A Hybrid Multiscale Model for Cancer Invasion of the Extracellular Matrix

Abstract

The ability to locally degrade the extracellular matrix (ECM) and interact with the tumor microenvironment is a key process distinguishing cancer cells from normal cells, and is a critical step in the metastatic spread of the tumor. The invasion of the surrounding tissue involves the coordinated action of the cancer cells, the ECM, the matrix degrading enzymes, and the epithelial-to-mesenchymal transition. In this paper, we present a mathematical model which describes the transition from an epithelial invasion strategy of the epithelial-like cells (ECs) to an individual invasion strategy for the mesenchymal-like cells (MCs). We achieve this by formulating a genuinely multiscale and hybrid system consisting of partial and stochastic differential equations that describe the evolution of the ECs and the MCs while accounting for the transitions between them. This approach allows one to reproduce, in a very natural way, fundamental qualitative features of the current biomedical understanding of cancer invasion that are not easily captured by classical modelling approaches, for example, the invasion of the ECM by self-generated gradients, and the formation of EC invasion islands outside of the main body of the tumor.

Modeling multiple taxis: Tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence

“…for (x 1 , x 2 ) ∈ Ω and ε = 0.3. The ECM in this case is a structured random matrix produced by an inductive process described in Appendix A; this was first introduced in [80]. We augment the model (2) with the sensitivity functions Figure 1.…”

A novel 3D atomistic-continuum cancer invasion model: In silico simulations of an in vitro organotypic invasion assay

“…This gives rise to M(t), which is another union of sub-sets, each of the size of a single cancer cell, cf. Sfakianakis et al (2020).…”

“…The spatio-temporal evolution of the mesenchymal-like cancer cells is dictated by the cell-particle based submodel. Similarly to the rest of the model, the methods and techniques used here are motivated by the work in Sfakianakis et al (2020) and the references therein.…”

“…We have proposed a three-dimensional model based on the two-dimensional model introduced in Sfakianakis et al (2020), that accounts for the phenotypic variation of cancer cells by distinguishing between an epithelial-like and a mesenchymal-like phenotype. The model addresses dynamic mutations between these two cell phenotypes in the form of EMT and its reverse process MET.…”

“…Andasari et al (2012); ; , overcomes this problem but the computational cost limits the number of cells that can be modelled. Building on the two-dimensional model by Sfakianakis et al (2020), we propose a three-dimensional model that represents the spatio-temporal evolution of epithelial-like and mesenchymal-like cancer cells in a biologically appropriate manner while retaining computational efficiency. This is achieved by modelling the epithelial-like cancer cells, which make up the bulk of the tumour, by a macroscopic density profile and their time evolution by a continuum partial differential equation (PDE) approach.…”