Computational and Mathematical Methods in Medicine

Computational and Mathematical Methods in Medicine / 2009 / Article

Original Article | Open Access

Volume 10 |Article ID 571494 | https://doi.org/10.1080/17486700802216301

Lisette de Pillis, K. Renee Fister, Weiqing Gu, Craig Collins, Michael Daub, David Gross, James Moore, Benjamin Preskill, "Mathematical Model Creation for Cancer Chemo-Immunotherapy", Computational and Mathematical Methods in Medicine, vol. 10, Article ID 571494, 20 pages, 2009. https://doi.org/10.1080/17486700802216301

Mathematical Model Creation for Cancer Chemo-Immunotherapy

Received23 Feb 2008
Accepted13 May 2008

Abstract

One of the most challenging tasks in constructing a mathematical model of cancer treatment is the calculation of biological parameters from empirical data. This task becomes increasingly difficult if a model involves several cell populations and treatment modalities. A sophisticated model constructed by de Pillis et al., Mixed immunotherapy and chemotherapy of tumours: Modelling, applications and biological interpretations, J. Theor. Biol. 238 (2006), pp. 841–862; involves tumour cells, specific and non-specific immune cells (natural killer (NK) cells, CD8+T cells and other lymphocytes) and employs chemotherapy and two types of immunotherapy (IL-2 supplementation and CD8+T-cell infusion) as treatment modalities. Despite the overall success of the aforementioned model, the problem of illustrating the effects of IL-2 on a growing tumour remains open. In this paper, we update the model of de Pillis et al. and then carefully identify appropriate values for the parameters of the new model according to recent empirical data. We determine new NK and tumour antigen-activated CD8+T-cell count equilibrium values; we complete IL-2 dynamics; and we modify the model in de Pillis et al. to allow for endogenous IL-2 production, IL-2-stimulated NK cell proliferation and IL-2-dependent CD8+T-cell self-regulations. Finally, we show that the potential patient-specific efficacy of immunotherapy may be dependent on experimentally determinable parameters.

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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