Two dimensional mathematical model of fluid flow in a growing solid tumor

Authors

Adriana Gracia, University of Texas-Pan American

Date of Award

12-2014

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Daniel N. Riahi

Second Advisor

Dr. Ranadhir Roy

Third Advisor

Dr. Virgil Pierce

Abstract

We investigate the problem of steady and unsteady fluid flow in a growing solid tumor. We develop a mathematical model for the two dimensional fluid flow in a spherical tumor where the spatial variations of the interstitial velocity, interstitial pressure and the drug concentration within the tumor are, in general, with respect to the radial distance and the latitudinal angle in the spherical coordinates. The expressions for radial and latitudinal variations of the interstitial velocity, interstitial pressure, and the two investigated drug concentrations were determined analytically. We calculated these quantities in the tumor as well as in a corresponding normal tissue. Depending on the types of the two considered drug concentrations, we determine the results about efficiency and the way drug delivery in the tumor takes place in absence or presence of the drugs’ interactions that could be significant in the presence of the two drugs in the tumor.

Comments

Copyright 2014 Adriana Gracia. All Rights Reserved.

https://www.proquest.com/dissertations-theses/two-dimensional-mathematical-model-fluid-flow/docview/1658783796/se-2

Granting Institution

University of Texas-Pan American