Date of Award

Summer 2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

Committee Director

Fang Hu

Committee Director

Jin Wang

Committee Member

Gene Hou

Committee Member

Yan Peng

Abstract

Modeling and Simulation plays a critical role in understanding complex physical and biological phenomena as it provides an efficient and controlled test environment, without the risk of costly experiments and clinical trials. In this dissertation, we present an extensive study of two such systems with integrated application: Fluid structure interaction (FSI) and virotherapy on tumor. Moreover, we substantiate a few preliminary results of FSI application on tumor.

The FSI problem comprises of fluid forces exerted on the solid body and the motion of the structure affecting the fluid flow. FSI problems are of great interest to applied industries, however they are also computationally challenging due to the complex structures involved and freely moving boundaries. We propose a partitioned approach to compute FSI that integrates the direct forcing technique with the Immersed Boundary Method which is able to handle complex rigid, moving, solid and elastic structures. We then propose and analyze a virotherapy model for tumor treatment that includes both the innate and adaptive immune cells which are then studied in a variety of settings. We demonstrate that immune responses, burst sizes, and repeated administration of viral doses on regular intervals play a huge role in the success of the virotherapy. A detailed stability analysis of the ODE tumor virotherapy model is also performed. We analyzed some of the biologically meaningful equilibrium analytically and computationally, whenever analytic solution was impossible. We confirm that tumor can be controlled by showing the existence of endemic equilibria that are locally (or globally if certain criteria are met) stable for a set of parameters. Finally, the FSI method is applied to multiple non-stationary discs to gain some insights in the behavior of the cellular aggregation. This will serve as a stepping stone to our future work of understanding the intra-cellular interaction among tumor cells.

ORCID

0000-0003-3234-2702

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