Mathematics and Computer Science, Volume 2

3Optimal Personalized Therapies in Colon Cancer Induced Immune Response using a Fokker-Planck Framework

Souvik Roy^⋆ and Suvra Pal

Department of Mathematics, The University of Texas at Arlington, Arlington, TX, USA

Abstract

In this paper, a new stochastic framework to determine optimal combination therapies in colon cancer-induced immune response is presented. The dynamics of colon cancer are described through an It¨o stochastic process, whose probability density function evolution is governed by the Fokker-Planck equation. An open-loop control optimization problem is pro- posed to determine the optimal combination therapies. Numerical results with combination therapies comprising of the chemotherapy drug Doxorubicin and immunotherapy drug IL-2 validate the proposed framework.

Keywords: Fokker-Planck optimization, non-linear conjugate gradient, immunotherapy, chemotherapy

3.1 Introduction

Colon cancer is a leading cause of global cancer related deaths [11]. The lack of early symptoms forces the detection of colon cancer to take place at the metastatic phase of the cancer [29]. Thus, it becomes important to devise fast and accurate treatment strategies for a cure. In this context, combination therapies have been clinically shown to be an effective strategy for combating cancer in comparison to monotherapy (see [18]). Conventional monotherapeutic techniques are indiscriminate in choosing actively growing cells that lead to the death of not only cancerous cells but also healthy ...