A genuinely hybrid, multiscale 3D cancer invasion and metastasis modelling framework

Dimitrios Katsaounis*, Nicholas Harbour, Thomas Williams, Mark Andrew Joseph Chaplain, Nikolaos Sfakianakis

*Corresponding author for this work

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We introduce in this paper substantial enhancements to a previously proposed hybrid multiscale cancer invasion modelling framework to better reflect the biological reality and dynamics of cancer. These model updates contribute to a more accurate representation of cancer dynamics, they provide deeper insights and enhance our predictive capabilities. Key updates include the integration of porous medium-like diffusion for the evolution of Epithelial-like Cancer Cells and other essential cellular constituents of the system, more realistic modelling of Epithelial–Mesenchymal Transition and Mesenchymal–Epithelial Transition models with the inclusion of Transforming Growth Factor beta within the tumour microenvironment, and the introduction of Compound Poisson Process in the Stochastic Differential Equations that describe the migration behaviour of the Mesenchymal-like Cancer Cells. Another innovative feature of the model is its extension into a multi-organ metastatic framework. This framework connects various organs through a circulatory network, enabling the study of how cancer cells spread to secondary sites.
Original languageEnglish
JournalBulletin of Mathematical Biology
Early online date25 Apr 2024
Publication statusE-pub ahead of print - 25 Apr 2024


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


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