Tumor growth models

Abstract

In this chapter, two of the most widely used tumor growth models (TGM) are studied: the logistic and Gompertz models. The chapter begins with a study of the logistic model and the generalized logistic model. A study of the immune system (IS) and the angiogenesis process is also presented, since both subsystems can influence tumor growth. The IS is responsible for the human organism’s defense against infections and diseases and may help to suppress tumors. However, it can also be affected by the tumor, leading to a balance between the tumor volume and the evolution of immunocompetent cell densities. The angiogenesis process corresponds to the formation of new blood vessels from preexisting ones, which can supply the tumor with oxygen and nutrients, thus allowing the tumor to grow. The overall model used for simulations is described, and typical intervals for the model parameters are presented. The overall model comprises the PK and PD models, as well as the models that represent the tumor growth and the subsystems that affect it (immune system and angiogenesis).