In a flat region of the ultrasound echo trace, the computer becomes
unable to move the select time window in the phase-jumping manner
described, since there is no signal slope to generate a feedback
signal. Therefore, the computer causes the window to drift
positively or negatively, corresponding to greater or lesser delay
into a pulse cycle, by applying a negative or positive voltage via
interconnect 296 and wire 341 to integrator input resistor 342.
When no drift is desired, the connection to wire 341 from within
the computer is interrupted by transistor switching.
The magnitude signal M1, at interconnect 360, is derived by gating
of the U'90 signal in switch 331, and by filter circuitry. When U'0
tracks a positive-going zero crossing, U'90 has a positive peak in
the same window interval. This peak region on wire 298 is sampled
by switch 331, which connects the voltage from A1 to B, and from
wire 298 to 350. Resistor 351 represents the input to a unity-gain,
two-pole lowpass filter. In calculating the filter transfer
function, the value of resistor 351 must be divided by the on-state
duty cycle of switch 331. On the opposite end of resistor 351 from
wire 350 is wire 352, which is connected in turn to resistor 353.
The opposite end of resistor 353 leads via wire 354 to the
non-inverting "+" input of operational amplifier 355, and to one
side of capacitor 356. The opposite side of capacitor 356 is
grounded via wire 357 to ground 358. The output of amplifier 355
feeds back via wire 359 to the inverting input, creating a
unity-gain voltage follower, so that the potential of 359 tracks
the potential of 354. It will be seen that grounded capacitor 356
in conjunction with resistors 351 and 353 creates a single-pole
lowpass filter, whose output is buffered by the op amp. The output
voltage on wire 359 is coupled via capacitor 361 to wire 352, which
joins resistors 351 and 353. This capacitor feedback path
introduces a second pole into the filter function, plus mild
positive feedback around the loop. This feedback can be used,
through proper component selection, to implement a two-pole
Butterworth filter characteristic. This well-known filter function
combines moderately sharp frequency cutoff with good phase
linearity and fast settling. Because of the high ultrasound
repetition rate and the low output bandwidth required, a
higher-order filter is unnecessary for removing pulse-rate "jitter"
from the filtered output. The implementation of the Butterworth
filter function with this topology is familiar to electrical
engineers. The filtered output appears on interconnect circle 360,
labeled "M1".
By circuit repetitions described, voltages N1 to N6 represent
propagation delay times for selected portions of repetitive
ultrasound echo traces. Voltages M1 to M6 represent the ultrasound
signal strengths in the vicinity of the selected trace portions.
The computer can adjust circuit phase-lock to almost any portion of
an echo trace that has a zero crossing in one of the signal phases
generated by filtering. Trace portions that may fail to track are
regions of very low signal amplitude or poor signal-to-noise ratio,
or regions where time-varying interfering echoes create signal
slope reversals. To minimize artifacts of multiple-reflection
interferences, and simultaneously to assure phase lock to opposing
artery walls in the vicinity of maximum vibrational response, the
computer seeks a strong signal region to track, with high
differential vibration amplitude. Specifically, it tries all
possible pairs of tracking points that fall within a
physiologically-possible range of depth and spacing, and it selects
for tracking the pair that maximizes the product of signal strength
and differential vibration amplitude. Since the polarities of
echoes from near and far arterial walls are reversed if the walls
are symmetric (because transitions to greater acoustic impedance on
the near side correspond to transitions to lower acoustic impedance
on the far side, and vice versa), the tracked slopes of near and
far walls are normally opposite, and may be as shown for segments
15, 16, 17 and 18, or the reverse, with negative tracked slopes on
the left and positive tracked slopes on the right, depending on
arterial wall structure and polarities of the ultrasound system
itself. Assymmetries in the artery may cause the system to track
same-slopes rather than opposite-slopes, or to track different
slope signs for different echo paths. Although the system is
designed so that tracked optimum waveform points are normally
displayed as zero-crossings, the system may track zero-crossings in
a 90.degree. or 270.degree. phase signal, meaning that the
displayed highlighted segment may be a maximum or minimum peak.
This choice could arise from variations in the overlap of echo
contributions from closely-spaced ultrasound reflectors. These
variations in phase tracking choices do not necessarily imply
unsuccessful functioning of the overall system. The operator must
be alert to assymmetries in the display, however, since these may
imply arterial wall irregularities that could cause errors in
analyses based on some degree of radial symmetry, at least of the
artery wall and immediate surroundings. The system may be
programmed to note assymmetries as it scans to select tracking echo
depths, and to alert the operator to assymmetries exceeding
threshold limits. The operator can respond to observed trace
irregularities or to system prompting by repositioning transducer
assembly 1 over a healthier, more uniform artery segment.
Referring now to FIG. 9, we see how these ultrasound signals are
interfaced to the computer. The signals are used directly (except
for lowpass filtering) for signal strength and depth data, and
indirectly, as demodulated vibration signals. Driver force and
acceleration signals are also processed for digital force and
velocity input.
The acceleration signal arrives via cable 2 as a balanced signal
from a strain gauge bridge in assembly 1. It arrives at
interconnect circle 420, labelled "AC" for ACceleration. Wires 421
and 422 carry the differential signal from circle 420 to the
inverting "-" and non-inverting "+" differential inputs of
amplifier 423, labeled "INS" for INStrumentation amplifier, an
amplifier designed for precise feedback-controlled gain with very
high common-mode signal rejection. This is useful for rejecting hum
and interference signals that usually appear as a common-mode
voltage on a symmetric twisted pair of wires.
The single-ended voltage output of amplifier 423 on wire 424
provides input for module 425, labeled "BPF/s". The letters "BPF"
designate the BandPass Filter function that is repeated for every
vibration input, in order to standardize frequency-dependencies of
amplitude and phase and cause these dependencies to cancel upon
complex-number division by the reference velocity signal. The
phase-correction aspect of the complex division takes place in the
demodulators using the velocity reference phase, while the
magnitude-correction aspect takes place digitally, in the computer.
The "/s" aspect of the "BPF/s" filter label represents integration
with respect to time, which is needed to transform the acceleration
signal to a velocity signal. In the Laplace transform domain,
integration becomes division by the transform variable "s". Hence,
the "BPF/s" filter labeling is chosen to designate a transfer
function combining integration with bandpass filtering, using
notation familiar to electrical engineers. Since
electronically-derived integrals inevitably drift over time, it is
useful to combine integration with filtering that cancels drift in
a single combined-function filter. In this way, the overall desired
filter function is achieved without compromise. Using similar
notation, filters 455 and 466, at the top of the figure, are
labeled "BPF.multidot.s". In the Laplace domain, multiplication by
"s" represents differentiation with respect to time. As with
integration, practical considerations prevent separate circuits
from performing time differentiation except over limited
bandwidths. Since high-frequency gain reduction is an aspect of the
BPF filter function, a single filter circuit combining bandpass
filtering with differentiation is feasible. The critical feature
about these filters is matching of the bandpass function. The
filters just described are easily detailed by electrical
engineers.
Continuing with the output of filter 425 via wire 426, the
continuous signal enters the "S" (Signal) port of demodulator
module 429, (not to be confused with the Switching ports of modules
210, 331 and 332 of FIG. 7.) The operation of module 429 and the
other demodulators in FIG. 9 was discussed under the heading "AC
Signal Demodulation", where the module labeling is explained in
conjunction with FIG. 6. Wire 426 also couples the band-limited
velocity signal to module 427, labeled "CLIP". This module clips
the voltage swing of the velocity signal typically from a few volts
to about 700 millivolts peak, on output wire 428, which extends up
through the diagram to all the zero-phase demodulator reference
inputs. The clipped amplitude is accurately in-phase with the
velocity signal, and is insensitive to velocity amplitude
variations. Wire 428 connects to the phase reference input of
demodulator module 429 at the terminal labeled "O". The demodulator
output from terminal "O" travels via wire 430 to multiplexer 444,
labeled "MUX", and enters at the input labeled "V" (Velocity). As
was explained earlier, there is only a zero-phase velocity signal,
since the 90.degree. signal is always zero. Module 431, labeled
"PLL" (Phase Lock Loop), generates a square wave on output wire
432, which travels up to all the 90.degree.-phase demodulator
reference inputs. This signal is similar to the signal on wire 428,
except that it leads the wire-428 waveform in phase by 90.degree..
Phase lock loop circuits for generating quadrature-phase signals
are familiar to electrical engineers. There are commercial
integrated circuits easily adapted to achieving the frequency range
and tracking speed requirements of module 431.
Like the acceleration signal, the vibration driver force signal
appears originally as a low-level differential voltage from a
semiconductor strain gauge bridge, conducted to interconnect circle
433, labeled "F" (Force), via a twisted wire pair in cable assembly
2. The pair ends at wires 434 and 435, which enter the inverting
"-" and non-inverting "+" differential inputs of instrumentation
amplifier 521, labeled "INS", like amplifier 423. The amplified,
single-ended signal travels via wire 436 to amplifier 520, to an
input labeled "+1" to indicate unity amplification. The
acceleration signal on wire 424 from amplifier 423 is applied to an
inverting input on amplifier 520, labeled "-e" (-error). The
purpose of this input is to subtract from the force signal the
mass-times-acceleration error signal associated with the moving
mass of the transducer assembly. Thus, as explained earlier, the
resultant force signal appearing an output wire 437 from amplifier
520 represents only the force actually applied to patient tissue.
(This correction can easily be accomplished in computer software,
working with the demodulated signals, but the circuit described
offers greater conceptual clarity by generating "pure" signals.)
Since only vibrational variations in the force signal are of
interest, the signal on wire 437 is applied to module 438, labeled
"BPF" (bandpass filter). Here the filter function need not be
modified by differentiation or integration. The filter output from
438 travels on wire 439 to the signal inputs, "S", of demodulator
assemblies 440 and 442. The phase reference input for demodulator
440 is the zero-phase reference on wire 428, while the reference
for demodulator 442 is the 90.degree.-phase reference on wire 432.
The "real" component derived from the zero-phase demodulation in
440 travels via wire 441 to the input of multiplexer 444 labeled
"FR" (Force, Real component). Similarly, the "imaginary" component
derived from the 90.degree.-phase demodulation in 442 travels via
wire 443 to the input of multiplexer 444 labeled "FI" (Force,
Imaginary component).
Processing of ultrasound depth signals is similar to processing of
force signals, except that filtering includes time-differentiation
to obtain velocity signals from the displacement signals. For near-
and far-wall depth signals N1 and N2, arriving via interconnect
circles 338 and 451, respectively, wires 450 and 452 conduct the
respective signals to differencing amplifier 453, to inputs labeled
"-1" and "+1" to designate inverting and non-inverting unity gain.
(Recall that the N2 signal is generated by a repetition of the
circuitry on the bottom of FIG. 7, but with opposite-polarity
ultrasound "U" signals interchanged at the inputs of multiplexer
290). The difference signal from amplifier 453 is carried via wire
454 to filter module 455, labeled "BPF.multidot.s" to designate
combined differentiation and bandpass filtering, as discussed
above. Not indicated in the filter labeling is the modification in
the filter function to offset the slight lag of the tracking loop
circuit on the bottom of FIG. 7, generating N1, and the repeated
circuitry generating N2. This compensation cannot be exact, since
the tracking circuit responds with variable time lag according to
signal slope, but the compensation is set for a typical ultrasound
signal slope. Since the computer monitors the signal strength
signals M1 through M6, which closely approximate the slopes of the
tracked zero-crossings, it can compute phase and amplitude errors
arising from slope values significantly different from the ones
anticipated in the fixed filter compensations. The compensated
signal from filter 455 travels via wire 456 to the signal inputs of
demodulators 457 and 459. The phase inputs arrive, respectively, on
wires 428 and 432, producing "real" and "imaginary" demodulated
signal outputs on wires 458 and 460, leading to inputs of
multiplexer 444 labeled "D1R" and "D1I" (Differential velocity
signal number 1, Real and Imaginary components).
Common-mode depth velocity is interfaced to the computer in the
same manner as differential depth velocity, except that the sum of
signals N1 and N2 is processed instead of the difference. The N1
and N2 signals, on interconnect circles labeled 338 and 451, are
coupled to wires 461 and 463, leading to summing inputs of
amplifier 464. The "+1" labeling of both inputs indicates
unity-gain summation. The sum, on output wire 465, goes to module
466, "BPF.multidot.s", whose function matches that of module 455
above, as mentioned. The filtered output on wire 467 travels to "S"
inputs of demodulator modules 468 and 470, whose phase reference
signals, O, arrive via wires 428 and 432. The "real" and
"imaginary" demodulated outputs travel via wires 469 and 471 to
inputs of multiplexer 444 labeled "C1R" and "C1I" (Common-mode
velocity signal number 1, Real and Imaginary components).
The depth signals N1 and N2, and the corresponding magnitude
signals M1 and M2, enter the multiplexer with less processing on
the right of multiplexer 444, for non-vibratory signal processing.
N1 and N2 inputs, via interconnects 338 and 451 as elsewhere,
travel via wires 480 and 484 to modules 481 and 485, labeled "LPF"
(LowPass Filter). These filters are typically both identical to the
two-pole Butterworth filter illustrated at the bottom of FIG. 7,
except for a changed input resistor, not corrected for input-switch
duty cycle. The filtered outputs travel via wires 482 and 486 to
inputs of multiplexer 444 labeled "N1F" and "N2F", where the "F"
designates "Filtered". Magnitude inputs M1 and M2 are already
filtered, and travel via wires 483 and 488 to multiplexer 444
inputs also labeled "M1" and "M2".
The N1, N2, M1 and M2 functions just described are repeated twice
more, for N3, N4, M3 and M4, and finally for N5, N6, M5 and M6. As
labeling in FIG. 9 indicates, this is accomplished by repeating the
portion of the circuit between the dashed horizontal lines twice,
in addition to the repetition shown, for a total of three
repetitions.
We now examine computer control of multiplexing functions. The
computer is indicated at box 500, labeled "CPU". The same label
applies to multiwire bus interconnect circle 295, carrying signals
to the multiplexer circuitry of FIG. 7 for control of ultrasound
tracking selection. The bus in FIG. 9 is labeled 501 for its lower
portion, leading to 295, to multiplexer 444, and to A to D
converter 503. Information flow to the multiplexer, telling which
analog input line to select, is essentially one way, as shown by
the wide arrow pointing into the multiplexer. The selected
multiplexer input is coupled to output wire 502, leading to the
analog input of A to D converter 503. This converter module samples
and digitizes the analog data for input to the computer at 500 via
bus 501. The bus connection to converter 503 operates
bidirectionally, since the computer sends data to 503 for timing of
the sampling and conversion process, and the resulting digitized
signals travel back from 503 to the computer.
Above computer block 500, wire 504 carries clock pulses to
interconnect circle 200, "CK", which appears in FIG. 7, carrying
timing pulses for the ultrasound event sequencer. Aside from
synchronization to the computer clock, the event sequence of module
202 (FIG. 7) is typically autonomous from the computer.
Multiwire bus 505, carrying the same data and address information
as bus 501, enters module 506, "DCO" (Digitally Controlled
Oscillator). A frequency-controlling binary number is transmitted
to 506, where it is stored on flip-flops between updates. The
oscillator itself typically uses the well known "state variable"
design approach of two integrators and an inverter wired in a loop,
with degenerative/regenerative feedback regulation to achieve a
desired AC output amplitude with very low distortion. Integrator
time constants are modified by placing a complementary-MOS
multiplying D to A converter in the input path of each integrator.
The digital input value held on the flip flops then modifies the
integration speed of both integrators, causing oscillation
frequency to vary directly with the frequency-control number. The
detailing of this module is easily accomplished by a skilled
electronics engineer. The oscillator output is split into a
balanced differential signal for transmission via wires 508 and 509
to interconnect circle 507, "VB", to the ViBraton driver in
assembly 1. Transmission is via a twisted pair of wires in cable
assembly 2 (wiring not shown). The differential drive is chosen to
keep drive currents out of signal ground wires and to minimize
electrostatic couplings, thus simplifying shielding and isolation
of drive and data signals.
Calibration Cuff Function
Sphygmomanometer cuff 11 (FIG. 1) is used optionally to reduce the
pressure differential across the wall of the artery
segment-under-test (e.g. part of carotid artery 40) by a known,
time varying amount, normally below diastolic pressure so that the
artery does not collapse. Cuff pressure change should be slow
enough to permit axial blood flow to and from the cuff region, with
resulting artery diameter change and pressure-differential
equilibration. Cuff pressure is varied in a pattern, e.g.
sinusoidal, designed to minimize the correlation between cuff and
blood pressure changes. Cuff pressure change and
vibration-determined blood pressure change can be correlated over
unequal numbers of complete cuff and cardiac cycles (e.g. 10 full
cuff cycles and a simultaneous 15 full cardiac cycles). The unequal
rhythms minimize unwanted correlations of the cuff rhythm with all
harmonics of the cardiac rhythm. Departure of the correlation slope
from unity indicates an error in vibration-determined pressure
change, leading to a calibration correction.
DESCRIPTION OF A WHOLE-ORGAN EMBODIMENT
A variation of the invention is adapted e.g. for measuring
mechanical properties of whole organs and internal pressures in
fluid-filled organs, e.g. urinary bladder, or edematous organs.
FIGS. 10a and 10b show that driver/sensor assembly 600 is a round
disc with six driver assemblies, 601 through 606, arrayed
hexagonally around the perimeter, and with single ultrasound
assembly 607 in the middle. The six matched driver assemblies are
each like the assembly of housing 60 and central moving element 61
of FIGS. 2 and 4. The description accompanying FIG. 4 applies to
these driver assemblies as well. All six assemblies are wired
electrically in parallel and generate parallel vibrational forces
against disk 608, to which they are affixed. Driver/sensor assembly
601 is shown in simplified cross-sectional view in FIG. 10b, to
clarify the orientation and relationship to the cross section of
FIG. 4. Ultrasound assembly 607 (shown in FIG. 10b in simplified
cross-section, to clarify orientation in the larger assembly) lies
in the center of disk 600. The same cross section appears in more
detail in FIG. 11. Interconnection to a computer/controller is
provided by cable 609 (FIGS. 10a, 10b). FIG. 10b shows assembly 600
lying on the surface of tissue 610, with contour 611 indicating the
upper boundary of an underlying organ.
In operation, assembly 600 is a three-dimensional-measurements
counterpart to assembly 1 of FIGS. 1, 2 and 3. Assembly 600 is
capable of sensing its vibrational velocity and the total
vibrational force exerted on underlying tissue. The force
measurement differs from assembly 1, which measures applied force
only over a central transducer segment. The single ultrasound
assembly of 600, lacking an acoustic lens, generates a roughly
columnar beam, with the only significant divergence with depth
arising from aperture diffraction. The beam has two-axis steering,
which is servo-controlled to lock onto and track an ultrasound echo
source over time.
An objective of the whole-organ embodiment is to induce vibrations
in an underlying organ, and then to measure, over a range of
frequencies, the surface mechanical impedance and the transfer
ratios from surface driver velocity to velocities of various
internal organ surfaces. The spectrum of responses is analyzed
using simulation algorithms, as described below. The simulation
outcome is a mathematical model of the vibrating system, with its
coefficients adjusted so computed responses match observed
responses. The adjusted model coefficients indicate the vibrational
parameters of the organ tissue, including density, viscosity and
shear modulus, and possibly including the frequency-dependences of
viscosity and shear modulus, as these parameters may be influenced
by visco-elastic creep. These parameters can be correlated with
normal or pathological tissue conditions, e.g. the changes
associated with scirrosis of the liver or with cystic kidney
disease.
A further use of the whole-organ embodiment of the invention is to
determine internal pressure in an organ, whether that pressure be
attributed to free liquid or semiliquid contents, e.g. in the
urinary bladder or the eye, or to abnormal fluid retention in cells
or in the interstices between cells. The elasticity associated with
a fluid pressure differential, whether abrupt across a thin organ
wall, or graduated from the center to the surface of an edematous
organ, gives a different series of vibration-mode resonant
frequencies than is associated with an elastic modulus. This
difference was discussed above in a cylindrical context for
distinguishing blood pressure from arterial wall stiffness in the
systemic artery pressure embodiment. Analogous differences exist
for other organ shapes. The measurements and analysis taught here
provide means for distinguishing fluid-pressure-related and
elastic-modulus-related elasticities, even in heavily over-damped
situations. Note that pressure-induced restoring impedance in a
roughly spherical organ varies as the product of radius times
pressure, whereas restoring impedance per-unit-length in a
cylindrical organ or vessel varies as pressure alone, independent
of radius.
Where fluid pressure effects vary over time between vibrational
measurements, even slowly over hours or days, the change can
provide pressure-baseline data, opening the way to the powerful
network algorithm, for determining organ mechanical impedance. The
three-dimensional network algorithm differs from the
two-dimensional cross-sectional network algorithm primarily in
depending on total surface-driver vibrational force, as opposed to
a representative force per-unit-length. This difference accounts
for the dissimilarities in the force measurement methods of this
whole-organ embodiment versus the systemic artery pressure
embodiment.
We now examine the steerable ultrasound assembly 607, shown from
above in FIG. 11a, and from the side in FIG. 11c. Two possible
magnetic field patterns for the perspective of FIG. 11a are
illustrated schematically, side by side, in FIG. 11b. In FIG. 11a,
we see a torroidal magnetic field generator surrounding a gimbaled
center assembly. The field generator consists of four curved
magnetic core elements 621 through 624, each mostly covered by
curved winding segments 625 through 628. Each core element is a
90.degree. segment of a torroid, and the wound elements abut to
form a complete torroidal core. Opposite windings are joined
electrically as pairs. Thus, windings 626 and 628 are wired to give
a magnetic field across the torroid center, sloping from upper
right to lower left, as illustrated on the left in FIG. 11b.
Similarly, windings 625 and 627 are wired for a field from upper
left to lower right, as on the right in FIG. 11b. Current reversals
change the field directions. Within saturation, power and bandwidth
limits, field strength and direction across the torroidal center
can be controlled continuously by controlling currents in the two
winding pairs.
Upper layer 630 of the gimbaled center assembly is an
axially-poled, disk-shaped permanent magnet. Magnetic fields from
the torroidal wound core generate torsional moments on the magnet,
tending to align the magnet axis to the cross-plane field. The
gimbal consists of jewel needles 631 and 632 (FIGS. 11a and 11c),
extending inward from the torroidal core on the left and right;
ring 633, seen from above (FIG. 11a) and in section (FIG. 11c),
with bearing cups for needles 631 and 631; needles 634 and 635
(FIG. 11a only), extending inward from ring 633 above and below;
and bearing cups for needles 634 and 635 in magnet 630. The gimbal
permits the magnet to tilt in response to the driving magnetic
field. Five thin, u-shaped spring wires restore the magnet to axial
alignment, so that the equilibrium deflection angle is a function
of applied field strength, and of temperature, which affects the
magnetic moment of the permanent magnet. Of these five, wire 636 is
illustrated in FIG. 11c. The five wires are arrayed with the
openings of the u-shapes pointing radially outward to the vertices
of an imaginary regular pentagon. Each wire is affixed to top
assembly cover 640 and to magnet 630. These spring wires provide
four signal leads for four 90.degree. metallization sectors of
piezoelectric ultrasound disk 641, plus a common ground lead. The
sector metallizations are numbered 642 through 645 as they are
exposed in the central cross-sectional view of FIG. 11a. These
metallizations are on the top of ultrasound transducer disk 641,
where the disk is affixed to magnet 630. The common ground
metallization covers the entire lower surface of disk 641, which is
bonded to quartz acoustic interface layer 650. This interface is in
turn bonded to acrylic plastic acoustic interface layer 651, whose
lower surface contacts fluid that envelops the gimbaled assembly.
The fluid is contained in an envelope whose top surface is cover
640 and whose bottom surface is cover 652. Cover 652 forms the
center of the lower surface of disk 608 (FIGS. 10a and 10b), and
contacts the patient. The ultrasound impedance of the cover is
close to that of the ultrasound-transmitting fluid and of human
tissue, to minimize ultrasound reflections.
The ultrasound assembly is aimed using digital control. Algorithms
regulate magnetic-drive field currents to produce desired aiming
motions, taking into account magnetic torques, restoring torques,
inertia and fluid-damping forces. The aiming mechanism as described
here operates open-loop, to the extent that magnet angular position
is calculated but not actually measured. Absolute angular accuracy
of the device is not critical. Angle-correcting feedback comes when
a desired ultrasound target is computer-identified and tracked,
using circuitry like that shown below the dashed line in FIG.
7.
Angular error signals for alignment to center an ultrasound echo
source are generated from the phase differentials of echo arrival
at the four sectors of the ultrasound disk. Sectors closer to the
echo source will give phase-leading echo responses, relative to
sectors farther from the echo source. The disk is aligned when the
four phases of the tracked signal match.
Circuitry to detect ultrasound phase error signals is outlined as
follows. The same ultrasound drive pulse voltage is applied to all
four sectors of disk 641. The return echo signal is received on two
separate channels, split between either left versus right sectors,
or up versus down sectors, depending on solid state switch
settings. The split alternates left-right and up-down on alternate
pulses. The two amplified channel outputs are summed to a
common-mode channel, which is processed like any of the ultrasound
channels of the systemic artery pressure embodiment, to permit
tracking of a zero-crossing. The left-right and up-down
differential signals are processed separately and sampled during
the zero-crossing time window pulse generated by the tracking
circuitry, like the pulse signal "I1" at 268 in FIG. 7. During the
window interval, the tracked common-mode ultrasound signal is
changing rapidly. The left-right and up-down differential
ultrasound signals in the same phase and time window reflect the
desired phase differentials. Both of these signals are sampled and
smoothed like signal "U'90" on wire 298 from multiplexer 290 of
FIG. 7. The sampled and filtered phase-differential signals are
analogous to the signal "M1" at 360, in terms of the generating
circuitry. The error signals represent a product of a non-linear
phase error term multiplied by echo signal strength. The
common-mode echo signal strength signal is used to correct the
strengths of the alignment error signals, resulting in parameters
that reflect angular misalignment in a consistent way. These
misalignment signals are data for the algorithm that determines the
currents to be sent to the torroidal magnetic driver. In this way,
an alignment lock can be established as soon as a zero-crossing
phase lock to an ultrasound feature is established.
The ultrasound system can scan its accessible angular sector and a
prescribed depth range, recording the approximate three-dimensional
locations of strong echo responses. Vibration responses are also
noted. The array of responses is studied, possibly by human
operators as well as the computer, and echoes representing desired
vibration-tracking targets are identified. Those targets are
subsequently re-located and tracked while driver frequency is
varied. The vibration data for each target consist of target
velocity and driver force, each resolved into 0.degree. and
90.degree. phase components relative to driver velocity. These
parameters are typically expressed as ratios to driver velocity
amplitude. The data are collected over an array of frequencies.
Force and velocity measurement for the whole-organ embodiment is
different from the systemic artery pressure embodiment. Since total
driver force is to be measured, rather than force from a portion of
the driver, it is possible to infer force from the electrical
responses of the electromagnetic vibration drivers, without using
separate force and acceleration transducers. Velocity can be
infrerred similarly. The inference is based on the driver coil
voltage developed in response to element motion. When a driver
reaction-mass element moves relative to the housing and driver
plate, the magnetic fluxes linking the coils are altered. A fixed,
rigid reference element, similar to the six driver elements, uses a
secondary coil current to cause the same flux change that is
induced by the average axial motion in the six driver elements. The
secondary current necessary to balance the reference-element
primary voltage against the voltage across the six drivers is a
measure of displacement response. This measure is used to determine
velocity and force response.
Implementation of this displacement-response measurement is
detailed in the circuit diagram of FIG. 12. From interconnect
circle 660, labeled "CPU" (computer), multiwire bus 661 carries a
control signal to module 662, labeled "DCO" (digitally controlled
oscillator). This oscillator is similar to module 506 of FIG. 9,
previously described, except that the output is single-ended rather
than differential. The frequency-controlled sinusoidal output is
coupled via wire 663 to interconnect circle 700, labeled "F"
(force). This signal, of known constant amplitude, provides the
0.degree. phase reference signal for demodulation, as did the
velocity signal on wire 426 of FIG. 9. A 90.degree. phase-lock-loop
uses this signal to develop a 90.degree. phase reference signal for
demodulation, as with the velocity signal in FIG. 9. Wire 663
couples to current amplifiers 666 and 667. The output of amplifier
666 is six times the current output of amplifier 667, and drives
the six parallel-connected electromagnetic drivers, 601 through
606, as joined together and to amplifier 666 by wire 668. The
opposite ends of the driver windings connect to wire 669, which is
grounded at 670. The lower current of amplifier 667 is coupled via
wire 675 to reference electromagnetic driver 676. This reference
driver matches the other six except that the housing and central
moving element are locked to fixed relative positions. The space
occupied by o-rings in the other six drivers is occupied by a
secondary winding in the reference driver. The difference between
the reference-driver primary voltage and the voltage across the six
parallel drivers is the voltage difference between wires 668 and
675. Wire 668 connects to the "+" input of high-gain AC
differential amplifier 677, while wire 675 connects to the "-"
input of the same amplifier. This amplifier includes high-pass
input filtering and feedback to nullify DC input offsets while
leaving operation at oscillator frequencies virtually unaffected.
The greatly-amplified AC difference signal is coupled from 677 via
output wire 678 to the input of current amplifier 679. The
resulting current output is coupled via wire 680 to the secondary
coil in reference-driver 676. Both primary and secondary windings
in 676 have their opposite ends connected to ground wire 681, which
is grounded at 682.
The function of the feedback loop through the secondary winding in
the reference driver is to determine the average vibrational change
in position of the magnet-plus-coil elements in the six parallel
drivers, relative to the housings and center-washers. Position
changes divert magnetic flux, inducing primary winding voltages
proportional to rates-of-change of flux. The feedback loop through
the reference secondary winding provides a secondary current such
that the AC magnetic flux imbalance in the reference driver almost
exactly matches the average of the motion-induced flux imbalances
in the six matched drivers. The secondary current needed to
accomplish the primary voltage balance is an accurate measure of
average relative position changes of the six moving driver
elements. The close flux matching achieved between the reference
driver and the average of the six moving drivers causes matched
magnetic non-linearities and matched parasitic eddy currents, so
that these artifacts are minimized in the feedback signal developed
on wire 678.
The voltage on wire 678, representing vibrational position change,
is coupled to the input of filter 685, labeled "BPF.multidot.s"
(bandpass filtering combined with time differentiation, the latter
indicated by the operator ".multidot.s"). This filter function was
discussed in relation to the systemic artery pressure embodiment of
FIG. 9. The output signal from filter 685 on wire 686 is coupled to
interconnect circle 687, labeled "V" (velocity). This signal
represents a relative average velocity of the driver housings and
center elements. This signal is demodulated with respect to
0.degree. and 90.degree. phase reference signals, like the force
signal on wire 439 of FIG. 9. The actual vibrational velocity of
plate 608, and the force applied by plate 608 in underlying patient
tissue, are deduced from the demodulated components of this "V"
signal. The velocity- and force-determining formula of the computer
takes into account the known reaction masses of the six drivers and
the restoring characteristics of the support o-rings in the
drivers. There is also a temperature correction factor, based on
the temperature-sensitivities of the permanent magnets in the six
driver elements. Temperature of the reference element is relatively
unimportant. A temperature sensor on plate 608 provides a signal
that is digitized and fed into the computer. The coefficients in
the algorithm to determine velocity and force are adjusted by a
calibration procedure in which the driver plate is placed against
loads of known mechanical impedance and electrical responses
measured at various frequencies.
DESCRIPTION OF AN OPTHALMIC PRESSURE EMBODIMENT
Another variation of the invention measures intraopthalmic pressure
by inducing, measuring and analyzing vibration responses, and by
measuring eyeball diameter. The system includes visual feedback
from the patient to measure opthalmic vibrational motions. The
computation system uses a simulation algorithm to interpret data. A
network algorithm can also be applied under certain circumstances
for refining and checking simulation results. Subsets of the data
suffice to determine pressure with fair accuracy, but the
combination of all the measurements taught here determine a more
precise pressure.
Vibrational excitation plus surface-velocity and force sensing
functions are combined in a single driver element. Vibration signal
decoding electronics are very similar to the whole organ
embodiment, as described with reference to FIG. 12. A single
magnetic driver, 800 in FIG. 13, replaces the function of the six
parallel-wired drivers 601 through 606 (FIG. 12). The reference
driver is electrically matched to the moving driver, but locked
against vibrational motion, as with the reference driver of the
whole organ embodiment. The drivers are typically smaller than
those used in the systemic artery pressure and whole organ
embodiments, but are otherwise similar in design. Drive currents to
the actual driver and reference driver are matched. Moving housing
801 of driver 800 makes direct contact with lower eyelid 802,
including vibrations through the lid into the eye, shown generally
at 805. The relatively heavy central winding and magnet structure
is coupled to rigid supporting post 804. The post is achored in an
adjustable support structure for resting the chin and ocular orbits
in a stable position. When the head is steadied, post 804 is
extended manually to bring housing 801 into gentle contact with the
lower eyelid of the open eye. Post 804 is then locked in place for
measurements. Velocity and force responses in the eye are deduced
from electrical responses of the coil in driver 800, using a
circuit similar to the FIG. 12 circuit. A difference is that the
amplitude of the digitally-controlled oscillator drive signal is
computer-controlled, as well as the frequency.
A first estimate of intra-opthalmic pressure can be derived using
the mechanical driver response alone. At vibration frequencies well
below the lowest resonant frequency (typically 30 Hz) of the
eyeball, measured mechanical impedance reflects primarily the
effective moving mass of the eyeball, moving substantially as a
rigid sphere partly surrounded by a soft semisolid characterized by
an additional moving mass, a velocity damping coefficient and a
restoring constant. The coupling is through the lower eyelid, which
behaves primarily like a spring at low frequencies. To better
characterize the effective eyelid spring constant, vibration
measurements are taken at higher frequencies between opthalmic
resonances, chosen such that the eyeball behaves as a comparatively
rigid body. These measurements complete, the driver explores
vibrational impedance responses in the vicinities of low-frequency
opthalmic resonances. Interpretation of the data depends on eyeball
diameter, on the effect of partly-surrounding tissue mass (which
varies with eyeball protrusion from the head) and on an average
tissue density that varies little and can be guessed. The
measurements well below resonance assist in estimating the
effective vibrating mass of the tissue that partly surrounds the
eyeball.
Interpretation of the mechanical vibration data is improved by a
measurement of opthalmic diameter. The curvature of sclera 808 (the
white of the eye) is measured by observing the reflections of two
lights on the sclera. Lights 810 and 811 appear as narrow, curved
line-sources of illumination, oriented roughly vertically to either
side of a display screen. (The lights must typically be spaced
further than 45.degree. from the eyeball-to-display center axis to
make the sclera reflections visible to the patient.) The curvature
of the lights is chosen to make the reflections on the sclera to
the left and right of cornea 806 appear approximately as straight
vertical lines. Tests are conducted in a dark-walled booth, to
minimize other reflections from the sclera. Clear display screen
812, between the two lights, is temporarily backed by a mirror.
Vertical cursors 813 and 814 are generated just in front of the
reflective mirror surface, e.g. using light-emitting diodes and
fiber optics. Switching of light-emitting diodes on different fiber
optic elements moves the visible cursor positions by small
increments. The positions are adjusted by the patient controlling
adjustment knobs, until the patient, looking in the mirror, sees
the light reflections on the sclera aligned to the two cursors. The
aligned cursor positions indicate the size of the eyeball. This
size measurement refines the interpretation of the
vibrational-impedance measurement, yielding an improved pressure
estimate.
To obtain further vibration response data, the mirror surface on
the back of screen 812 is replaced by a black surface. Lights 810
and 811 are switched off, as are the diodes illuminating cursor
lines 813 and 814. The display now consists of strobed horizontal
line 820, synchronously-strobed dots 821 and 822 above and below
the center of line 820, and independently-strobed dot 823 in the
middle of line 820. Peak strobe intensity must be fairly high, so
that flash tubes are typically used for this function instead of
light-emitting diodes. Line 820 is strobed in two alternating
colors, e.g. red and blue-green. The strobe flashes are synchronous
with the vibration drive signal, with (e.g.) the red and blue-green
strobe times separated by a 180.degree. relative phase angle. As
the eyeball vibrates, the cornea tilts and causes the image of the
strobe display to move up and down on the retina. When the patient
observes the red-strobed line converged with the blue-green-strobed
line to form an apparent white line, this indicates that the moving
line image on the retina is crossing the same position, moving in
opposite directions, at the times of the strobe flashes. The phase
of the red flash (and consequently of the opposite-phase blue-green
flash) is computer-set to a specific timing angle relative to the
force computed to be effectively driving the opthalmic vibration
mode of interest. The patient adjusts a knob that controls driver
frequency (via the computer), in order to converge the red and
blue-green strobe lines. Convergence indicates that the
zero-crossings of the vibrational displacement of the cornea and
lens are in-phase with the computer-controlled strobe-timing phase.
By repeatedly resetting the strobe phase angle relative to computed
vibrational force and allowing the patient to adjust frequency to
reconverge the lines, the computer determines values for the
opthalmic vibrational phase response angle as a function of
frequency.
Dot 821 flashes blue-green with the blue-green flash of line 820,
while dot 822 flashes red with the red flash of line 820. The
apparent visual positions of dots 821 and 822 are not perturbed by
vibrational motion when the colors of line 820 are converged. To
measure angular response amplitude of the cornea and lens, dot 823
is strobed alternately red and blue-green 90.degree. out-of-phase
with the respective blue-green and red flashes of line 120 and
single-color dots 821 and 822. When the phase adjustment has
converged the center line, the two color images of dot 823 appear
to have a maximum vibration-induced angular separation. The user
adjusts the vibration driver amplitude, thereby adjusting the
perceived dot separation to converge the red flash of dot 823 with
the blue-green flash of dot 821, and the blue-green flash of dot
823 with the red flash of dot 822, to form two white dots. To the
extent that angular image response of the eye depends on angular
deflection of corneal surface 806 and on the well-known refractive
index of the cornea (or of the type of contact lens resting on the
cornea, which must be provided as computer input), this amplitude
adjustment step tells the computer the excitation required to
achieve a reference angular tilt response amplitude of the cornea.
The amplitude response scaling equation is adjusted for the typical
effect of lens vibrational movement on the observed angular
response. Given the opthalmic radius-curvature, these angular
response sensitivity measurements may be converted to displacement
amplitude responses elsewhere on the eye. The resulting data tell
the computer substantially the same thing that ultrasound data tell
the computer in the whole organ embodiment, namely, the amplitudes
and phases of organ vibration velocities associated with
surface-measured forces and velocities at a number of frequencies.
(As mentioned, a miniature variant of the whole-organ embodiment
can determine intraopthalmic pressure using ultrasound instead of
visual measurements.)
A final refinement permits application of the network algorithm to
intraophthalmic pressure determination. Applicability of this
refinement depends on a combination of pulsatile pressure-change
amplitude in the eye, patient visual acuity, and the maximum
opthalmic vibration amplitude determined to be safe. Since the
intraopthalmic pressure pulsates somewhat with blood pressure,
convergence of line 820 will not be steady. The patient is asked to
adjust frequency until line convergence is achieved at one peak of
the opthalmic pressure waveform, with the red line moving above the
blue-green line at other times. The patient is then asked to adjust
frequency for convergence at the opposite extreme of the pressure
waveform, with the red line moving below the blue-green line at
other times. This frequency-separation at constant phase is easily
translated into phase-separation at constant frequency, given the
results of other measurements. Finally, the patient is asked to
adjust the angular separation of dots 821 and 822 (e.g. by
mechanical adjustment of the strobe optics) to match the peak
separation observed from pressure-induced variation in convergence
of line 820. This adjused spacing, measured and
digitally-interfaced, tells the computer the amplitude of the
pulsatile response-variation measurement. This completes the data
collection needed for applying the network algorithm, thus further
refining the pressure determination.
The vibration amplitudes and energy levels allowable in this
embodiment must be restricted for safety reasons, particularly to
avoid risk of retinal detachment. For this reason, the visual
display screen subtends a small visual angle and illumination is
made quite bright, to maximize visual acuity for small-vibration
observations. The vibration driver system can sense approximate
response amplitudes and precise applied vibrational power levels
without the benefit of visual observations. The system is designed
both to monitor and restrict maximum excitation levels, and to be
electrically incapable of delivering dangerous vibrational energy
levels.
There are time-varying display alternatives to the stroboscopic
display described above, e.g. an oscilloscope with horizontal
sinusoidal beam deflection at the driver frequency. Vibrational
response of the eyeball to the driver acting above or below the
cornea will cause a vertical deflection of the prescribed spot,
resulting in a perceived lissajous ellipse or circle if the spot
deflection frequency matches opthalmic excitation frequency. The
appearance of a circle or ellipse with vertical and horizontal
symmetry axes then indicates a+or-90.degree. phase angle between
spot deflection and opthalmic vibration response, while the
appearance of a sloping line segment indicates a 0.degree. or
180.degree. phase angle. Many designs for variable displays
synchronized to vibration driver excitations can produce perceived
colors and geometric patterns indicative of opthalmic vibration
responses.
DESCRIPTION OF THE PULMONARY ARTERY PRESSURE EMBODIMENT
Another variation of the invention is adapted for measuring blood
pressure in the right pulmonary artery, in the vicinity where the
artery crosses roughly horizontally at right angles to the
esophagus. Vibration driver/sensor assembly 900 of FIG. 14 is
swallowed and positioned partway down the esophagus, opposite
pulmonary artery segment 901, shown in section. The esophageal wall
is indicated by dashed line 928. The assembly is rotated and
adjusted vertically via flexible cable 902.
The assembly, shown cut open, contains a pair of defocused
ultrasound transducer assemblies, 903 and 904, which are very
similar in construction, relative positioning and function to
assemblies 62 and 65 of FIGS. 2 and 3, described in conjunction
with the systemic artery pressure embodiment. By manual axial
positioning of assembly 900, the operator matches the depths of two
artery-wall echo traces on an oscilloscope, as with traces 13 and
14 of FIGS. 1 and 7. Rotational alignment achieves maximum echo
signal strength from the artery-wall target. This is accomplished
in much the same way that the operator adjusts assembly 1 of the
systemic artery pressure embodiment to align with the underlying
artery, using a digital signal-strength readout.
Vibrational excitation is generated through length-change of
assembly 900, as curved end caps 905 and 906 vibrate axially.
Cylindrical housing 907 stretches to allow the relative motion of
the end caps. This housing is a composite structure of compliant
polymer (e.g. silicone rubber) with circumferential filaments (e.g.
fiberglass) that minimize diameter changes but affect bending and
length change minimally. Cable 902 emerges into curving segment 908
passing through cap 905 and into housing 907, providing vibration
decoupling between external cable 902 and cap 905. Flexible
membrane 909, bridging the circular gap between cable 902 and cap
905, is curved into 905 to roll with axial cap motion for vibration
decoupling. Thrust between the end caps is supported by rigid tube
910, which terminates in end plugs from which emerge thin, short
flexible rod segments 911 and 912, whose proportions give high
bending compliance with low axial compliance and no buckling under
working axial loads. Axial drive is provided by two magnetic driver
assemblies consisting of housings 913 and 915, which move axially
relative to their central magnet/winding assemblies terminating in
pedestals 914 and 916. Rod segments 911 and 912 terminate in
pedestals 914 and 196, transferring thrust from the pedestals to
tube 922 while allowing limited bending of the housing and end
caps. The driver housing and pedestal are analogous to housing 801
and pedestal 804 of FIG. 13, as described in relation to the
opthalmic pressure embodiment. Detection of relative vibrational
motion of the end caps is by analysis of driver electrical
responses, using circuitry similar to that used in the whole organ
and opthalmic pressure embodiments.
End-segment motion compresses and decompresses the gas (e.g. air)
in housing 907 without significantly perturbing the housing
diameter, so that vibrational excitation is analogous to an
acoustic suspension loudspeaker with twin drivers at the ends of a
closed cabinet of rigid diameter. A net volume-change vibration
drive is desired, since this motion induces a vibration field that
attenuates more gradually and smoothly over space than
constant-volume vibration modes. The hoop stiffness of housing 907
prevents radius-change from offsetting volume changes caused by
end-motion, while the high bending flexibility (within angular
limits) prevents housing rigidity from interacting significantly
with tissue vibrations that bend the housing.
As the relatively rigid and heavy spinal column lies immediately
dorsal to assembly 900, on the right in FIG. 14, the tissue
displacements off moving end caps 905 and 906 normally interact to
produce significant lateral translational vibrations and bending
vibrations in the assembly. Acceleration sensors 917, 918 and 919
detect left-right lateral vibrations near the top, center and
bottom regions, respectively, of assembly 900, thus quantifying
translational and bending motions in a plane substantially
perpendicular to the axis of artery 901. The ultrasound-detected
arterial motions are minimally affected by un-measured vibration
components.
To provide still more data, fluid pressure sensor 920 is placed
adjacent to acceleration sensor 918, on the assembly surface
closest to artery 901. This sensor detects pressure exerted on the
sensor assembly surface adjacent to the artery, responding from DC
up through the vibration-frequency band of the drivers. Hence, the
sensor can feel the low-frequency push as artery 901 expands with
each heartbeat, and it can feel the effects of changing tissue
stresses related to the diameter-change of the artery. In this way,
the low-frequency pulsations of the artery itself are examined as a
vibrational excitation that indicates properties of the artery and
its near surroundings.
Cable 908 enters tube 910. The ultrasound coaxial cable travels via
tube 910 to assembly 921, which contains high frequency
transformers and transistor switches like those in assembly 56 of
FIGS. 2 and 3. The switches couple ultrasound signals either via
wire pair 922 between 921 and ultrasound assembly 903, or via wire
pair 923 between 921 and ultrasound assembly 904, depending on a
selection control voltage, as discussed in the analogous situation
for the systemic artery pressure embodiment. Flexible wire braid
924, originating from cable 908 (which extends from cable 902),
emerges from tube 910 to couple power and signals to and from
acceleration transducer 919. Likewise braid 926, also originating
from cable 908, emerges from tube 910 to couple power and signals
to and from assembly 918, and similarly for braid 927 and assembly
920. Similar braid 925 emerges directly from cable 908 to couple to
acceleration transducer 917.
The system gathers substantial data about the artery, including
both frequency-baseline and pressure-baseline variations. Because
of lag between pressure and diameter responses observed in the
pulmonary artery (apparently caused by visco-elastic creep response
in the artery wall), vibrations are sometimes measurable at equal
radii and with sufficient pressure separation to permit solution of
the network algorithm to useful accuracy. Preliminary to network
solution, simulation algorithm techniques are applied to translate
the three-dimensional vibration field problem into an equivalent
two-dimensional problem, amenable to network techniques taught in
conjunction with the systemic artery pressure embodiment.
Application of the simulation algorithm involves representing the
system as interacting simple vibrating shapes. At a distance, the
vibration fields from end caps 905 and 906 appear very similar to
the fields of two spheres vibrating in the simplest volume-change
mode. The spinal column to the right of assembly 900 in the diagram
acts like a partial vibration mirror, creating the effect of a
second image-pair of vibrating spheres. The field strength, phase
and apparent distance (presumed directly to the right) of these
image spheres from assembly 900 are inferred from the translational
motions of acceleration sensors 918, 919 and 920. The resulting
effective four-source field induces smoothly-tapering Mode 1 and
Mode 2 excitations in the pulmonary artery, with minimal excitation
of Mode 3 and above. Designing for the correct spacing between end
caps 905 and 906 relative to their expected distance to the right
of artery 901 helps to minimize average Mode 3 excitation. As there
are pressure and stress variations axially along the artery, there
is axial vibrational flow, resulting in net cross-section area
change in the ultrasound plane. This appears as Mode 0 vibrational
excitation in the ultrasound plane. The Mode 1 and Mode 2
vibrations vary slowly enough with respect to axial distance along
the artery that axial motion associated with axial rate-of-change
of these modes can be ignored. Hence, Mode 1 and Mode 2 excitations
are treated as simple two-dimensional modes locally, anywhere along
the artery length. The three-axis ultrasound system provides enough
data to resolve Mode 0 from Mode 2 unambiguously in the ultrasound
plane without symmetry assumptions (not the case with Mode 1 and
Mode 3 excitation), since Mode 0 motion is described entirely by a
single amplitude and a single phase (unlike Modes 1, 2 and 3, each
of which can exhibit two amplitudes and two phases because of the
possible differing-axis excitations).
The excitatory field of the four vibrating spheres can be resolved
computationally, at any point along the artery length, into an
axial translation, a transverse translation (observed as Mode 1), a
transverse two-dimensional shear in the cross-sectional plane
(observed as Mode 2), and a shear component associated with Mode 0
motion in the cross-sectional plane, accompanied by an axial
velocity gradient. Of these vibration components, the transverse
shear component associated with Mode 2 excitation accounts for most
of the vibrational energy flow that is pressure-sensitive. Focusing
on this component, a network algorithm solution is obtained, using
pressure-baseline data at constant diameter. From the four-source
vibration field model, the axial variation in Mode 2 excitation is
estimated and an effective excited length calculated as follows.
The Mode 2 excitation amplitude as a function of axial position is
divided by the amplitude computed for the ultrasound-plane. This
amplitude ratio is squared (giving an energy ratio) and integrated
with respect to distance over the length of the pulmonary artery.
The resulting integral is the effective excited length. For network
algorithm solution, driver force and velocity may be interpreted as
axial force and relative axial velocity of the end caps.
Two-dimensional force associated with the ultrasound-measured
vibrations is axial force divided by the effective excited length
just described. The network algorithm is then solved by the methods
shown in the context of the systemic artery pressure embodiment.
(If the image-pair vibration is significantly phase-shifted from
the primary pair, a more complicated network algorithm may be
needed, taking into account differing effective excited arterial
lengths for two different vibration phases.) Network solution data
feed into the analytic function fit algorithm, yielding values for
absolute pressure.
Further computational refinements provide a consistency check for
the network solution, as well as an estimate for tissue elasticity
around the pulmonary artery, which can mimic blood pressure
significantly for the low pressure range of concern (typically
below 30 mm Hg). The heart-rate pulsations sensed by
surface-pressure sensor 910 help give an estimate of tissue elastic
modulus near the artery. The measured pressure response is
sensitive to tissue shear stresses acting normal to the sensor
surface. Correlating these stresses with pulsating
ultrasound-measured artery diameter and distance gives an
indication of tissue elasticity.
The network solution gives an estimate of changing blood pressure
that can be correlated with pulsatile diameter changes to estimate
artery diameter elasticity. The four-source vibration simulation
predicts Mode 0 excitation along the artery length. Combining this
prediction with ultrasound-measured Mode 0 response and with an
elastic tube vibration model (based on Fourier analysis and the
elastic tube theory that has been used to study pulse wave
propagation in arteries), an independent estimate of diameter
elasticity is obtained. Comparing these two elasticity estimates
gives a consistency check.
Since the network solution just described relies on data showing
pressure differences at equal diameters, and since the lag between
pressure and diameter changes can be small, the accuracy of the
data for this simplest kind of network solution may be compromised.
Better results then require diameter-correction procedures
analogous to those described for the systemic artery pressure
embodiment. Since Mode 0 vibrations are sensitive to diameter
pulsations, Mode 0 energetics may need to be simulated and
incorporated into a network algorithm with diameter-change
correction. This simulation is approached using methods indicated
above and under "Simulation Algorithms". Note that methods taught
for applying a two-dimensional network algorithm to a
three-dimensional flow situation are applicable e.g. in the
systemic artery pressure embodiment, for correcting computations
where flow does not accurately approximate a two-dimensional
field.
OTHER EMBODIMENTS
Systems Simplified by Low Damping
If vibrations are not strongly damped by tissue viscosity, phase
varies little through most of the vibration field, and effective
vibrating mass is hardly affected by viscous shear forces. Then
pressure is related simply to geometry, average density and a
resonant frequency where organ excitation force is in phase with
response velocity. This is useful e.g. in a simplified
intraopthalmic pressure embodiment taking advantage of low damping
and the fact that driver force is altered minimally by transmission
through the eyelid. The user adjusts frequency to converge a line
strobed at force maxima, thus matching the phases of driver force
and opthalmic velocity response. A simple formula relates adjusted
frequency, opthalmic radius and estimated effective average density
to pressure. The system achieves useful accuracy without a
determination of driver velocity.
Expanded Digital Processing
The signal processing so far described uses analog circuits up to
the outputs of the demodulator modules. From there, digital
algorithms take over to solve the mathematical equations described
in the text. The analog-digital interface boundary can be moved.
For example, the simultaneous network equations can be solved by
analog computation. For economy and flexibility, however, there are
advantages to expanding digital processing in the invention,
eliminating analog circuitry and moving the A to D interface toward
the sensors. For example, the audio-band signals entering the
circuitry of FIG. 9 can be sampled and digitized directly and the
demodulation functions moved into the digital domain. Even direct
sampling and digitization of ultrasound signals is possible, though
not necessarily a good approach. Digital demodulation involves
digital multiplication of signal quantities and formation of
averages using fixed weighting factors. By careful sequencing of
sampling and computation in relation to analog signal phases,
multiplications by arbitrary quantities can be reduced.
Microprocessor computation time is typically minimized by
algorithms that use sorting, summing, differencing, halving and
doubling of quantities to minimize multiplications by multi-bit
quantities. Pre-scaling of variables to permit fixed-point
arithmetic rather than floating-point also saves time.
Mathematically inexact approximations of processes described here
often yield adequate results while conserving computer power. Thus,
the economy and feasibility or real-time digital processing is
influenced profoundly by good software design.
Multiple Simultaneous Frequency Processing
The circuitry described so far induces, measures and analyzes
responses at only one frequency at a time. With additional
circuitry or added computation function, it is possible to excite
responses and analyze data at several frequencies simultaneously.
This approach has the advantage that a full spectrum of response
data containing both pressure and frequency baseline information
can be gathered at once, e.g. during a single heartbeat, reducing
or eliminating reliance on analyzing matched pressure cycles.
Multi-frequency digital signal processing often need not keep pace
with real-time events, since frequency baseline data is typically
needed only for calibration of the sensor-patient coupling.
Real-time blood pressure monitoring (either systemic or pulmonary)
typically requires processing only at a single frequency. Hence,
the computer can store multi-frequency signal data rapidly during a
calibration heartbeat and process the data over a longer period of
time.
Multi-frequency processing is described as a modification and
extension of the analog processing and data acquisition of FIG. 7
and accompanying text. The demodulation and signal-generation
processes described can be implemented digitally as well as by
analog modules. In one approach, several sinusoid oscillators
operate simultaneously at different frequencies. The outputs are
summed and amplified to energize the vibration driver. The response
data then contains multiple frequencies. To analyze data at one of
the oscillator frequencies, that oscillator output is used
separately as a demodulator phase reference signal. A quadrature
sinusoid at the same frequency is also derived. The audio-band
response signals are demodulated with respect to the two
reference-frequency phases. (Depending on bandwidths, it may be
necessary to use demodulation multipliers that are linear in both
quadrants, to avoid unwanted distortion products.) With proper
filtering and sufficient frequency spacing, the demodulator outputs
represent responses only at the frequency of the phase-reference
sinusoid. Hence, a second set of demodulators using a second
sinusoidal frequency reference yields independent response data at
that frequency, and so on. Note that a response signal, e.g.
velocity or force, is no longer appropriate to use as a demodulator
phase reference, since such a signal contains several frequencies.
After all signal quantities are demodulated at a given frequency
for both reference phases, one signal quantity, generally
complex-valued, may be chosen as a reference and complex-divided
into the other signal quantities, as an optional scaling
procedure.
Multi-Sensor, Multi-Driver Systems
The amount and accuracy of information yielded by a system to
excite, measure and analyze vibrations depends on the number and
quality of measurements taken. A system capable of inducing
vibrations from many points and detecting many independent response
parameters can ultimately resolve more physiological data than a
simple system. Computation methods described under "Simulation
Algorithms" are applicable in such complex environments.
One possible multi-sensor, multi-driver system can be described in
terms of a multiplicity of modules like the one of FIGS. 10 and 11,
as described for whole-organ measurements. Each driver/sensor
module should include means for sensing its location and
orientation is space as it contacts the patient. Location sensing
is accomplished e.g. using three spring-retracted cables extending
straight to each module, with the cable payout lengths measured.
Orientation sensing can be gyroscopic. The ultrasound transducers
of the modules operate in a sequence that avoids unwanted
interference while organ dimensions and vibration parameters are
evaluated along multiple paths. The vibration drivers are activated
e.g. one at a time to perform frequency sweeps. The activated
driver measures its own force and velocity output, while inactive
drivers sense force and velocity passively at their surfaces. As
the drivers perform their frequency sweeps, the system gathers
sufficient vibration data to constrain the unknown parameters of a
detailed simulation model. Ultrasound dimension data aids in
constraining the model. Once the simulation parameters are adjusted
to provide good agreement between modeled and measured responses,
those parameters give a detailed picture of the mechanical
properties of the tissues and organs under study.
Simulation Algorithms
This section discusses mathematical simulations of vibrational flow
in visco-elastic, incompressible tissues. At each point in the
tissue, flow is a vector velocity, and each vector direction
component is represented by a complex number, characterizing
vibrational amplitude and phase. The vibration field equations,
involving pressure gradients and shear stresses, are separable into
component equations involving pressure without shear effects, and
shear stresses without pressure effects. Shear forces are
associated with viscosity and elasticity, but the two properties
are easily combined into a single, frequency-dependent complex
coefficient. Shear-induced velocities tend to be confined to
boundary layers whose influence drops off rapidly with distance, so
that shear velocity fields can often be ignored at a distance from
a vibrating object. The deeper-penetrating pressure fields are
simpler to compute than shear fields. In many instances, only the
pressure field need be computed in detail.
Both the pressure and shear equations have relatively simple
solutions for parallel planar layers and two-dimensional flow, or
for concentric cylinders or concentric spheres. To compute
interactions among spheres, cylinders and flat-surfaced vibrators
requires translation of vibration fields between the coordinates of
different symmetries. In this translation, orthogonality between
vibration modes breaks down, so that a single mode in one symmetry
influences a number of modes in another symmetry. A combination of
Fourier analysis and solutions of simultaneous linear equations
frequently suffices to solve boundary constraint problems for
interacting geometries.
Iterative functional minimization procedures finally determine
best-fit parameters of a simulated vibrating system, in order to
match actual body vibration measurements with their simulated
counterparts. The best-fit parameters reveal fluid pressures and
the tissue properties of organs and blood vessels.
Mathematical Simplifications
Two related topics of classical mechanics overlap in simulation
analysis for this invention: the theory of viscous fluid flow, and
the theory of elastic solids. For the vibrations of interest with
this invention, compressibility is negligible, so that all shape
deformations of tissue may be described as shear deformations--an
important simplification. Because the analysis is concerned only
with low-amplitude, low-velocity vibrations, fluid and elastic
behaviors are non-turbulent and linear, a further simplification.
Because vibrations are small, the shapes of vibrating objects
change only negligibly within the limits of a cycle, permitting the
simplifying approximation that in certain aspects of analysis,
boundary shapes are considered constant despite vibrations.
Dimensional Analysis
The Reynolds number is a familiar non-dimensional parameter of
fluid dynamics, expressing a ratio of inertial to viscous forces.
If two flow situations involve similar boundary shapes and matched
Reynolds numbers, then the flow velocity fields will be
geometrically similar (other effects being equal). In the
small-vibration context, fluid flow Reynolds numbers are
essentially zero, implying that inertia is dominated by viscosity.
Vibrational flow analysis differs greatly from steady flow
analysis, however, since inertia must be overcome with each
reversal of flow direction. Hence, vibration frequency multiplies
the effect of inertia. A different non-dimensional scale parameter
is useful for expressing the vibrational ratio of inertial to
viscous forces. The Reynolds number is expressed as a flow velocity
multiplied by a size-defining length (e.g. a water pipe radius),
all divided by the kinematic viscosity of the fluid. For a
vibrational counterpart to the Reynolds number, substitute
frequency multiplied by length where velocity was used. Hence, a
constant product of frequency times length-squared, divided by
kinematic viscosity, implies vibrational flow similarity.
The square-root of this Reynolds number analog is especially useful
for analysis. We designate this number "R", suggesting Radius,
since the parameter expresses radius in units of a characteristic
length over which inertia and viscous forces are comparable. This
characteristic length is the denominator square-root expression of
Eq. 36, and divides dimensional radius "r", the numerator. The
terms under the square root are angular frequency "f" and kinematic
viscosity "nu".
(In the specialized context of pulsating axial fluid flow in tubes,
this number is called the "Womersley Frequency paramter"--see
Womersley, J. R., "An Elastic Tube Theory of Pulse Transmission and
Oscillatory Flow in Mammalian Arteries", WADC Tech. Rep., 56-614,
1957.)
The parameter "R" arises in correcting the vibration analysis for
changing arterial diameter. When radius "r" varies, a constant
equivalent frequency and radius is maintained if the product
"f.multidot.r.sup.2 " is held constant. We see that this maintains
"R" constant. In the simplified case of an artery with a
zero-thickness wall in uniform surroundings, this adjustment
maintains a similar flow geometry and an identical impedance from
inertia and viscosity. Thus, maintaining a constant
f.multidot.r.sup.2 product can be useful for isolating the effect
of pressure change on an impedance measurement when pressure and
radius change interdependently.
Now consider an arterial wall of significant thickness. Assume that
"f" is adjusted with changing "r" of the midpoint in the wall
thickness, in order to maintain the midpoint "R" constant. Since
wall cross-section is constant, wall thickness varies as 1/r.
Hence, non-dimensional wall thickness, proportioned to constant
"R", varies as 1/r.sup.2. To correct vibration measurements for
this change in proportions calls for simulation methods to be
shown.
Separability of Basic Flow Equations
The analysis begins with familiar fluid flow equations expressing
two constraints:
(1) Continuity of an incompressible medium demands that for any
fixed volume in the medium, the net flow influx through the surface
of the volume must be zero at all times;
(2) Newton's Law, Force=(Mass.times.Acceleration), must be
satisfied for any fluid element in each coordinate direction. The
Newton's Law equations are frequently referred to as the momentum
equations.
To satisfy Newton's Law, there are two important sources of force
to consider: pressure, and shear stresses. The latter are caused by
the viscosity and elasticity of the medium. There is a very
important theorem for dealing with pressure and shear stresses.
(The theorem, discovered independently in developing this
invention, may be previously known, but if so, it is not widely
known and is not reported in advanced texts on fluid mechanics.)
The theorem states that inside a region of uniform density,
viscosity and shear modulus, a flow geometry determined by both
pressure and shear stresses can be separated into two component
flow geometries. The first component geometry is determined
entirely by pressure gradients and density, independent of shear
effects. To solve for this geometry, the powerful theory of
potential flow is applicable. The second component geometry is
determined entirely by shear forces and density, independent of
pressure effects. The shear field equations are simplified by the
absence of pressure gradients. Each component flow solution must
obey the equation of continuity. The correct overall flow velocity
field is the specific combination of the potential flow and shear
flow solutions that matches the motions of the boundary of the
uniform region.
The independence of the potential flow equations from viscosity and
elasticity is counter-intuitive. Viscosity and elasticity induce
non-zero shear stresses in a potential flow field, but
surprisingly, these stresses balance to give no net force on any
volume entirely within the uniform medium. Shear stresses become
unbalanced, creating a net force, only at boundaries of
discontinuity in fluid and elastic properties, or where
non-vibrational tension in a tissue layer (e.g. as caused by fluid
pressure containment) causes a restoration force toward an
equilibrium shape.
The velocity potential function of non-viscous steady flow analysis
is an abstraction, having no obvious physical counterpart. In
vibrational flow, the velocity potential corresponds to vibrational
pressure. The vibrational pressure gradient results directly in
fluid acceleration. Fluid velocity lags acceleration by
90.degree..
Given this separation of the Newton's Law equations for flow in a
visco-elastic medium, we may discuss separate potential and shear
flow solutions for geometries of interest. Wherever tissues with
differing properties come in contact, the vibrational flow
solutions for regions on either side of the interface must give
matching velocities at the boundary, and the net effect of
pressures and shear stresses must balance both parallel and normal
to the interface. It is possible for vibrational pressure to be
discontinuous across a boundary, provided that the discontinuity is
offset by an opposite discontinuity in vibrational stress acting
normal to the boundary surface. This vibrational stress
discontinuity can arise from vibrational shear forces or from
non-vibrational tension (e.g. from pressure containment)
interacting with vibrationally-changing curvature. There must be no
cross-boundary discontinuity in shear stresses paralleling a
boundary surface.
The vibrational flow simulation task is largely to determine the
combinations of potential and shear flow solutions within regions
that match properly at the boundaries. For symmetric geometries
such as concentric spherical or cylindrical tissues, this matching
task reduces to evaluating flow functions and solving simultaneous
linear equations, generally no more than four complex-valued
equations at a time. When non-concentric geometries interact (e.g.
a flat disk vibrator perturbing an underlying spherical organ), the
vibrations in the coordinates of one geometry must be translated
into vibration components in the coordinates of the other geometry.
Through this translation, a single vibration mode in one geometry
generally excites a series of modes in the interacting geometry.
Hence, orthogonality of vibration modes vanishes with loss of
symmetry. Solutions come to involve systems of many simultaneous
equations. The mode translations from geometry to geometry
generally involve Fourier analysis or comparable
function-correlation integrals. A concrete example is sketched
below.
Complex Viscosity Incorporates Elasticity
In the context of arterial blood pressure determination, tissue
viscosity is important, and elasticity other than pressure-induced
elasticity is negligible, except possibly within a hardened
arterial wall. For probing the much lower pressure range of the
pulmonary artery, tissue elasticity is significant. For vibrational
probing of organs, tissue elasticity is one of the most important
diagnostic parameters. Consequently, organ-probing driver
frequencies range low enough to bring out tissue elasticity
effects, which become increasingly dominant at low frequencies.
Elasticity is a tendency of a substance to return from deformation
to an original shape. Viscosity is a tendency of a substance to
resist any rate-of-deformation in shape. Elasticity stores energy,
while viscosity dissipates energy. In visco-elastic tissues,
elasticity and viscosity are not simply additive, since there is
usually elastic "creep". With creep, a tissue deformed from a shape
forgets that original shape progressively over time,
re-equilibrating toward the new shape. Since creep dissipates
stored mechanical energy, creep causes a time-dependent viscosity,
as well as a time-dependent elasticity.
The relationship of creep to elasticity and viscosity is more
easily described in the frequency domain. If there is elastic
creep, then the shear modulus decreases with decreasing frequency,
to reflect how the tissue progressively forgets a previous shape
with increasing duration of the deformation cycle. As shear modulus
decreases, viscosity increases to reflect the added dissipation of
stored mechanical energy.
The relationship between elastic modulus and viscosity as functions
of frequency can be described in terms of the analytic properties
of a complex viscosity function whose real part is ordinary
viscosity and whose imaginary part relates to shear modulus. We
designate ordinary absolute viscosity by "mu", and complex
viscosity by "MU", whose real and imaginary parts are called "MUr"
and "MUi". MUi is expressed in terms of shear modulus "Y", divided
by the complex quantity "j.multidot.f", for "j"="square root of
-1", and "f"="radian frequency". In Eq. 37, both mu and Y are
functions of f, being invariant with respect to f only in the
absence of creep:
The function "MU" of the argument "j.multidot.f" is analytic, that
is, it has a unique complex derivative. The j.multidot.f argument
is imaginary for a pure frequency signal but may take on any
complex value for the purposes of mathematical analysis. The
properties of analytic functions relate mu and Y in this context.
The analytic function fit algorithm and the Hilbert Transform (both
described previously) apply to analyzing the frequency
interdependence of elasticity and viscosity.
Complex kinematic viscosity "NU" is defined as absolute viscosity
"MU" divided by density ".rho.":
One may write the equations for vibrational viscous flow, and by
substituting a complex viscosity coefficient for ordinary
viscosity, the equations apply to visco-elastic flow. This
technique works even for many non-Newtonian fluids like cake batter
and silicone putty, fluids that exhibit short-term memory, or
decaying elastic behavior. The difficulties fall away in part
because at any fixed frequency, the combined effects of elasticity
and creep separate neatly into an elastic component, appearing in
the imaginary part of the complex viscosity coefficient, and a
viscous component, appearing in the real part. The other
simplification is that many non-Newtonian fluids are difficult to
deal with because of non-linear or non-isotropic behaviors
manifested only with large shear deformations. These behaviors
often disappear for small-amplitude vibrations.
There are minor limitations to the analytic simplification being
described here, as applied to the analysis of living tissues.
Certain tissues are highly non-isotropic, even in their responses
to small vibrations. This is seldom a problem in the context of
this invention. For example, striate muscle tissue is
non-isotropic, having differing viscous and elastic properties
along the fibers and across them. The properties are symmetric for
the two directions within a cross section cutting perpendicular to
the length of the fibers. In analyzing vibration fields in a plane
of symmetry, that plane is usually the plane of isotropic behavior.
Where anisotropic tissues appear in thin layers, the anisotropy
between in-plane and across-plane directions is of little
consequence to vibration analysis on a relatively large scale.
Thus, many anisotropic sheathings of connective tissue can be
treated as if they were isotropic, with negligible error.
Planar, Cylindrical and Spherical Solutions
There are three symmetries of flow geometry that yield to
particularly simple analysis: concentric cylinder symmetry;
concentric sphere symmetry with vibration symmetric through an
axis; and planar symmetry with long waves standing or traveling
along a flat surface and penetrating into the medium below. In all
three cases, flow geometry may be described in two dimensions, in
an appropriate cross-section. Symmetry takes care of the remaining
dimension. Further, for these particular symmetries, the
two-dimensional partial differential equations split neatly into
separate ordinary differential equations for each coordinate. The
overall solution is the product of the component solutions.
Once the separability of potential and shear functions is
recognized and once the complex viscosity coefficient described
above is incorporated as a tool, mathematicians can readily set up
and solve the planar-wave vibration equations. Therefore, only a
sketch is provided here. The potential-flow solutions are the
familiar equations for sinusoidal surface waves on a non-viscous
liquid. For each wavelength, one solution decays exponentially with
depth and the other solution grows exponentially with depth.
Vibrational phase is independent of depth. These solutions are
expressed elegantly in terms of the complex exponential function.
The undamped shear solutions are known as Rayleigh waves. The less
familiar damped shear solutions involve a sinusoidal function along
the surface, multiplied by the exponential function of depth, but
with a complex exponential argument. Again, there are two depth
functions at a given surface wavelength, one growing with depth and
the other decaying with depth. Shear vibrational phase is not
constant with depth, and the vibration field is not analytic, i.e.
the complex velocity function is not related directly to a function
having a unique complex derivative.
Combining planar vibration solutions in a double complex Fourier
series, it is possible to model a vibration field having
two-dimensional symmetry in a uniform medium below a flat surface
vibrator. This technique is useful in conjunction with embodiments
of the invention that deal with a shallow artery whose diameter
changes significantly with changing pressure. The double Fourier
series consists of a potential flow series and a shear flow series,
both including only solutions that decay with depth. The sum of the
two series solutions must match the motion of the vibrator, and
elsewhere the sum must obey the boundary constraints of a free
surface. For a finite series, the solution will be approximate and
periodic over surface length, representing an infinite row of
vibrators spaced widely enough not to interfere seriously with each
other. The technique can be extended to multiple, parallel tissue
layers, in which case layers with a lower boundary must be
represented by quadruple Fourier series solutions, involving
potential and shear flow functions that increase and decay with
depth.
The cylindrical and spherical solutions are very similar to each
other in form. They consist of a function of angle multiplied by a
function of radius. The angle functions are a discrete series of
vibration modes, such as are illustrated in FIG. 6. The radial
functions are solutions to second-order homogeneous ordinary
differential equations. Associated with any mode number
(corresponding to a given surface wavelength in the planar case)
are exactly four radial solutions--two potential and two shear. One
potential and one shear solution diverge at infinit radius. The
other potential and the other shear solution diverge at zero
radius. Since these solutions are difficult, their determination
procedures are outlined here.
To express and solve these cylindrical and spherical equations in
the most general form, we must extend our definition of
non-dimensional radius "R" from Eq. 36 to the case of complex
kinematic viscosity "NU", of Eq. 38, according to Eq. 39;
We further characterize the ratio of elastic to viscous components
of complex NU by the ratio "q" of Eq. 40:
With these definitions, we can write the equations governing
potential and shear flow for cylindrical and spherical geometries.
We begin with the cylindrical case. If "u" is velocity in a radial
direction and "v" is velocity in a tangential direction, associated
with non-dimensional radius "R" and angle ".theta.", then we
have:
We have split u and v into radial complex amplitude functions, U
and V, multiplied by circumferential sine and cosine functions for
Mode n, and finally multiplied by the complex EXPonential function
giving the dependence on frequency and time. Adding a real constant
to the cosine and sine arguments rotates the mode shape in space.
Vibrational phase shift and amplitude adjustment to satisfy
boundary constraints is accomplished by multiplying U and V
solutions by an appropriate complex scaling coefficient.
There are two types of U solutions, potential and shear solutions
"Up" and "Us". These are solutions to the following equations:
The difference between the potential and shear equations is the
addition of the elasticity correction, q, and the imaginary unit,
j, to the shear equation. The imaginary j-term in Eq. 44 causes the
solutions to spiral in the complex plane about the R-axis. The
potential flow equation contains no imaginary terms. The potential
flow solution is real, exhibiting no "spiraling", i.e. no
vibrational phase shifts with changing R. In fact, for any given
Mode n, any potential solution can be expressed as a linear
combination of exactly two potential flow functions (allowing for
complex scaling coefficients), R.sup.n-1 and R.sup.-n-1. Similarly,
for a given Mode n and elasticity correction q, all shear solutions
can be expressed in terms of just two shear flow functions. These
can be evaluated by numerical integration along the R-axis, using
almost any integration procedure (e.g. Runge-Kutta or, as is
especially efficient here, a Taylor series incrementation). Let the
solution that diverges at infinity and converges at zero be called
the "zero-solution". Similarly, let the solution that diverges at
zero and converges at infinity be called the "infinity-solution".
To obtain the zero-solution for any range of R exceeding a given
minimum Rmin, start at an R below Rmin with an arbitrary initial
solution (e.g. Us=1, .delta.Us/.delta.R=0) and integrate for
increasing R. The first integration steps will give a combination
of both solutions, but the infinity-solution will decay rapidly
while the desired zero-solution will grow rapidly, to dominate the
entire solution. It is always possible to pick a positive starting
R that is small enough to give arbitrarily good separation of the
zero-solution from the infinity-solution above a given Rmin.
Evaluate complex Us and .delta.Us/.delta.R over a range above Rmin,
for Rmin>1, and store the results in two tabulated functions, Us
and .delta.Us/.delta.R, of the argument R. Tabulate points for R=1.
Standarize the magnitudes and phases by dividing each tabular entry
by the original complex value obtained for Us at R=1. In this way,
the function is standardized to Us=1 at R=1. This tabular function
may be defined as the zero-solution. Similarly, the
infinity-solution for any range of R below a given Rmax and for a
given q and Mode n is evaluated by starting with with an arbitrary
initial U and .delta. U/.delta.R. Beginning from R sufficiently
above Rmax>1, integrate for decreasing R. The desired
infinity-solution quickly dominates. As before, tabulate the
function below Rmax and rescale the function and derivative results
to standardize to Us=1 at R=1. This gives the
infinity-solution.
For rapid computation of the two shear functions, pre-compute and
store an array of function tables as described in the paragraph
above, for needed Modes n (typically not past n=4), and for the
needed range of q. These tables may be stored in read-only memory
or loaded into random-access memory along with the microprocessor
control program. Let the q-spacing be small enough to permit
accurate polynomial spline interpolation along that array axis.
(Interpolation of the complex logarithm of the function and
derivative may prove more accurate). The R-spacing can be fairly
large. To evaluate, say, the infinity-solution for given R and q,
pick the next-larger tabulated R in the infinity-solution tables,
interpolate along the q-axis of the array to the desired q, and
then use numerical integration to move back from the tabulated R to
the desired R. To evaluate a desired zero-solution, use the
zero-solution tables, pick the next-lower tabulated R, interpolate
to the desired q, and integrate forward to the desired R. Using
this technique, it is not necessary to integrate far enough to
obtain separation of the two solutions, for the tabular values of
Us and .delta.Us/.delta.R used for starting already provide the
desired separation. Tabular spacing of R is clearly a tradeoff
between memory allocation and function computation time. The
absolute magintudes and phases of the solutions obtained are always
scaled to fit a boundary condition. One normally needs to know only
the complex ratio of a U-function going from one R to another R,
corresponding to inner and outer boundaries of a continuous region
of tissue. The non-dimensional R parameters are always computed
first, starting with actual radius r and solving for R in Eq.
39.
Because of desirable mathematical properties of the differential
equations just given, the solutions are consistent with the
continuity constraint, or incompressibility condition. The
V-solution is obtained from any U-solution (either Up or Us) by
applying the continuity constraint. This is expressed simply:
The equations governing vibrational flow for spherical symmetry
with the vibration axis corresponding to the spherical axis are
similar, but somewhat more involved. In place of the trigonometric
functions "cos (n.multidot..theta.)" and "sin (n.multidot..theta.)"
of Eqs. 41 and 42, we substitute functions designated,
respectively, "C(.theta.)" and "S(.theta.)". The functions C and S
are different for each Mode number n. These functions are solutions
to Eqs. 46 and 47:
The number "N" must be chosen to give a function periodicity of
2.multidot.pi, in order that C and S be single-valued for a given
angular position. The eigenvalues of N that satisfy this closure
condition correspond to Mode numbers n. Solutions for N, C and S as
functions of n are given in Table 1 for n from 0 to 3.
TABLE 1 ______________________________________ Spherical Vibration
Functions of Angle ______________________________________ n N C S 0
0 1 0 1 2 cos(.theta.) sin(.theta.) 2 6 1/4 + (3/4)cos(2.theta.)
(1/4)sin(2.theta.) 3 12 (3/8)cos(.theta.) + (5/8)cos(3.theta.)
(1/32)sin(.theta.)sin(3.theta.)
______________________________________
The mode shapes are slightly distorted from the single-component
sinusoids of the cylindrical solutions, although the mode shape
graphs appear very similar to the drawings of FIG. 6. Given these
angle functions, we now move on to the spherical radial functions U
and V, keeping the same notation as for the analogous cylindrical
equations above:
As before, the shear equations differ from the potential equations
only in the addition of the q-term and the imaginary unit, j. The
functional behavior is quite similar to the cylindrical cases. For
a given n and corresponding eigenvalue N, the two potential
solutions are power-law functions of R, as is easily shown by
substitution. The two shear solutions converge at zero and
infinity, and they spiral about the R-axis in the complex
plane.
As before, V comes from any U solution using the continuity
equation. The solution shown is independent of Mode number n or the
eigenvalue N, since these parameters are incorporated into the
definition of the functions C and S. Hence, we have simply:
Regions Dominated by Potential Flow
We can see some important generalized function properties embodied
in the examples of these vibration field solutions for cylindrical
and spherical symmetry. Observe that the shear flow solutions are
much more localized in their influence than the potential
solutions. Consider the flow field exterior to a cylinder driven to
vibrate by an interior energy source. If the medium surrounding the
cylinder is approximated as uniform to infinity, then only the
infinity-solution to the differential equations gives appropriate
convergence. This shear solution goes to zero roughly exponentially
with increasing R, while the corresponding potential solution
converges to zero only as a negative power of R (determined by Mode
number n). Hence, far from a surface, the potential field
dominates. This comparison holds for spheres and for other shapes
as well. The comparison fails for periodic surface waves, but when
these waves are combined using Fourier techniques to represent the
field of a long vibrator plate, the properties discussed here
emerge. Hence, the generalization about local shear fields and
relatively penetrating potential fields applies where a flat
circular vibration driver is placed above a roughly spherical
organ, as in the embodiment of the invention for probing whole
organs. Let us see how this is useful.
If an organ below a circular vibrator plate is relatively deep,
then the shear-flow field of the vibration driver will affect the
organ much less than the potential field. Unless large tissue
discontinuities generate local shear flow fields in the organ's
vicinity, the field coupled to the organ can be approximated by a
pure potential field. The potential flow solution for a flat disk
was solved decades ago as an exercise in acoustics, and is easy to
compute on a microprocessor. The task at hand is to compute an
"effective vibrator" whose size and vibration amplitude and phase
are corrected, relative to the actual driver plate, to account for
the effects of the boundary shear field on the potential field
propagated to greater depths. The shear flow solution is
computable, given a big enough computer and some time, but a
compact synthesis of the result needs to be expressed for rapid
microprocessor computation.
Large-computer shear flow solutions can be classified according to
the vibration damping factor encountered at the driver, and
according to the log-log slope of imaginary driver impedance
plotted against frequency. These two non-dimensional parameters,
combined with plate diameter and impedance magnitude as scaling
factors, define the effective average density, viscosity and shear
modulus of tissue below the driver. For any combination of the two
non-dimensional parameters just given, the vibration field outside
the vibrator shear-flow region can be approximated by an equivalent
effective vibrator of adjusted diameter, vibrating at an adjusted
amplitude and phase angle relative to the actual vibrator. In this
way, the effect of the local shear boundary layer on the
deep-penetrating vibration field is expressed compactly as three
empirical non-dimensional functions (diameter ratio, amplitude
ratio and phase angle increment) of two non-dimensional arguments
(driver damping factor and the log-log slope just mentioned). These
three functions are derived in advance, using large-computer
simulations, and the values are stored in three two-dimensional
arrays. The microprocessor evaluates the vibrator correction
factors rapidly using polynomial spline interpolation in two
dimensions, from the tables. The potential flow field for the
adjusted effective vibrating plate is given by a simple
mathematical expression.
Interacting Vibration Fields
The principle of linear superposition of function solutions,
combined with mode shape analysis resembling Fourier analysis,
provides a means for combining the cylindrical, spherical and
planar vibration field techniques and quantifying interactions that
cross from one symmetry to another. To indicate how, let us
continue the simplified example of a circular vibration driver
plate interacting with a roughly spherical organ of unifom tissue
in substantially uniform surroundings. We now sketch very briefly a
complete system simulation.
To begin the solution, computationally "remove" the organ and fill
that volume with tissue like the tissue that surrounds the organ.
Now compute the potential field sent by the driver into the
underlying uniform tissue, using the "effective vibrator" method.
At the boundary of the "missing" organ, compute the potential
vibration field velocity components in terms of the spherical organ
coordinates, R (fixed at the organ surface radius) and .theta. (=0
when pointing toward the driver plate). Resolve these velocities
into radial and tangential directions. Similarly determine the
first and second derivatives of radial and tangential velocities
with respect to coordinates R and .theta..
The next task is to compute forces, resolved into the radial and
tangential Mode shapes described by the functions C and S, as
defined above. Start by computing pressure and shear stresses over
the spherical surface. Getting from velocity derivatives to shear
stresses resolved across the organ boundary surface requires tensor
stress analysis, a well-known area of applied mathematics. To
integrate pressures and stresses over the organ surface, in order
to define mode-forces, requires careful application of the
mode-force definition discussed in relation to the systemic artery
pressure embodiment and Eq. 1. Given the various normal and
tangential mode-forces, we now determine transfer impedances, Zt,
from the vibrator plate to the organ. For each Mode, there are two
such impedances to compute, Ztn and Ztt, for normal and tangential
Zt. Double the mode-force values described just above. (If the
motion at the organ surface is stopped by making the organ rigid,
this has the effect of doubling the surface forces, relative to
those computed for the organ volume filled with tissue like the
surrounding tissue. Stopping the organ motion sets V2 of the
network algorithm equations to zero.) For each Mode, set the
doubled normal and tangential forces equal to V1.multidot.Ztn and
V1.multidot.Ztt, using actual (not "effective") driver plate
velocity V1. Finally, divide through these two equations by V1,
yielding Ztn and Ztt, for the given Mode.
Now we can put the organ back in place, computationally. For the
symmetry of the organ in its surroundings, the spherical vibration
functions and tensor stress analysis are used to compute network
terminal-2 normal and tangential self-impedances, Z2n and Z2t, for
each Mode number. To get a pure normal-velocity vibration to
compute Z2n requires a particular linear combination of potential
and shear flow functions. A different linear combination of the
same functions gives the pure tangential-velocity vibration to
compute Z2t. Only zero-solutions may be used inside the organ, and
only infinity-solutions outside the organ. The final step is to
solve for actual normal and tangential vibration velocity
responses, based on V1, on the transfer impedances, and on the
self-impedances, for each mode and at any frequency. These results
are all predicated on assumed densities, viscosities and shear
moduli for the organ and its surroundings, and on the geometry.
Using transfer impedances, the force experienced by the vibration
driver plate is corrected for the presence of the organ.
Matching Empirical Data
The measurement system tells the computer the driver impedances and
induced motions it actually observes at a number of frequencies.
The task now is to adjust the parameters of the simulation model so
that computed and observed parameters match as closely as possible.
There are a number of well-known generalized algorithms available
for minimizing function-fit errors. It is clear that rapid
simulation methods are essential if a generalized simulation of any
complexity is to be matched to real-world data in a reasonable
time. If a good fit between simulated and empirical measurements
can be obtained over a range of frequencies, this lends confidence
that the simulation parameters represent actual properties of the
organ and surrounding tissues.
* * * * *