Discrete ARMA Model Applied for Tumor Growth Inhibition Modeling and LQR-based Chemotherapy Optimization

Mathematical models for tumor growth inhibition (TGI) are an important tool in the battle against cancer allowing preclinical evaluation of potential anti-cancer drugs and treatment schedules. In this article, an autoregressive moving average (ARMA) model for cancer tumor growth is estimated based on laboratory data of TGI in mice and presented. The model was proven capable of describing with accuracy the tumor growth under single-agent chemotherapy. At the same time, an optimal control problem was formulated to identify optimal drug dosages. The linear quadratic regulator (LQR) controller was used with success in optimizing both periodic and intermittent chemotherapy treatment schedules reducing the tumor mass while keeping dosages under acceptable toxicity