A hybrid multiscale model for cancer invasion of the extracellular matrix

Nikolaos Sfakianakis*, Anotida Madzvamuse, Mark Andrew Joseph Chaplain

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)824–850
JournalMultiscale Modeling and Simulation
Issue number2
Early online date13 May 2020
Publication statusPublished - 2020


  • Cancer invasion
  • Multiscale modelling
  • Hybrid continuum-discrete
  • Coupled partial and stochastic partial differential equations


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