U.S. patent application number 11/494299 was filed with the patent office on 2008-09-18 for systems and methods for evaluating vessels.
Invention is credited to Marco A. Costa, Olusegun Johnson Ilegbusi, Jannick Rolland.
Application Number | 20080228086 11/494299 |
Document ID | / |
Family ID | 39763403 |
Filed Date | 2008-09-18 |
United States Patent
Application |
20080228086 |
Kind Code |
A1 |
Ilegbusi; Olusegun Johnson ;
et al. |
September 18, 2008 |
Systems and methods for evaluating vessels
Abstract
Disclosed are systems and methods for evaluating body vessels.
Images of the vessel are captured, analyzing to generate a
three-dimensional model of the vessel, and the data associated with
the three-dimensional model is analyzed. In cases in which the
vessel is a coronary artery, the vessel model can be analyzed to
determine the vulnerability of plaques within the artery to
rupture. In some embodiments, the images are optical coherence
tomography images. In some embodiments, the images are captured
with an optical catheter that includes a tracking device. In some
embodiments, the analysis includes flow and/or structural
analysis.
Inventors: |
Ilegbusi; Olusegun Johnson;
(Oviedo, FL) ; Rolland; Jannick; (Chuluota,
FL) ; Costa; Marco A.; (Ponte Vedra Beach,
FL) |
Correspondence
Address: |
THOMAS, KAYDEN, HORSTEMEYER & RISLEY, LLP
600 GALLERIA PARKWAY, S.E., STE 1500
ATLANTA
GA
30339-5994
US
|
Family ID: |
39763403 |
Appl. No.: |
11/494299 |
Filed: |
July 27, 2006 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60773486 |
Feb 15, 2006 |
|
|
|
Current U.S.
Class: |
600/479 |
Current CPC
Class: |
A61B 8/543 20130101;
A61B 5/0075 20130101; A61B 5/061 20130101; A61B 5/7285 20130101;
A61B 6/4417 20130101; A61B 6/541 20130101; A61B 5/0071 20130101;
A61B 5/6852 20130101; A61B 5/0084 20130101; A61B 5/0066 20130101;
A61B 5/0086 20130101; A61B 6/5247 20130101; A61B 8/4416
20130101 |
Class at
Publication: |
600/479 |
International
Class: |
A61B 6/00 20060101
A61B006/00 |
Claims
1. A method for evaluating a vessel comprising: capturing optical
coherence tomography (OCT) images of the vessel; analyzing the OCT
images to generate a three-dimensional model of the vessel; and
conducting analysis on data associated with the three-dimensional
model.
2. The method of claim 1, wherein capturing OCT images of the
vessel comprises capturing OCT images of the vessel with an optical
catheter positioned within the vessel.
3. The method of claim 1, further comprising capturing fluorescence
spectroscopy images of the vessel.
4. The method of claim 1, wherein conducting analysis comprises
conducting flow analysis in relation to fluid flow through the
vessel.
5. The method of claim 1, wherein conducting analysis comprises
conducting structural analysis in relation to walls of the
vessel.
6. The method of claim 1, wherein the vessel is an artery and
conducting analysis comprises conducting analysis on the artery to
determine the vulnerability of plaques within the artery to
rupture.
7. A computer-readable medium comprising a system for evaluating a
vessel, the computer-readable medium, comprising: logic configured
to capture optical coherence tomography (OCT) images of the vessel;
logic configured to analyze the OCT images to generate a
three-dimensional model of the vessel; and logic configured to
conduct analysis on data associated with the three-dimensional
model.
8. The computer-readable medium of claim 7, wherein the logic
configured to capture OCT images of the vessel comprises logic
configured to capture OCT images of the vessel with an optical
catheter positioned within the vessel.
9. The computer-readable medium of claim 7, further comprising
logic configured to capture fluorescence spectroscopy images of the
vessel.
10. The computer-readable medium of claim 7, wherein the logic
configured to conduct analysis comprises logic configured to
conduct flow analysis in relation to fluid flow through the
vessel.
11. The computer-readable medium of claim 7, wherein the logic
configured to conduct analysis comprises logic configured to
conduct structural analysis in relation to walls of the vessel.
12. The computer-readable medium of claim 7, wherein the vessel is
an artery and the logic configured to conduct analysis comprises
logic configured to conduct analysis on the artery to determine the
vulnerability of plaques within the artery to rupture.
13. A method for evaluating a vessel comprising: capturing images
of the vessel by an optical catheter positioned within the vessel;
simultaneously determining a position and orientation of the
catheter with information generated by a tracking device of the
catheter; analyzing the images to generate a three-dimensional
model of the vessel; and conducting analysis on data associated
with the three-dimensional model.
14. The method of claim 13, wherein capturing images of the vessel
comprises capturing optical coherence tomography (OCT) images of
the vessel.
15. The method of claim 14, wherein capturing images of the vessel
further comprises capturing fluorescence spectroscopy images of the
vessel.
16. The method of claim 13, wherein conducting analysis comprises
conducting flow analysis in relation to fluid flow through the
vessel.
17. The method of claim 13, wherein conducting analysis comprises
conducting structural analysis in relation to walls of the
vessel.
18. The method of claim 13, wherein the vessel is an artery and
conducting analysis comprises conducting analysis on the artery to
determine the vulnerability of plaques within the artery to
rupture.
19. A computer-readable medium comprising a system for evaluating a
vessel, the computer-readable medium comprising: logic configured
to process images of the vessel captured by an optical catheter
positioned within the vessel; logic configured to simultaneously
determine a position and orientation of the catheter with
information generated by a tracking device provided within the
catheter; logic configured to analyze the images to generate a
three-dimensional model of the vessel; and logic configured to
conduct analysis on data associated with the three-dimensional
model.
20. The computer-readable medium of claim 19, wherein logic
configured to process images of the vessel comprises logic
configured to process optical coherence tomography (OCT) images of
the vessel.
21. The computer-readable medium of claim 20, wherein the logic
configured to process images of the vessel further comprises logic
configured to process fluorescence spectroscopy images of the
vessel captured by the catheter.
22. The computer-readable medium of claim 19, wherein the logic
configured to conduct analysis comprises logic configured to
conduct flow analysis in relation to fluid flow through the
vessel.
23. The computer-readable medium of claim 19, wherein the logic
configured to conducting analysis comprises logic configured to
conduct structural analysis in relation to walls of the vessel.
24. The computer-readable medium of claim 19, wherein the vessel is
an artery and the logic configured to conduct analysis comprises
logic configured to conduct analysis on the artery to determine the
vulnerability of plaques within the artery to rupture.
25. An optical catheter comprising: an internal optical system
configured to capture images of a vessel in which the catheter is
positioned; and a tracking device that determines the position and
orientation of the catheter within the vessel simultaneous of image
capture.
26. The catheter of claim 25, wherein the tracking device is
capable of collecting positional and orientation data within 6
degrees of freedom.
27. The catheter of claim 25, wherein the catheter is configured to
capture images about an axis of the catheter along 360.degree..
28. The catheter of claim 25, wherein the catheter is sized and
configured to be positioned within a coronary artery and capture
images of the arterial walls and plaques formed within the
artery.
29. The catheter of claim 25, wherein the catheter is configured to
capture optical coherence tomography (OCT) images of the
vessel.
30. The catheter of claim 29, wherein the catheter is further
configured to capture fluorescence spectroscopy images of the
vessel.
31. A method for evaluating a vessel comprising: capturing images
of the vessel; analyzing the images to generate a three-dimensional
model of the vessel; and conducting analysis on data associated
with the three-dimensional model, the analysis including flow
analysis in relation to fluid flow through the vessel and
structural analysis in relation to walls of the vessel.
32. The method of claim 31, wherein capturing images of the vessel
comprises capturing optical coherence tomography (OCT) images of
the vessel with the optical catheter.
33. The method of claim 32, wherein capturing images of the vessel
further comprises capturing fluorescence spectroscopy images of the
vessel.
34. The method of claim 31, wherein the vessel is an artery and
conducting analysis comprises conducting the flow analysis and the
structural analysis to determine the vulnerability of plaques
within the artery to rupture.
35. The method of claim 31, wherein conducting analysis further
comprises developing a flow-structure index that is indicative of
likelihood of plaque rupture.
36. The method of claim 31, wherein conducting the flow analysis
and the structural analysis is performed in an iterative process in
which the structural analysis influences the flow analysis and vice
versa.
37. A computer-readable medium comprising a system for evaluating a
vessel comprising: logic configured to capture images of the
vessel; logic configured to analyze the images to generate a
three-dimensional model of the vessel; and logic configured to
conduct analysis on data associated with the three-dimensional
model, the analysis including flow analysis in relation to fluid
flow through the vessel and structural analysis in relation to
walls of the vessel.
38. The computer-readable medium of claim 37, wherein the logic
configured to capture images of the vessel comprises logic
configured to capture optical coherence tomography (OCT) images of
the vessel with the optical catheter.
39. The computer-readable medium of claim 38, wherein the logic
configured to capture images of the vessel further comprises logic
configured to capture fluorescence spectroscopy images of the
vessel.
40. The computer-readable medium of claim 37, wherein the vessel is
an artery and the logic configured to conduct analysis comprises
logic configured to conduct the flow analysis and the structural
analysis to determine the vulnerability of plaques within the
artery to rupture.
41. The computer-readable medium of claim 37, wherein the logic
configured to conduct analysis further comprises logic configured
to develop a flow-structure index that is indicative of likelihood
of plaque rupture.
42. The computer-readable medium of claim 37, wherein the logic
configured to conduct the flow analysis and the structural analysis
performs the analysis in an iterative process in which the
structural analysis influences the flow analysis and vice versa.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application claims priority to copending U.S.
provisional application Ser. No. 60/773,486, entitled, "Optical
Apparatuses and Methods," filed Feb. 15, 2006, and U.S. utility
application Ser. No. 11/417,599, entitled, "Optical Probes For
Imaging Narrow Vessels Or Lumens," filed May 4, 2006, both of which
are hereby incorporated by reference in their entirety.
BACKGROUND
[0002] Cardiovascular disease (CVD) is the single most common cause
of fatality in the developed world. In 2005, the American Heart
Association estimated that approximately 865,000 Americans will
acquire a new acute coronary syndrome (ACS) each year and that
another 700,000 will have a stroke, with similar pathophysiology.
From the pool of patients with acute coronary syndrome, about 22
percent of men and about 46 percent of women develop disabling
heart failure within the following 6 years. It is expected that by
the year 2020, cardiovascular disease will claim 25 million deaths
annually worldwide with coronary artery disease representing half
of those deaths.
[0003] Arterial plaque rupture is the most common complication
associated with atherosclerosis, and accounts for approximately 70%
of fatal coronary events. The transition into unstable plaques is
characterized by the presence of active inflammation
(monocyte/macrophage infiltration), thinning of the fibrous cap of
the plaque, development of a large lipid necrotic core, and
endothelial denudation with superficial platelet aggregation.
Although such a condition is serious, it can be treated, at least
in some cases, with aggressive therapy intended to prevent a
catastrophic vascular event if the existence and location of the
vulnerable plaque are detected.
[0004] Techniques currently exist that are used in an attempt to
detect vulnerable plaques. Unfortunately, such plaques often may
not be detected by such techniques for various reasons, including
poor resolution of the imaging modality, slow system response, and
complexity. Thus, the practice of such techniques may not result in
the detection of plaques that, if otherwise detected, could
possibly be treated. It can therefore be appreciated that one goal
is to develop systems and methodologies that would enable such
detection, especially for real-time or near real-time applications.
If such systems and methodologies could be developed, they would
have a major impact on morbidity and mortality related to
atherosclerotic disease.
SUMMARY
[0005] Disclosed are systems and methods for evaluating body
vessels. In one embodiment, a system and a method relate to
capturing optical coherence tomography (OCT) images of the vessel,
analyzing the OCT images to generate a three-dimensional model of
the vessel, and conducting analysis on data associated with the
three-dimensional model.
[0006] In another embodiment, a system and a method relate to
capturing images of the vessel by an optical catheter positioned
within the vessel, simultaneously determining a position and
orientation of the catheter with information generated by a
tracking device of the catheter, analyzing the images to generate a
three-dimensional model of the vessel, and conducting analysis on
data associated with the three-dimensional model.
[0007] In a further embodiment, a system and method relate to
capturing images of the vessel, analyzing the images to generate a
three-dimensional model of the vessel, and conducting analysis on
data associated with the three-dimensional model, the analysis
including flow analysis in relation to fluid flow through the
vessel and structural analysis in relation to walls of the
vessel.
[0008] In one embodiment, an optical catheter includes an internal
optical system configured to capture images of a vessel in which
the catheter is positioned, and a tracking device that determines
the position and orientation of the catheter within the vessel
simultaneous of image capture.
BRIEF DESCRIPTION OF THE FIGURES
[0009] The components in the drawings are not necessarily to scale,
emphasis instead being placed upon clearly illustrating the
principles of the present disclosure. In the drawings, like
reference numerals designate corresponding parts throughout the
several views.
[0010] FIG. 1 is a block diagram of a device that comprises an
embodiment of a system for evaluating a vessel.
[0011] FIG. 2 is a flow diagram of an embodiment of a method for
evaluating a vessel.
[0012] FIG. 3 is a perspective view of an embodiment of an optical
catheter that can be used to capture image data relating to a
vessel.
[0013] FIG. 4 is a side view of the optical catheter of FIG. 3 that
shows an internal optical system of the catheter.
[0014] FIGS. 5A and 5B illustrate use of the optical catheter shown
in FIGS. 3 and 4 within a vessel.
[0015] FIG. 6 is an example three-dimensional body reconstruction
of a coronary artery segment.
[0016] FIG. 7 is a cross-section of the coronary artery of FIG. 6
taken at plane A of FIG. 6.
[0017] FIG. 8 is an example three-dimensional grid reconstruction
of a coronary artery segment.
[0018] FIG. 9 is a flow diagram of an embodiment of a method for
acquiring and analyzing images of a vessel.
[0019] FIG. 10 is a further example three-dimensional grid
reconstruction of a coronary artery segment.
[0020] FIG. 11 shows a velocity field determined at four
longitudinal cross-sections of the lumen of the coronary artery
segment of FIG. 10 taken at 45.degree. intervals.
[0021] FIG. 12 shows a distribution of wall shear stress for the
coronary artery segment of FIG. 10.
[0022] FIG. 13 shows a distribution of wall shear stress gradient
for the coronary artery segment of FIG. 10.
[0023] FIG. 14 shows a distribution skin friction coefficient for
the coronary artery segment of FIG. 10.
[0024] FIG. 15 is an example representation of a coronary artery
segment including the artery lumen and the arterial wall/plaque
structure.
[0025] FIG. 16 illustrates a predicted flow pattern for an artery
segment.
[0026] FIG. 17 illustrates distributions of shear stress for 20%,
40%, and 70% stenosis.
[0027] FIGS. 18A and 18B illustrate predicted stress distributions
obtained from structural analysis.
[0028] FIGS. 19A and 19B illustrate maximum shear stress and
circumferential stress within the arterial wall/plaque
structure.
[0029] FIGS. 20A and 20B illustrate stress ratio distributions
R.sub.1 and R.sub.2.
[0030] FIGS. 21A and 21B illustrate the stress ratio distributions
R.sub.3 and R.sub.4.
[0031] FIG. 22 illustrates a characterization of stenotic plaque
vulnerability.
DETAILED DESCRIPTION
Introduction
[0032] As described above, current technologies may be ineffective
in enabling identification of vulnerable arterial plaques. Given
that such plaques could be treated if detected, it can be
appreciated that there is a need for systems and methods that could
be used for early identification of vulnerable plaques.
[0033] In the following, described are various embodiments of
systems and methods for evaluating vessels, such as human coronary
arteries. As described below, images of an artery can be captured
with imaging apparatus and used to identify plaques within the
artery. In cases in which the images are high-resolution images,
for example when optical coherence tomography (OCT) is used to
capture the images, the images may reveal great detail as to the
structure of the plaques and, therefore, may provide reliable data
for flow and structural analyses and provide an indication as to
plaque vulnerability. As is also described below, the captured
image data can be used to construct a three-dimensional
reconstruction or model of the artery. In embodiments in which the
image data is collected using an internal catheter, the
construction of such a model can be greatly simplified through use
of a tracking device that provides position and orientation
information regarding the catheter. Once the three-dimensional
model of the artery has been constructed, various analyses, such as
fluid analysis and structural analysis, can be conducted to assist
in the identification and/or evaluation of arterial plaques. In
some embodiments, fluid and structural analyses are used
concurrently to make a plaque vulnerability determination or
otherwise characterize the plaque.
[0034] Although evaluation of coronary arteries is discussed in
detail in this disclosure, it is to be appreciated that the
disclosed systems and methods can be used to evaluate other
arterial or non-arterial conditions. In addition, the disclosed
systems and methods may be used in conjunction with other body
vessels, or other biological or non-biological vessels as the case
may warrant. Furthermore, although particular embodiments of
systems and methods are described in the following, those
embodiments are mere example implementations of the systems and
methods and it is noted that other embodiments are possible. All
such embodiments are intended to be within the scope of this
disclosure. The terminology used in this disclosure is selected for
the purpose of describing the disclosed systems and methods and is
not intended to limit the breadth of the disclosure.
System and Method Overview
[0035] Beginning with FIG. 1, illustrated is a computer system 100
that includes a computer-readable medium in the form of computer
memory 102. As will be appreciated from the following disclosure,
the particular configuration of the computer system 100 and the
memory 102 are not critical. By way of example, however, the
computer system 100 comprises a desktop, laptop, or server computer
that includes the computing and processing power necessary to
conduct the data collection and manipulation described in the
following. Although the computer system 100 can comprise a single
computer, the system can, alternatively, comprise two or more such
computers. For example, multiple networked computers can be used,
if desired. Also by way of example, the memory 102 can comprise a
combination of volatile and non-volatile memory components. For
instance, the memory 102 may comprise one or more hard disks and
one or more random access memory (RAM) components. In addition, the
memory 102 can comprise read-only memory (e.g., Flash memory) and
one or more removable memory components, such as a floppy disk, a
CD-ROM, or a memory card.
[0036] Stored within memory 102 is an evaluation system 104. The
evaluation system 104 comprises several modules that serve discrete
purposes within the system during evaluation of a vessel. In the
embodiment shown in FIG. 1, the system 104 includes an imaging
acquisition module 106, an image analysis module 108, a flow
analysis module 110, and a structural analysis module 112. Although
the various modules 104-112 are illustrated in FIG. 1 as being
independent, the modules can comprise part of a single program that
is used to evaluate vessels. Accordingly, two or more of the
modules 104-112 may be combined or otherwise linked with each
other. As is further indicated in FIG. 1, the image acquisition
module 106 can be coupled to imaging apparatus 114 that are used to
capture images of the vessel.
[0037] The image acquisition module 106 comprises the logic that is
used to control operation of the imaging apparatus 114 and/or
collect and store images captured by the imaging apparatus. In some
embodiments, the image acquisition module 106 also collects
tracking data relevant to the image capture process. The nature of
the image acquisition module 106 may depend upon the nature of the
imaging apparatus 114. By way of example, the imaging apparatus 114
can comprise ultrasound imaging apparatus, optical coherence
tomography (OCT) imaging apparatus, fluorescence spectroscopy
imaging apparatus, magnetic resonance imaging (MRI) apparatus, a
combination of those apparatuses, or other suitable imaging
apparatus. An example part of one suitable imaging apparatus is
described in relation to FIGS. 3 and 4 below.
[0038] The image analysis module 108 digitizes and processes the
images captured with the imaging apparatus 114. In addition, the
image analysis module 108 processes any tracking data that may have
been collected during image acquisition. Through such processing,
the image analysis module 108 quantifies morphologic information
pertaining to the vessel including the luminal geometry and any
vessel landmarks, such as plaque size and location. That data is
then used by the image analysis module 108 to construct a
three-dimensional reconstruction or model of the vessel.
[0039] The flow analysis module 110 is configured to use the
morphologic information generated by the image analysis module 108
to delineate the flow domain for fluid flow studies, e.g.,
hemodynamics, within the vessel lumen. The spatial and/or temporal
distribution of flow variables, such as velocity, pressure, wall
shear stress, cell distribution, distribution of blood
constituents, etc., can be obtained by the flow analysis module 110
through solution of appropriate governing equations, subject to
appropriate boundary and initial conditions. The method of solution
of those equations can be analytical or computational, and may rely
on principles of computational fluid dynamics (CFD). The flow
analysis module 110 may use numerical methods based on
discretization of the reconstructed vessel into the computational
grids or control volumes over which the governing equations are
integrated and solved. In other embodiments, the flow analysis may
utilize a meshless method which does not require discretization of
the vessel into computational grids. In the case of arterial
analysis, hemodynamic indices can be related to atherosclerosis
plaque development and vulnerability. In addition, the flow
analysis module can use special features to represent coronary
interventional procedures such as stented arteries.
[0040] In embodiments in which the structural analysis module 112
is provided, that module can use the morphologic data generated by
the image analysis module 108 to develop a stress analysis model
within the arterial wall in order to investigate the coupled
flow-structure interaction within the artery. Such analysis can be
conducted simultaneous to the fluid flow analysis. Where the
captured images are high-resolution images, a media-plaque boundary
can be delineated that is used in the analysis. In some
embodiments, the structural analysis module 112 can comprise an
integral part of the flow analysis module 110. As is described in
greater detail below, there may be two-way implicit coupling of the
structural analysis module 112 and the flow analysis module 110
such that the analysis conducted by one module influences the other
and vice versa. Specifically, variables calculated in the flow
analysis module 110, such as pressure, can be provided to the
structural analysis module 112, which calculates vessel and plaque
deformation and stresses. The calculated deformations can then be
used by the flow analysis module 110 to update the flow domain and
recalculate using the new deformed geometry. Iterations can then be
performed between the flow analysis module 110 and structural
analysis module 112 until convergence is achieved.
[0041] FIG. 2 provides an overview of an example method for
evaluating a vessel. Beginning with block 200, images of a vessel
under evaluation are captured and stored. As described above, the
vessel can, for example, comprise an artery which may have plaques
that are vulnerable to rupture. In addition to the images, any
tracking information relevant to the image acquisition can be
collected, as indicated in block 202. In some embodiments, the
tracking information comprises x-ray data collected during
intravascular ultrasound (IVUS). In embodiments in which images are
captured with an optical catheter, the tracking information can
comprise position and orientation information collected from an
internal tracking device of the catheter. In other embodiments,
however, such "tracking" information is not needed. For example,
when MRI is used, no separate tracking information is necessary
given that MRI provides three-dimensional image data directly. As
mentioned above, the images, and any tracking information that was
captured, can be collected and stored by the image acquisition
module 106.
[0042] Referring next to block 204, a three-dimensional
reconstruction or model of the vessel is generated. The model can
be generated by the image analysis module 108 using the images and
any tracking information collected by the image acquisition module
106. At this point, as indicated in block 206, fluid flow analysis
can be performed, for example by the flow analysis module 110 using
data from the three-dimensional model. In some embodiments,
structural analysis can also be performed, as indicated in block
208. As noted above, the structural analysis can be performed by
the structural analysis module 112 simultaneous to the flow
analysis. Notably, however, flow analysis alone may be sufficient
in some cases to evaluate the vessel and any features of concern,
such as plaques. In cases in which structural analysis is
performed, however, results from the structural analysis may
influence the flow analysis and vice versa. Therefore, as indicated
in decision block 210, flow in the method may return to block 206
if all flow and structural analyses have not been completed.
Operating in that manner, the flow and structural analyses can be
performed in an iterative process.
[0043] Once all flow and/or structural analysis has been performed,
one or more determinations can be made as to the vessel and/or any
features of concern, such as plaques, as indicated in block 212. In
some embodiments, the determinations can be made manually by a
person skilled in interpreting the results of the various analysis
that was conducted. In other embodiments, the determinations can
be, at least partially, automated. For example, the flow analysis
module 110 and/or the structural analysis module 112 can be further
configured to provide a quantification of the likelihood of a given
plaque rupturing. As described below, the quantification can, for
example, take the form of an index that indicates the
susceptibility of the plaque to such rupture.
Image Acquisition and Analysis
[0044] As described in the foregoing, images of the vessel under
evaluation can be obtained using various imaging technologies. For
example, one or more of ultrasound, OCT, fluorescence spectroscopy,
and MRI can be used. One suitable method for collecting image data
of an artery comprises intravascular ultrasound (IVUS), which is
performed using an intravascular catheter that captures images of
the artery from within the artery. A description of one method for
performing IVUS and analyzing the captured data is described in a
paper entitled "Reproducibility of Coronary Lumen, Plaque, and
Vessel Reconstruction and of Endothelial Shear Stress Measurements
In Vivo in Humans," by Ahmet U. Coskun, Ph.D. et al., 2003 which is
hereby incorporated by reference into the present disclosure. In
that method, IVUS image data is obtained with simultaneous biplane
coronary angiography (BCA) in which two, preferably orthogonal,
frames of biplane angiograms are taken at the same instant of time.
During image acquisition, an IVUS catheter is advanced into the
target coronary artery and intracoronary nitroglycerin is
administered. A diluted contrast solution is injected at sufficient
concentration to allow the simultaneous visualization of the
arterial lumen and the IVUS catheter core just before the IVUS
pullback while BCA is performed. Images of both projections are
digitally recorded for approximately 3 to 4 seconds at a rate of 15
frames per second.
[0045] The IVUS and BCA images are ECG-gated to obtain
end-diastolic images, which are marked to guide the software
algorithms. The calibration points, which are used to correct
geometric distortions, the starting point of IVUS pullback, and the
traces of IVUS catheter core and lumen are marked on the digital
BCA images. On each IVUS image, 12 guide marks positioned
30.degree. apart around the IVUS catheter core can be used to trace
the lumen and the external elastic membrane (EEM) borders. The EEM
is the discrete interface at the border between the media and the
adventitia, and it is represented as a thin echolucent line on the
IVUS image. The distance between the EEM and lumen borders define
the plaque thickness (plaque plus media or atheroma thickness).
[0046] Fusion of the IVUS and BCA images is then performed to
determine the three-dimensional arterial geometry. Briefly, the BCA
images are first rectified using a calibration grid to correct the
geometrical distortions that occur during imaging. The physical
three-dimensional path of the IVUS transducer during pullback is
determined using the corresponding angiographic projections in BCA.
The reconstructed path of the IVUS catheter core serves as the stem
on which the three-dimensional vessel geometry is built. The
three-dimensional position of each ECG-gated IVUS frame is
determined from the trajectory of the catheter pullback, the known
speed of the mechanical IVUS pullback speed, and the ECG signal.
The normal direction of each frame is determined from the
corresponding tangential direction of the catheter core since the
IVUS image is perpendicular to the core axis. The IVUS images are
segmented to extract the boundary of lumen and EEM and are
interactively edited as needed. The three-dimensional
reconstruction is completed by positioning the lumen and EEM
boundary along the IVUS path while correcting for rotation of the
IVUS caused by twisting of the catheter. Approximately 200-400 IVUS
images are used to recreate each arterial segment, depending on its
length and the heart rate. Once the lumen is reconstructed using
the acquired data, a portion of the reconstructed segment, which is
free of significant side branches and available in both pullbacks,
is selected as the segment of interest to be used in the flow
and/or structural analyses.
[0047] A further example of performing IVUS/BCA and analyzing the
captured data is described in a paper entitled "Reconstruction and
Spatial Filtering of 3-D Geometry of Coronary Artery Segments," by
A. U. Coskun, Ph.D. et al., 2000, which is also hereby incorporated
by reference into the present disclosure.
[0048] Although IVUS is a viable methodology for image acquisition,
OCT provides advantages that are not realizable with IVUS. OCT,
like ultrasound, produces images from backscattered "echoes," but
uses infrared (IR) or near infrared (NIR) light that is reflected
from internal microstructures within tissues or other materials
under evaluation. Interferometric techniques are then used to
extract the reflected optical signals from the IR or NIR light used
in OCT. The output, measured by an interferometer, is computer
processed to produce high-resolution, real-time, cross-sectional or
three-dimensional images of the tissue. The IR or NIR light is
emitted from a high-intensity light source, such as a
super-luminescent diode or a laser. By way of example, a Gaussian
beam having a central wavelength of approximately 800 nanometers
(nm) to 1500 nm can be used. Notably, video rates can be achieved
in cases in which Fourier-domain OCT is performed.
[0049] Significantly, OCT provides higher resolution images than
ultrasound and, therefore, provides more information about the
structure and composition of the walls and plaques of an artery.
More particularly, OCT can provide images that reveal the
boundaries of the structural components of the vessel walls and
plaque and therefore provides more information that is relevant to
the evaluation of the vulnerability of the plaque to rupture.
[0050] For a detailed discussion of OCT as used in biological
applications, reference can be made to a paper entitled "Optical
Coherence Tomography (OCT)," by Ulrich Gerckens et al., 2003, which
is hereby incorporated by reference into the present
disclosure.
[0051] In some embodiments, OCT can be combined with two-photon
fluorescence spectroscopy to obtain even more information about the
artery and plaque composition. With appropriate tuning and
focusing, IR or NIR light can be concentrated on microstructures of
the artery and/or plaque so as to cause two-photon excitation of
the microstructures that results in emission of fluorescent
light.
[0052] Although BCA can be used to determine the position and
orientation of an IVUS or OCT catheter and, therefore, the position
and orientation of the images captured with the catheter, reliance
upon BCA presents several disadvantages. First, BCA is expensive to
perform and requires expensive and cumbersome equipment that is
possessed by only a few hospitals. Second, it is potentially
harmful to the patient given that the patient is exposed to a
relatively large dose of radiation. In view of those drawbacks, it
may be desirable in some embodiments to equip the catheter with a
tracking device that automatically provides real-time information
as to the position and orientation of the catheter while it
captures images within the vessel.
[0053] FIG. 3 illustrates an optical probe or catheter 300 that can
form part of the imaging apparatus 114 shown in FIG. 1. In the
example embodiment of FIG. 3, the catheter 300 is an OCT catheter
that incorporates microtracking capability. As shown in FIG. 3, the
catheter 300 includes a generally cylindrical outer housing 302.
The outer housing 302 is elongated and comprises a proximal end
304, a distal end 306, and an outer periphery 308 that extends
between the two ends. In the illustrated embodiment, an imaging
window 310 is provided along the outer periphery 308 adjacent the
distal end 306 of the catheter 300. Visible through the imaging
window 310 in FIG. 3 are components of an internal optical system
of the catheter (see FIG. 4). The imaging window 310 extends along
the circumference of the outer housing 302 so as to permit
360.degree. viewing using the internal optical system.
[0054] The optical catheter 300 is dimensioned such that it may be
used in narrow, for example small diameter, vessels. By way of
example, the optical catheter 300 has an outer diameter of
approximately 1 millimeter (mm) to 2 mm, and a length of
approximately 20 mm from its proximal end 304 to its distal end
306.
[0055] Extending from the proximal end 304 of the optical catheter
300 is a flexible cord 312 that transmits light to and receives
light signals from the internal optical system. The outer diameter
of the cord 312 can be smaller than that of the housing 302, and
the length of the cord can depend upon the particular application
in which the catheter 300 is used. Generally speaking, however, the
cord 312 is long enough to extend the catheter 300 to a site to be
imaged while the cord is still connected to a light source (not
shown) that transmits light through the cord to the catheter.
[0056] The materials used to construct the optical catheter 300 can
be selected to suit the particular application in which it is used.
In biological applications, biocompatible materials are used to
construct the catheter 300. For example, the outer housing 302 of
the catheter 300 can be made of stainless steel or a biocompatible
polymeric material. The imaging window 310 can be made of a
suitable transparent material, such as glass, sapphire, or a clear,
biocompatible polymeric material. In some embodiments, the material
used to form the imaging window 310 can also be used to form a
portion or the entirety of outer housing 302.
[0057] The cord 312 can comprise a tube made of a resilient and/or
flexible material, such as a biocompatible polymeric material. In
some embodiments, the cord 312 can comprise a tube composed of an
inner metallic shaft, coil, or braid, for example formed of
stainless steel or nitinol, that is surrounded by an impermeable
polymeric sheath. Such an embodiment provides additional column
strength and kink resistance to the cord 312 to facilitate
advancing the catheter 300 to the imaging site. In addition, the
outer housing 302 and/or the cord 312 can be coated with a
lubricious coating to facilitate insertion and withdrawal of the
catheter 300.
[0058] FIG. 4 illustrates the interior 400 of the optical catheter
300. As shown in that figure, the catheter 300 houses an internal
optical system 402. In the embodiment of FIG. 4, the optical system
402 comprises collimation optics including a collimating lens 404,
axicon optics including an axicon lens 406, imaging optics
including a first imaging lens 408 and a second imaging lens 410,
and a mirror 412. Each of the collimating lens 404, axicon lens
406, and first imaging lens 408 are fixedly mounted within the
housing 302 using appropriate mounting fixtures (not shown).
Substantially any mounting fixtures that secure the lenses in place
and that do not undesirably obstruct the transmission of light
through the optical system 402 can be used. The second imaging lens
410 is fixedly mounted to the mirror 412 with a mounting arm 414
that extends from the mirror. The mirror 412 is, in turn, mounted
to a shaft 416 of a micromotor 418 that is fixedly mounted adjacent
the distal end 306 of the catheter 300. As shown in FIG. 4, the
mirror 412 is mounted to the shaft 416 such that the mirror
reflects light rays transmitted by the first imaging lens 408
toward the distal end 306 of the catheter 300, and reflects light
rays transmitted back from the second imaging lens 410 toward the
center of the catheter. Extending through the cord 312 is an
optical waveguide 420, such as a single-mode optical fiber.
[0059] As is further shown in FIG. 4, the optical catheter 300
includes a tracking device in the form of a microtracker 422. The
microtracker 422 provides real-time position and orientation
information relating to the catheter 300 such that BCA is not
required to determine the position and orientation of the images
that are captured by the catheter. Such operation enables tracking
of the catheter (e.g., catheter tip) in three-dimensional space in
terms of X, Y, Z, yaw, pitch, and roll, thereby providing six
degrees-of-freedom (6DOF).
[0060] By way of example, the microtracker 422 comprises the
InertiaCube.TM. from InterSense. The InertiaCube.TM. is an
integrated digital smart-sensor module based on
micro-electro-mechanical systems (MEMS) technology involving no
moving parts. By using sourceless (i.e., self-referenced) inertial
sensors as a primary means of tracking motion, high update rates,
desirable smoothness, predictive capability, and excellent immunity
to various forms of external interference are possible. The
InertiaCube.TM. also has integral solid-state magnetometers which
sense components of earth's magnetic field along three
perpendicular axes. Those magnetometer readings can be used as a
digital electronic compass for correcting yaw drift in a sourceless
orientation tracking modality. The technology used by the
mircrotracker 422 is described in one or more of the following
patents, each of which is hereby incorporated by reference into the
present disclosure: U.S. Pat. No. 7,000,469, U.S. Pat. No.
6,922,632, U.S. Pat. No. 6,757,068, U.S. Pat. No. 6,681,629, U.S.
Pat. No. 6,474,159, and U.S. Pat. No. 6,314,055.
[0061] With the above-described configuration, light from a
high-intensity light source (not shown) is transmitted by the
optical waveguide 420 to the collimating lens 404, to the first
imaging lens 408, to the mirror 412, to the second imaging lens
410, and then out from the optical catheter 300 to the imaging site
(not shown). When the micromotor 418 is activated, it rotates the
shaft 416 and, therefore, axially rotates the mirror 412 and the
second imaging lens 410 about a longitudinal central axis of the
catheter 300 such that images can be captured substantially through
360.degree. relative to that axis (i.e., the central axis extending
from the proximal end 304 to the distal end 306). In addition,
positional and orientation information is collected from the
microtracker 422 for the purposes of interpreting the images
captured by the catheter 300.
[0062] FIGS. 5A and 5B illustrate an example of use of the optical
catheter 300 within a vessel 500. By way of example, the vessel 500
comprises a coronary artery. Referring first to FIG. 5A, the
optical catheter 300 is shown positioned within the vessel 500. The
catheter 300 could have been positioned by introducing the catheter
into the vessel 300 using a needle or trocar (not shown). Once so
introduced, the catheter 300 can be placed into position along the
vessel 500 by advancing the catheter using the cord 312, for
example in the direction indicated by arrow 502. The position and
orientation information regarding the catheter 300 can be
communicated, for example, to the image acquisition module 106
(FIG. 1) with the microtracker 422. Optionally, appropriate
external visualization techniques, such as BCA or other x-ray
imaging, can further be used to guide in the practitioner
positioning the catheter 300 at the desired imaging site.
[0063] Once the optical catheter 300 is positioned as desired, the
inner surface 504 and/or interior 506 of the wall that forms the
vessel 500 can be imaged using the catheter. In FIG. 5A, the
interior 506 of a bottom portion 508 of the vessel 500 is imaged
with the catheter 300. As is apparent from that figure, the focal
zone of the optical system 402 coincides with the wall interior 506
such that a given depth of the wall can be imaged without the need
to adjust focus. By way of example, a resolution of approximately 5
microns (.mu.m) can be achieved across a focal line or depth up to
approximately 2 mm. For instance, in one embodiment, a resolution
of 4.8 .mu.m can be achieved for a focal line or depth of 1.5
mm.
[0064] Turning to FIG. 5B, the mirror 412 and second imaging lens
410 have been rotated 180.degree. relative to their positions
illustrated in FIG. 5A such that a second portion 510 of the vessel
wall is imaged. Again, the wall interior 506 is imaged across a
depth instead of at a discrete point such that dynamic focusing is
unnecessary. Although only two portions 508 and 510 of the wall 506
have been illustrated as being imaged using the optical catheter
300, it is to be understood that the entire circumference of the
vessel 500 can be imaged in the same manner due to the 360.degree.
rotation capability of the mirror 412 and the second imaging lens
410. Therefore, in some embodiments, images may be continually
captured as the mirror 412 and second imaging lens 410 are
continuously rotated or "swept" by the micromotor 418.
[0065] FIG. 6 is an example three-dimensional body reconstruction
of a coronary artery segment 600. In FIG. 6, a portion of the
artery segment 600 is shown removed to reveal an inner lumen 602 of
the artery that is defined by the artery wall 604. FIG. 7
illustrates a cross-section of a portion of the segment 600 taken
at plane A in FIG. 6. As can be appreciated from FIG. 7, the
thickness of the artery wall 604 varies due to plaque 700
formation. In particular, the plaque 700 reduces the
cross-sectional area of the lumen 602 so as to restrict the flow of
blood through the artery.
[0066] FIG. 8 is an example three-dimensional grid reconstruction
of a coronary artery segment 800, along with multiple
cross-sections 802. As described below, such a grid reconstruction
can be useful in conducting various analyses, such as flow
analysis.
[0067] In view of the foregoing discussion, a method for acquiring
and analyzing images can be described as provided in the flow
diagram of FIG. 9. Beginning with block 900, images of the vessel
under evaluation are captured with a catheter that is positioned
within the vessel. By way of example, the catheter can have a
configuration similar to that of the catheter 300 described in
relation to FIGS. 3-5. Accordingly, in some embodiments, the
catheter captures image data used to generate OCT and/or
fluorescence spectroscopy images. Simultaneous to the image
capture, the position and orientation of the catheter are
determined by a microtracker provided within the catheter, as
indicated in block 902.
[0068] The image data and the tracking information (i.e., position
and orientation information) are collected, as indicated in block
904. Next, the image data and the tracking information are
correlated, as indicated in block 906, such that a
three-dimensional reconstruction or model of the vessel can be
constructed, as indicated in block 908.
Flow Analysis
[0069] Once a three-dimensional model of the vessel has been
constructed in the manner described above, the morphological
information provided by the model is used to define the flow and/or
structural domains for analyses of hemodynamics and structural
evolution of the arterial wall-plaque assembly. The following
describes an example method for performing flow analysis.
[0070] Local hemodynamic factors play a significant role in the
development of atherosclerosis. It has increasingly been recognized
that knowledge of the relationship between blood flow and disease
pattern is essential to understanding the role of arterial fluid
dynamics on the genesis and progression of atherosclerosis. While
invasive animal studies can be used to follow dynamic plaque
development, they do not provide local hemodynamic information and
the techniques may not be applicable to humans. Experiments to
elucidate the interactions between flow variables and endothelium
can be readily conducted in vitro. However, understanding the
clinical significance of those basic interactions depends on
developing suitable methodologies for calculating and measuring
intra-coronary flow in vivo, and on understanding the relationships
between flow variables and the formation, morphology, and
composition of complex plaque forms.
[0071] The nature and effect of the changing shear stresses
existing along the longitudinal axis of the coronary artery have
not been previously studied in detail. Nevertheless, such
characteristics may be extremely important in identifying the
natural history of a particular coronary plaque and its likelihood
to become vulnerable and rupture. In the following technique, the
relationships between local hemodynamic factors and atherogenesis
and restenosis are evaluated. In particular, the technique is used
to obtain the profiles of the endothelial shear stress and related
flow indicators in the coronary artery segments of patients with
cardiovascular disease.
[0072] In one embodiment, a reconstructed luminal segment is
divided into N.sub.z equal small slices each with thickness
.DELTA.s, for use in generating computational grids. The
intermediate slabs between the image frames are obtained by linear
interpolation. Next, each slice is divided into N.sub..theta. equal
intervals in the angular direction and NT intervals in the radial
direction. A power law distribution is used for the radial
divisions in order to concentrate grids in the important near-wall
region. Finally, the slices are combined in three-dimensional space
to form the computational mesh.
[0073] In other embodiments, only the locations of the boundaries
of the reconstructed vessel are required. The internal points
needed in conjunction with the boundary points are generated using
appropriate meshless method such as Radial Basis Function (RBF)
interpolation for the analysis.
[0074] In a simplified flow analysis approach, it is assumed that
the arterial wall is stiff and wall movement is neglected. Blood is
considered incompressible and homogeneous. Although blood viscosity
is generally shear rate dependent, it is assumed to be Newtonian in
the present computations because the non-Newtonian effect is known
to be significant only when the shear rate is less than 50/second.
In addition, the pulsatility of the coronary blood flow is
neglected for computational economy. Thus, the simulations are
based on steady flow at the present stage. Although this assumption
may seem to be an over-simplification, it has been shown that there
is insignificant difference in pressure drop between steady and
pulsatile flows when the Reynolds number is less than 200.
Moreover, flow separation characteristics do not change
significantly at low Reynolds numbers (Re<500) for steady and
pulsatile flows.
[0075] Within the above framework, blood flow in the coronary
artery can be described by a set of transport equations for mass
and momentum conservation. For an orthogonal coordinate system, the
continuity (conservation of mass) equation gives:
.gradient.{right arrow over (V)}=0 [Equation 1]
where V is the gradient operator and V is the velocity vector.
Conservation of linear momentum (steady Navier-Stokes equations) in
vector form is:
.rho.{right arrow over (V)}.gradient.{right arrow over
(V)}=-.gradient.p+.mu..gradient..sup.2{right arrow over (V)}
[Equation 2]
where .gradient..sup.2.gradient..gradient., p p is the pressure,
.mu. is the dynamic viscosity, and .rho. is the density. A no-slip
condition is assumed to prevail at the surface, giving:
{right arrow over (V)}.sub.wall=0 [Equation 3]
[0076] For convenience, the outlet section is taken as zero gage
pressure, thus:
p.sub.out=0 [Equation 4]
[0077] A uniform mass flux is specified at the inlet, such
that:
{right arrow over (V)}{right arrow over (n)}.sub.in=Q/A.sub.in
[Equation 5]
where A.sub.in is the inlet cross-sectional area, n.sub.in is the
unit normal vector, and Q is the volumetric flow rate.
[0078] Equations [1] and [2], coupled with the boundary conditions
[3]-[5], are integrated over the luminal volume using the
finite-domain scheme and a body fitted coordinate (BFC) system
embodied in the PHOENICS computer code. The numerical accuracy of
the results is assured by systematic grid refinement. The
computations are considered to be fully converged when the maximum
change in the velocity at a monitored location between two
successive iterations is less than 0.1%.
[0079] Once the flow field has been computed, the results are
processed to obtain final indicator functions on the luminal
surface. In addition, the variation of local mean radius, R.sub.m,
(radius of a circle of the same cross-sectional area as the lumen
at a specific location) with path length, s, is determined from the
reconstructed lumen data. Then, abrupt changes of radius are
determined and local minimas are identified as possible locations
of stenosis. Finally, the computed results and stenosis locations
are displayed on the lumen surface for analysis.
[0080] The viscosity is estimated from the correlation of Walburn
and Schneck:
.mu.=C.sub.1exp(C.sub.2H)exp(C.sub.4TPMA/H.sup.2)(C.sub.5{dot over
(.gamma.)}).sup.C.sup.3.sup.H [Equation 6]
where C.sub.1=0.797 cP, C.sub.2=0.0608, C.sub.3=-0.00499,
C.sub.4=145.85 dl/g, C.sub.5=1 s, H is Hematocrit in percent, and
TPMA is total proteins minus albumin content including globulins
and fiboringen. The shear rate is set to an average value defined
by:
{dot over
(.gamma.)}.sub.c=2V.sub.av/R.sub.av=2Q/(.pi.R.sub.av.sup.3)
[Equation 7]
V.sub.av is the mean velocity and R.sub.av is the volume average
radius of the lumen:
R av = 1 L .intg. S = 0 L R m s [ Equation 8 ] ##EQU00001##
[0081] An example artery segment reconstruction 1000 of an actual
artery that was evaluated is shown in FIG. 10. As is apparent in
the reconstruction, the lumen cross-sections are considerably
irregular due to plaque growth and stenosis in the diseased
arteries. Due to the complexity and irregularity of the artery
segment, a fine grid system is desirable to represent the detailed
structure. Grid independence tests indicate that a slab thickness
of about .DELTA.s=300 .mu.m is sufficiently accurate for the axial
resolution coupled with 40 grids in the circumferential direction
and 16 grids in the radial direction.
[0082] It is noted that the total number of computational nodes can
exceed 100,000. This number is quite large in comparison to several
other numerical studies, which usually fall in the range 6,000 to
20,000 nodes. One reason for this difference is that actual
arteries are much more complex than the tube models or models
generated from replicas of previous studies. Another reason is
that, because the goal is accurate shear stress measurement, grid
independence is performed on velocity gradients rather than
velocity field, in contrast to many studies. Gradients generally
have lower accuracy than field variables in numerical computations,
and thus require finer grid structure for grid independence.
[0083] Since the full three-dimensional flow field cannot readily
be represented in two dimensions, the velocity field is presented
at four longitudinal cross-sections of the lumen at 45.degree.
intervals. To enhance the details, the lumen radius is exaggerated
three fold. The resulting flow field 1100 is presented in FIG. 11
with each velocity field depicted for each of the four
cross-sections 1102. It is observed that the imposed uniform inlet
flow quickly develops toward parabolic and does not have much
effect on the flow pattern in the remainder of the segment
considered. The eccentric flow profile due to curvature at the
bends and the jet-like core flow downstream of the luminal
narrowings are quite evident, as indicated in the figure. In
contrast to several previous numerical and experimental studies, no
secondary vortex or reverse flow is observed in the diseased
artery, most likely because the blood flow rates were measured at
rest and are much smaller than the previous studies and because
flow pulsatility is neglected in the simulations. Additionally,
segments with branches were excluded.
[0084] Shear stress .tau. is the product of the dynamic viscosity
.mu., and the shear rate, {dot over (.gamma.)}, i.e.,
.tau.=.mu.{dot over (.gamma.)}. The shear rate {dot over (.gamma.)}
is related to the strain rate tensor:
.gamma.= {square root over (.PI./2)} and
.PI.=.parallel..gradient.{right arrow over (V)}+(.gradient.{right
arrow over (V)}).sup.T.parallel. [Equation 9]
where the superscript, T, represents the transpose operator. The
shear rate calculated using Equation [9] is always positive. It
thus slightly differ from previous formulations, which assumes the
sign of the flow. The wall shear stress, WSS, (or endothelial shear
stress) is the shear stress evaluated at the luminal surface.
[0085] FIG. 12 shows the distribution 1200 of the wall shear stress
1200. In order to show the complete lumen on a two-dimensional
surface, the artery has been opened up along a longitudinal cut
through an arbitrary plane (.theta.=0) as if it were a pathology
specimen. The details are enhanced by exaggerating the luminal
radius by a factor of three. In one study, the magnitude of WSS is
found to be in the range 0.3-5.5 Pa (3-55 dynes/cm.sup.2) and it is
within 1-2 Pa (10-20 dynes/cm.sup.2) on most parts of the surface,
which is consistent with the physiological values. The eccentric
flow at the curvature points cause relatively low WSS at the inner
side of the curvature and relatively high WSS at the outer side of
the curvature. As expected, the stenosed regions have the highest
shear stresses because of flow acceleration at these narrow
sections. The jet-like core flow at the downstream of the luminal
narrowings cause low WSS regions because of low velocity near the
lumen wall. The results indicate that in diseased arteries the
shear stress pattern is very complex with closely adjoining regions
of high and low wall shear stress. Studies have shown that
atherogenesis is initially localized to regions of low shear
stress. Thus, the regions of low shear stresses observed adjacent
to the stenoses may be vulnerable to new plaque growth.
[0086] Lei et al. postulated that the wall shear stress gradient,
WSSG, defined as the gradient of WSS in the direction of the
luminal axis, is the single best indicator of abnormal hemodynamics
influencing atherogenesis. This postulate was based on a
two-dimensional simulation of a branching straight tube. WSSG can
be computed to investigate the influence of arterial geometry.
[0087] Assuming the flow direction is the positive direction, WSSG
can be calculated from:
W S S G = .differential. W S S .differential. s = .mu.
.differential. .gamma. . .differential. s wall [ Equation 10 ]
##EQU00002##
where the direction, s, is the path length along the lumen starting
at the inlet section. FIG. 13 shows the distribution of WSSG on the
luminal surface. As with FIG. 12, the results are plotted on the
"opened-up" lumen. WSSG exhibits abrupt changes at the stenosed
regions. Specifically, it changes sign at the narrow sections but
with very minimal circumferential variation. This trend appears to
be primarily due to the narrowing of the lumen. Ordinarily, a sign
change would be expected in WSSG profile at the locations of flow
reversal. However, no flow reversal was observed in any of the
coronary artery segments that were investigated.
[0088] Endothelial cell functions and atherosclerosis are related
to shear stress, and disease is initiated primarily at regions of
low shear stress. The arterial tree varies considerably in
diameter, flow rate, and viscosity. On the other hand, wall shear
stress in a healthy native artery remains in the physiological
range, e.g., about 1.5 Pa (15 dynes/cm2). The changes in WSS along
the artery appear mostly due to variations in local dynamics
related to branching and curvatures. Thus, it can be helpful to
scale (normalize) the results to reflect the effect of changes in
local dynamics at different segments of the arterial tree.
[0089] To achieve this, the definition of skin friction coefficient
C.sub.F can be introduced. That coefficient is WSS divided by the
kinetic energy of the fluid and multiplied by the local Reynolds
number Re, thus:
C F = 2 W S S .rho. U m 2 Re , where Re = 2 .rho. U m R m .mu. Re [
Equation 11 ] ##EQU00003##
[0090] In equation [11], U.sub.m is the mean velocity at the local
cross-section. The value of C.sub.F is constant and equal to 16 for
fully-developed laminar flow in a straight tube (Poiseuille flow).
Hence, the value of C.sub.F may be a good indication of changes in
local dynamics of flow affecting the wall shear stress.
[0091] FIG. 14 illustrates the distribution 1400 of C.sub.F on the
luminal wall for the considered case. The results exhibit local
characteristics that differ from those of WSS. The maximum WSS is
36. The values of C.sub.p at the narrowed locations are all around
16 and they are quite close to each other. Thus, for the
investigated case, values of C.sub.p are in the range 5-25
indicating that local dynamics can cause flow changes much
different from those expected from Poiseuille Law, which is widely
(and erroneously) used in wall shear stress calculations.
[0092] In view of the above, it can be appreciated that the
location, growth, and vulnerability of arterial plaques can, in
some cases, be predicted relative to the shear stresses imposed
upon the plaques from blood flow. In some embodiments, the shear
stress information can be used by a physician or other skilled
practitioner along with the images of the plaques to evaluate how
likely it is that the plaques will rupture. For example, if a given
plaque (1) has a thin cap, and (2) is subjected to relatively high
shear stresses, it may be concluded that the plaque is vulnerable
to rupture and appropriate measures, such as invasive surgery, may
be performed to prevent that rupture.
Flow-Structure Analysis
[0093] As is apparent from the foregoing, the stresses imposed upon
an artery and, therefore, the possibility of plaque rupture, can be
evaluated through analysis of blood flow and shear stress within
the artery. As described above, the walls of the artery can be
assumed to be rigid. In reality, however, healthy artery walls are
flexible and elastic. Therefore, flow analysis assuming rigid walls
may not provide the most accurate information regarding blood flow
through the artery and/or the stresses that are imposed upon the
artery walls and plaques. Notably, assuming that an entire artery
segment is flexible and elastic similarly does not yield completely
accurate information because plaque formation can result in the
artery becoming much more plastic, particularly when the plaques
calcify and harden.
[0094] In view of the above, more accurate results can be obtained
by taking into account fluid flow through the artery as well as the
structural properties of the artery and its plaques. When flow
analysis is combined with structural analysis, plaque vulnerability
can be assessed with greater accuracy. In particular, the spatial
and temporal distribution of the hemodynamic variables (velocity,
pressure, stresses), local hemodynamics, and plaque characteristics
can be predicted and used more reliably to make determinations as
to the vulnerability of a plaque to rupture.
[0095] Studies have been performed to explore the possible
mechanisms that are responsible for the sudden change of a stable
atherosclerotic plaque to an unstable and life-threatening
atherothrombotic lesion, known as plaque tearing or disruption. For
example, assessments have been made as to the type of plaques that
could progress to occlusion and the other types that were likely to
become vulnerable to disruption and/or thrombosis. Less obstructive
plaques were found to be more lipid-rich and vulnerable to rupture
than larger plaques. Furthermore, the smaller, rather than the
larger, plaques were more likely to lead to acute clinical events
in the case of abrupt occlusion because they were less frequently
subjected to preventive therapy. Those findings suggest that plaque
tearing tends to occur at the locations where the fibrous cap is
thinned, and therefore weakest and most vulnerable. Those locations
are coincident with the regions of the stress concentrations
resulting from biomechanical and hemodynamic forces.
[0096] Among the other determinants of plaque vulnerability to
rupture, structural stress is essential in understanding the
stenosis tearing mechanism. Increased biomechanical stresses in the
arterial wall can lead to the rupture of the fibrous cap and,
subsequently, myocardial infarction or stroke. By investigating the
correlation between different stages of plaque formation and
patterns of mechanical stress, vulnerable plaques can be identified
and treated before they rupture.
[0097] Described in the following is a study of the effects of
fluid and structural properties on arteries and arterial plaques.
Referring to FIG. 15, a diseased artery model 1500 was used that
comprises a lumen 1502 having an obstruction 1504 that represents a
stenosis. A small lipid core 1506 primarily comprising cholesterol
is embedded within the stenosis 1504. The volume of the lipid core
1506 is less than 15% of the stenosis 1504. In the figure, L and Ls
represent the artery segment length and the stenosis length,
respectively. The nominal stenosis severity, S.sub.t, and
eccentricity of the stenosis models, Ec, are defined as
follows:
S t = ( D i - D s ) / D t .times. 100 ( % ) [ Equation 12 ] Ec = e
( D i - D s ) / 2 .times. 100 ( % ) [ Equation 13 ]
##EQU00004##
where D.sub.i and D.sub.s are, respectively, the inner diameter of
the occluded section and the minimum diameter of the section,
and
e = 1 2 ( D i - D s ) [ Equation 14 ] ##EQU00005##
[0098] In the study, the model 1500 was assumed to have a total
length of 110 mm, a stenosis length of 10 mm, an inner diameter of
4 mm, and a wall thickness 0.5 mm. Five models of stenosis levels
of 20%, 30%, 40%, 50%, and 70% were considered, representing native
(20% stenosis), moderate (30%, 40% and 50% stenosis), and severe
(70% stenosis) cases. The eccentricity was assumed to be 100% in
all cases to reflect common diseased arteries.
[0099] The mathematical model assumes bi-linear isotropic,
incompressible material properties. Specifically, employed were the
bi-linear models of Beatties et al. for the stenosis constituents,
which are defined by the stress-strain curve and the two modulis
E.sub.1 and E.sub.2 for the stress values that are less than and
greater than the yield stress Y, respectively. That model was
chosen because it is an optimization scheme in the sense that it
gives a good approximation of the non-linear behavior of the
material under internal pressure and shear stress. In addition,
that model is readily implemented in multi-purpose software for
simulating fluid structure interactions.
[0100] Trilateral and quadrilateral finite elements were generated
for the solid and fluid parts of the arterial segment, resulting in
8505 to 9354 elements. Unlike pervious studies, the internal
luminal pressure was not prescribed but rather computed from the
flow module and distributed over the inner surface. The input
parameters used in the study are summarized in Table 1.
TABLE-US-00001 TABLE 1 Principal input parameters used for the
computation Inlet Velocity 0.2 m/s Outlet Gage Pressure, 0 Pa Pois-
Density Kinematic Modulus Yield Modulus sion's .rho. - Kg/
Viscosity E.sub.1 - kN/ Stress E.sub.2 - kN/ Ratio Materials
m.sup.3 .upsilon. - m.sup.2/s m.sup.2 Y m.sup.2 .theta. Blood-like
1050 3.6 .times. 10.sup.-6 Artery 61.5 8.4 245 0.45 Plaque 483 39.6
1820 0.45 Lipid core 3.81 0.69 38.8 0.45
[0101] Previous studies have shown the prevalence of shear stress
and structural stresses on plaque rupture, and the maximum
principal stresses (MPS) and Von Mises stresses (VMS) were
predicted. Then, by correlation with the concept of buckling in
material failure study, ratios of the wall shear stresses (WSS)
obtained from the flow model to each of the above structural
stresses were computed for analysis. The following equilibrium and
boundary conditions have been used for the artery wall models:
.sigma..sub.ij,j.sup.S=0 [Equation 15]
.sigma..sub.ij.sup.Sn.sub.j|inner
surf=.sigma..sub.ij.sup.fn.sub.j|inner surf [Equation 16]
d.sup.Sinner surf|=d.sup.f|innersurf [Equation 17]
d.sub.--.sub.Y.sup.S|outersurf=0 [Equation 18]
d.sub.--.sub.X.sup.S|inlet,outersurf=0 [Equation 19]
where d.sup.S(d.sub.--.sub.x.sup.S,d.sub.--.sub.Y.sup.s), d.sup.f,
.sigma..sub.ij.sup.S, .sigma..sub.ij.sup.f are the displacements (X
and Y directions respectively) and stress tensors for solid and
fluid, respectively.
[0102] The maximum principal stresses (MPS), structural maximum
shear stresses (MSS), circumferential stresses (SZZ), and Von Mises
stresses (VMS) were predicted. Then, the ratios of the luminal wall
shear stresses (SS) obtained from the flow model to each of the
above structural stresses were computed for analysis.
[0103] The study considered steady, viscous, incompressible flow in
the asymmetric diseased artery model shown in FIG. 15. A lipid pool
1506 is considered due to the clinical observations that its
characteristics may be closely linked to plaque vulnerability and
may increase the magnitude of stress distribution over the fibrous
cap. The fluid is assumed to be Newtonian at that stage. The
Navier-Stokes equations for two-dimensional flow with compliant
walls were solved using the CFD-ACE-GUI flow solver.
[0104] The governing equations solved in the study for the steady
flow behavior are Navier-Stokes equations and can be expressed
as:
[0105] Flow Direction:
.gradient. ( V .fwdarw. u ) = 1 .rho. [ - .differential. p
.differential. x + .gradient. ( .mu. .gradient. u ) ] [ Equation 20
] ##EQU00006##
[0106] Transverse Direction:
.gradient. ( V .fwdarw. u ) = 1 .rho. [ - .differential. p
.differential. y + .gradient. ( .mu. .gradient. u ) ] [ Equation 21
] ##EQU00007##
In those equations, p is the static pressure and .tau..sub.ij is
the viscous stress tensor.
[0107] For boundary conditions, assumed are no-slip on the walls,
no fluid penetration into the wall, and that the inlet and outlet
of the segment have no axial displacement. The inlet velocity and
outlet pressure are prescribed as indicated in Table 1, and are
represented mathematically as:
u = ( 0 , 0 ) [ Equation 22 ] .differential. u .differential. x
inlet , outlet = ( 0 , 0 ) [ Equation 23 ] u x = 0 = u in = 0.2 m /
s [ Equation 24 ] p x = 1 = p out = 0.0 Nm - 2 [ Equation 25 ]
##EQU00008##
where u is the inflow velocity, p.sub.out the pressure at the
outlet, and .PI. is the interface between fluid and structure
domains.
[0108] The viscous stresses are related to the deformation rates
for the assumed Newtonian flow, thus:
.tau. xx = 2 .mu. .differential. .mu. .differential. x - 2 3 .mu. (
.gradient. V .fwdarw. ) [ Equation 26 ] .tau. yy = 2 .mu.
.differential. v .differential. y - 2 3 .mu. ( .gradient. V
.fwdarw. ) [ Equation 27 ] .tau. xy = .tau. yx = .mu.
.differential. .mu. .differential. y + .differential. v
.differential. x [ Equation 28 ] ##EQU00009##
The velocity gradients and pressure distributions were computed and
recorded.
[0109] The CFD code employed for the study (CFD-ACE-GUI) used a
two-way implicit coupling between the fluid and structure modules.
The pressures and velocities obtained from the flow modules are
sent to the stress module at every 10 iterations where deformations
and stresses are calculated. Then, these deformations are sent back
to the flow module, where the solution is recalculated on the new
deformed geometry. Iterations are performed until convergence is
obtained. The convergence criteria chosen in the study continued
the iterative solution until the calculated difference between the
mass inflow and mass outflow rates were negligible (less than
0.001%). Typically, the ratio of this difference to the prescribed
mass inflow rate was less than 0.1%.
[0110] Fluid-Flow Analysis
[0111] An example predicted flow pattern in the lumen is presented
in FIG. 16 (for a 70% stenosis level). At substantially any level
of stenosis, the predicted velocity profile is parabolic upstream
of the stenosis. Then, the velocity increases within the
constricted section above the stenosis with the maximum value
ranging from 0.34 m/s for 20% stenosis to 0.85 m/s for 70%
stenosis. The parabolic profile is progressively distorted as the
plaque severity increases. A small re-circulation vortex develops
in the lee region of the stenosis, the size and the strength of
which increase with the stenosis severity. For the most severe
stenosis (70%) a second re-circulation vortex develops on the upper
surface (on the upper right of FIG. 16C). The re-circulation
vortices are characterized by negative velocity. Those results
indicate that the flow has become fully developed over the 12D
length upstream of the stenosis as expected. The maximum velocity
is located within the narrowest section above the stenosis.
[0112] A flow re-circulation occurs just distal to the stenosis due
to a decrease in pressure in the expanding flow channel and the
no-slip condition on the surface. A second re-circulation vortex
occurs for the severe (70%) stenosis case due to the combination of
flow momentum and the inertia force created by the first
re-circulation vortex. In other words, the pull by the first vortex
creates a vacuum on the opposite side of the channel, which is
rapidly filled with backward flow due to the balance of momentum.
The requirement for mass and momentum conservation provides the
re-circulation vortex. This re-circulation is important because it
impacts the deposition of atherogenesis constituents such as
low-density lipoproteins (LDL) in the lumen. The deposition
mediated by both the low shear stress (SS) and the increased
residence time of the constituents in the recirculation zone. This
resident time increases with the size of the re-circulation
vortex.
[0113] Results of the pressure study show that pressure increases
on the upstream with stenosis severity ranging from 40 to 250 Pa
for 20% and 70% stenosis, respectively. The pressure decreases
rapidly as the velocity gradient increases on the upstream segment.
The opposite effects occur on the downstream of the plaque where
the pressure increases as the velocity gradient decreases. Also, it
is noted that in the case of 70% stenosis, the pressure remains
negative on the downstream until it recovers from the outlet. The
minimum pressure is not located on the tip of the stenosis but
slightly on the downstream side.
[0114] The distribution of shear stress (SS) for 20%, 40%, and 70%
stenosis as a function of X/D is presented in FIG. 17. The
parameter X/D on the horizontal coordinate represents the
dimensionless distance along the solid-liquid interface as
explained previously. The vertical double dashes represent the
location of symmetric vertical plane (SP) passing through the top
of stenosis.
[0115] FIG. 17 shows that the shear stress increases with the
stenosis level at the upstream side of the stenosis. The wall shear
stress rises monotonically to a maximum in the upstream section,
then drops to the lowest value before oscillating to a constant
value. The location where the stress drops from the maximum is
quite distinct for the stenosis levels above 40%. The shear stress
increases with stenosis severity, and its maximum occurs just
before the symmetric vertical plane.
[0116] The shear stress increases at the upstream side of the
lesion due to the flow acceleration resulting from channel
reduction. The predicted sharp drop in the shear stress
distribution and the minimum value after the drop have been
observed by previous in studies. However, unlike these studies, the
minimum value for the 70% stenosis model remained positive due to
the physiological velocity we imposed at the inlet. The minimum
stress following the drop value is located at the reattachment
point downstream of the symmetric vertical plane. The shear stress
(SS) is predicted on the plaque shoulder slightly upstream of the
symmetric vertical plane (SP). This results is consistent with
clinically observed location of plaque rupture.
[0117] Structural Analysis
[0118] The stress distributions predicted from structural analysis
are illustrated in FIGS. 18A and 18B. The figures show the maximum
principal stress (MPS) and Von Mises stress (VMS) for 20% and 70%
stenosis levels, respectively. Those stresses describe the total
stresses that a material endures for a given applied pressure. The
horizontal axis X/D represents the dimensionless distance along on
the solid-liquid interface. The interface considered in these plots
lies just within the fibrous cap to fully account for the
structural effects and stretches from the proximal to the distal
ends of the stenosis (X/D=12.5 to 15.02). The vertical axis
represents the predicted structural stress obtained in N/m.sup.2.
The vertical double dash represents the location of the symmetric
vertical plane (SP) passing through the top of the stenosis.
[0119] The results indicate that, within the fibrous cap, the MPS
starts with high positive values at the proximal end of the
stenosis and subsequently drops rapidly to negative values. The
initial high values are due to stress continuity with the upstream
disease free arterial wall to the diseased segment. The incoming
flow compresses the plaque proximally while the upstream wall
segment is under tension. This compression produced the observed
negative MPS. Peaks of MPS extension are also present in the model
as shown in the graph. The main MPS peak for 70% stenoses is
located on the SP, and upstream of the SP for 20% stenosis. This
trend is due to the lipid pool reaction to the external
compression. The MPS increases with stenosis severity on SP due to
the low pressure above the plaque. Specifically, the lesion
sustains important compression on its upstream side then deforms on
its top where there is less resistance in order to balance the
surrounding forces. The drop in the MPS curve at the end is
associated with the compression of the disease-free artery wall
distal of the stenosis.
[0120] The Von Mises stress (VMS) curves show three consecutive
peaks: one on each side of the SP and one on the SP. The peaks on
both sides of the SP increase with the stenosis severity while the
peak on the SP is relatively high for 20% stenosis (70 N/m.sup.2)
and significantly rises up to (.about.350 N/m.sup.2) for 70%
stenosis.
[0121] The maximum shear stress (MSS) and circumferential stress
(SZZ) for different stenosis levels and 20% and 70% stenosis are
shown in FIGS. 19A and 19B, respectively. Maximum shear stress
(MSS) is meant to describe the stress in the planes 45% away from
the MPS plane, where the structural shear stress is maximal. Also,
circumferential stress (SZZ) describes the stress in the direction
perpendicular to the model and pointing out of the screen. The
horizontal axis represents the ratio X/D as explained above. The
vertical axis represents the structural stress obtained in
N/m.sup.2.
[0122] The results indicate that, as for MPS, circumferential
stress (SZZ) starts with high positive values and decrease to
negative values. The positive SZZ values are due to the stress
continuity with the upstream disease-free arterial wall segment to
the diseased segment. Negative SZZ values are compressive stresses
due to the internal pressure obliquely distributed over the
diseased segment unlike on the disease-free segments where they are
radial. On both sides upstream and downstream of the diseased
segment, SZZ acts in the opposite direction. A peak of SZZ
extension identified with positive value is also observed in the
graph at the SP for stenosis greater than 30% stenosis. It is
important to note that, similar to the MPS curve, SZZ rises with
stenosis severity.
[0123] Similar to what has been previously shown in the Von Mises
stress (VMS) results, the maximum shear stress (MSS) curve present
three consecutive peaks, one on each side of the SP and one on the
SP. The peaks on both sides of the SP increase with the stenosis
severity, while the peak on the SP is relatively high for mild
stenosis (20% stenosis) and significantly rises for severe stenosis
(70% stenosis).
[0124] Fluid-Structure Interaction (FSI)
[0125] Next, appropriate fluid-structure interaction (FSI)
parameters are established to characterize plaque rupture from the
various stresses obtained above. The parameters identified for
investigation are the stress ratios R.sub.1 and R.sub.2 R.sub.1 is
the ratio of shear stress to maximum principal stress (SSIMPS), and
R.sub.2 is the ratio of shear stress to Von Mises Stress (SSIVMS).
FIGS. 20A and 20B show the distributions of the stress ratios
R.sub.1 and R.sub.2 distributions.
[0126] The reasoning behind selecting the endothelial fluid shear
stress ratio parameter is threefold. The first reason is the
successive compression and extension of structural stress
distribution in the plaque, as explained above. Second, several
studies have shown that shear stress and structural stress play
important roles in plaque disruption. Third, the analogy of plaque
rupture with the mechanism of buckling in material failure allows
one to relate endothelial shear stress in a stenosed artery to
perturbation transverse force in buckling, and the internal
pressure in plaque to compressive pressure in buckling.
[0127] The ratio distributions presented in FIGS. 20A and 20B are
for 20% and 70% stenosis levels, respectively. The distance X is
measured along the solid-liquid interface and D is the nominal
diameter of the normal artery segment proximal to the lesion.
[0128] The results indicate that the stress ratio R.sub.1, has
multiple positive and negative peaks. Those peaks are located where
R.sub.1, is infinite. That trend is expected since the maximum
principal stress (MPS) is zero at these locations. R.sub.1 is
negative between the two infinites prior to the mid plane SP due to
the compressive MPS. Between the peak before and on the SP, R.sub.1
is low and positive for severe stenosis (70%) but remains negative
for mild stenosis (20%).
[0129] Stress ratio R.sub.2 curves have two peaks upstream of the
SP and one downstream. The first peak is more interesting to
investigate for three reasons. First, it occurs on the shoulder
where plaques are most likely to rupture. Second, the first peak's
base is larger than the others. Third, the first peak varies with
the stenosis severity. A close look at both ratios reveals that, at
the location of the first peak of R.sub.2, the ratio R.sub.1
changes with the stenosis level.
[0130] Stress ratios R.sub.3 and R.sub.4 distributions are
presented in FIGS. 21A and 21B. R.sub.3 is the ratio of wall shear
stress to maximum shear stress (SS/MSS), and R.sub.4 is the ratio
of wall shear stress to circumferential stress (SS/SZZ). As for the
cases above, the ratio distributions presented below are for two
stenosis levels: 20% and 70% stenosis corresponding to the FIGS.
21A and 21B, respectively.
[0131] The results shown in FIGS. 21A and 21B indicate that,
similar to R.sub.1, R.sub.4, multiple positive and negative peaks
are evident. Those peaks are located where R.sub.4 is infinite.
This trend is expected since circumferential stress (SZZ) is zero
at these locations. Between the two, R.sub.4 infinites prior to the
mid plane SP, and R.sub.4 is negative due to the compressive SZZ.
At the vicinity of the SP, R.sub.4 remains almost unchanged and
close to zero. After the SP, R.sub.4 for severe (70%) stenosis
becomes discontinuous and changes sign at approximately 1/3 the
distance from the base of the lesion, downstream of the SP.
[0132] The stress ratio R.sub.3 curves have similarities with
R.sub.2, and the characteristics previously cited for R.sub.2 can
be applied to R.sub.3. In addition, it is noted that, at the
location of the first peak of the ratio R.sub.3, the stress ratio
R.sub.4 changes with the stenosis level.
[0133] The fluid structure interaction parameters that were
computed to characterize the stenotic plaque vulnerability are
summarized in FIG. 22. In that figure, the horizontal axis
represents the percentage of the stenosis, and the vertical axis
represents the monitored stress ratio. Specifically, the plots
represent the values of R.sub.1 and R.sub.4 at monitored locations
for stenosis levels of 20%, 30%, 40%, 50%, and 70% stenosis. The
monitored locations were the X/D locations where the first R.sub.2
and R.sub.3 maximum occur upstream of the mid plan (SP) in FIGS. 20
and 21, respectively. Those locations were selected because they
are situated on plaque shoulder where plaque rupture most likely
takes place, and the magnitude of the stress ratios varies with
stenosis severity.
R.sub.1=|R.sub.1{(X/D).sub.R2.sub.max}| [Equation 29]
R.sub.4=|R.sub.4{(X/D).sub.R3.sub.Max}| [Equation 30]
The monitored R.sub.1 and R.sub.4 values are presented in FIG. 22
for comparison.
[0134] The results show that although the two methods to
characterize plaque rupture R.sub.1.sub.--.sub.Monitored and
R.sub.4.sub.--.sub.Monitored exhibit the same trend,
R.sub.1.sub.--.sub.Monitored is consistently larger than
R.sub.4.sub.--.sub.Monitored. In general, the predicted FSI indices
are low for both mild (e.g. 20%) and severe (e.g. 70%) stenosis.
Interestingly, those indices reach a maximum between the extreme
stenosis levels at typically approximately 40% to 45% stenosis.
This stenosis range can be considered prone to rupture as it is
consistent with medical observation. In other words, this result
indicates that the FSI indices investigated here can serve to
characterize plaque vulnerability. Plaques typically remain
asymptomatic until the stenosis level exceeds about 70% of the
lumen. However, it has been suggested that nearly 68% of myocardial
infarction patients had less than 50% stenosis. The results
presented here suggest lipid-laden plaques of 40% to 45% stenosis
may be vulnerable to sudden rupture of the fibrous cap.
[0135] By carefully monitoring the stress ratio either R.sub.1 or
R.sub.4 at the location of maximum stress ratio R.sub.2 or R.sub.3,
respectively, an experimental study can establish the stability
value of R.sub.1.sub.--.sub.Cr, or R.sub.4.sub.--.sub.Cr (critical
value) for atheroma rupture. These critical stress ratios combine
the interaction of flow and structural parameters on plaque
characteristic, and are referred to as the flow-structure
interaction (FSI) stability indices.
[0136] The FSI indices can be to be associated with the plaque
location where the stress ratios become infinite in order for the
indices to be more meaningful. Specifically, if there is no
discontinuity for either R.sub.1 or R.sub.4 distribution, the
plaque is likely to be stable. Likewise, if there is discontinuity
for R.sub.1 or R.sub.4 and their magnitude at the location of
maximum R.sub.2 or R.sub.3, respectively, is smaller than a
threshold (e.g., determined experimentally), the plaque is likely
stable. Otherwise, the plaque can be deemed unstable and vulnerable
to rupture.
[0137] As with the flow analysis described above, the arterial
plaques rupture can, in some cases, be predicted relative to the
shear stresses imposed upon the plaques from blood flow and
relative to the structural characteristics of the plaques. In some
embodiments, the shear stress information and structural
information can be used by a physician or other skilled
practitioner along with the images of the plaques to evaluate how
likely it is that the plaques will rupture. For example, if a given
plaque (1) has a thin cap, (2) is subjected to relatively high
shear stresses, and (3) has a structure that is likely to fail, it
may be concluded that the plaque is vulnerable to rupture and
appropriate measures, such as invasive surgery, may be performed to
prevent that rupture. In other embodiments, a physician or other
skilled practitioner can make a determination as to plaque
vulnerability to rupture in view of a fluid-structure interaction
index that is automatically generated by the evaluation system. In
such a case, the vulnerability determination may be simplified
and/or made with greater consistency. Establishing such an index
may require consideration of other facts of plaque vulnerability
such as the detailed plaque characteristics including fibrious cap
thickness, lipid pool size and eccentricity, calcium composition,
and so forth.
[0138] As noted above, while particular embodiments have been
described in this disclosure, alternative embodiments are possible.
All alternative embodiments are intended to be covered by the
present disclosure.
* * * * *