A Computational Model for Atherosclerosis

1 April 2022

Abstract

Even though our societies have managed to make huge jumps in the understanding of human biology, still cardiovascular diseases remain the main cause of death compared to any other disorder. Two main categories exist in the field of cardiovascular diseases, these refer to the atherosclerotic and non-atherosclerotic disorders [PMO+16]. These disorders are pathological phenomena with complicated dynamic cell processes still not fully understood. To understand these interactions, computational and mathematical models are developed from researchers trying to describe the factors which significantly lead to this pathogenesis. This master thesis focuses on the development of a computational model which couples mechanics and biology to describe the atherosclerotic disorder and plaque formation. The core of this thesis compared to most of the studies in the literature is to include the influence of vasa vasorum vessels in plaque formation. The inspiration for this model comes from a recent publication of [SHW21], which made a first try of describing this phenomenon. This thesis represents a refined model of atherosclerosis. In this master thesis from a mechanical point of view the artery is defined as a 3-layered structure referring to intima, media & adventitia each owning individual material parameters. Furthermore the formulation of pre-stretch is included allowing the description of the biological phenomenon of homeostasis existing in organs and tissues. From a biological point of view cells are taken into account. In the first chapter, fundamentals of continuum mechanics and finite element method for finite strain formulation are represented. Since arteries are anisotropic materials with fibers in their matrix, the basic theory of composite materials will be introduced. Furthermore the multiplicative decomposition of the deformation gradient for finite strain theory is presented, having an important role in the later formulation of the computational model. The biological reactions which lead to the plaque formulation play a significant role in this thesis. Therefore the biological processes and different types of cells are explained. In addition fundamentals of basic diffusion theory will be introduced, because these type of equations allow to model cell movement. As next, the new computational model is described, including the motivation for this new approach along with the equations and steps which need to be conducted in order to obtain the desired results. In the following Chap.[4], features of the proposed model are presented and the results are compared to the literature. Special focus is hereby laid on the developed stresses, total deformation around the plaque area and also the evolution and behaviour of cells concentrations. The thesis ends with the conclusion in Chap.[5] and a glimpse in the future for a further extension of this theory

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