These selections of models are described in the paper: Cellular interactions constrain tumor growth by Jeffrey West and Paul K. Newton

Significance: A mathematical model relating tumor heterogeneity at the cellular level to tumor growth at the macroscopic level is described based on a statistical mechanics framework. The model takes into account the number of accessible states available to each cell as well as their long-range coupling (population cooperation) to other cells. We show that the degree to which cell populations cooperate determines the number of independent cell states, which in turn dictates the macroscopic (volumetric) growth law. It follows that targeting cell-to-cell interactions or functional coupling among cell populations could be a way of mitigating and controlling tumor growth.

Abstract: A tumor is made up of a heterogeneous collection of cell types, all competing on a fitness landscape mediated by microenvironmental conditions that dictate their interactions. Despite the fact that much is known about cell signaling, cellular cooperation, and the functional constraints that affect cellular behavior, the specifics of how these constraints (and the range over which they act) affect the macroscopic tumor growth laws that govern total volume, mass, and carrying capacity remain poorly understood. We develop a statistical mechanics approach that focuses on the total number of possible states each cell can occupy and show how different assumptions on correlations of these states give rise to the many different macroscopic tumor growth laws used in the literature. Although it is widely understood that molecular and cellular heterogeneity within a tumor is a driver of growth, here we emphasize that focusing on the functional coupling of states at the cellular level is what determines macroscopic growth characteristics.