Date of Award

5-2020

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Advisor

Jian Du

Second Advisor

Ersoy Subasi

Third Advisor

Ugur Abdulla

Fourth Advisor

Jay Kovats

Abstract

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. The formation of a thrombus in arteries is a very complex process whose workings are subjects of intense research. In this dissertation, we investigate the biomechanics of platelet aggregation in large arteries using a two-phase continuum computational model. The model tracks the number densities of various platelet populations, the concentration of one platelet-activating chemical, as well as the number densities of inter-platelet bonds. Through the formation of elastic bonds, platelets can cohere with one another to form a platelet thrombus. The movement of the bound platelets is different from the background blood flow. The interaction between a growing thrombus and the moving blood is modeled through an interphase drag term. The mechanical properties of the thrombus are closely related to the platelet packing densities, the stiffness and number density of interplatelet bonds, as well as the stresses generated by those bonds under deformation. Under large hydrodynamic forces in large arteries, the kinematic and mechanical properties of platelet bonds are crucial for the thrombus growth and stability. The main conclusions from our simulation results are: (1) With approximately the same porosity values, thrombi formed under arterial shear rates are likely to have much higher permeabilities than those formed under static conditions. Otherwise, stable clots fail to form due to the large drag forces from the background flow. Our simulation data is consistent with recent experimental measurements. (2) Under large drag forces, a stable clot formation is possible with a significant increase in the bond formation rate. Correspondingly, the platelet packing density in the thrombus is much lower than the value for thrombus formed under low drag. (3) Within fast moving blood flow, platelet activating chemicals are quickly carried away from the injury along the downstream direction. This may significantly limit the thrombus growth in the direction normal to the vessel wall if platelets have to be activated by a soluble agonist before they can form cohesive bonds and become bound. The growth of a thrombus can be drastically boosted if shear-dependent platelet binding/activation is introduced in the model through vWF mediate bond formation.

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