Chapter 4: Single species growth

As alluded to in Chapter 2, cancer is an incredibly complex disease, characterized by an array of cellular and micro-environmental defects that allow the cells to escape homeostatic control and to grow without bound. Molecular biology is aiming to unravel those defects, thus improving our understanding of the pathways that lead to the development of cancers and identifying possible drug targets for therapies. It is, however, equally important to understand the laws and principles according to which tumor cell populations grow. This fundamental aspect of cancer research is the focus of the current chapter. Different tumor growth patterns have been identified experimentally and clinically over the years. Mathematical models have been constructed to describe those observed patterns. The tumor growth models are partly rooted in ecological models that study the growth dynamics of single species populations. The simplest growth law is exponential growth, which results from unbounded reproduction of cells. More realistic models have introduced density dependence in a variety of ways, and included specific biological details to account for specific observations. This chapter reviews the main tumor growth models that have been described, and relates each growth model to experimental data. This is done in the context of a historic time-line [Rodriguez-Brenes et al. (2013)], describing the models in the chronological order in which they have been published. This timeline is summarized graphically in figure 4.1, and can be consulted for reference while reading the rest of this chapter.