U.S. patent application number 15/527467 was filed with the patent office on 2017-12-14 for blood pressure and arterial compliance estimation from arterial segments.
This patent application is currently assigned to Rochester Institute of Technology. The applicant listed for this patent is David A. Borkholder, Alexander S. Liberson, Jeffrey S. Lillie. Invention is credited to David A. Borkholder, Alexander S. Liberson, Jeffrey S. Lillie.
Application Number | 20170354331 15/527467 |
Document ID | / |
Family ID | 56014473 |
Filed Date | 2017-12-14 |
United States Patent
Application |
20170354331 |
Kind Code |
A1 |
Borkholder; David A. ; et
al. |
December 14, 2017 |
Blood Pressure and Arterial Compliance Estimation from Arterial
Segments
Abstract
A noninvasive method for monitoring the blood pressure and
arterial compliance of a patient based on measurements of a flow
velocity and a pulse wave velocity is described. An embodiment uses
a photoplethysmograph and includes a method to monitor the dynamic
behavior of the arterial blood flow, coupled with a hemodynamic
mathematical model of the arterial blood flow motion in a fully
nonlinear vessel. A derived mathematical model creates the patient
specific dependence of a blood pressure versus PWV and blood
velocity, which allows continuous monitoring of arterial blood
pressure.
Inventors: |
Borkholder; David A.;
(Canandaigua, NY) ; Liberson; Alexander S.;
(Pittsford, NY) ; Lillie; Jeffrey S.; (Mendon,
NY) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Borkholder; David A.
Liberson; Alexander S.
Lillie; Jeffrey S. |
Canandaigua
Pittsford
Mendon |
NY
NY
NY |
US
US
US |
|
|
Assignee: |
Rochester Institute of
Technology
Rochester
NY
|
Family ID: |
56014473 |
Appl. No.: |
15/527467 |
Filed: |
November 17, 2015 |
PCT Filed: |
November 17, 2015 |
PCT NO: |
PCT/US15/61190 |
371 Date: |
May 17, 2017 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62080740 |
Nov 17, 2014 |
|
|
|
62080738 |
Nov 17, 2014 |
|
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
A61B 5/02007 20130101;
A61B 5/02125 20130101; A61B 5/0295 20130101; G09B 23/30 20130101;
A61B 5/0456 20130101; A61B 5/0285 20130101; G09B 23/288 20130101;
G09B 23/28 20130101; A61B 5/7278 20130101; A61B 5/021 20130101 |
International
Class: |
A61B 5/021 20060101
A61B005/021; G09B 23/28 20060101 G09B023/28; A61B 5/02 20060101
A61B005/02; G09B 23/30 20060101 G09B023/30; A61B 5/0285 20060101
A61B005/0285 |
Claims
1. A method for determining material characteristics for an artery,
the method comprising: providing at least three values for each of
blood pressure, internal radius, and external radius of an arterial
segment or segments of a subject; applying a base model of
fluid-structure interaction incorporating conservation of mass and
momentum for the fluid, and non-linear elasticity of the structure;
and running a mathematical optimization on the base model to
provide a calibrated model to determine material characteristics of
the arterial segment or segments.
2. The method of claim 1, wherein the material characteristics are
a and c, R.sub.m, where a is a reduced material constant, a = a 11
- a 12 2 a 22 , ##EQU00023## a.sub.11, a.sub.12, a.sub.22 are the
constants characterizing anisotropy of arterial wall, c is a
material constant, and R.sub.m is a mean wall radius in a load free
state.
3. The method of claim 1, wherein the mathematical optimization
provides the best fit for the equations ac .lamda. .theta. k 2 e aE
.theta. k 2 E .theta. k - p k ri k h k = 0 , ##EQU00024## k=1,2, .
. . , N to determine a, c, and R.sub.m.
4. A method for determining at least one of a blood pressure and an
arterial compliance parameter of a subject, the method comprising;
providing a value for pulse wave velocity within an arterial
segment or segments of a subject; providing a value for flow
velocity within the arterial segment or segments of the subject;
providing a value for blood density of the subject; providing the
material characteristics of an artery; and applying a calibrated
model of fluid-structure interaction incorporating conservation of
mass and momentum for the fluid, and non-linear elasticity of the
structure, to calculate at least one of blood pressure and an
arterial compliance parameter of the subject using the provided
values.
5. The method of claim 4, wherein the flow velocity is measured
directly from the subject.
6. The method of claim 4, wherein the flow velocity is estimated
based on PWV for the subject.
7. The method of claim 4, wherein the blood pressure is
systolic.
8. The method of claim 4, wherein the blood pressure is
diastolic.
9. The method of claim 4, wherein a peak pulse wave velocity is
associated with a systolic pressure.
10. The method of claim 4, wherein a minimum pulse wave velocity is
associated with a diastolic pressure.
11. The method of claim 4, wherein a peak flow velocity is
associated with a systolic blood pressure.
12. The method of claim 4, wherein a minimum flow velocity is
associated with a diastolic blood pressure.
Description
CROSS REFERENCE
[0001] This application claims the benefit of the filing date of
U.S. Provisional Patent Application Ser. No. 62/080,740, filed Nov.
17, 2014, and U.S. Provisional Patent Application Ser. No.
62/080,738, filed Nov. 17, 2014, each of which are hereby
incorporated by reference in their entirety.
FIELD
[0002] The disclosure relates to methods for at least one of blood
pressure and arterial compliance estimation from arterial
segments.
BACKGROUND
[0003] The pulse wave, generated by left ventricular ejection,
propagates at a velocity that has been identified as an important
marker of atherosclerosis and cardiovascular risk. Increased pulse
wave velocity (PWV) indicates an increased risk of stroke and
coronary heart disease. This velocity is considered a surrogate
marker for arterial compliance, is highly reproducible, and is
widely used to assess the elastic properties of the arterial tree.
Research shows that measurement of pulse wave velocity as an
indirect estimate of aortic compliance could allow for early
identification of patients at risk for cardiovascular disease. The
ability to identify these patients would lead to better risk
stratification and earlier, more cost-effective preventative
therapy. Several studies have shown the influence of blood pressure
and left ventricular ejection time (LVET) on pulse wave
velocity.
[0004] Over the past decades, there has been ongoing research for
better theoretical prediction of PWV. The clinical relationship
between PWV and arterial stiffness is often based on classic linear
models or the combination of the linear models, and measured
results with an incorporated correction factor. Whereas linear
models predict PWV as a function of only geometric and physical
properties of the fluid and the wall, there is strong empirical
evidence that PWV is also correlated to pressure and ejection
time.
[0005] There exist no models that accurately describe PWV and flow
accounting for the nonlinearities in an arterial segment. A model
that would enable solution of the inverse problem of determination
of blood pressure and aortic compliance for a PWV measure has yet
to be developed.
SUMMARY
[0006] In accordance with one aspect of the present invention,
there is provided a method for determining material characteristics
for an artery, the method including providing at least three values
for each of blood pressure, internal radius, and external radius of
an arterial segment or segments of a subject; applying a base model
of fluid-structure interaction incorporating conservation of mass
and momentum for the fluid, and non-linear elasticity of the
structure; and running a mathematical optimization on the base
model to provide a calibrated model to determine material
characteristics of the arterial segment or segments.
[0007] In accordance with another aspect of the present invention,
there is provided a method for determining at least one of a blood
pressure and an arterial compliance parameter of a subject, the
method including providing a value for pulse wave velocity within
an arterial segment or segments of a subject; providing a value for
flow velocity within the arterial segment or segments of the
subject; providing a value for blood density of the subject;
providing the material characteristics of an artery; and applying a
calibrated model of fluid-structure interaction incorporating
conservation of mass and momentum for the fluid, and non-linear
elasticity of the structure, to calculate at least one of blood
pressure and an arterial compliance parameter of the subject using
the provided values.
[0008] These and other aspects of the present disclosure will
become apparent upon a review of the following detailed description
and the claims appended thereto.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] FIG. 1 is a diagram on the longitudinal cross section of the
arterial wall at diastolic (10) and systolic (11) pressure;
[0010] FIG. 2 is a graph of the dependence of distensibilty on
transmural pressure and a flow velocity;
[0011] FIG. 3 is a flowchart depicting creation of a blood pressure
and distensibility lookup table;
[0012] FIG. 4 is a format of a lookup table for blood pressure and
distensibility;
[0013] FIG. 5 is a flowchart depicting a method for determining
blood pressure of a subject based on a PWV measure using a lookup
table;
[0014] FIG. 6 is a flowchart depicting a method for determining
arterial compliance of a subject based on a PWV measure using a
lookup table;
[0015] FIG. 7 is an illustration of pressure pulse measurement on
two locations in the same artery for determination of a systolic
and diastolic PWV; and
[0016] FIG. 8 is a flowchart depicting a method for determining the
material characteristics of an arterial segment.
DETAILED DESCRIPTION
[0017] A fully nonlinear model of pressure and flow propagation in
arterial segments is disclosed that enables determination of blood
pressure and arterial compliance based on measures of pulse wave
velocity and flow velocity following a calibration. The approach
allows for determination of systolic and diastolic blood pressure.
The approach allows for determination of a systolic and diastolic
aortic compliance.
[0018] A noninvasive method for monitoring the blood pressure and
arterial compliance of a patient based on measurements of a flow
velocity and a pulse wave velocity is described. An embodiment uses
a photoplethysmograph and includes a method to monitor the dynamic
behavior of the arterial blood flow, coupled with a hemodynamic
mathematical model of the arterial blood flow motion in a fully
nonlinear vessel. A derived mathematical model creates the patient
specific dependence of a blood pressure versus PWV and blood flow
velocity, which allows continuous monitoring of arterial blood
pressure. The calibrated mathematical model presents an arterial
compliance and a distensibility as a clinical marker of arterial
stiffness. The disclosure is applicable for fully nonlinear elastic
vessels that are commonly found in the major arteries, as well as
smaller vessels that operate closer to the linear elastic
regime.
[0019] The disclosure includes a fully nonlinear basic model for
blood pressure wave propagation in compliant arteries. A nonlinear
traveling wave model was used to investigate mechanisms underlying
the effects of pressure, ejection time, ejection volume, geometric,
and physical properties on PWV. A patient calibration procedure was
developed that involves measurement of blood pressure and arterial
dimensions (internal and external radii). An embodiment includes
blood pressure prediction using the model, per patient calibration,
and the measurement of flow velocity and pressure wave velocity. An
embodiment includes arterial compliance determination using the
model, per patient calibration, and the measurement of flow
velocity and pressure wave velocity.
[0020] A basic mathematical fluid-structure interaction model for
pulse wave velocity (PWV) propagation incorporates the dynamics of
incompressible flow in a compliant vessel. This one dimensional
model simulating blood flow in arteries effectively describes
pulsatile flow in terms of averages across the section flow
parameters. Although it is not able to provide the details of flow
separation, recirculation, or shear stress analysis, it accurately
represents the overall and average pulsatile flow characteristics,
particularly PWV.
[0021] Conservation of mass and momentum results in the following
system of one dimensional equations
.differential. A .differential. t + .differential. .differential. z
( uA ) = 0 ( 1 ) .differential. u .differential. t + .differential.
.differential. z ( u 2 2 + p .rho. ) = 0 ( 2 ) ##EQU00001##
where t is time, z is the axial coordinate shown in FIG. 1, A=A
(z,t) is the arterial cross-sectional area, u=u(z,t) is the blood
flow velocity, .rho. is blood density, p=p(z,t) is blood
pressure.
[0022] For an impermeable thin walled membrane, neglecting inertia
forces, the vessel pressure-strain relationship is maintained by
equilibrium condition as a function p=p(.eta.), based on relevant
constitutive relations where 11 is the circumferential strain
(ratio of wall deflection to zero stress arterial radius (R)).
Noting that A=.pi.R.sup.2(1+.eta.).sup.2, and assuming that
transmural pressure is a smooth function of a wall normal
deflection (derivative
p.sub..eta.=.differential.p/.differential..eta. exists at any
point), the total system of equations can be presented in the
following non-conservative form
.differential. U .differential. t + H ( U ) .differential. U
.differential. z = 0 ( 3 ) where U = [ .eta. u ] ; H = [ u 1 +
.eta. 2 p .eta. .rho. u ] ( 4 ) ##EQU00002##
[0023] We find the eigenvalues of H(U) to be real and distinct. PWV
is associated with the forward running wave velocity, i.e., the
largest eigenvalue, hence it is identified as
PWV = u + 1 + .eta. 2 .rho. p .eta. ( 5 ) ##EQU00003##
[0024] The partial derivative p.sub.ii indicates sensitivity of
pressure with respect to the wall normal deflection, and has a
clear interpretation as tangent (incremental) moduli in finite
strain deformation. In the general case, equation (5) is
supplemented by appropriate constituent equations for a
hyperelastic anisotropic arterial wall, accounting for finite
deformation.
[0025] It is assumed that arterial wall is hyperelastic,
incompressible, anisotropic, and undergoing finite deformation.
After a few original loading cycles (preconditioning) the arterial
behavior follows some repeatable, hysteresis free pattern with a
typical exponential stiffening effect regarded as pseudo elastic.
The strain energy density function W for the pseudo elastic
constitutive relation may be presented in the form
W=1/2c(e.sup.Q-1) (6)
where c is a material coefficient, and Q is the quadratic function
of the Green-Lagrange strain components. For the finite inflation
and extension of a thin walled cylindrical artery the following
strain energy function is used
Q=a.sub.11E.sub..theta..sup.2+2a.sub.12E.sub..theta.E.sub.z+a.sub.22E.su-
b.z.sup.2 (7)
where c, a.sub.11, a.sub.12, a.sub.22 are material constants. The
Cauchy stress components in circumferential and axial directions
are:
.sigma. .theta. = .lamda. .theta. 2 .differential. W .differential.
E .theta. = c .lamda. .theta. 2 e Q s .theta. , s .theta. = a 11 E
.theta. + a 12 E z .sigma. z = .lamda. z 2 .differential. W
.differential. E z = c .lamda. z 2 e Q s z , s z = a 12 E .theta. +
a 22 E z ( 8 ) ##EQU00004##
[0026] With the geometry of the reference state determined, we
define R, Z, H--as an internal radius, axial coordinate and a wall
thickness in a stress free configuration, r,z,h--internal radius,
axial coordinate and a wall thickness in a physiologically loaded
configuration. The corresponding principal stretch ratios are
.lamda..sub..theta.=r/R,.lamda..sub.z=dz/dZ,.lamda..sub.r=h/H
(9)
[0027] Assuming isochoric deformation incorporate the
incompressibility condition as
.lamda..sub.z.lamda..sub..theta..lamda..sub.r=1 (10)
[0028] The Green-Lagrangian strain components relate to the
principal stretch ratios of Eq. 12 by
E.sub.i=1/2(.lamda..sub.i.sup.2-1), (i=.theta., z, r) (11)
[0029] For the membrane thin walled cylindrical artery undergoing
finite inflation and axial deformation, the load-stress relations
follow from the static conditions
.sigma. .theta. = pr h = pR .lamda. .theta. H .lamda. r = pR H
.lamda. .theta. 2 .lamda. z .sigma. z = F 2 .pi. RH .lamda. z = f
.lamda. z ( 12 ) ##EQU00005##
where F is the axial pretension force and f is the axial pre-stress
per unit of cross section area of a load free vessel. A
substitution back into equation (8) yields the desired
relations:
.lamda. z - 1 ce Q s .theta. = pR H c .lamda. z e Q s z = f ( 13 )
##EQU00006##
[0030] The solution of equations (13), (11), (7) results in a
load-strain relations, which with account of the identity
.lamda. .theta. = r R = r - R R + 1 = .eta. + 1 ##EQU00007##
converts into the p=p(.eta.) function, required by (5) to predict a
wave front speed of propagation, i.e., PWV.
[0031] Arterial stiffness, or its reciprocals, arterial compliance
and distensibility, may provide indication of vascular changes that
predispose to the development of major vascular disease. In an
isolated arterial segment filled with a moving fluid, compliance is
defined as a change of a volume V for a given change of a pressure,
and distensibilty as a compliance divided by initial volume. As
functions of pressure the local (tangent) compliance C and
distensibility D are defined as
C = dV dp , D = C V = dV Vdp ( 14 ) ##EQU00008##
[0032] Equations (14) determine arterial wall properties as local
functions of transmural pressure.
[0033] We present equations (14) in the following equivalent
form
C = dV / d .eta. dp / d .eta. = 2 V p .eta. , D = C V = 2 p .eta. (
15 ) ##EQU00009##
[0034] The classical results are generalized for the case of a
hyperelastic arterial wall with account of finite deformation and
flow velocity. To proceed, determine p.sub..eta. from Equation (5)
and substitute in Equation (15), arriving at the following
relations
D = 1 + .eta. .rho. ( PWV - u ) 2 , C = VD ( 16 ) ##EQU00010##
[0035] FIG. 2 illustrates the dependency of distensibility on
pressure and flow velocity. Since PWV is monotonically increasing
with pressure, distensibility is a decreasing function. Unlike the
classical Bramwell-Hill model, which being linked to the
Moens-Korteweg wave speed predicts arterial distensibility as a
constant irrespective to the pressure level, the present model
predicts distensibility as a function of PWV, pressure and a blood
flow.
[0036] Arterial constants can be defined based on the developed
mathematical model. The Cauchy stress components based on Fung's
energy are presented in equations (6), (7), and (8). Neglecting
longitudinal stress (.sigma.=0) in equation (8), we obtain
E z = - a 12 a 22 E .theta. ( 17 ) ##EQU00011##
where the ratio
a 12 a 22 ##EQU00012##
is a counterpart of a Poisson coefficient in a linear isotropic
elasticity.
[0037] It follows from Equations (7), (17) that a circumferential
stress is a function of a circumferential strain and two material
constants, a and c
.sigma. .theta. = ac .lamda. .theta. 2 e aE .theta. 2 E .theta. (
18 ) Q = aE .theta. 2 ( 19 ) a = a 11 - a 12 2 a 22 ( 20 )
##EQU00013##
[0038] The governing equation specifies an equilibrium
condition
.sigma. .theta. = ac .lamda. .theta. 2 e aE .theta. 2 E .theta. =
pr i h h = r o - r i ; r m = r i + r o 2 .lamda. .theta. = r m R m
; E .theta. = .lamda. .theta. 2 - 1 2 ( 21 ) ##EQU00014##
where p is the transmural pressure, r.sub.i is the internal radius,
r.sub.o is the outer radius, and h is the wall thickness. Let us
define r.sub.m as the mid radius of a loaded vessel, and R.sub.m as
the mid radius for a stress free vessel. Measuring r.sub.i and
r.sub.o corresponding to the pressure p leaves us with three
unknowns (a, c, R.sub.m) which need to be determined as a part of a
calibration procedure. The calibration provides a calibrated model
which can be individualized for each subject.
[0039] An embodiment of the calibration includes the use of
published values for a population or segment of a population.
Referenced values for material constants c, a.sub.11, a.sub.12,
a.sub.22 can be used to calculate the material constant a based on
equation (20). The material constant c is used directly. A
reference value for the mid radius in the stress free state
(R.sub.m) is used along with a reference value for the arterial
wall thickness (h) and associated mid radius (r.sub.m) for the
loaded wall. The material parameters (a, c, R.sub.m) along with the
product of wall thickness and mid radius for the loaded wall
(hr.sub.m) can then be used to determine at least one of blood
pressure and arterial compliance, e.g., distensibility, of a
subject by measuring PWV and flow velocity.
[0040] Another embodiment of the calibration is disclosed as
follows and described in FIG. 8. Assuming we have k measurements of
the radius and pressure during a cardiac cycle or cycles, the
following four variables are defined (r.sub.i.sub.k, r.sub.o.sub.k,
r.sub.m.sub.k, p.sub.k). By using these sampled variables
circumferential stress can be presented as a function of three
unknowns
.sigma..sub..theta.=.sigma..sub..theta.(a, c, R.sub.m) (22)
[0041] Now using a mathematical optimization, e.g., a least square
(LS) minimization technique identifies (a, c,R.sub.m)
LS = k [ .sigma. .theta. ( a , c , R m ) - p k ri k h k ] 2
.fwdarw. min ( a , c , R m ) ( 23 ) ##EQU00015##
[0042] The following nonlinear calibration method describes one
approach that may be completed to determine arterial constants.
[0043] Step 1: Obtain k measurements, k.gtoreq.3, for blood
pressure-p.sub.k, internal radius-r.sub.ik; outer radius-r.sub.ok,
calculate mean radii r.sub.mk=0.5(r.sub.ik+r.sub.ok) and wall
thicknesses h.sub.k=r.sub.ok-r.sub.ik. example, tonometry could be
used to measure a continuous blood pressure to create the array of
blood pressures, and Doppler speckle ultrasound could be used to
measure artery radii to create the corresponding array of r.sub.ik,
r.sub.ok.
[0044] Step 2: Run a least square minimization as in equation (23)
to identify the three constants (two material constants a, c and
the mean radius R.sub.m, in a load free condition). Substituting
.sigma..sub..theta. in equation (23) with equation (18) results
in
LS = k [ ac .lamda. .theta. k 2 e aE .theta. k 2 E .theta. k - p k
ri k h k ] 2 .fwdarw. min ( a , c , R m ) ( 24 ) ##EQU00016##
where
.lamda. .theta. k = r mk R m ; E .theta. k = .lamda. .theta. k 2 -
1 2 . ##EQU00017##
LS is a function of measured parameters p.sub.k, r.sub.ik,
r.sub.mk, h.sub.k and unknown properties (a,c,R.sub.m), determined
from the minimization procedure. Since we have 3 unknowns, at least
3 sets of pressure and associated outer and inner radii are
required.
[0045] In an embodiment, a calibrated model can be used to
determine at least one of blood pressure and arterial compliance,
e.g., distensibility, of a subject by measuring PWV and flow
velocity.
[0046] With the three material properties (a,c,R.sub.m) and the
constant product (hr.sub.m) a blood pressure may be estimated based
on the equilibrium equation (21) rearranged to
p = ac .lamda. .theta. 2 e aE .theta. 2 E .theta. h r i ( 25 )
##EQU00018##
where the stretch ratio (.lamda..sub..theta.) can be defined in
terms of .eta.
.lamda. .theta. = r m R m = ( r m - R m R m + 1 ) = .eta. + 1 ( 26
) ##EQU00019##
[0047] The circumferential strain (E.sub..theta.) can be defined in
terms of .eta.
E.sub..theta.=(.lamda..sub..theta..sup.2-1)/2=.eta.(.eta.+2)/2
(27)
[0048] Wall thickness follows from incompressibility conditions
hr.sub.m=h.sub.kr.sub.mk (28)
where from
h = h k r mk r m = h k r mk R m .lamda. .theta. = h k r mk R m (
.eta. + 1 ) ( 29 ) ##EQU00020##
[0049] Internal Radius
r.sub.i=r.sub.m-0.5h=.lamda..sub..theta.R.sub.m-0.5h=(.eta.+1)R.sub.m-0.-
5h (30)
[0050] These formulations provide a relationship between pressure
(p), circumferential strain (.eta.), two arterial material
parameters (a and c) and two arterial geometric parameters (R.sub.m
and the constant product h.sub.kr.sub.mk).
[0051] Equation (5) for PWV in arterial tissues can be
re-arranged
p.sub..eta.(1+.eta.)=2.rho.*PWV.sub.f.sup.2 (31)
where a flow corrected PWV (PWV.sub.f) has been introduced
(PWV.sub.f=PWV-u).
[0052] This relation can be used in combination with equation (16)
to define distensibility D in terms of the p.sub..eta.
D=.sup.2/.sub.p.sub..eta. (32)
[0053] In an embodiment, a lookup table can be created for
convenience to enable determination of a blood pressure and
distensibility based on the 4 arterial parameters (can be subject
specific) and measurement of PWV and flow velocity. A blood density
.rho. is either measured or a value is assumed based on age and
gender. As illustrated in an embodiment shown in FIG. 3, the steps
to create the blood pressure and distensibility lookup table are as
follows:
[0054] Set .eta.=0.
[0055] Using equation (26) calculate circumferential stretch ratio
.lamda..sub..theta..
[0056] Using equation (27) calculate circumferential strain
E.sub..theta..
[0057] Using equation (29) and any h.sub.kr.sub.mk product from the
calibration, calculate wall thickness h.
[0058] Using equation (30) calculate the internal radius
r.sub.i.
[0059] Using equation (25) calculate pressure p.
[0060] While .eta.<0.5, .eta.=.eta.+0.005, go back to
calculation of the circumferential stretch ratio or else
continue.
[0061] Calculate the array for p.sub.n using the slope of the
(p,.eta.) curve.
[0062] Using equation (31) and the array of values for .eta. and
p.sub.n calculate a 1D array for p.sub..eta.(1+.eta.).
[0063] Using equation (31) and the array of p.sub..eta., calculate
D for each value of .eta..
[0064] An example resultant array is shown in FIG. 4. This lookup
table enables determination of a subject blood pressure and
distensibility by measuring PWV.sub.f and identifying the row
(either directly or by interpolation) where
p.sub..eta.(1+.eta.)=2.rho.*PWV.sub.f.sup.2. This row also contains
other relevant arterial parameters such as E.sub..theta.,
.lamda..sub..theta., h, and r, which can be extracted for that
individual based on the measured PWV.sub.f. Note that for
determination of a systolic blood pressure and distensibility, a
systolic PWV and a maximum flow velocity is used to calculate
PWV.sub.f. For determination of a diastolic blood pressure and
distensibility, a diastolic PWV and a minimum (or zero) flow
velocity is used to calculate PWV.sub.f. Intermediate values of
blood pressure and distensibility may also be determined based on
the associated intermediate values of PWV.sub.f and flow
velocity.
[0065] A method for monitoring a blood pressure of a subject is
disclosed. The model is calibrated for the subject (or population)
by a non-linear calibration. For example, a non-linear calibration
as illustrated in FIG. 3 can be performed. Once the calibration is
complete, a patient specific lookup table can be formed for
convenience as described in FIG. 3 and as shown in FIG. 4. The
method for monitoring a subject's real time blood pressure is shown
in FIG. 5. An ECG measurement can be made for use as a timing
reference for start of the pulse wave transit time, or to be used
as a reference for determining acceptance time windows for other
waveform features, or for averaging waveforms. An arterial flow
velocity is measured providing minimum and maximum flow velocities,
although a minimum could be assumed to be zero. An average flow
velocity can also be measured. The flow velocity can also be
estimated based on other measures or as a percentage of PWV. The
pulse wave velocity is measured, ideally providing both a systolic
and diastolic PWV. The subject (or population based) blood density
.rho. are then used with the lookup table of FIG. 4 to estimate
blood pressure. The arrays of associated blood pressure (p),
PWV.sub.f and distensibility (D) can also be used directly or with
interpolation to estimate p and D based on the PWV.sub.f measure.
The systolic PWV and the peak flow velocity are used to estimate a
systolic blood pressure, while a diastolic PWV and the minimum flow
velocity are used to estimate a diastolic blood pressure. Although
other estimates and combinations may be used to estimate an average
or systolic or diastolic blood pressure. PWV can be measured at the
foot and the systolic flow velocity (u) can be added to it as an
estimate of systolic PWV.sub.f. Diastolic pressure could use the
raw PWV measured at the foot and use either the minimum flow
velocity or assume u=0. Other empirical or relational estimates for
the systolic and diastolic PWV.sub.f can also be used.
[0066] Determination of PWV includes measurement of the transit
time of the pulse wave between two points, and a measure or
estimate of the distance traveled. The PWV is the distance
travelled divided by the time difference. This can be done by
extracting the foot (FIG. 1, item 12) or peak (FIG. 1, item 13) of
the pressure wave in two locations (proximal, distal) of the same
artery, calculating the time difference between these two extracted
features, and measuring the distance between these two measurement
points. In one embodiment, this is done in the radial artery as
shown in FIG. 7 with measurements items 80 (proximal) and 81
(distal). Use of the foot location on the pressure or PPG waveform
(items 801 and 810) will correlate to a diastolic PWV, while use of
the peak location (items 802 and 811) will correlate to a systolic
PWV. Two different arteries can also be used with a measurement or
estimate of the arterial path distance between the two measurement
points. The PWV can also be measured using the heart as the
proximal measurement point with an electrocardiogram feature (e.g.,
the ECG r-wave) as the first time point, or by sensing when the
aortic valve opens using a feature on measured waveforms or images
such as the ballistocardiogram (BCG), ultrasound imaging, Doppler
ultrasound, impedance plethysmography (IPG), or
photoplethysmography (PPG) on the chest over the aorta. The distal
pressure wave is then used as above to extract a second time point.
The arterial distance between the aortic root and the distal
measurement point is used in the calculation of PWV. This can be
measured or estimated, and may be based on subject characteristics
such as height, weight age and gender. The distal pressure wave can
be measured using sensors such as tonometry, an arterial cuff,
ultrasound, RF based arterial wall tracking, and PPG.
[0067] In some embodiments, the wave will propagate across multiple
arterial segments between the proximal and distal points of
pressure measurement. This measurement can be used in at least two
ways. In the first form, average properties of the vessel segments,
radius, and modulus will be considered so that the result
corresponds to bulk average of the segment. In the second, the
properties of individual arterial segments are determined. First,
use the model to determine the relative transit time through each
sequential arterial segment based on geometrical properties of each
segment and assuming a similar pressure within all segments. Then
using a solution method, such as minimization of a least squares or
another method, solve for the PWV within each segment by
recognizing that the total transit time (measured) is the sum of
the transit time through each segment.
[0068] Measurement of flow velocity can be done using Doppler
ultrasound, an inductive coil, MRI or CT scan with contrast agents.
The flow velocity can be captured as a continuous wave, as a peak
value, or a minimum value (including u=0). It is also possible to
estimate flow velocity using related measures or with a scale
factor. For example PWV can be measured using previously described
techniques and flow velocity is then estimated as a percentage of
PWV (for example u=0.2 PWV). Aortic flow velocity can be estimated
through left ventricular ejection time (LVET), ejection volume
(EV), and aortic cross-sectional area (CA) where u=EV/(LVET*CA).
Left ventricular ejection time (LVET) can be measured or estimated
using a number of sensors (e.g. PPG, heart sound). Using PPG for
example, the measure of LVET is the length of time from the foot of
the PPG wave (FIG. 1 item 12) to the dicrotic notch (item 14).
Using heart sound, LVET is the time between the first and second
heart sound. Ejection volume can be based on direct measurement for
the subject (e.g. ultrasound, thermal dilution, etc) at rest and at
exercise with subsequent scaling based on heart rate. The
cross-sectional area can be directly measured by ultrasound
imaging, MRI, or CT scans. EV and CA can also be based on subject
specific parameters such as age, gender, height and weight. EV can
also be measured or estimated using features from the BCG such as
the amplitude of the j-wave or m-wave. An estimate of flow velocity
in the periphery can be made based on scaling of the blood volume
in that arterial tree branch, and relative arterial size as
compared to the aorta. Although a direct measurement of flow
velocity or an estimate based on PWV is preferred in the
periphery.
[0069] Pressure can be measured using any approved technique, for
example, brachial cuff, tonometry, or intra-arterial catheter.
Ideally a continuous method (e.g., tonometry, intra-arterial) is
used with a method of time synchronization to the flow and PWV
measures (e.g. via ECG). However serial measures can also be used.
Here the pressure p can be systolic, diastolic, or any intermediate
pressure (e.g., mean pressure) when coupled with the appropriate
flow velocity (u). For example, systolic pressure could be
associated with the peak flow velocity, and diastolic pressure
could be associated with the lowest (or zero) flow velocity, or an
average pressure could be associated with an average flow
velocity.
[0070] An optional ECG can be measured across the chest or wrists.
Other locations are also possible such as ear lobes, behind the
ears, buttocks, thighs, fingers, feet or toes. PPG can be measured
at the chest or wrist. Other locations such as the ear lobes,
fingers, forehead, buttocks, thighs, and toes also work. Video
analysis methods examining changes in skin color can also be used
to obtain a PPG waveform. Flow velocity can be measured at the
chest or wrist. Other locations for flow velocity measure are also
possible such as the neck, arm and legs.
[0071] In one embodiment, the pulse transit time is measured based
on aortic valve opening determined by the J-wave of the BCG
waveform, and a PPG foot measured (e.g., FIG. 1, item 12) from the
thigh. The ECG r-wave may be used as a reference for determining
acceptance windows for BCG and PPG feature delineations, or as a
starting point for a PWV measure. The aorta distance is estimated
from aortic root along the path of the aorta to the femoral artery
at the thigh PPG measurement location. The PWV is calculated by
dividing the aorta distance by the measured time difference (BCG
J-wave to PPG foot). The minimum and maximum flow velocity is
measured by ultrasound Doppler at the aortic root. A blood density
.rho. is assumed based on age and gender of the subject. Using the
measured PWV.sub.f as shown in FIG. 5 the lookup table of FIG. 4 is
used to determine the associated pressure. To calculate p.sub.d the
minimum measured flow velocity can be used in combination with an
estimate of diastolic PWV, where diastolic PWV is calculated based
on the BCG J-wave to PPG foot time difference. To calculate p.sub.s
the peak flow velocity or a percentage of the peak flow velocity
can be used in combination with an estimate of systolic PWV, where
the systolic PWV is calculated based on the peak flow velocity time
point to the PPG peak time difference. Under conditions where flow
velocity is not measured, diastolic flow velocity can be assumed to
be 0, while systolic flow velocity can be estimated as a percentage
of PWV (e.g .about.20%).
[0072] In another embodiment, the pulse transit time is measured
from the carotid artery using tonometry, to the pressure pulse
measured at thigh with a thigh cuff. The arterial distance is
estimated from aortic root along the path of the aorta to the
femoral artery at the thigh cuff measurement location. The PWV is
calculated by dividing the arterial distance by the measured time
difference. The foot to foot timing on the measured pressure pulses
(e.g., FIG. 7 items 801 and 810) is used to determine a diastolic
pulse transit time and to calculate a diastolic PWV. The peak to
peak timing (e.g., FIG. 7, items 802 and 811) is used to determine
a systolic pulse transit time and to calculate a systolic PWV. The
peak flow velocity is estimated at 20% of the systolic PWV while
the minimum flow velocity is estimated at zero. A blood density
.rho. is assumed based on age and gender of the subject. Using the
measured PWV.sub.f, as shown in FIG. 5, the lookup table of FIG. 4
is used to determine the associated pressure. To calculate p.sub.d
the minimum measured flow velocity can be used in combination with
the diastolic PWV. To calculate p.sub.s the peak flow velocity is
used in combination with the systolic PWV.
[0073] A method for monitoring an arterial compliance of a subject
is disclosed. The model is calibrated for the subject (or
population) by a non-linear calibration. For example, a non-linear
calibration as illustrated in FIG. 8 can be performed. Once the
calibration is complete, a patient specific lookup table can be
formed for convenience described in FIG. 3 and as shown in FIG. 4.
The method for monitoring a subject's arterial compliance is shown
in FIG. 6. An optional ECG measurement can be made for use as a
timing reference for start of the pulse wave transit time, or to be
used as a reference for determining acceptance time windows for
other waveform features, or for averaging waveforms. An arterial
flow velocity is measured providing minimum and maximum flow
velocities, although a minimum could be assumed to be zero. An
average flow velocity can also be measured. The flow velocity can
also be estimated based on other measures or as a percentage of
PWV. The pulse wave velocity is measured, ideally providing both a
systolic and diastolic PWV. The subject (or population based) blood
density .rho. is then used with the patient specific lookup FIG. 4,
to determine compliance as shown in FIG. 6 and equation 16.
[0074] The systolic PWV and the peak flow velocity are used to
determine a systolic distensibility, while a diastolic PWV and the
minimum flow velocity are used to estimate a diastolic
distensibility. Although other estimates and combinations may be
used to determine the subject distensibility parameter.
[0075] In one embodiment, the pulse transit time is measured based
on aortic valve opening determined by the J-wave of the BCG
waveform, and a PPG foot measured (e.g., FIG. 1, item 12) from the
thigh. The aorta distance is estimated from aortic root to femoral
artery at the thigh PPG measurement location. The PWV is calculated
by dividing the aorta distance by the measured time difference (BCG
J-wave to PPG foot). The minimum flow velocity is assumed to be
zero, enabling distensibility calculation without a direct flow
measurement. The flow corrected PWV is calculated (in this
embodiment PWV.sub.f=PWV since u=0). A blood density .rho. is
assumed based on age and gender of the subject with the patient
specific lookup FIG. 4 to determine compliance as shown in FIG. 6
and equation 16. Measures of a systolic PWV, peak flow velocity,
may also be used to determine D.
[0076] In another embodiment, the pulse transit time is measured
from the carotid artery using tonometry, to the pressure pulse
measured at thigh with a thigh cuff. The arterial distance is
estimated from aortic root along the path of the aorta to the
femoral artery at the thigh cuff measurement location. The PWV is
calculated by dividing the arterial distance by the measured time
difference. The foot to foot timing on the measured pressure pulses
(e.g., FIG. 8 items 801 and 810) are used to determine a diastolic
pulse transit time and to calculate a diastolic PWV. The peak to
peak timing (e.g., FIG. 7, items 802 and 811) is used to determine
a systolic pulse transit time and to calculate a systolic PWV. The
peak flow velocity is estimated at 20% of the systolic PWV while
the minimum flow velocity is estimated at zero. A blood density p
is assumed based on age and gender of the subject with the patient
specific lookup FIG. 4 to determine compliance as shown in FIG. 6
and equation 16.
[0077] The disclosure will be further illustrated with reference to
the following specific examples. It is understood that these
examples are given by way of illustration and are not meant to
limit the disclosure or the claims to follow.
EXAMPLE
[0078] Paper Example, Blood Pressure and Distensibility
[0079] This paper example uses referenced values for an aorta
c=120123 Pa, a.sub.11=0.320, a.sub.12=0.068, a.sub.22=0.451. The
reduced constant `a` is calculated based on equation 20 (a=0.31).
In addition reference values were used for the mid radius for the
stress free vessel R.sub.m=0.009 m, the aortic wall thickness
h=0.00211 m, and the mid radius of the loaded wall r.sub.m=0.011. A
computer routine executed the functions outlined in FIG. 3 to
calculate an array of p.sub..eta.(1+.eta.), D, and the associated
pressures (p) for each value of .eta.. Equation (31) was then used
along with a reference value of blood density .rho.=060 kg/m.sup.3
to create an array of associated PWV.sub.f for each value of .eta..
The pulse transit time is measured based on time synchronized
tonometry at the carotid artery and at the femoral artery, each
providing a pressure pulse waveform. The equivalent aortic distance
between the two measurement points is measured at for example 1.0
m. The foot to foot time difference between the two tonometry
waveforms is measured at for example 200 nis. The diastolic PWV is
then calculated as 1.0 m/200 ms=0.5 m/s. From the same tonometry
waveforms the peak to peak time difference is measured at for
example 140 ms. The systolic PWV is then calculated as 1.00 m/140
ms=7.14 m/s. Flow velocity is measured using Doppler ultrasound at
the aortic root, with the minimum taken as the diastolic flow
velocity u.sub.d=0.00 .sup.m/.sub.s, and the maximum taken as the
systolic flow velocity u.sub.s=1.10 .sup.m/.sub.s. A flow corrected
PWV is calculate at systolic blood pressure (PWV.sub.f=7.14
m/s-1.10 m/s=6.04 m/s) with the associated systolic blood pressure
determined from the array as p.sub.s=138 mmHg. A flow corrected PWV
is calculate at diastolic blood pressure (PWV.sub.f=5.0 m/s-0.0
m/s=5.0 m/s) with the associated diastolic blood pressure
determined from the array as p.sub.d=84 mmHg. The arterial
compliance parameter distensibility (D) is determined from the
systolic and diastolic PWV.sub.f measures and the associated array
elements. In this paper example the diastolic distensibility is
identified as
D = 57.6 1 MPa , ##EQU00021##
and the systolic distensibility is identified as
D = 31.3 1 MPa . ##EQU00022##
* * * * *