Mathematical modeling of an optimal oncotherapy for malignant tumors

Abstract

The paper presents a mathematical model of the optimal treatment for malignant neoplasms. The neoplasm is considered as a distributed parameter object. The scheme for an optimal oncotherapy using a system of partial differential equations of parabolic type is analyzed. The authors propose a solution to the problem using Bellman optimization and the method of adjustable parameters. The optimal control law of the oncotherapy mode is derived. The main results include a scheme for the formation of the Bellman optimal strategy for regulation of control parameters and dynamic parameters, under which the target conditions are guaranteed over time. The work describes an optimization criterion that reflects the total costs of the control system for the oncological treatment. Simulation results demonstrate the efficiency of the optimal control of treatment process. The results of this work can be used in modern clinical practice at the stage of predictive selection of the most effective treatment strategy.