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Atherosclerosis Modeling: A System Biology
Approach to Disease Management
Brendan M. Leung

Abstract— Cardiovascular diseases (CVD) are the
leading cause of death in many developed countries. Many
CVDs are caused atherosclerosis. Although the pathophysiology of atherosclerosis is well understood, it remains
a challenge to predict the severity of atherosclerosis and
prognosis based on individual risk factors. The advent in
system biology provides novel approaches in compiling and
understanding the predictive strategies in CVD
managment. In this paper, we investigate the feasibility of
predicting the pathology and prognosis of atherosclerosis
based on recent studies genomic, proteomic, metabolic and
numerical modeling of the circulatory system.
Index Terms—Cardiovascular disease, atherosclerosis,
system biology, mathematical modeling, environmental
stress, risk factors
I. INTRODUCTION
A
is the underlying cause of may
cardiovascular diseases, including myocadioinfarction
(MI), atheroembolism, atherosclerotic aneurysm, stroke and
congestive heart failure (CHF). It is a progressive arterial
degenerative disease that may develops as early as childhood.
Together it causes more deaths in Canada than any other
diseases. It is also a tremendous economic burden costing the
Canadian healthcare system $18 billion dollars 1994. Thus
there exist strong motivations to prevent and control the spread
of such condition in the general public.
The pathology of atherosclerosis is well described in
literature [1]. Atherosclerosis is one of many different types of
arteiosclerotic lesions, and it has essentially two components
to its development. The first part of the cause is contributed by
fatty streaks found in arterial walls. These are lesions
beginning in childhood and can be described as collection of
foamy lipid-laden macrophage and smooth muscles beneath
the intimal layer of arteries [2]. Eventually these lesions grow
into fibrolipid plaques and begin promoting platelets
aggregations, where a lipid core is formed surrounded by
macrophage, platelets and smooth muscles cell due to intimal
hyperplasia.
THEROSCLEROSIS
This article is submitted as a course requirement for BME1450, IBBME,
University of Toronto, 2003.
Brendan M. Leung is a M.A.Sc candidate at the Institute of Biomedical
and Biomaterial Engineering, University of Toronto.
The formations of fibrolipid plaque give rise to the second
morphological change in the affected artery. The plaques cause
stenosis, or the narrowing of arterial lumen. Mechanically
stenosis can be lead to an increase in vessel wall stress. The
damage in tissue stretching causes the intimal layer of the
artery to overgrow and increase in thickness in response to
stenosis. The thickening of intimal layer worsens the flow
properties of atherosclerotic vessels, since most of the
overgrowth is directed towards the lumen. Moreover, intimal
hyperplasia result in a lost of vascular elasticity and promoted
calcium deposition, which will lead to calcification and
hardening of the artery.
II. RISK FACTORS IN ATHEROSCLEROSIS
Many of the risk factors for atherosclerosis are commonly
associated with cardiovascular diseases. Some of these factors
including age, ethnicity, sex and family medical history cannot
be manipulated by the patients. While others such as smoking,
hypertension, plasma low-density lipoprotein (LDL) level,
obesity and diabetes (type I and II), can either be avoided or
controlled by medication.
In most patients, atherosclerosis presents no symptom until
the arteries affected are severely obstructed, leading to
hypoxia in downstream tissues, causing stroke or heart attack.
Thus it is extremely valuable. There are many tests and indices
commonly used by clinicians to assess the severity of these
risk factors for individual patient. Blood pressure and LDL
level are frequently measured to correlate the susceptibility of
the patients to develop atherosclerosis. Statistic of clinical
observations across different age, sex and ethnic groups has
also give rise to some prediction of decease progression
comparing to the general population. While these results are
good indicators for individual risk factors, they fail to provide
an overall picture and prediction concerning the progression of
the disease. It would be invaluable to devise a systematic
approach to evaluate the condition both in terms of treatment
and prevention.
III. SYSTEM BIOLOGY APPROACH TO ATHEROSCLEROSIS
The notion of viewing disease in a system approach became
a reality as the Human Genome Project moves towards
completion. The basic component required to analyze a
disease using system biology is to define the systems involved.
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Table 1: Sources and databases of cardiovascular transcriptome and proteome
In the case of atherosclerosis, there are two related system that
needs to be identified. The first system is the disease
pathology. It was mentioned previously that the make up of the
disease fairly is well described as far as the types of cells
involved and pathology is concerned. The second system of
interest is the human system in which the disease lies. The
genes that make up various components of the human system
are currently being uncovered by the Human Genome Project.
Their functions will also be elucidated by proteomic studies
following the post-genomic era. Functional analysis gives rise
to metabolic pathways which generate the basis for normal
physiology and pathophysiology comparison. In essence, we
can consider the disease model for atherosclerosis as two
systems, one with in another. The power of incorporating the
human genome into the modeling process means that
personalized predictions can be made given the state of the
individual as measured using existing parameters such as
blood cholesterol level, blood pressure and life styles.
A.
Systemic Modeling
Once the systems involved are defined, we can define the
parameters that interact and perturb the system. As mentioned
previously, some risk factors in atherosclerosis are related to
the human system, such as age, sex and ethnicity. Attempts has
been made to models the effect these factors on the
cardiovascular system. The effect to aging is probably the most
studied systemic cause of atherosclerosis. Non-disease specific
mathematical modeling on aging has been attempted [3-4].
Although the results from these studies are invaluable toward
the understanding of systemic aging, models that deal more
specifically with organ degeneration is needed as a disease
prediction tool.
The first step in creating such model is to elucidate tissue
specific gene expression pattern, so-call tissue transcriptome,
similar to that done in BodyMap Database for cardiac myocyte
and aortic tissue [5]. Natural it would also be of interest to
understand the tissue proteome, the protein expression pattern.
Some databases containing cardiovascular gene and protein
expressions are listed in Table 1 [6].
Building on the knowledge of genomics and proteomic, the
physiology of the cardiovascular system may be incorporated.
One such study attempted to model the normal physiology of
cardiomyocyte based on the DiFrancesco-Noble model of the
Purkinje fiber [6], derived from the Hodgkin-Huxley model of
the squid axon form the 60’s. The model aims to create a
virtual myocyte in which intra and extra cellular calcium level,
membrane ionic potential, membrane transport proteins and
bioenergetics via the tricarboxylic acid cycle (a.k.a. Krebs
cycle) are all taken into consideration in cellular function and
contraction. Such model has been validated and used to model
normal versus disease state myocytes.
An even more ambitious attempt was made by Hunter et al.
[7] from the University of Auckland, New Zealand, where they
combined the anatomy of the heart, electrical properties of
membrane ionic channels, soft tissue theory described by
mechanical elastic deformation equations, homodynamic
models based on Navier-Stokes equations and metabolic
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pathways of cardiomyocytes to generate an overall picture to
describe a beating heart. The exploitation of knowledge from
the vast number of bio-physical disciplines reiterates the
complexity of biological systems. The resulting model was
very comprehensive and was able to integrate the various submodels dealing different physical parameters such as stress,
electrical potential, flow rate and metabolic state in a 3dimensional fashion using the large deformation mechanic
model.
B.
Environmental Modeling
While systemic modeling deals mainly with normal
physiology and pathogenesis, environmental modeling takes
into consideration the causal as well as degenerative effect of
risk factors. While modern clinical practices focus on
monitoring and controlling these risks in order to lower their
impacts, it does not provide patients and clinicians with a
predictive treatment due to the lack of understanding. In such
case a model based on measurable risk factor such as blood
pressure and plasma LDL level would be useful. While
monitoring of arterial blood flow is not a common clinical
“check-up” procedure, one may use blood pressure to relate
the flow regime occurring in the arteries. However,
popularization of non-invasive flow measurement techniques
such as ultra-sound Doppler, laser Doppler anemometry and
functional magnetic resonance imaging may allow for routine
arterial flow monitoring.
Perktold et al. have used numerical modeling to investigate
local arterial flow conditions associated with atherosclerotic
lesions [8]. It was hypothesized that hemadynamic is related to
platelet aggregation and vessel wall modification. Platelets in
regions of the arteries where turbulent whirls are found
experience an increased resident time in contact with the
endothelium, thus may promotes plaque formation and growth.
Aortic cell morphology can be altered by wall shear stress,
especially in regions where flow rate and direction changes
with pulsate motion of the heart. Local flow pattern chances
mass transfer properties of the endothelium, in turn, such
vessel wall permeability and arterial mass transfer contributes
to vessel wall shear stress and transendothelium
macromolecules transport. The results may lead to intimalmedial remodeling, the first step observed in atherogenesis [9].
The modeling process relies on the basic engineering
concepts in fluid mechanic. Blood was modeled as a
incompressible, elastic non-Newtonian fluid, and a viscous
flow equation was applied (Nanvier-Stokes). The use of
computational fluid dynamic (CFD) allows for the
identification of two types or near wall flow patters which are
of interest in disease development. It can be seen here that
system biology approach to disease modeling act as a
discovery tool for basic pathogenesis and pathophysiology.
Future modeling may also consider the elastic properties on
aorta under pressure (current model assumes rigid wall).
The effects of plasma cholesterol level on atherosclerosis
were under intense investigation over the past two decades.
However there remains to be limited effort in creating a
computational model correlating cholesterol level and
atherosclerosis. A study done by Nedeljkovic et al. [10]
attempted to correlate intimal-medial thickening, a hallmark of
atherosclerosis, with plasma triglyceride and cholesterol
indices. The following mathematical relationship was
observed:
IMT = 0.005 x TG-0.008 x Chol + 0.28
where IMT, TG and Chol are intimal-medial thickening,
triglyceride and cholesterol indices used in the study. While
the model is empirical and by no mean transferable between
populations, it does provide a basis to understand the impact
current laboratory tests results on the disease state.
As described before, the effects of blood cholesterol level
maybe due in part to the transendothelial transport mechanism,
which is heavily dependent on local flow condition. It was
observed that mass transfer in the vicinity of stenosis and
bifurcation are different that other areas of the arteries [11].
Modeling based on convective mass transport in arterial blood
reveals a polarized boundary layer on the arterial wall with
respect to LDL concentration, as illustrated on figure 1. The
modeling data of LDL accumulation provides a better
correlation between measured plasma LDL level and actual
local surface LDL concentration.
Figure 1: Polarization of LDL concentration at the vessel wall boundary layer as modeled
using mass transfer equations. [13]
Work done by Back et al. [12] shows that region distal to
stenosis suffers hypoxia and increased LDL perfusion. The
conceivable effect on stenotic plaque enlargement can be
model using a combination of measured plasma LDL level and
CFD analysis described before.
IV. INTEGRATION OF MODELS: GENERATING A TOOL FOR
DISEASE PREDICTION.
Currently a unified model that incorporate systemic
model and environmental model for the purpose of
atherosclerosis progression prediction does not exist.
However, gathering from the many advances in individual
sciences concerned in vascular biology, it is a feasible and
practical approach to develop diagnostic models for the
treatment of atherosclerosis. Present clinical measurements
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of blood pressure and plasma LDL levels may be
incorporated into the combined model to predict the
effective arterial wall surface cholesterol level and better
assess the risk of progression of fibrolipid plaques. On the
other hand, genomic and proteomic modeling of arterial
aging may be included when modeling the hemadynamics in
the patients’ arteries, hence giving a more accurate
prediction of arterial wall LDL concentration mention
above.
To bring the disease modeling concept to an even more
proactive level, one can imagine the long term arterial
health modeling based on the measured parameters and the
patients’ genomic make-up. The concept of preventive
disease management may also be applied in other
degenerative conditions and may provide vast benefit to
public health.
V. CONCLUSION
The current paper put forth the idea of preventive
medicine using a system biology approach to devise models
that reflect the state of health of patients’ arteries. The
advents in numerical modeling and genomic / proteomic
discoveries allows for sophisticated models to be developed,
thus the unification of models as a diagnostic tool is deemed
both feasible and practical.
REFERENCES
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