Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

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

Pages: 915 - 943, Volume 18, Issue 4, June 2013      doi:10.3934/dcdsb.2013.18.915

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Lisette dePillis - Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, United States (email)
Trevor Caldwell - Harvey Mudd College, Claremont, CA 91711, United States (email)
Elizabeth Sarapata - Harvey Mudd College, Claremont, CA 91711, United States (email)
Heather Williams - Harvey Mudd College, Claremont, CA 91711, United States (email)

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.

Keywords:  Renal cell carcinoma, regulatory T cells, sunitinib, immune system, mathematical modeling.
Mathematics Subject Classification:  Primary: 92C50; Secondary: 92C37, 97M10, 97M60.

Received: February 2012;      Revised: August 2012;      Available Online: February 2013.