| Abstract: | The accumulation of low density lipoproteins within the arterial wall is associated
with process of atherogenesis. Moreover, it is commonly accepted, that
the development of the atherosclerotic plaque is enhanced by the biomechanical
factors, such as hypertension and low wall shear stress.
In addition to medical experiments, computational simulations of the LDL
transport in the vascular wall are an important tool in the study of atherosclerosis.
Simulations of the LDL transport affected by that biomechanical factors can
improve the understanding of mechanisms responsible for the atherogenesis. In
this thesis the extended theoretical model of the LDL transport in the arterial
wall is introduced. Proposed model for the first time take into account two mentioned
biomechanical factors simultaneously. In this model arterial wall is considered
as a medium composed of four homogeneous porous layers. The transport of
macromolecules in such structure is described by the volume-averaged advectiondiffusion-
reaction equation.
The first part of the thesis contains biological and physical basis of the modeling.
In this part the process of atherogenesis affected by biomechanical factors is
presented. Then the transport processes in porous media are discussed.
In the main part of this thesis the extended four layer model of the LDL transport
in the arterial wall is presented. In this section, differences between proposed
model and other models, known from literature are emphasized. Moreover, the
procedure of transport parameters estimation is described in details. It is important
because in literature there are some extremely different transport parameters
sets for the LDL transport in the vessel wall. The most important part of this
section is the description of methods, which allow to impose biomechanical factors
to the modelling.
In the next part of the thesis results obtained in the modeling are discussed.
This section is divided into two main parts. In the first one the influence of biomechanical
factors on one-dimensional LDL concentration profiles within the arterial
wall is investigated. In the second part, the example of applying the proposed
model to analysis of clinical data is presented. The CT based geometry of the
right coronary artery was used in calculations.
To sum up, in the thesis it has been shown that it is possible to accurate
model the LDL transport with good agreement with experiments. It can be the
first step for clinical usage of theoretical calculations of the LDL transport in
the arterial wall. Moreover, the analysis of the influence of biomechanical factors
on this transport has allowed us to draw conclusions about reasons of the LDL
accumulation process in the vessel wall. |