Cellular Potts Modeling of Tumor Growth, Tumor Invasion, and Tumor Evolution

Abstract

Despite a growing wealth of available molecular data, the growth of tumors, invasion of tumors into healthy tissue, and response of tumors to therapies are still poorly understood. Although genetic mutations are in general the first step in the development of a cancer, for the mutated cell to persist in a tissue, it must compete against the other, healthy or diseased cells, for example by becoming more motile, adhesive, or multiplying faster. Thus, the cellular phenotype determines the success of a cancer cell in competition with its neighbors, irrespective of the genetic mutations or physiological alterations that gave rise to the altered phenotype. What phenotypes can make a cell “successful” in an environment of healthy and cancerous cells, and how? A widely used tool for getting more insight into that question is cell-based modeling. Cell-based models constitute a class of computational, agent-based models that mimic biophysical and molecular interactions between cells. One of the most widely used cell-based modeling formalisms is the cellular Potts model (CPM), a lattice-based, multi particle cell-based modeling approach. The CPM has become a popular and accessible method for modeling mechanisms of multicellular processes including cell sorting, gastrulation, or angiogenesis. The CPM accounts for biophysical cellular properties, including cell proliferation, cell motility, and cell adhesion, which play a key role in cancer. Multiscale models are constructed by extending the agents with intracellular processes including metabolism, growth, and signaling. Here we review the use of the CPM for modeling tumor growth, tumor invasion, and tumor progression. We argue that the accessibility and flexibility of the CPM, and its accurate, yet coarse-grained and computationally efficient representation of cell and tissue biophysics, make the CPM the method of choice for modeling cellular processes in tumor development.

Tumor growth in complex, evolving microenvironmental geometries: A diffuse domain approach

“…Continuum models such as single-phase and multiphase mixture models treat tumors as a collection of cells at larger scales and principles from continuum mechanics such as mass and momentum conservation are used to construct partial differential equations and integro-differential equations governing the motion of cell densities, or volume fractions, stresses and cell velocities. See, for example, the recent reviews (Ribba et al, 2004; Quaranta et al, 2005; Hatzikirou et al, 2005; Nagy, 2005; Wodarz et al, 2005; Byrne et al, 2006; Fasano et al, 2006; van Leeuwen et al, 2007; Roose et al, 2007; Graziano et al, 2007; Harpold et al, 2007; Drasdo and H ö hme, 2007; Friedman et al, 2007; Sanga et al, 2007; Anderson and Quaranta, 2008; Bellomo et al, 2008; Cristini et al, 2008; Deisboeck et al, 2009; Byrne, 2010; Rejniak and McCawley, 2010; Lowengrub et al, 2010; Deisboeck et al, 2011; Frieboes et al, 2011; Kim et al, 2011; Kam et al, 2012; Hatzikirou et al, 2012; Szab ó et al, 2013; Baldock et al, 2013; Katira et al, 2013) for a collection of recent results.…”

On a structured multiscale model for acid-mediated tumor invasion: The effects of adhesion and proliferation

“…There is a plethora of mathematical models related to tumor invasion and accounting in a more or less direct way for cell-cell and cell-matrix adhesions. Most of them describe individual cell behavior and are discrete -in their majority lattice based (e.g., [29,59], also see [15] for a comprehensive review) or off-lattice (see e.g., [18,53]). The so-called hybrid models have a semidiscrete character: They specify the evolution of cells in a discrete, individual-based way and couple it to that of some tactic signal (e.g., chemoattractant concentration, density of ECM fibers), the latter being modeled in a continuous way via some reaction-(diffusion) equation, see e.g., [2,36,54].…”

Systems morphodynamics: understanding the development of tissue hardware

“…Fletcher [16] provides an introductory overview of some approaches to modelling epithelial morphogenesis, while Salbreux [17] shows how one type of model, the vertex model, can be applied in increasingly sophisticated ways to tissues in two dimensions and three dimensions. Shvartsman [18] presents application of a vertex approach to a specific morphogenetic process in Drosophila, illustrating the effect of patterning-chemical morphogenesis-on the mechanical morphogenesis that follows. A particular recognition should be made here that the articles included cover only very few of the approaches to modelling mechanical morphogenesis, and the omission of specific articles emphasizing other approaches, such as Cellular Potts, Finite-element or Agent-based is simply a result of the exigencies of editing a theme issue and should by no means be taken as a preference or prejudice of the editors.…”