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SB3C2016
Summer Biomechanics, Bioengineering and Biotransport Conference
June 29–July 2, 2016, National Harbor, MD, USA
TOWARDS NON-INVASIVE, COMPUTATIONAL MODELING OF THE TRANSPORT OF THROMBO-EMBOLI
AND ATHERO-EMBOLI ALONG ARTERIES
Debanjan Mukherjee and Shawn C. Shadden
Department of Mechanical Engineering
University of California, Berkeley
Berkeley, CA, USA
INTRODUCTION
Floating aggregates of cellular or acellular material (emboli) consti-
tute a leading cause of ischemic stroke. They are also associated with a
range of other complications, including deep vein thrombosis, pulmonary
embolism, and athero-embolic renal disease. In addition, embolization
during endovascular or surgical procedures leads to adverse peri-operative
and post-operative effects, reducing treatment efficacy. Emboli causing
stroke are mostly fragments of clots (thrombo-emboli), or cholesterol
based fragments from ruptured plaques (athero-emboli), originating from
heart or valvular diseases, or diseases of the large arteries including the
aorta. These emboli are transported to vessels distal to their point of origin
by blood flow. Large artery hemodynamics is characterized by unsteady,
pulsatile, chaotic flow. Predictive understanding of transport trends for em-
boli carried by such flows therefore continues to pose challenges. Specif-
ically for stroke, the most prominent diagnosis process relies on the pres-
ence of a potential major cardiac source of embolus, with the absence of
significant arterial disease [1]. Thus when cardiac and arterial sources of
embolism co-exist, identification of stroke etiology becomes difficult. This
complication leads to a substantial proportion of stroke cases (30-40%) to
be categorized as “Cryptogenic”. The identification of embolism source is
important for long-term treatment and management of the patient’s condi-
tion.
In view of the aforementioned complexities and challenges, we de-
scribe here a computational framework for investigating the transport of
small and medium sized emboli across large arteries. The framework com-
prises a combination of large artery hemodynamics, discrete particle dy-
namics, and a sampling-based computational method (Figure 1). The de-
veloped tool will serve as a non-invasive probe into anatomically realistic
vasculature, and help derive evidence regarding the i) transport mechan-
ics of emboli across chaotic, large artery hemodynamics, ii) size/inertia
dependent trends in embolus distribution to the brain (or other potential
occlusion sites), and iii) relation between embolism source and embolus
destination for stroke etiology. We present here illustrative numerical ev-
idence regarding these objectives, derived from numerical experiments on
real patient anatomical models.
METHODS
For our study, four representative patient datasets were selected from
a database of Computed Tomography (CT) scan images. Vessel lumen was
reconstructed from the images for the entire vasculature from the aortic si-
nus to the major cerebral arteries connected at the Circle of Willis. These
were thereafter translated into a three-dimensional computer model, and
discretized into a computational mesh comprised of an unstructured grid
of linear tetrahedral elements. Blood was assumed to be a Newtonian fluid
with density 1025 kg/m3, and viscosity 0.004 Pa.s. A Petrov-Galerkin
stabilized finite element solver was employed to solve the continuity and
Navier-Stokes equations [2], and compute the velocity and pressure fields.
A pulsatile, volumetric waveform derived from clinical data was specified
at the inlet of the aorta in the form of a cross-sectional plug profile. The
outlet boundary conditions were set using single element Windkessel re-
sistors. Resistance values were calculated based on volumetric blood flow
to the vessels obtained from measured data, or from proportionality rela-
tionship with vessel cross-sectional area. A mean brachial pressure of 93
mm/Hg was assumed.
FIGURE 1: Illustration of the overall computational framework.
Individual emboli are modeled as spherical particles with a nominal
density of 1100.0 kg/m3. The particle motion is modeled using a modified
form of the Maxey-Riley equation[3], which is derived from a superpo-
sition of the steady and unsteady forces on the particle arising from the
background flow as well as the disturbed flow around the particle. Near-
wall, shear-induced lift forces were considered, and a one-way coupled
framework for integrating the particle motion equations based on the ob-
tained velocity and pressure fields from hemodynamics simulations was
employed.
Potential sites of embolization were generated by spatially sampling
the aorta inlet, and the walls of the ascending aorta and the aortic arch up
until the proximal end of the descending aorta. Particles of diameters rang-
ing from 100 - 1000 microns were released across 8 instances during a sin-
gle cardiac cycle. These ensured that particle sizes were not large relative
to the vessel diameters, and could translocate past the M1,A1,P1 segments
of the middle, anterior, and posterior cerebral arteries respectively.
RESULTS
The fraction of particles distributed across the six major cerebral ar-
teries connected at the Circle of Willis were scaled by the volumetric blood
flow received by these arteries, and compared between cardiogenic and
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SB³C2016-970
FIGURE 2: Variations in distribution fractions to the cerebral
arteries between cardiogenic and aortogenic emboli.
aortogenic cases. Typically, radiological evidences employed in diagnos-
tics involve identifying lesion patterns in the brain vasculature, which is di-
rectly related to the cerebral arteries to which the embolic particles travel.
Hence, we present the comparison of distribution fractions in terms of the
different cerebral vasculature regions in the brain in Figure 2. In terms
of left vs right propensity of embolization, a more pronounced right brain
preference is observed for cardiogenic emboli, over and above the volu-
metric blood flow received by the right cerebral arteries. When compared
amongst the anterior, middle, and posterior arteries, we observe that while
the aortogenic cases have greater variability, the median values (red lines)
indicate that aortogenic emboli arrive at the posterior arteries notably in
excess of volumetric blood flow as compared to cardiogenic emboli.
FIGURE 3: Surface map of embolus source and its tendency to
send emboli to the head for aortogenic emboli.
Based on the particle trajectories, and the spatial sampling of the aorta
inlet and aorta wall, an inverse map can be constructed now to explore the
source-destination relationship, and the critical locations along the aorta
leading to embolization to the brain. For all the patients considered, this
surface heat-map has been compiled in Figure 3. Locations marked red
are the ones with highest observed tendency of sending an embolus to the
brain, while the locations marked blue are those that never sent any em-
bolus to the brain. Observations indicate that embolization events along
the greater curve of the aortic arch have the most potential to send em-
boli to the brain. The next major location is along the base of the arch or
the lesser curve of the aorta. As the arch progresses distal to the left sub-
clavian, there are increasing number of locations which do not send any
emboli to the brain.
In our prior studies [4], we have illustrated the effect of particle in-
ertia and its interaction with helical flow in arteries on their distribution
across arterial bifurcations. Our computational tool enables further investi-
gations regarding the mechanics of the fluid-particle interactions and their
role in embolus transport. As an illustrative example, we present prelim-
inary results from our experiments for assessing the role of shear-driven
lift forces in Figure 4. Characteristic unsteady, swirling flow patterns for
FIGURE 4: Forces on emboli from their interaction with char-
acteristic unsteady flow, and their role in transport.
one of the patient models has been depicted for peak systole and mid di-
astole. For this patient, samples of embolic particles were advected with
and without the inclusion of shear-driven lift forces, for both aortogenic
and cardiogenic cases. The sample statistics for an integrated measure of
the various fluid-interaction forces for each particle for one cardiac cycle
have been presented. It is seen that cumulative levels of lift and drag are
notably smaller in comparison to the unsteady added mass, and stresses
from undisturbed flow. However, lift still leads to noticeable difference
in transport fractions for aortogenic emboli. This is possibly because of
the important role that shear-driven lift plays in drawing aortogenic em-
boli from the aorta wall into the bulk blood flow and affecting its transport.
Further numerical experiments to obtain more detailed numerical evidence
on the role of these forces are currently underway.
DISCUSSION
The implications of the developed framework, and the numerical ev-
idence obtained, are multi-fold. Firstly, it enables exploring the difference
between cardiogenic and aortogenic emboli in terms of their distribution
across the major cerebral arteries. This is valuable for understanding stroke
etiology, especially when competing embolus sources exist. Secondly,
for aortogenic emboli, exploring the source-destination mapping provides
valuable insights into the aspect of site-specificity. Additionally, this has
valuable implications for improving treatment outcomes of procedures like
percutaneous coronary intervention, for which silent strokes caused by aor-
tic wall trauma and embolization may be more common than recognized
[5]. Such a computational tool can thus advance state-of-the-art in terms of
understanding complications due to emboli transported along the arteries.
Currently, we are continuing investigations in terms of a) extending our
experiments to a broader set of patient models, b) including aspects like
anatomical variations, and embolus composition in the computations, and
c) deriving clinically significant statistics from the computational model.
ACKNOWLEDGMENTS
This research was supported by the American Heart Association,
Award No. 13GRNT17070095.
REFERENCES
[1] Ferro, J.M., et al. Lancet Neurol., 9(11):1085-1096, 2010.
[2] Simvascular, www.simvascular.org, 2015.
[3] Maxey, M.R., Riley, J.J., Phys. Fluids, 26(4):883-889, 1983
[4] Mukherjee, D., et al., Theor. Comp. Fluid. Dyn. 2015
[5] Hamon, M.D., et al., Circulation, 118(6):678-683, 2008
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