Therapy Optimization in Population Dynamics Models

Cell subpopulations dealt with in the preceding chapter were the result of compartmentalizing the model. In this chapter we focus on growth of cancer cells and the associated vascular system and interactions with the immune system. Therefore, though the variables will still describe the amount of cells of different type, there will be no flux from one type to another. We start with introduction of standard models of population dynamics, with exponential, Gompertzian, and logistic growth. The difference between stochastic and deterministic approach to model population size is explained, a point often misinterpreted in various sources. Then, the angiogenic aspects of cancer growth are discussed, followed by several models of cancer growth including vascularization. Consequently, the problem of optimization of antiangiogenic and combined therapies is analyzed. Finally, models of gene and immunotherapy in cancer treatments are briefly reviewed. In addition to discussion of optimal treatment protocols, the focus of this chapter is on the formal, system engineering-based analysis of dynamical properties of systems under investigation, such as stability and controllability.