Optimizing cancer treatment using optimal control theory

Abstract

Cancer is a complex group of diseases characterized by uncontrolled cell growth that can spread throughout the body, leading to serious health issues. Traditional treatments mainly include chemotherapy, surgery, and radiotherapy. Although combining different therapies is becoming more common, predicting how these treatments will interact and what side effects they may cause, such as gastrointestinal or neurological problems, can be challenging. This research applies optimal control theory (OCT) to create precise and personalized treatment plans for cancer patients. OCT helps identify the most effective doses of chemotherapy and immunotherapy by forecasting how various treatment combinations will impact tumor growth and the immune response over time. It optimizes the integration of chemotherapy with immunotherapy to minimize side effects while maximizing therapeutic benefits. The study proposes a model for managing malignant tumors using a mix of immunotherapy, vaccines, and chemotherapy. The aim is to develop the best treatment plan that reduces new tumor growth while keeping healthy cells stable. It also takes into account individual differences among patients, including variations in tumor biology and immune responses in both younger and older individuals. To do this, we compared different optimal control strategies: interior point optimization (IPOPT), an open-source tool for nonlinear optimization; state-dependent Riccati equation (SDRE), which adapts linear control methods for nonlinear situations; and approximate sequence Riccati equation (ASRE), a globally optimal feedback control approach for nonlinear systems. The optimization criterion showed that the proposed work achieved a cost value of 52.3573 for IPOPT, compared with 52.424 for both SDRE and ASRE. For $ \mathrm{C}\mathrm{D}{8}^{+} $ T cells, the proposed method maintained a consistent value of 1.6499 for continuous (C) and dosed (D) across all techniques. Tumor cell counts had a C value of 0.0007 for IPOPT, compared with 0.0006 for ISDRE and ASRE, with D values remaining at 0 across all methods. This comparison demonstrates the successful use of control theory techniques and highlights their potential for developing personalized and effective treatment strategies for complex cancer cases. By optimizing treatment schedules and dosages, OCT can help minimize the side effects of cancer therapies, thereby enhancing patients' overall quality of life.

Keywords

• optimal control theory
• interior point optimization
• state-dependent riccati equation
• approximate sequence riccati equation
• cancer treatment