U.S. patent application number 09/734058 was filed with the patent office on 2001-05-10 for ultrasonic systems and methods for contrast agent concentration measureament.
This patent application is currently assigned to Riverside Research Institute. Invention is credited to Deng, Cheri Xiaoyu, Lizzi, Frederic Louis.
Application Number | 20010001108 09/734058 |
Document ID | / |
Family ID | 26775105 |
Filed Date | 2001-05-10 |
United States Patent
Application |
20010001108 |
Kind Code |
A1 |
Lizzi, Frederic Louis ; et
al. |
May 10, 2001 |
Ultrasonic systems and methods for contrast agent concentration
measureament
Abstract
The concentration and/or radii of a contrast agent in a fluid
can be estimated by acquiring ultrasound spectral data, performing
spectral analysis to generate a linear estimation of the power
spectrum, and correlating at least one spectral parameter to a
predetermined distribution function for the contrast agent. If the
mean radius squared of particles is known, then the concentration
of contrast agent particles can be calculated. If the concentration
is constant, then relative variations in mean radius squared can be
determined.
Inventors: |
Lizzi, Frederic Louis;
(Tenafly, NJ) ; Deng, Cheri Xiaoyu; (Edison,
NJ) |
Correspondence
Address: |
BAKER BOTTS L.L.P.
44TH FLOOR
30 ROCKEFELLER PLAZA
NEW YORK
NY
10112-4498
US
|
Assignee: |
Riverside Research
Institute
|
Family ID: |
26775105 |
Appl. No.: |
09/734058 |
Filed: |
December 11, 2000 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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09734058 |
Dec 11, 2000 |
|
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09318882 |
May 26, 1999 |
|
|
|
6186951 |
|
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60086748 |
May 26, 1998 |
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Current U.S.
Class: |
600/458 ;
600/449 |
Current CPC
Class: |
A61B 8/481 20130101;
A61B 8/06 20130101; G01S 15/8952 20130101; G01S 7/52041 20130101;
G01S 15/899 20130101 |
Class at
Publication: |
600/458 ;
600/449 |
International
Class: |
A61B 008/14; A61B
008/02 |
Claims
What is claimed is:
1. A method of determining the concentration of a contrast agent in
a fluid in a region comprising: acquiring backscatter data from the
region; extracting spectral parameters from the backscatter data;
and estimating a contrast agent concentration using at least one
spectral parameter and a predetermined distribution function for
the contrast agent.
2. The method of determining the concentration of a contrast agent
in a fluid in a region as defined by claim 1, wherein the at least
one spectral parameter is derived from a linear regression of
spectral data as a function of frequency.
3. The method of determining the concentration of a contrast agent
in a fluid in a region as defined by claim 1, further comprising
the step of providing a visual indication of said concentration
estimation.
4. A method of calculating the function C<r.sup.2>, where C
is the concentration of contrast agent particles and
<r.sup.2> is the mean of the radius squared of contrast agent
particles in a region of a fluid, comprising: acquiring backscatter
data from the region; extracting at least one spectral parameter
from the RF backscatter data, and estimating the function
C<r.sup.2> using the spectral parameters.
5. The method as defined by claim 4, wherein the at least one
spectral parameter is derived from a linear regression analysis of
the backscatter data as a function of frequency.
6. The method as defined by claim 4 further comprising the step of
providing a visual indication of the estimated function
C<r.sup.2>.
Description
SPECIFICATION
1. This application is a divisional application of Ser. No.
09/318,882 which was filed on May 26, 1999 entitled ULTRASONIC
SYSTEMS AND METHODS FOR FLUID PERFUSION AND FLOW RATE MEASUREMENT,
which claimed priority to U.S. Provisional patent application
entitled Ultrasonic Contrast Methods for Perfusion Quantification,
Ser. No. 60/086,748, which was filed on May 26, 1998.
FIELD OF THE INVENTION
2. The present invention relates generally to ultrasonic imaging,
and more particularly relates to methods for measuring blood flow
rate and perfusion employing ultrasound contrast agents.
BACKGROUND OF THE INVENTION
3. The accurate measurement of blood flow and blood perfusion is of
great clinical importance for evaluating physiologic function and
clinical conditions. Noninvasive Doppler sonography has been used
to provide information on blood velocity and techniques have been
developed to estimate volumetric blood flow rates from Doppler
velocity measurements. Measurement of volumetric blood flow using
traditional Doppler generally requires the determination of vessel
size, beam/vessel angle and some estimate of the spatial variations
in velocity. These requirements limit the accuracy of volumetric
flow rate assessments because of the many sources of error in the
velocity estimation using Doppler methods, such as errors in the
estimation of vessel diameter and beam/vessel angle.
4. Ultrasonic contrast agents, which most commonly take the form of
encapsulated gaseous micro-bubbles, which scatter ultrasound
effectively, have been demonstrated to enhance ultrasonic images of
blood and Doppler signals. With recent improvements in their
ability to persist over longer periods of time, ultrasonic contrast
agents hold great potential for improved blood flow and perfusion
measurements in local tissue regions and organs. As their
interactions with ultrasound are radically different from blood or
soft tissue, the application of ultrasonic contrast agents opens
new ground for developing new and better methods for quantification
and characterization of fluid flow.
5. Ultrasound contrast agents can be used as blood volume contrast
agents because they become distributed within the vascular space,
travel at the same velocity as the blood flow rate or velocity, and
remain relatively stable in the body during clinical observation
periods. These characteristics provide the potential for mean flow
rate estimation based on the indicator dilution principle using the
contrast time-video intensity curve in ultrasonic images following
a bolus injection. Such a process is described in the article
"Mathematical Modeling of the Dilution Curves for Ultrasonic
Contrast Agents," by C. M. Sehgal et al., J. Ultrasound Med.,
16:471-479, 1997. However, current ultrasound methods that use the
time-intensity curve in ultrasonic images following a bolus
injection of a contrast medium are somewhat limited at present
because 1) the interaction of ultrasound with contrast agents is
not well understood; 2) the lack of knowledge of the number
concentration of contrast agent and the rate of delivery, sometimes
referred to as the "input function"; and 3) video intensity in
ultrasonic images is a nonlinear conversion of returned echo
amplitude from scatterers. Thus, improved methods of flow rate
measurement using such contrast agents are required.
SUMMARY OF THE INVENTION
6. It is an object of the present invention to provide improved
methods for determining the concentration of contrast agents in a
fluid.
7. In accordance with the present invention, a method of
determining the concentration of a contrast agent in a fluid in a
region is provided which includes acquiring backscatter data from
the region; extracting spectral parameters from the backscatter
data; and estimating a contrast agent concentration using at least
one spectral parameter and a predetermined distribution function
for the contrast agent.
8. Preferably, the spectral parameter is derived from a linear
regression of spectral data as a function of frequency.
9. Also in accordance with the invention, a method of calculating
the function C<r.sup.2> is provided, where C is the
concentration of contrast agent particles and <r.sup.2> is
the mean of the radius squared of contrast agent particles in a
region of a fluid. The method includes acquiring backscatter data
from the region; extracting at least one spectral parameter from
the RF backscatter data; and estimating the function
C<r.sup.2> using the spectral parameters.
10. The methods described can be further enhanced by spectrum
analysis procedures applied to radio-frequency (RF) echo signals
(backscatter) received from contrast agent particles. The computed
spectra can be analyzed with linear regression procedures to derive
a spectral parameter, such as an intercept value, that is
proportional to C<r.sup.2> where C is the concentration of
contrast agent particles and <r.sup.2> is the mean value of
their squared radii.
BRIEF DESCRIPTION OF THE DRAWING
11. Further objects, features and advantages of the invention will
become apparent from the following detailed description taken in
conjunction with the accompanying figures showing illustrative
embodiments of the invention, in which
12. FIG. 1 is a block diagram of an ultrasonic imaging system,
suitable for practicing methods in accordance with the present
invention;
13. FIGS. 2A-C are schematic diagrams pictorially illustrating a
first method in accordance with the present invention;
14. FIG. 3 is a block diagram of an alternate embodiment of an
ultrasonic imaging system, suitable for practicing methods in
accordance with the present invention;
15. FIGS. 4A-C are schematic diagrams pictorially illustrating a
method in accordance with the present invention.
16. FIGS. 5A-5D are related graphs illustrating the effect of an
ultrasonic pressure wave on a contrast agent and an exemplary
coherent relationship between a high-pressure ultrasound signal and
a diagnostic ultrasound signal. In particular, FIG. 5A is a graph
of high-pressure transducer output pressure versus time; FIG. 5B is
a graph of contrast agent diameter versus time, coherent to FIG.
5A; FIG. 5C is a pictorial representation of contrast agent
diameter versus time, coherent with FIG. 5A, and FIG. 5D is a graph
of two applied diagnostic pressure pulses versus time, coherent
with FIG. 5A.
17. FIGS. 6A-C are schematic diagrams pictorially illustrating a
method in accordance with the present invention.
18. FIG. 7 is a graph of calibrated power spectra for an exemplary
contrast agent, Albunex.RTM., with various radii;
19. FIGS. 8A and 8B are graphs of spectral slope and intercept
value, respectively, versus contrast agent (Albunex.RTM.) particles
over a frequency of 5.5 to 9.0 MHz;
20. FIGS. 9A and 9B are graphs of spectral slope and intercept
value, respectively, versus contrast agent (Albunex.RTM.) particles
over a frequency of 10 to 55 MHz;
21. FIGS. 10A and 10B are graphs of theoretical spectral amplitude
in decibels versus frequency for polydisperse Albunex particles
over frequency ranges of 5.5-9.0 MHz and 10 to 55 MHz,
respectively; and
22. FIG. 11 is a histogram graph of normalized size distributions
versus particle radius.
23. Throughout the figures, the same reference numerals and
characters, unless otherwise stated, are used to denote like
features, elements, components or portions of the illustrated
embodiments. Moreover, while the subject invention will now be
described in detail with reference to the figures, it is done so in
connection with the illustrative embodiments. It is intended that
changes and modifications can be made to the described embodiments
without departing from the true scope and spirit of the subject
invention as defined by the appended claims.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
24. Ultrasonic imaging is an important and cost effective medical
diagnostic tool. By introducing an ultrasonic contrast agent, the
features of fluid-carrying tissue can be observed with enhanced
clarity. In a present method, a contrast agent is introduced into a
fluid stream, it is selectively eliminated or diminished by the
application of a focused pulse of relatively low frequency
ultrasonic energy and the restoration or movement of the region of
diminished contrast agent is monitored, preferably using high
frequency ultrasound, to determine the flow rate or perfusion rate
of the fluid.
25. FIG. 1 illustrates a simplified block diagram of a system for
performing a perfusion rate measurement method in accordance with
the present invention. A fluid carrying conduit 100, such as an
artery, is illustrated as supplying a fluid, such as blood, to a
perfusion region 101. A contrast agent is introduced in the conduit
100 at an upstream location 102 such that the contrast agent is
carried into and distributed throughout the region 101 by
perfusion. Perfusion is achieved in tissue through a network of
capillaries 103 distributed throughout the tissue. The ultrasonic
contrast agent 200 generally takes the form of microbubbles whose
physical properties, such as density and compressibility, differ
substantially from those of the fluid and surrounding tissue, such
that ultrasonic scattering is increased. While the conduit 100 is
typically a vascular region, such as an artery, and the fluid being
monitored is usually blood, the present methods are generally
applicable to any fluid in any conduit. As such, the present
systems and methods are applicable to monitoring industrial fluid
transport systems as well as biological systems. While not limited
to any particular contrast agent, Albunex.RTM., manufactured
Molecular Biosystems, Incorporated of San Diego, Calif., and
Aerosomes (Definity), available from Dupont Pharmaceuticals, are
suitable contrast agents for practicing the present methods. The
presence and initial stable distribution of the contrast agent in
the region 101 can be determined by low level ultrasound
monitoring. FIG. 2A pictorially represents the region 101 in which
a stable distribution of a contrast agent 200 has been
achieved.
26. Ultrasound signals having a high peak pressure amplitude
(hereinafter "high-pressure" ultrasound) has a destructive, and/or
disruptive, effect on typical contrast agents which modifies the
physical properties of the contrast agent. The contrast agents'
microbubbles generally respond to a pressure wave in approximately
an inverse relationship to the applied ultrasound pressure, as
shown in FIG. 5A-C. Further, when a pressure wave of sufficient
amplitude is applied at a frequency near a resonant frequency of
the microbubbles of the contrast agent 200, the microbubbles can be
destroyed. Using this phenomenon as an advantage, a high-pressure
transducer 104 is directed to a target position 106 in the region
101. The high-pressure transducer 104 is responsive to a
high-pressure excitation unit 108 and controller 110, such that a
defined pulse of focused ultrasonic energy in the form of a
pressure wave can be delivered to the target position 106 within
the region 101. The high-pressure transducer 104 generally emits a
pulse of ultrasonic energy in the frequency range of 0.5-7 MHz,
which is selected depending on the resonant frequency of the
selected contrast agent. The effect of the pulse from the
high-pressure transducer 104 is the modification or destruction of
a large portion of the contrast agent 200 within the target
position 106, as illustrated in FIG. 2B. While depicted in two
dimensions, the zone of diminished backscatter which is created has
a volume which can be estimated in vivo based on the depth of the
target position 106, the power of the applied ultrasonic pulse, and
the focal properties of the high-pressure transducer 104
27. The system of FIG. 1 also includes a diagnostic ultrasonic
transducer assembly 112 which is similarly directed to the target
region 106. This transducer assembly can include mechanical scan
drives or an electronically controlled array to scan a diagnostic
beam signal and form a cross-sectional scan image in a plane
containing the beam from the transducer 104. In FIG. 1, the
diagnostic ultrasonic transducer assembly 112 is shown as coaxially
located with the high-pressure transducer 104. However, the two
transducers can be adjacent and angularly directed to the common
target position 106 or opposite one another and directed to the
common target position 106. Alternatively, the operation of the
high pressure transducer 104 and diagnostic transducer 112 can be
provided for in a common assembly, such as a broadband ultrasound
array. An ultrasound driver/processor 114 is operatively coupled to
the diagnostic ultrasonic transducer assembly 112 and generates the
ultrasonic driving signals therefor and receives RF backscatter
signals therefrom under the control of controller 110. Preferably,
the diagnostic ultrasonic transducer assembly 112 employs high
frequency ultrasound to establish digitally generated B-mode image
data. A commercially available system, such as the HDI Ultramark 9
available from ATL Ultrasound, Inc. of Bothell, Wash., is suitable
for this operation.
28. By monitoring the target region 106 before, during and after
the interval when contrast agent is depleted from a region, the
time which is required for the contrast agent to return to its
original level can be determined. This is illustrated as time
T.sub.2 in FIG. 2C. Further, since the volume of the contrast agent
void can be readily estimated based on the expected in-situ power
and focal properties of the pressure wave from the high-pressure
transducer 104, the volumetric flow can also be determined.
Alternatively, the volume of the zone of diminished backscatter can
be estimated by evaluating ultrasound images of the zone using the
diagnostic transducer assembly 112 before substantial replenishment
of the contrast agent has occurred. Thus, the perfusion rate
(volume of blood/time/tissue volume) can be ascertained.
29. The above described perfusion rate measurements can be
performed using a dual-frequency band ultrasonic method which uses
high-frequency pulses to monitor the alteration of contrast agent
particles which result from the application of simultaneously
applied low frequency ultrasound waves. This method combines the
fine spatial resolution achievable at high center frequencies, such
as 10 MHz, with the more pronounced contrast agent modifications
that are caused at lower frequencies, near 1 MHz, which are closer
to the contrast agents' resonant frequency. Such dual band methods
also enhance the detectability of contrast agent particles at
frequencies much higher than their resonant frequency, where their
backscatter enhancement is generally relatively low.
30. Preferably, the dual-band method uses two beams that are
coaxial or at least substantially coaxial. The high frequency pulse
preferably occurs at a selected time/phase interval in the low
frequency pulse; usually at intervals which are selected to occur
near a low-frequency positive 500 or negative pressure peak 502. As
illustrated in FIG. 5A through FIG. 5C, the contrast agent
particles radii are minimum 504 and maximum 506, respectively at
these temporal points. The backscatter measured with the high
frequency pulse is correspondingly high (large particle radius) or
low (small particle radius) at these respective phase
relationships. As the contrast agent is modified to a greater
extent than the surrounding tissue, only regions with contrast
agents will exhibit significant backscatter changes associated with
the low-frequency pressure. Thus, contrast agents can be sensed at
high frequencies by comparing RF backscatter data taken on
sequential low-frequency pulses where the high-frequency pulse is
firstly provided at a positive pressure peak of the low frequency
pulse and secondly provided at a negative pressure peak of the low
frequency pulse. For example, the acquired RF backscatter data from
these respective points can be aligned and subtracted, producing a
non-negative result only from regions where contrast agent was
present, thus enhancing the imaging capability of the ultrasound
system. Such a method can be practiced using the apparatus of FIG.
1, where the controller 110 controls the time and phase of delivery
of the signals to the high pressure transducer 104 and diagnostic
transducer 114.
31. The dual band method can also be used in a second mode to sense
the degree of contrast agent depletion produced by the low
frequency pulse from the high pressure transducer 104. In this
mode, a high-frequency pulse from the diagnostic transducer 112
occurs before the low frequency pulse, to establish an initial
backscatter level in the region occupied by contrast agents as well
as in distal regions whose backscatter echo signals are diminished
because of the attenuation characteristic of contrast agents. A
second high frequency pulse is launched from the diagnostic
transducer 112 subsequent to the low frequency pulse and
corresponding backscattered echo signals are compared to those from
the first high-frequency pulse to determine alterations in contrast
agent backscatter, caused by the preceding low frequency,
high-pressure pulse. Alterations in the backscatter from distal
tissues can also be examined to detect changes in intervening
contrast-agent attenuation caused by modifications in contrast
agents due to the low frequency pulse. The high-frequency pulse
examination can be repeated at a series of time intervals following
the low frequency pulse to monitor the temporal return of all
backscatter levels to their initial values as new contrast agent
particles enter the insonified region.
32. FIG. 3 illustrates an alternate embodiment of a system also in
accordance with the present invention, which is particularly well
suited for fluid flow rate (change in distance over change in time)
measurements. The system is substantially similar to that described
in connection with FIG. 1 except that the high-pressure transducer
104 is directed a first target zone 300 and the diagnostic
transducer assembly 112 is directed to a second target zone 302,
which is downstream from the first target zone 300. As with the
system of FIG. 1, a contrast agent is injected into the fluid
stream in conduit 100 at a location which is upstream of the
high-pressure transducer 104, and is monitored to determine when a
constant level of the contrast agent 200 is present, which is
depicted as T.sub.0 in FIG. 4A. At a time T.sub.1, a pulse of
ultrasonic energy is delivered by the high-pressure transducer 104
to the first target zone 300 in order to substantially reduce or
modify the contrast agent 200 in a defined region of the fluid
stream, as illustrated in FIG. 4B. The region where contrast-agent
backscatter has been reduced provides reduced ultrasonic scattering
and lower level return signals to the diagnostic transducer
assembly 112. This region is referred to herein as a zone of
reduced ultrasonic backscatter.
33. The fluid flowing past the second target region 302 is
monitored by the diagnostic transducer assembly 112 to determine
the time required (t) for the zone of reduced ultrasonic
backscatter to flow into the second target region 302, as shown in
FIG. 4C. Since the separation distance (d) between the
high-pressure transducer 104 and diagnostic transducer assembly 112
is defined by the system setup, and therefore is known, once the
time (t) that is required for the zone of reduced ultrasonic
backscatter to traverse this separation distance is determined, the
fluid flow rate, or velocity (V), can easily be determined by the
equation, V=d/t.
34. In the foregoing methods and apparatus, reference has been made
to the modification of physical parameters of the contrast agent in
response to an applied high-pressure ultrasound signal. This
modification generally takes the form of contrast agent destruction
and/or contrast agent radius alteration. Referring to FIGS. 5A-5C,
it is observed that in the presence of the low frequency ultrasonic
pressure wave from the high-pressure transducer 104 the diameter of
the microbubbles of the contrast agent 200 is not constant. Rather,
the diameter varies in a substantially inverse relationship to the
applied pressure wave, as is illustrated graphically in FIG. 5B and
pictorially in FIG. 5C. Because the radii of the contrast agent
particles varies over the cycle of the high-pressure signal, the
backscatter of the contrast agent also varies. Thus, phase coherent
operation of the high pressure transducer 104 and diagnostic
transducer 112, gas illustrated in the graph of FIG. 5D, is desired
in some applications. This operation can be achieved in the
apparatus of FIG. 1 since the controller 110 provides the driving
signals for both the high pressure transducer 104 and diagnostic
transducer 112. In addition, the substantially coaxial relationship
of the high pressure transducer 104 and diagnostic transducer 112,
as illustrated in FIG. 1, provides that the path length of the
signals from the two transducers is substantially equal along the
common signal beam path, thus providing for the coherent signal
relationship to be maintained over a large target area.
35. Since most conventional high-pressure transducers generally
provide a single focal point, generally only a single zone of
reduced ultrasonic backscatter is created in the fluid stream, as
is illustrated in FIGS. 4A-C. However, certain known transducers
can generate two or more simultaneous focal regions of
high-pressure at predetermined positions, thereby creating two or
more zones of reduced ultrasonic backscatter within the fluid
stream. In this case, which is illustrated in FIGS. 6A-C, the
distance between focal regions 300A and 300B is known. Therefore,
by measuring the time that is required for both the first and
second contrast agent zones of reduced ultrasonic backscatter to
cross a given measurement point 302, the velocity of the fluid can
be determined. This method has an advantage in that the separation
between the first target regions 300A, 300B and second target
region 300 need not be tightly controlled, as it is the spacing and
time interval between consecutive regions of reduced ultrasonic
backscatter generated at 300A and 300B which is being measured at
point 300. As an alternate to using a transducer with simultaneous
multiple focal regions, two or more high-pressure transducers
spaced apart can be used.
Quantitative Backscatter Analysis
36. The methods and apparatus described in the preceding sections
have generally employed an initial measured contrast level as a
baseline for subsequent relative measurements following a contrast
agent depletion operation. However, it is also possible to
characterize and quantify the level of contrast agent in a region
in absolute terms using the present invention. The following
discussion sets forth the mathematical foundation for such
quantitative analysis.
37. A useful starting point for analyzing contrast agent scattering
is the Rayleigh-Plesset-Noltingk-Neppriras-Poritsky (RPNNP)
equation, set forth in the article "Numerical Studies of the
Spectrum of Low-Intensity Ultrasound Scattered by Bubbles" by B. C.
Eatock et al. J. Accoust. Soc. Am. 77:1672-1701; 1985, which
describes the radial motion of a free spherical bubble in a liquid
driven by a sound field as: 1 0 R 2 R t 2 + 3 2 0 ( R t ) 2 = P go
( R 0 R ) 3 + P v - P a - 2 ' R - 2 f 0 R R t - p ( t ) , ( 1 )
38. where .rho..sub.0 is the density of the surrounding medium, R
is the radius of the bubble at time t, R.sub.0 the initial radius,
P.sub.go the initial gas pressure inside the bubble, .GAMMA. the
polytropic exponent of gas, P.sub.a the ambient pressure, .sigma.'
the surface tension coefficient, p(t) the time-varying acoustic
pressure, f the frequency of the incident acoustic field, and
.delta. the total damping coefficient. A Rayleigh-Plesset like
equation has been developed by C. Church for an encapsulated bubble
(such as Albunex) by incorporating the effects of a thin elastic
solid layer, as described in "The Effects of an Elastic Solid
Surface Layer on the Radial Pulsations of Gas Bubbles," J. Acount.
Soc. Am. 97:1510-1521, 1995 (hereinafter, "Church"). This reference
derives an analytical solution of the equation for relatively
low-pressure amplitudes by using a perturbation method and assuming
a summation of harmonics as the solution.
39. Using Church's definition for the scattering cross section for
a bubble of radius R,
.sigma.(f,R)=4.pi.r.sup.2.vertline.p.sub.s.vertline..sup.2/.vertline.p.ver-
tline..sup.2, (2)
40. where p.sub.s is the scattered pressure which can be computed
from R(t), the solution of the bubble dynamics equation (eq. 1).
The total scattering cross section of a collection of bubbles is
proportional to the concentration of bubbles (number of particles
per unit volume), when the interaction among bubbles can be
ignored. The calibrated spectrum analysis method discussed below
incorporates the scattering cross section obtained from the bubble
dynamics equation.
41. First, consider the calibrated complex spectrum S.sub.m of
radio frequency (rf) echoes from a range-gated contrast-agent
region of length L. The range gate is located at a range r in the
focal volume of a transducer with aperture radius .alpha. and focal
length equal to r. This spectrum is computed by multiplying the RF
signals with a Hamming function and performing a Fast Fourier
Transform (FFT). The resulting spectrum is divided by a calibration
spectrum derived from a planar reflective surface (e.g., of an
optically flat glass plate in a water tank in the transducer's
focal plane). This calibration procedure removes the spectrum of
the launched pulse from the measurement. Under the above
conditions, the spectrum is found to involve a convolution (*) with
the spectrum of the gating function S.sub.G 2 S m ( f , R ) s G ( k
) * a 2 4 ( f , R ) - j 2 k r r 2 C ( x ) F 2 ( y , z ) x , ( 3
)
42. where the wave-number k=2.pi.f/c, f is temporal frequency, c is
the propagation velocity in the surrounding fluid, and {right arrow
over (x)} is a spatial coordinate vector (x is the axial
propagation coordinate, y and z are cross-range coordinates).
.sigma.(f,R) is the frequency-dependent scattering coefficient of a
single contrast agent particle of radius R. The concentration
function C({right arrow over (x)}) includes a collection of delta
functions which describe the random location of each contrast agent
particle of radius R. F.sup.2 is the two-way beam directivity
function [2J.sub.1(k.alpha. sin .theta.)/(k.alpha. sin
.theta.)].sup.2 where sin.theta.=(z.sup.2+y.sup.2)- .sup.1/2/r and
J.sub.1() denotes a Bessel function of the 1st kind and 1st
order.
43. Because contrast agent particles are spatially distributed in a
random manner, C({right arrow over (x)}) is a stochastic function
and S.sub.m, set forth in equation 3, represents a single
realization of the backscatter. The average calibrated power
spectrum is then computed by averaging M independent measurements
of .vertline.S.sub.m.vertline..sup.2- . Independent measurements
can be obtained along adjacent scan lines (separated by a
beam-width) or by single-line measurements obtained at temporal
intervals that permit new groups of contrast agents to enter the
beam. This average power spectrum is an estimate of the "true"
ensemble power spectrum S={overscore (S.sub.mS*.sub.m)} where
S*.sub.m is the complex conjugate of S.sub.m and the superscript
bar denotes expected value.
44. The ensemble average power spectrum S is computed as: 3 S ( f ,
R ) = a 4 ( f , R ) 16 r 4 k 2 R C ( x ) R F 2 ( y , z ) - j 2 k x
x * R G ( x ) - j 2 k x x ( 4 )
45. where .DELTA.{right arrow over (x)} denotes lagged spatial
coordinates .DELTA.x, .DELTA.y, and .DELTA.z; R.sub.c is the
spatial auto-correlation function (ACF) of the concentration
function C({right arrow over (x)}); R.sub.F.sup.2 is the
cross-range ACF of the beam directivity function F.sup.2 and
R.sub.G the axial ACF of the gating function.
46. For contrast agent particles with independent, uniformly random
positions, the concentration function ACF is
R.sub.C(.DELTA.{right arrow over (x)})={overscore
(C)}.delta.(.DELTA.{righ- t arrow over (x)})+{overscore (C)}.sup.2,
(5)
47. where {overscore (C)} is the average concentration (number of
particles per unit volume) of particles of radius R and
.delta.(.DELTA.{right arrow over (x)}) denotes the product of delta
functions .delta.(.DELTA.x), .delta.(.DELTA.y), and
.delta.(.DELTA.z). The directivity function ACF is approximately a
Gaussian function of (.DELTA.y.sup.2+.DELTA.z.sup.2) with 4 R F 2 (
0 , 0 ) 0.361 4 r 2 k 2 a 2 .
48. The gating function ACF depends on the gating function; for a
Hamming function of length L, R.sub.G(0)=0.4L. We treat the case in
which L is large so that the bandwidth of the second integral in
eq. 4 is much smaller than the bandwidth of the first integral, 5 S
( f , R ) = k 2 a 4 16 r 4 C _ ( f , R ) R F 2 ( 0 , 0 ) R G ( 0 )
= 0.036 C _ ( f , R ) a 2 L r 2 . ( 6 )
49. Equation 6 shows that the calibrated spectra of contrast
particles of radius R are related to the scattering cross section
of a single particle multiplied by the number of particles of that
radius and factors associated with the transducer (i.e., aperture
radius .alpha., range/focal length r), and the analysis gate (L).
We also obtain similar results for the focal volumes of rectangular
phased arrays.
50. A normalized size-distribution function n(R) (.intg.n(R)dR=1)
is employed to describe contrast agent suspensions containing
independent particles with different radii. The total
contrast-agent particle concentration is {overscore (C)}.sub.T,
and, {overscore (C)}={overscore (C)}.sub.Tn(R)dR represents the
number of particles of radius between R and R+dR within a unit
volume. Therefore, for contrast agent suspensions containing
independent particles with different radii, the calibrated power
spectrum is equal to the weighted sum of constituent power spectra
computed from equation 6 for particles of each radius, 6 S ( f ) =
0.036 a 2 L r 2 C _ T ( f , R ) n ( R ) R . ( 7 )
51. Useful summary spectral parameters can be derived by 1)
expressing calibrated spectra (equation 7) in dB and 2) computing
linear regression parameters over the useable bandwidth. This
approach can be used to derive spectral intercept (dB,
extrapolation to zero frequency) and spectral slope (dB/MHz). Such
techniques are discussed in further detail in commonly assigned
U.S. Pat. No. 4,858,124 to Lizzi et al., which is expressly
incorporated herein by reference. The calibrated power spectrum can
be expressed in dB as 7 S db ( f ) = 10 log ( 0.036 a 2 L r 2 ) +
10 log ( C _ T ) + 10 log ( ( f , R ) n ( R ) R ) . ( 8 )
52. Applying a linear regression to equation 8 and noting that the
linear regression operators for intercept, INT(.multidot.), and
slope, SLP(.multidot.), are linear. The result for the linear fit
is:
S.sub.db(f).congruent.I.sub.1+I.sub.2+I.sub.3+m.multidot.f, (9)
53. where the intercept I consists of three terms: 8 I 1 = 10 log (
0.036 a 2 L r 2 ) ,
54. I.sub.2=10 log({overscore (C)}.sub.T), and I.sub.3=INT[10
log(.intg..sigma.(f,R)n(R)dR)]. The slope m=SLP[10
log(.intg..sigma.(f,R)n(R)dR)]. The intercept components are
related to known system constants (I.sub.1), total particle
concentration (I.sub.2), and the weighted-average scattering
cross-section (I.sub.3) which also determines the slope m. In
addition, I.sub.3 and m of the linear fit also depend on the
frequency band being analyzed.
55. The above results show that I.sub.2 is the only term affected
by {overscore (C)}.sub.T. Thus, the intercept is related in a
simple fashion to the total concentration {overscore (C)}.sub.T
and, as discussed below, can be used to estimate {overscore
(C)}.sub.T. The slope is independent of {overscore (C)}.sub.T and
system parameters, and is affected only by the frequency-dependent
scattering of contrast agent particles and their radius
distribution.
56. The following section presents spectral intercept and slope
computed for an exemplary Albunex.RTM. contrast agent, over several
frequency ranges. These values are calculated without intervening
attenuation effects. If intervening attenuation is present it will
multiply calculated values of S by exp(-.beta.r). Typically, the
effective tissue attenuation coefficient .beta.(nepers/cm) is
approximately linearly proportional to frequency. In this case, the
measured power spectrum (in dB) will exhibit a linear fit S' equal
to
S'=I+mf-2.alpha.'fr=1+(m-2.alpha.'r)f, (10)
57. where the attenuation coefficient .alpha.' is now expressed in
dB/MHz/cm. Thus, attenuation lowers the measured slope by a factor
of 2 .alpha.'r (dB/MHz) but, most importantly, it does not affect
the spectral intercept I. Thus, unlike other backscatter
parameters, results for intercept are independent of attenuation in
intervening tissue.
58. Church's theoretical formulation for the scattering cross
section .sigma.(f, R) and shell parameters reported for
Albunex.RTM., is used to evaluate calibrated power spectra and
spectral parameters for Albunex.RTM.. Results were obtained for
Albunex.RTM. populations with a single radius or a distribution of
radii over the relevant frequency band.
59. Albunex.RTM. particles with a single radius {overscore (R)} are
analyzed by substituting n(R)=.delta.(R-{overscore (R)}) into
equation 8, where .delta. represents Kronecker delta function, and
obtaining the calibrated spectrum as 9 S db ( f ) = 10 log ( 0.036
a 2 L r 2 ) + 10 log ( C _ T ) + 10 log [ ( f , R _ ) ] . ( 11
)
60. From this equation, spectra over a frequency range of 1 MHz to
60 MHz can be computed for Albunex.RTM. particles of different
radii (from 0.5 to 3.25 .mu.m, and k{overscore (R)}<1 for the
frequency range); we included the parameters of our Very High
Frequency Ultrasound (VHFU) system used in our experiments
(.alpha.=0.3 cm, r=1.2 cm, L=0.03 cm). We also set {overscore
(C)}.sub.T=1/cm.sup.3 (I.sub.2=0). (A change of concentration will
affect only the spectral magnitude, not the spectral shape or
slope.) Results are shown in FIG. 7. The spectra initially rise
rapidly with frequency, and some (for larger radii, e.g. 3.25
.mu.m) exhibit resonance peaks below 10 MHz before leveling off at
higher frequencies. At these higher frequencies, the spectra
approach frequency-independent constants for all analyzed radii, a
fact indicating that the scattering cross-section
.sigma.(f,{overscore (R)}) depends only on radius, not frequency,
at these high frequencies.
61. The calculation of spectral parameters, requires selection of
several representative bandwidths, computed linear fits to spectra
in dB, and derived plots of spectral slope and intercept versus.
particle radius. FIGS. 8A and 8B show the results for the 5.5 to
9.0 MHz band (relevant to data acquired using the ATL HDI
ultrasound system). Note that spectral slope changes abruptly from
2 dB/MHz to negative values as particle radius becomes larger than
2 .mu.m. For radii larger than about 2 .mu.m, intercept varies as
10 log({overscore (R)}.sup.2), as indicated by the dotted line.
FIGS. 9A and 9B show results for the 10 to 55 MHz band. For radii
larger than about 1.5 .mu.m, spectral slope is relatively constant
(near zero) and intercept is proportional to 10 log({overscore
(R)}.sup.2). Using equation (9), we found that, for VHFU
frequencies,
62. .sigma.(f,{overscore (R)}).congruent.4.pi.{overscore (R)}.sup.2
for {overscore (R)}.gtoreq.1.5 .mu.m, (12)
63.
64. indicating that the scattering cross-section of reasonable
large contrast agent particles depends only on radius at VHFU
frequencies.
65. Spectra were also computed for each frequency band in the
distribution of a range of Albunex.RTM. particle sizes. Results of
these spectral computations are plotted in FIG. 9, along with
linear regression fits for a total concentration of
1.times.10.sup.7/cm.sup.3. The calibrated power spectrum is the
weighted average of the spectra of contrast agent particles of all
radii; therefore, as expected, the resulting spectrum is fairly
flat over our VHFU frequency band. The size distribution affects
the intercept but does not significantly affect the slope over this
frequency band.
66. FIGS. 8A, 8B and 9A, 9B can be used in practice to extract
concentration information assuming that all Albunex.RTM. particles
have the same radius. For poly-disperse Albunex.RTM. particles with
known particle size distribution, the concentration can be
estimated by matching the theoretical results of slope and
intercept with measured results. Further, the intercept depends
strongly on {overscore (C)}.sub.T{overscore (R)}.sup.2, a fact
indicating that the details of the distribution function n(R) might
not be so important; as described next, we found that we can treat
different distribution functions in simple terms to obtain
estimation of concentration information.
67. A .GAMMA.-distribution function is used to represent the
normalized size distribution of Albunex.RTM. particles 10 n ( R ) =
{ A ( R - R 0 ) - 1 - ( R - R 0 ) R > R 0 0 R R 0 , ( 13 )
68. where .alpha., .beta., and R.sub.0 are parameters determining
the shape of the function, and A is a normalizing constant for the
distribution. This function closely matches the distribution
measured by Church when R.sub.0=0.5 .mu.m, .alpha.=1.5, and
.beta.=0.8/R.sub.0. Different size distributions are examined by
varying parameters .alpha. and .beta. while keeping R.sub.0 at 0.5
.mu.m. FIG. 11 illustrates the .GAMMA.-distributions we considered
as well as a uniform distribution function (from 0.5 to 3 .mu.m). A
calibrated power spectra is calculated for these distribution
functions with a total concentration of 5.times.10.sup.7/cm.sup.3
and our VHFU parameters (I.sub.1+I.sub.2=35.3 dB). For comparison,
we also calculate approximate intercept, using equation 12, as
=I.sub.1+10 log ({overscore (C)}.sub.T)+10
log(4.pi.<R.sup.2<), (14)
69. where <R.sup.2> is the mean square radius computed from
the size distribution. Results are summarized in Table 1. Comparing
I with in Table 1, it is seen that equation 12 is a very good
approximation (to within about 1 dB) for the scattering cross
section. The spectral slope and intercept are not sensitive to the
details of size distribution over this frequency range and the
intercept is affected primarily by the mean square radius
<R.sup.2>.
1TABLE 1 Distributions and spectral results .GAMMA.- Slope
functions <R>(.mu.m) <R.sup.2>(.mu.m.sup.2) (dB/MHz)
I(dB) {tilde over (I)}(dB) I-{tilde over (I)}(dB) 1: .alpha. = 1.45
2.72 8 .times. 10.sup.-4 -29.7 -29.4 -0.3 1.5, .beta. = 0.8/R.sub.0
2: .alpha. = 1.10 1.51 0.021 -33.7 -32.0 -1.7 1.5, .beta. =
1.3/R.sub.0 3: .alpha. = 1.50 2.77 3 .times. 10.sup.-4 -29.6 -29.3
-0.3 2, .beta. = 1/R.sub.0 4: .alpha. = 2.00 4.75 -0.008 -26.6
-27.0 0.4 3, .beta. = 1/R.sub.0 5: uni- 1.75 3.42 -0.01 -28.0 -26.9
-1.1 form, 0.5.about.3 .mu.m
70. Thus, the absolute value of {overscore
(C)}.sub.T<R.sup.2> is estimated to within about 1 dB from
intercept even for such different distribution functions. Thus, the
value of {overscore (C)}.sub.T<R.sup.2> is a suitable measure
of "effective concentration," which can be used for flow, volume
and perfusion estimation.
71. The above-described quantitative backscatter analysis
techniques can be used to estimate the concentration of contrast
agent in a region. This method can be used in any application where
a concentration estimate is desired, including use in conjunction
with the flow rate and perfusion rate techniques previously
described.
72. As set forth herein, the present invention provides apparatus
and methods for performing perfusion rate measurements using
ultrasound techniques by introducing a contrast agent into a
region, depleting the contrast agent from a known volume of the
region using a destructive pulse of ultrasound energy, and then
monitoring the recovery of the contrast agent within the region
using non-destructive ultrasound energy.
73. The present invention also provides apparatus and methods for
performing flow rate measurements of a fluid in a conduit using
ultrasound techniques by introducing a contrast agent into an
upstream location of the conduit, depleting the contrast agent from
a first downstream location in the conduit using a pulse of
ultrasound energy to create a zone of reduced ultrasonic
backscatter in the fluid stream, and then monitoring a second
downstream location to detect the arrival of the zone of reduced
ultrasonic backscatter using non-destructive ultrasound energy.
74. It is also an aspect of the present invention that first and
second ultrasound transducers are operated in a phase coherent
manner such that a predetermined phase relationship in the signals
provided by the transducers is maintained. By maintaining a
predetermined phase relationship, improved contrast agent
measurements can be performed.
75. The concentration and/or radii of a contrast agent in a fluid
can also be determined using ultrasound apparatus and methods in
accordance with the present invention. By acquiring ultrasound
spectral data, performing spectral analysis to generate a linear
estimation of the power spectrum, and correlating at least one
spectral parameter to a predetermined distribution function for the
contrast agent, effective concentration levels can be estimated. If
the mean radius squared of particles is known, then the
concentration of contrast agent particles can be calculated. If the
concentration is constant, then relative variations in mean radius
squared can be determined.
76. Although the present invention has been described in connection
with specific exemplary embodiments, it should be understood that
various changes, substitutions and alterations can be made to the
disclosed embodiments without departing from the spirit and scope
of the invention as set forth in the appended claims.
* * * * *