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

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

doi:10.1007/s11538-024-01286-0

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

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Article number	64
Journal	Bulletin of Mathematical Biology
Volume	86
Issue number	6
Early online date	25 Apr 2024
DOIs	https://doi.org/10.1007/s11538-024-01286-0
Publication status	Published - 1 Jun 2025

Keywords

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

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This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1007/s11538-024-01286-0Licence: CC BY

Katsaounis_2024_BMB_Genuinely-hybrid_CC
Copyright © The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Final published version, 3.14 MBLicence: CC BY

Multiscale modelling of cancer invasion and metastasis: integrating stochastic and continuum approaches
Katsaounis, D. (Author), Sfakianakis, N. (Supervisor) & Chaplain, M. A. J. (Supervisor), 2 Dec 2025
Student thesis: Doctoral Thesis (PhD)

Cite this

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

abstract = "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.",

keywords = "Cancer invasion, Multiscale modelling, Hybrid continuum-discrete, Coupled partial and stochastic partial differential equations",

author = "Dimitrios Katsaounis and Nicholas Harbour and Thomas Williams and Chaplain, {Mark Andrew Joseph} and Nikolaos Sfakianakis",

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AU - Katsaounis, Dimitrios

AU - Harbour, Nicholas

AU - Williams, Thomas

AU - Chaplain, Mark Andrew Joseph

AU - Sfakianakis, Nikolaos

PY - 2025/6/1

Y1 - 2025/6/1

N2 - 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.

AB - 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.

KW - Cancer invasion

KW - Multiscale modelling

KW - Hybrid continuum-discrete

KW - Coupled partial and stochastic partial differential equations

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JO - Bulletin of Mathematical Biology

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

Abstract

Keywords

UN SDGs

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Student theses

Multiscale modelling of cancer invasion and metastasis: integrating stochastic and continuum approaches

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