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Modeling Blood Flow in a Brain Tumor Treated Concurrently with Radiotherapy and Chemotherapy

1Mathematics Department, University of Texas-Pan American, Edinburg, Texas

Applied Mathematics and Physics. 2013, Vol. 1 No. 3, 67-77
DOI: 10.12691/amp-1-3-4
Copyright © 2013 Science and Education Publishing

Cite this paper:
Ranadhir Roy, Daniel N Riahi. Modeling Blood Flow in a Brain Tumor Treated Concurrently with Radiotherapy and Chemotherapy. Applied Mathematics and Physics. 2013; 1(3):67-77. doi: 10.12691/amp-1-3-4.

Correspondence to: Ranadhir Roy, Mathematics Department, University of Texas-Pan American, Edinburg, Texas. Email:


Blood flow through a tumor plays a critical role in tumor growth and cancer therapies. Hence, fluid dynamics is an appropriate method to study blood flow through a tumor. Drug transport in the tumor interstitial depends on convection and diffusion. To investigate characteristics of blood flow through a spherical tumor, a coupled convection-diffusion models for simulating the interactions between two anti cancer drugs has been developed in this paper. This model provides the computational transportation to evaluate systematically and quantitatively the effects of interactions on the concentration within the tumor. Mathematical expressions for the spatial variations of the interstitial velocity and interstitial pressure are developed and calculated analytically, while variations of drug concentrations within a tumor are determined numerically in this paper. We determined the way interstitial pressure and velocity vary in the radial direction, which agreed with the experiments, as well as we studied the way one drug concentration changes in the presence or absence of a second drug within the tumor. We found that the concentration of a drug in the tumor could be improved in the presence of another drug in the tumor.