Date of Award

7-2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Advisor

Jian Du

Second Advisor

Linxia Gu

Third Advisor

Ugur G. Abdulla

Fourth Advisor

Tariel I. Kiguradze

Abstract

Platelet aggregation is one of the major components of blood clotting. The proximal cause of most heart attacks and many strokes is the rapid formation of a blood clot (thrombus) in response to the rupture or erosion of an arterial atherosclerotic plaque. In the context of a stenotic artery (i.e., an artery whose lumen is partially blocked by the plaque) understanding how the thrombus forms presents additional challenges because of the extremely high shear rates and stresses present as a consequence of the constriction. In this dissertation, we use a two-phase continuum model to investigate the stability of an existing platelet thrombus within a stenotic channel. In the computational model, the thrombus is modeled as a viscoelastic material that moves differently from the bulk flow. The frictional drag force between the thrombus and the background fluid is dependent on the porosity/permeability of the thrombus. On the other hand, the model directly tracks the formation and breaking of different inter-platelet bonds, which determine the thrombus elasticity and its capability to resist flow. Accurate and efficient numerical algorithms are developed to solve the system of model equations with solid boundaries of irregular shape. Our simulation results illustrate that the mechanical stability of thrombi is closely related to flow conditions, number/type of molecular bonds between platelets, and the porosity values.

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