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" Finite Element Simulation of Atherosclerotic Plaque through Morphoelasticity "
Mohammad Mirzaei, Navid
Fok, Pak-Wing
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Latin Dissertation
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| Language of Document
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English
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| Record Number
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1054566
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| Doc. No
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TL53683
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| Main Entry
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Mohammad Mirzaei, Navid
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| Title & Author
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Finite Element Simulation of Atherosclerotic Plaque through Morphoelasticity\ Mohammad Mirzaei, NavidFok, Pak-Wing
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| College
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University of Delaware
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| Date
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2020
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| Degree
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Ph.D.
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| student score
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2020
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| Note
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120 p.
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| Abstract
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Atherosclerosis is a disease which can cause a narrowing of the blood vessels therefore reducing the blood flow. It is one of the leading causes of death in the world. Under-standing the behavior and dynamics of the vessel wall before and after atherosclerosis has been a motivation for many studies. We investigate this phenomenon as a combi-nation of mechanical deformation of the vessel wall along with cell and chemical dynamics that occur within. In chapter 2 of this thesis, we investigate this phenomenon as a pure mechanical deformation to learn how growth anisotropy affects the deformation of the arterial wall. We consider the vessel wall as a growing hyperelastic material with three layers. To describe tissue growth, we use morphoelasticity as the mathematical framework. Then we investigate the effect of anisotropic growth on arterial wall remodeling in five different cases: pure radial, pure circumferential, pure axial, isotropic and general anisotropic growth. We speculate that the nature of anisotropy is inclined towards the growth direction that requires the least amount of energy. We propose a scheme that minimizes the energy with respect to the displacement and growth anisotropy. In chapter 3, we utilize our results to see the effect of the most energetically favorable growth on an essential mechanical property of the vessel wall: the opening angle which is a measure of residual strain. We use a general 3D domain and investigate the changes in the opening angle with respect to growth in each separate direction. We notice that the growth in the circumferential direction has a more significant effect on the opening angle than the other two directions. We also compare the opening angle and the strain in the most energetically favorable anisotropic case with an isotropic growth regime. Due to the geometry of the cross section (specifically the axial length of the domain) the anisotropic and isotropic growth show similar results. Finally in chapter 4, we use an integrated model that also includes cell and chemical dynamics that occur within the arterial wall. The growth tensor now is a function of Platelet Derived Growth Factor (PDGF). In this part, we explore the distribution of oxidized lipids, macrophages, foam cells, oxygen and necrotic cells in the intima at each growth step via a system of partial differential equations. Altogether, this allows us to observe intimal thickening as a result of PDGF-induced vessel growth along with histological changes within the wall such as the development of necrotic zones. Our simulations show results similar to the images acquired from ultrasound scans.
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| Descriptor
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Applied mathematics
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Biomechanics
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Fok, Pak-Wing
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University of Delaware
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