Mathematical modeling of regulatory T cell effects on renal cell carcinoma treatment

Lisette dePillis; Trevor Caldwell; Elizabeth Sarapata; Heather Williams

doi:10.3934/dcdsb.2013.18.915

Article Contents

2013, Volume 18, Issue 4: 915-943. Doi: 10.3934/dcdsb.2013.18.915 open access

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Mathematical modeling of regulatory T cell effects on renal cell carcinoma treatment

1.
Department of Mathematics, Harvey Mudd College, Claremont, CA 91711
2.
Harvey Mudd College, Claremont, CA 91711

Received: February 2012

Revised: August 2012

Published: June 2013

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Abstract

We present a mathematical model to study the effects of the regulatory T cells (T$_{\textrm{reg}}$) on Renal Cell Carcinoma (RCC) treatment with sunitinib. The drug sunitinib inhibits the natural self-regulation of the immune system, allowing the effector components of the immune system to function for longer periods of time. This mathematical model builds upon our non-linear ODE model by de Pillis et al. (2009) [13] to incorporate sunitinib treatment, regulatory T cell dynamics, and RCC-specific parameters. The model also elucidates the roles of certain RCC-specific parameters in determining key differences between in silico patients whose immune profiles allowed them to respond well to sunitinib treatment, and those whose profiles did not.
Simulations from our model are able to produce results that reflect clinical outcomes to sunitinib treatment such as: (1) sunitinib treatments following standard protocols led to improved tumor control (over no treatment) in about 40% of patients; (2) sunitinib treatments at double the standard dose led to a greater response rate in about 15% the patient population; (3) simulations of patient response indicated improved responses to sunitinib treatment when the patient's immune strength scaling and the immune system strength coefficients parameters were low, allowing for a slightly stronger natural immune response.

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Mathematics Subject Classification: Primary: 92C50; Secondary: 92C37, 97M10, 97M60.

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