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Prediction of the cancer patients' response to their therapeutical treatment with non-linear forecasting techniques

Liliopoulos Sotirios

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Summary

This thesis delves into the complexity of cancer, necessitating a multidisciplinary approach for effective understanding and treatment. Central to this exploration is the use of mathematical tumor modeling to understand and predict the growth of solid tumors under a variety of therapeutic interventions. First, an introduction to the key concepts underlying the dynamics of cancer and a thorough review of current treatment modalities is presented. A comprehensive review of state-of-the-art mathematical models that portray tumor growth in both unperturbed and perturbed scenarios, focusing on chemotherapy, immunotherapy, and their combination also takes place. A key part of this work is the application of optimal control theory to refine cancer therapy protocols. This includes a detailed examination of the clinically acclaimed Simeoni et al.’s tumor growth inhibition (TGI) model. That model is enhanced in this thesis with a novel formulation, the augmented Simeoni et al.’s TGI model, which also incorporates the drug pharmacokinetics. An optimal non-linear control problem is then introduced and solved, based on that novel formulation, using the state-dependent Riccati equation (SDRE) methodology to identify the most effective chemotherapy strategies for tumor eradication. Additionally, this thesis presents the Adaptive Neuro-Fuzzy Inference System (ANFIS) and introduces three ANFIS TGI model structures for mathematical modeling of tumor growth under chemotherapy. Further, a novel method for modeling TGI under the efficacy of single and in combination chemotherapy drugs is proposed. Specifically, two autoregressive with exogenous inputs (ARX) TGI models for solid tumor growth are identified and evaluated. The parameters of these models estimated using non-linear optimization and laboratory experimental data, have shown high accuracy in fitting experimental tumor growth data under chemotherapy effects, being a pioneering contribution of this work. The use of linear quadratic regulator (LQR) optimal control based on those ARX TGI models is then introduced and explored for determining optimal chemotherapy dosages under various periodic and intermittent treatment schedules. Finally, all the presented in this thesis TGI models' capability for short-term adaptive tumor growth predictions incorporating also moving (sliding) window techniques, is thoroughly investigated giving accurate and significative for the clinical practice and the new anticancer drug discovery research TGI prediction results. All the simulation results are presented and extensively discussed, leading to insightful conclusions.

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