A Fokker-Planck feedback control framework for optimal personalized therapies in colon cancer-induced angiogenesis

TL;DR

This paper introduces a novel Fokker-Planck based framework for designing personalized, optimal combination therapies for colon cancer-induced angiogenesis, integrating stochastic modeling, parameter estimation, and feedback control.

Contribution

It develops a three-step method combining stochastic modeling, parameter identification, and feedback control to optimize personalized cancer treatments.

Findings

Numerical results show effective optimization of combination therapies.

The framework accurately estimates patient-specific tumor parameters.

The approach demonstrates potential for personalized cancer therapy planning.

Abstract

In this paper, a new framework for obtaining personalized optimal treatment strategies in colon cancer-induced angiogenesis is presented. The dynamics of colon cancer is given by a It\'o stochastic process, which helps in modeling the randomness present in the system. The stochastic dynamics is then represented by the Fokker-Planck (FP) partial differential equation (PDE) that governs the evolution of the associated probability density function. The optimal therapies are obtained using a three step procedure. First, a finite dimensional FP-constrained optimization problem is formulated that takes input individual noisy patient data, and is solved to obtain the unknown parameters corresponding to the individual tumor characteristics. Next, a sensitivity analysis of the optimal parameter set is used to determine the parameters to be controlled, thus, helping in assessing the types of treatment therapies. Finally, a feedback FP control problem is solved to determine the optimal combination therapies. Numerical results with the combination drug, comprising of Bevacizumab and Capecitabine, demonstrate the efficiency of the proposed framework.