U.S. patent application number 16/397218 was filed with the patent office on 2019-08-15 for systems and methods for simulation of hemodialysis access and optimization.
This patent application is currently assigned to HeartFlow, Inc.. The applicant listed for this patent is HeartFlow, Inc.. Invention is credited to Leo Grady, Sethuraman SANKARAN, Charles A. Taylor, Christopher K. Zarins.
Application Number | 20190247124 16/397218 |
Document ID | / |
Family ID | 55852965 |
Filed Date | 2019-08-15 |
United States Patent
Application |
20190247124 |
Kind Code |
A1 |
SANKARAN; Sethuraman ; et
al. |
August 15, 2019 |
SYSTEMS AND METHODS FOR SIMULATION OF HEMODIALYSIS ACCESS AND
OPTIMIZATION
Abstract
Systems and methods are disclosed for simulating or optimizing
hemodialysis access. One method includes receiving a
patient-specific anatomic model of a patient's vasculature;
computing a pre-treatment hemodynamic characteristic of a
pre-treatment geometry of a portion of the anatomic model;
simulating a post-treatment geometry of a vascular access in the
portion of the anatomic model; computing a post-treatment
hemodynamic characteristic of the post-treatment geometry of the
portion of the anatomic model having the vascular access; and
generating a representation of the pre-treatment hemodynamic
characteristic or the post-treatment hemodynamic
characteristic.
Inventors: |
SANKARAN; Sethuraman; (Palo
Alto, CA) ; Grady; Leo; (Millbrae, CA) ;
Taylor; Charles A.; (Atherton, CA) ; Zarins;
Christopher K.; (Menlo Park, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
HeartFlow, Inc. |
Redwood City |
CA |
US |
|
|
Assignee: |
HeartFlow, Inc.
|
Family ID: |
55852965 |
Appl. No.: |
16/397218 |
Filed: |
April 29, 2019 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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15054622 |
Feb 26, 2016 |
10314654 |
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16397218 |
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14595503 |
Jan 13, 2015 |
9336354 |
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15054622 |
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62074698 |
Nov 4, 2014 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G16H 50/50 20180101;
A61B 2034/105 20160201; A61B 2034/104 20160201; G16H 50/30
20180101; A61M 1/3655 20130101; A61M 1/3661 20140204; A61M 1/3653
20130101; A61M 1/3659 20140204; A61M 1/00 20130101; A61B 34/10
20160201 |
International
Class: |
A61B 34/10 20060101
A61B034/10; G16H 50/50 20060101 G16H050/50; A61M 1/36 20060101
A61M001/36; A61M 1/00 20060101 A61M001/00 |
Claims
1-20. (canceled)
21. A computer-implemented method of simulating or optimizing
hemodialysis access, the method comprising: receiving a
patient-specific anatomic model of a patient's vasculature;
modifying the geometry of the received patient-specific anatomic
model such that the geometry of the received patient-specific
anatomic model defines a post-treatment geometry of a vascular
access; determining a computational model of a hemodynamic
characteristic of the modified anatomic model; computing a
post-treatment hemodynamic characteristic using the determined
computational model; and outputting or generating a representation
of the post-treatment hemodynamic characteristic.
22. The computer-implemented method of claim 21, wherein the
hemodynamic characteristic includes blood pressure, blood velocity,
or cardiac output.
23. The computer-implemented method of claim 21, further
comprising: receiving or determining a geometry of a planned
treatment defining the vascular access; and modifying the received
patient-specific anatomic model such that the post-treatment
geometry is based on the geometry of the planned treatment.
24. The computer-implemented method of claim 23, wherein the
planned treatment includes a graft.
25. The computer-implemented method of claim 21, further
comprising: receiving or measuring one or more candidate locations
of the received patient-specific anatomic model, wherein the
portion of the received patient-specific anatomic model is selected
from one of the one or more candidate locations.
26. The computer-implemented method of claim 21, further
comprising: defining a cost function for optimizing the vascular
access; and solving the cost function using the post-treatment
hemodynamic characteristic.
27. The computer-implemented method of claim 21, further
comprising: receiving one or more infeasible surgical geometries
for the hemodialysis access, and computing the post-treatment
hemodynamic characteristic using the one or more infeasible
geometries as constraints for the simulating of the post-treatment
geometry.
28. The computer-implemented method of claim 21, further
comprising: selecting a treatment or treatment location of the
vascular access based on the post-treatment hemodynamic
characteristic.
29. A system for simulating or optimizing hemodialysis access, the
system comprising: a data storage device storing instructions for
simulating or optimizing hemodialysis access; and a processor
configured to execute the instructions to perform a method
including: receiving a patient-specific anatomic model of a
patient's vasculature; modifying the geometry of the received
patient-specific anatomic model such that the geometry of the
received patient-specific anatomic model defines a post-treatment
geometry of a vascular access; determining a computational model of
a hemodynamic characteristic of the modified anatomic model;
computing a post-treatment hemodynamic characteristic using the
determined computational model; and outputting or generating a
representation of the post-treatment hemodynamic
characteristic.
30. The system of claim 29, wherein the hemodynamic characteristic
includes blood pressure, blood velocity, or cardiac output.
31. The system of claim 29, wherein the system is further
configured for: receiving or determining a geometry of a planned
treatment defining the vascular access; and modifying the received
patient-specific anatomic model such that the post-treatment
geometry is based on the geometry of the planned treatment.
32. The system of claim 31, wherein the planned treatment includes
a graft.
33. The system of claim 29, wherein the system is further
configured for: receiving or measuring one or more candidate
locations of the received patient-specific anatomic model, wherein
the portion of the received patient-specific anatomic model is
selected from one of the one or more candidate locations.
34. The system of claim 29, wherein the system is further
configured for: defining a cost function for optimizing the
vascular access; and solving the cost function using the
post-treatment hemodynamic characteristic.
35. The system of claim 29, wherein the system is further
configured for: receiving one or more infeasible surgical
geometries for the hemodialysis access, and computing the
post-treatment hemodynamic characteristic using the one or more
infeasible geometries as constraints for the simulating of the
post-treatment geometry.
36. The system of claim 29, wherein the system is further
configured for: selecting a treatment or treatment location of the
vascular access based on the post-treatment hemodynamic
characteristic.
37. A non-transitory computer readable medium for use on a computer
system containing computer-executable programming instructions for
performing a method of simulating or optimizing hemodialysis
access, the method comprising: receiving a patient-specific
anatomic model of a patient's vasculature; modifying the geometry
of the received patient-specific anatomic model such that the
geometry of the received patient-specific anatomic model defines a
post-treatment geometry of a vascular access; determining a
computational model of a hemodynamic characteristic of the modified
anatomic model; computing a post-treatment hemodynamic
characteristic using the determined computational model; and
outputting or generating a representation of the post-treatment
hemodynamic characteristic.
38. The non-transitory computer readable medium of claim 37,
wherein the hemodynamic characteristic includes blood pressure,
blood velocity, or cardiac output.
39. The non-transitory computer readable medium of claim 37, the
method further comprising: receiving or determining a geometry of a
planned treatment defining the vascular access; and modifying the
received patient-specific anatomic model such that the
post-treatment geometry is based on the geometry of the planned
treatment.
40. The non-transitory computer readable medium of claim 39,
wherein the planned treatment includes a graft.
Description
RELATED APPLICATION(S)
[0001] This application claims priority to U.S. Provisional
Application No. 62/074,698 filed Nov. 4, 2014, the entire
disclosure of which is hereby incorporated herein by reference in
its entirety.
FIELD OF THE DISCLOSURE
[0002] Various embodiments of the present disclosure relate
generally to disease assessment, treatment planning, and related
methods. More specifically, particular embodiments of the present
disclosure relate to systems and methods for simulating and
optimizing hemodialysis access.
BACKGROUND
[0003] Hemodialysis is a process in which an external machine is
used to filter blood to remove excess salt and harmful wastes. For
example, blood may be sent to a hemodialysis machine and back to
the patient's circulation. The blood may enter and exit a body via
a vascular access. For instance, a vascular access for the blood
may be created by introducing cannulas into a patient's vein. Blood
may then be sent to a hemodialysis machine and back to the
patient's circulation via the cannulas. To enable ease of
cannulation and ensure availability of many candidate access sites,
a larger vein may be used. This may be possible by shunting
arterial blood flow through veins. Two kinds of vascular access
procedures include--arteriovenous fistula (AVF) (in which an artery
and a vein may be directly connected) and arteriovenous graft (AVG)
(in which a synthetic graft may be attached between an artery and a
vein). Demand for cardiac output may change from before and after
treatment (e.g., pre- and post-shunting of blood flow). For
example, the arteriovenous connection may increase blood pressure
and blood flow in the veins. The veins may slowly adapt to this
shunting by enlarging in diameter and increasing in thickness. This
adaptation process might take anywhere from one month to a year.
Once adapted, many different candidate sites may be available for
repeated cannulation and hemodialysis.
[0004] However, the change in cardiac workload for the heart
post-treatment may create a health risk. For instance, shunting the
blood flow from an artery to a vein may reduce overall system
resistance, thus changing hemodynamics in a way that increases
cardiac output. This increased demand for cardiac output may result
in a larger workload for the heart, and may be linked to an
increased risk of congestive heart failure. Further, treatment may
change vessel geometry, thus altering regions in vessels that may
be prone to thrombosis. An optimal AVG may minimize regions of
disturbed hemodynamics and, consequently, minimize regions prone to
thrombosis.
[0005] Thus, a desire exists to ensure that there is enough blood
flow to allow successful dialysis and maintain sufficient perfusion
to extremities, and at the same time, ensure that change to
hemodynamics is minimal so that cardiac demand may not increase to
a point that endangers a patient. Furthermore, a desire exists to
improve treatment planning by optimizing vascular access graft
locations and/or vascular access graft types. The present
disclosure is directed to improving treatment planning by
predicting changes in hemodynamics that may result from vascular
access procedures.
[0006] The foregoing general description and the following detailed
description are exemplary and explanatory only and are not
restrictive of the disclosure.
SUMMARY
[0007] According to certain aspects of the present disclosure,
systems and methods are disclosed for simulating and optimizing
hemodialysis access.
[0008] One method includes: receiving a patient-specific anatomic
model of a patient's vasculature; computing a pre-treatment
hemodynamic characteristic of a pre-treatment geometry of a portion
of the anatomic model; simulating a post-treatment geometry of a
vascular access in the portion of the anatomic model; computing a
post-treatment hemodynamic characteristic of the post-treatment
geometry of the portion of the anatomic model having the vascular
access; and generating a representation of the pre-treatment
hemodynamic characteristic or the post-treatment hemodynamic
characteristic.
[0009] In accordance with another embodiment, a system for
simulating or optimizing hemodialysis access: a data storage device
storing instructions for simulating or optimizing hemodialysis
access; and a processor configured for: receiving a
patient-specific anatomic model of a patient's vasculature;
computing a pre-treatment hemodynamic characteristic of a
pre-treatment geometry of a portion of the anatomic model;
simulating a post-treatment geometry of a vascular access in the
portion of the anatomic model; computing a post-treatment
hemodynamic characteristic of the post-treatment geometry of the
portion of the anatomic model having the vascular access; and
generating a representation of the pre-treatment hemodynamic
characteristic or the post-treatment hemodynamic
characteristic.
[0010] In accordance with another embodiment, a non-transitory
computer readable medium for use on a computer system containing
computer-executable programming instructions for performing a
method of simulating or optimizing hemodialysis access, the method
comprising: receiving a patient-specific anatomic model of a
patient's vasculature; computing a pre-treatment hemodynamic
characteristic of a pre-treatment geometry of a portion of the
anatomic model; simulating a post-treatment geometry of a vascular
access in the portion of the anatomic model; computing a
post-treatment hemodynamic characteristic of the post-treatment
geometry of the portion of the anatomic model having the vascular
access; and generating a representation of the pre-treatment
hemodynamic characteristic or the post-treatment hemodynamic
characteristic.
[0011] Additional objects and advantages of the disclosed
embodiments will be set forth in part in the description that
follows, and in part will be apparent from the description, or may
be learned by practice of the disclosed embodiments. The objects
and advantages of the disclosed embodiments will be realized and
attained by means of the elements and combinations particularly
pointed out in the appended claims.
[0012] It is to be understood that both the foregoing general
description and the following detailed description are exemplary
and explanatory only and are not restrictive of the disclosed
embodiments, as claimed.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] The accompanying drawings, which are incorporated in and
constitute a part of this specification, illustrate various
exemplary embodiments and together with the description, serve to
explain the principles of the disclosed embodiments.
[0014] FIG. 1 is a block diagram of an exemplary system and network
for simulating or optimizing hemodialysis access, according to an
exemplary embodiment of the present disclosure.
[0015] FIG. 2A is a block diagram of an exemplary method of
simulating hemodialysis access, according to an exemplary
embodiment of the present disclosure.
[0016] FIG. 2B is a block diagram of an exemplary method of
optimizing hemodialysis access, according to an exemplary
embodiment of the present disclosure.
[0017] FIG. 3A is a block diagram of an exemplary method of
performing predictive modeling and simulation of an AVG, a specific
embodiment of simulating hemodialysis access according to an
exemplary embodiment of the present disclosure.
[0018] FIG. 3B is a block diagram of an exemplary method of
optimizing an AVG, according to an exemplary embodiment of the
present disclosure.
DESCRIPTION OF THE EMBODIMENTS
[0019] Reference will now be made in detail to the exemplary
embodiments of the disclosure, examples of which are illustrated in
the accompanying drawings. Wherever possible, the same reference
numbers will be used throughout the drawings to refer to the same
or like parts.
[0020] Shunting of blood flow from an artery to a vein via AVGs or
AVFs may reduce overall systemic resistance, thus causing increased
cardiac output. This increased demand for cardiac output may result
in a larger workload for the heart, which may be linked to an
increased risk of congestive heart failure. Thus, a goal of
vascular access may include increasing blood flow to the veins,
while maintaining sufficient perfusion to extremities and ensuring
that cardiac demand may not increase to a dangerous level. Further,
an optimal AVG may minimize regions of disturbed hemodynamics so
that regions prone to thrombosis may be minimized as well.
[0021] The present disclosure includes systems and methods for
simulating and optimizing hemodialysis access in order to better
provide vascular access that improves blood flow but does not
endanger the patient. For example, the simulations and
optimizations include evaluating or comparing various location(s)
for the vascular access, as well as graft or fistula geometries.
Each "treatment" may include vascular access at one location,
multiple locations, a single graft or fistula, multiple grafts or
fistulas, or a combination thereof. One embodiment may include
evaluating various treatments, e.g., by simulating and comparing
pre- or post-treatment blood flow for different treatments.
[0022] One embodiment may further include performing optimization
for the hemodialysis access. For example, the optimization may
include defining a cost function for determining an optimal
hemodialysis characteristic (e.g., blood flow). The cost function
may incorporate pre- and post-treatment calculations from the
simulations of blood flow for different treatments. In one case,
selecting or finding an optimal hemodialysis access treatment may
include performing optimization over all possible vascular grafts
(e.g., including graft types and/or graft locations in the patient
vasculature) to minimize the cost function. In another case, the
optimization may be performed for a subset of available vascular
access grafts to minimize a cost function.
[0023] For example, the increase in cardiac demand due to an AVG or
an AVF may be modeled by performing a pre-dialysis blood-flow
simulation with the original geometry, e.g., by solving 3D
Navier-Stokes equations, reduced order models, or using machine
learning methods. Resistance boundary condition(s) relating blood
pressure to flow rate may be provided at the model boundaries. At
the aortic inlet surface, cardiac flow and pressure may be coupled
to the systemic circulation using a ventricular elastance function.
The ventricular elastance function may reflect the relationship
between cardiac flow, pressure, and systemic circulation since
pressure may be based on ventricular volume which, in turn, may be
related to a flow-rate using an elastance function.
[0024] Hemodynamics post-treatment may be computed by solving the
same equations using a modified geometry reflecting the procedure
based on geometric variables that determine the AVG or the AVF. The
resulting aortic pressure and flow rate, as well as the area
enclosed in the left ventricle PV loop, may be used to estimate the
changes in cardiac workload, post-treatment. The post-treatment
cardiac demand and other hemodynamic quantities of interest may be
reported to a user (e.g., a physician).
[0025] Hemodynamic quantities of interest may include blood flow,
e.g., volume of blood or velocity of blood through a patient's
vasculature or portion of a patient's vasculature. Other
hemodynamic characteristics that may be quantities of interest may
include shear stress and/or particle residence time through an AVG.
Shear stress and particle residence time through a particular AVG
may be observed to provide sufficient blood flow to allow
successful dialysis, while reducing the risk of thrombosis in the
AVG over time when it is not being used for dialysis. Yet another
example of hemodynamic characteristics may include distal perfusion
pressure and flow in arteries past a fistula. For example,
evaluating distal perfusion and flow in vessel locations past an
AVF may help to identify whether a graft may "steal" blood from the
extremity causing ischemia/symptoms or gangrene in fingers.
[0026] Such methods may help in treatment planning and predicting
changes in hemodynamics that result from vascular access
procedures.
[0027] Referring now to the figures, FIG. 1 depicts a block diagram
of an exemplary system 100 and network for simulating or optimizing
hemodialysis access, according to an exemplary embodiment.
Specifically, FIG. 1 depicts a plurality of physicians 102 and
third party providers 104, any of whom may be connected to an
electronic network 101, such as the Internet, through one or more
computers, servers, and/or handheld mobile devices. Physicians 102
and/or third party providers 104 may create or otherwise obtain
images of one or more patients' anatomy. The physicians 102 and/or
third party providers 104 may also obtain any combination of
patient-specific information, such as age, medical history, blood
pressure, blood viscosity, patient activity or exercise level, etc.
Physicians 102 and/or third party providers 104 may transmit the
anatomical images and/or patient-specific information to server
systems 106 over the electronic network 101. Server systems 106 may
include storage devices for storing images and data received from
physicians 102 and/or third party providers 104. Server systems 106
may also include processing devices for processing images and data
stored in the storage devices. For the present disclosure,
"patient" may refer to any individual of interest.
[0028] FIGS. 2A and 2B depict flowcharts of a general embodiment
for simulating hemodialysis access and optimizing hemodialysis
access, respectively. FIG. 3A depicts a flowchart of a specific
embodiment for simulating hemodialysis access. FIG. 3B depicts a
flowchart of a specific embodiment for optimizing hemodialysis
access.
[0029] FIG. 2A is a block diagram of an exemplary method 200 of
simulating hemodialysis access, according to an exemplary
embodiment. The method of FIG. 2A may be performed by server
systems 106, based on information, images, and data received from
physicians 102 and/or third party providers 104 over electronic
network 101.
[0030] In one embodiment, step 201 may include acquiring a digital
representation of a system of interest (e.g., of an individual's
anatomy) and reconstructing a computational model (e.g.,
representing the functioning of the system of interest). For
example, the digital representation may include an artery and a
vein that may be anastomosed or shunted, as well as all vessels
branching off the arteriovenous system encompassing arteries and
veins of a system of interest. In one embodiment, the vessels may
be traced back to the aorta. A three dimensional model of the
arteries may be reconstructed, e.g., by computing centerlines
through the model and segmenting the arteries and veins across
centerlines.
[0031] In one embodiment, step 201 may further include acquiring
candidate parameters for anastomoses (e.g., location of an
anastomosis). Step 201 may also include acquiring infeasible
surgeries or any extraneous constraints that may make certain
surgical configurations infeasible.
[0032] In one embodiment, step 203 may include computing
hemodynamics of a pre-treatment AV system geometry. Blood flow
characteristics in the reconstructed geometry may be computed by
solving the Navier-Stokes equations. For example, the computation
may include constructing a finite element mesh over the
reconstructed geometry (e.g., from step 201) and specifying
appropriate boundary conditions that relate blood pressure to flow
rate at outlet surfaces. The boundary conditions may be calculated
based on local tissue perfusion demand. Other boundary conditions,
including capacitance of micro-vessels, may also be provided. At
the aortic inlet, a time-varying elastance function of the left
ventricle may be given as input. Otherwise, blood pressure or
velocity may be provided as input at inlet surfaces.
[0033] Alternatively or in addition, step 203 may include using a
reduced order model to solve for the hemodynamics and related
quantities of interest. The reduced order model may involve
combining the Poiseulle's law with non-linear stenosis pressure
loss models, as well as Bernoulli's equation to account for kinetic
energy of blood. Alternately or in addition, step 203 may involve
solving the one dimensional wave equation.
[0034] Alternatively or in addition, step 203 may include using a
machine learning approach to solve for the hemodynamics (e.g., as
described in U.S. Nonprovisional application Ser. No. 13/895,893
filed May 16, 2013, the entire disclosure of which is hereby
incorporated by reference in its entirety). Features of the
computational model that affect hemodynamics may be calculated. In
some cases, a regressor computed using a database of 3D simulations
may be used to map the inputs to hemodynamic quantities of interest
(e.g., as described in the application).
[0035] In one embodiment, step 205 may include simulating and
computing hemodynamics for a post-treatment anatomy geometry.
Post-treatment patient geometry may be created by altering the
segmentation at the candidate anastomoses sites to mimic the
planned treatment geometry. Any of the three broad classes of
methods described in step 203 may be used to calculate hemodynamic
quantities of interest post-treatment.
[0036] In one embodiment, step 207 may include outputting the
results of the simulation. For example, the difference in
hemodynamics pre-treatment versus post-treatment may be displayed
or reported to a user (e.g., a physician). In one embodiment, step
207 may further include creating a rendering for the comparison,
including graphical, pictorial, and/or interactive features.
[0037] FIG. 2B is a block diagram of an exemplary method 220 of
optimizing hemodialysis access, according to an exemplary
embodiment. The method of FIG. 2B may be performed by server
systems 106, based on information, images, and data received from
physicians 102 and/or third party providers 104 over electronic
network 101.
[0038] Simulations may offer a viable alternative to calculating
optimal treatment geometry, including one or more AVGs and/or AVFs
at one or more locations. Optimal parameters may be computed by
minimizing a cost function. In one embodiment, step 221 may include
defining, receiving, or identifying a cost function for optimizing
hemodialysis access. For example, a general cost function may be
defined as:
C=.alpha..sub.1C.sub.output(pre,post).alpha..sub.2C.sub.flow+.alpha..sub-
.3C.sub.hemo+.alpha..sub.4C.sub.clot+.alpha..sub.5C.sub.other
C.sub.output(pre, post) may be a function of the cardiac output of
the heart, C.sub.flow may be a function of blood flow through the
veins and flow through arteries distal to shunt location,
C.sub.hemo may be a function of risk of clot formation near shunt
location, and C.sub.other may be a function of any other
problem-specific cost function that may depend on the hemodynamics.
More specifically, the cost function may be defined as:
C=.alpha..sub.1(E.sub.post-E.sub.pre)-.alpha..sub.2(Q.sub.dialyzer).alph-
a..sub.3(H.sub.post-H.sub.pre)+.alpha..sub.4(T.sub.post-T.sub.pre)+.SIGMA.-
.sub.i=1.sup.N.beta..sub.if.sub.i(P,v)
[0039] .alpha..sub.1, .alpha..sub.2, .alpha..sub.3, and
.alpha..sub.4 may include weights for different cost functions.
.alpha..sub.2, .alpha..sub.3, and .alpha..sub.4 may have different
units and a user may choose to pick values based on patient-history
(e.g., for a patient who has had previous coronary artery bypass
graft surgery, .alpha..sub.2, .alpha..sub.3 and .beta..sub.i may be
taken to be zero so that only the first term may be used in the
optimization). E in the first term may include the difference
between cardiac outputs (E.sub.post-E.sub.pre), which may be
defined as:
E=.intg.PdV
[0040] P and V may be defined as pressure and volume of left
ventricle. The second term, Q.sub.dialyzer may include the flow
through the dialyzer intended to be maximized. H in the third term
(H.sub.post-H.sub.pre), may include terms which quantify disturbed
hemodynamics. For instance, H may be an area of low wall shear
stresses defined as:
H=.intg.I(.tau.<.tau..sub.c)dA
[0041] .tau. may be the local WSS and .tau..sub.c may be the
critical cutoff, below which surfaces may be deemed disturbed.
[0042] Furthermore, thrombosis of a graft may contribute to AVG
failure. In one embodiment, the cost function may include a term
(e.g., "T") that indicates a propensity for thrombosis, e.g., by
modeling blood rheology or clotting. Various coagulation models T
based on hemodynamics and blood viscosity may be used to account
for one or more characteristics of blood that may promote or
inhibit intravascular coagulation, for instance: blood composition,
factors that influence activation or inhibition of platelets,
factors that influence activation or inhibition of a clotting
cascade (e.g., at any point in a multilayered cascade),
anti-coagulant presence or usage versus no anti-coagulation
presence or usage, viscosity of blood (since dialysis patients may
be anemic), etc. Factors that influence activation or inhibition of
platelets may include, for example, initiation of platelet
aggregation inhibition. The coagulation models may further account
for shear rate and/or chemical pathways, for instance, in modeling
the blood flow of a patient using anticoagulants.
[0043] In one embodiment, T may be calculated by advecting
particles using the blood velocity field calculated from the
hemodynamics. For example, particles may be defined based on a
platelet activation function, which, in turn, may be defined based
on a velocity gradient (e.g., with a deformation tensor). For
instance, an active platelet may be identified when an activation
threshold is crossed. Calculating T may then involve tracing the
evolution or activity of the active platelet over time. Another
exemplary platelet activation model may include a power law model
based on shear stresses, in which advecting particles may involve
releasing simulated blood cells at the inlet of a problem geometry
and propagating the cells based on the blood velocity field to
trace the path of the simulated blood cells over a period of time.
Such a power law model may be used to calculate the residence time
of the blood cells, which quantifies the propensity of the blood
cells to form clots. For instance, the higher the residence time,
the higher the propensity for thrombus formation. A patient's blood
viscosity may affect the velocity field and, consequently, the
residence time.
[0044] Any other term encoding hemodynamic quantities of interest
that may be added to the cost function, which may be represented by
the term .SIGMA..sub.i=1.sup.N.beta..sub.if.sub.i(P,v). Non-linear
combinations of the terms may also be used.
[0045] To find an optimal treatment, one embodiment of step 223 may
include selecting or identifying an optimization method to find the
parameters that minimize the cost function C. Any optimization
method, including (i) derivative-free optimization techniques
(e.g., pattern search, Nelder-Mead algorithm, etc.), (ii)
gradient-based quasi-Newtonian algorithm (e.g., BFGS), or (iii)
global optimization methods (e.g., evolutionary search algorithm)
may be used to find the optima. Constraints may be incorporated by
mapping parameters in the constraint region to a very high value
(e.g., 10{circumflex over ( )}10). Step 225 may include performing
the optimization method, and step 227 may include outputting the
results of the optimization method and/or updating or changing the
cost function to solve for a different optima.
[0046] FIG. 3A is a block diagram of an exemplary method 300 of
performing predictive modeling and simulation of an AVG between the
brachial artery and antecubital vein, which is one exemplary
embodiment of simulating hemodialysis access. FIG. 3B is a block
diagram of an exemplary method 320 of optimizing an AVG, according
to an exemplary embodiment. The methods of FIGS. 3A and 3B may be
performed by server systems 106, based on information, images, and
data received from physicians 102 and/or third party providers 104
over electronic network 101. Exemplary methods 300 and 320 may
apply to an AVG between any other artery and vein as well.
Furthermore, exemplary methods 300 and 320 may be extended to an
AVF where graft-specific parameters, e.g., radius, may be removed
from the optimization parameter set.
[0047] In one embodiment, step 301 may include acquiring a digital
representation of a system (e.g., a patient's vasculature or
anatomy of interest) and reconstructing a computational model to
represent a hemodynamic characteristic of the system. For example,
the system and computational model may include a portion of a
patient's aorta, brachial artery, antecubital vein, and (if
available) other arteries, e.g., cephalic, subclavian, and radial
artery. A three dimensional model of the brachial artery and
antecubital vein, part of the aorta, and other visible arteries and
veins may be reconstructed using a combination of automated
algorithms and manual editing.
[0048] Step 301 may further include receiving or measuring
available graft radii. Candidate sites or parameters for
anastomoses in the artery and veins may also be measured or
received as input, and infeasible surgical geometries may be used
as constraints.
[0049] In one embodiment, step 303 may include computing
hemodynamics in the model pre-AVG implantation. Blood flow
simulations in the reconstructed geometry (e.g., from step 301) may
be performed by constructing a finite element mesh of the
computational model. Blood pressure and velocities may be
calculated at the vertices of the finite element mesh, e.g., by
solving the Navier-Stokes equations. At the inlet to the model, the
aortic inlet flow and blood pressure may be coupled to a
reduced-order heart model driven by a ventricular elastance
function. At the outlets, resistance boundary conditions which
relate blood pressure to flow-rate may be prescribed. These values
may be obtained for different arteries by determining the ratio of
population-averaged nominal pressure to nominal flow-rate. For
instance, pressure and flow-rate for the radial artery may be
.about.150 mm Hg and .about.600 ml/min, respectively. Hemodynamic
quantities of interest may be calculated from blood pressure and
velocity found using the Navier-Stokes equations.
[0050] In one embodiment, step 305 may include modeling a virtual
AVG. For example, step 305 may include constructing a virtual model
of the AVG by inserting a graft at candidate sites (e.g., sites
provided in step 301). This may be performed by creating a
cylindrical vessel of the radius (e.g., from step 301) and creating
an anastomosis using the cylindrical vessel and a series of Boolean
operations on the computational geometry constructed from step 301.
Alternatively, if an implicit representation of the
patient-specific geometry is available, an implicit model of a
cylindrical graft may be used to model the geometric changes
associated with inserting a graft. In one embodiment, this
procedure may be performed twice, once at the brachial artery and
once at the antecubital vein. A finite element mesh of the new
geometry may be constructed.
[0051] In one embodiment, step 307 may include calculating
hemodynamic quantities of interest post-implantation of an AVG. In
one embodiment, step 309 may include reporting a comparison of the
pre-AVG hemodynamic quantities of interest to modeled post-AVG
hemodynamic quantities of interest. For example, step 309 may
include reporting the comparison for one or more of the candidate
AVG parameters that were provided as input in step 301.
[0052] Regarding FIG. 3B, method 320 shown in FIG. 3B may include
optimizing the radius and location of an AVG. In one embodiment,
step 321 of method 320 may include defining a cost function for
optimizing AVG implantation. The cost function may include
parameters that contribute to AVG optimization. For example, one
parameter may include graft radius. Graft radius may affect
shunting resistance of the AVG. A higher graft radius may result in
larger blood flow being shunted through the AVG. Length, as well as
curvature of vascular graft, may also be treated as a parameter.
The curvature of the graft may be important since the graft may go
down the forearm, take a 180.degree. turn, and return to the
antecubital space. Further, the angle of the AVG may impact the
local hemodynamics and may result in adverse hemodynamics, e.g.,
flow stasis, recirculation, etc. Location of anastomosis may be
another parameter which impacts the outcome of treatment. The graft
may take various different pathways, e.g., depending on the
location of the arterial and venous anastomosis. A desired output
of the model may include a choice of an optimal site for
anastomosis. An exemplary cost function may be defined as
C = ( E post - E pre ) E pre - ( Q dialyzer ) Q max - ( Q distal )
Q max + ( H post - H pre ) H pre + ( T - T pre ) T pre
##EQU00001##
[0053] The first, second, and last terms of the above equation may
be the same as defined in the general embodiment (and normalized by
their nominal value). An AVG-specific term (e.g., Q.sub.distal) may
be added to ensure that most of the flow is not shunted and that
enough blood flow goes to the extremities. This may help prevent a
condition where a patient loses sensation or has compromised
circulation in extremities soon after the surgery. Specifically,
Q.sub.distal may be the blood flow distal to the arterial
anastomosis site.
[0054] In one embodiment, step 323 may include receiving, creating,
or identifying a termination criterion. In one embodiment, step 325
may include using a derivative-free Nelder-Mead optimization method
to compute parameters that may minimize the cost function. A random
initial parameter set may be chosen. Subsequently, at each step in
the Nelder-Mead algorithm, a new parameter may be identified by
constructing simplexes using existing points and choosing an
operation between reflection, reduction, contraction or reduction.
In one embodiment, step 327 may include determining whether the
computed parameters from step 325 meet a termination criterion and
performing step 325 successively until the termination criterion is
reached. In one embodiment, step 329 may include outputting the
parameters computed where the termination criterion was met, as
optimal therapy parameters, e.g., to an electronic storage medium
and/or to a user interface.
[0055] Hemodialysis may present its own set of risks, including
cardiovascular risks stemming from dialysis access. Various access
treatments may change vessel geometry, altering hemodynamics and
causing thrombosis or dangerous levels of cardiac demand. A desire
exists to ensure that there is enough blood flow to allow
successful dialysis while also ensuring that change to hemodynamics
does not endanger a patient. The present disclosure thus provides
systems and methods to improve treatment planning by predicting
changes in hemodynamics that may result from vascular access
procedures. The systems and methods include simulating access
treatments and comparing results from the simulations to provide
optimal treatments for a patient.
[0056] Other embodiments of the invention will be apparent to those
skilled in the art from consideration of the specification and
practice of the invention disclosed herein. It is intended that the
specification and examples be considered as exemplary only, with a
true scope and spirit of the invention being indicated by the
following claims.
* * * * *