A level-set approach for a multi-scale cancer invasion model

TL;DR

This paper introduces a novel multiscale modeling approach for cancer invasion, combining level-set and finite element methods to better understand tumor growth and morphology changes.

Contribution

It develops a new macro-scale boundary movement law derived from micro-scale dynamics within a multiscale framework, enhancing modeling accuracy.

Findings

Effective numerical implementation using cut-cell finite element method.

Improved understanding of tumor boundary evolution.

Potential for more accurate cancer invasion simulations.

Abstract

Central to the quest for a deeper understanding of the cancer growth and spread process, the naturally multiscale character of cancer invasion demands appropriate multiscale modelling and analysis approach. The cross-talk between the tissue scale (macro-scale) cancer cell population dynamics and the cell-scale (micro-scale) proteolytic molecular processes along the tumour boundary plays a particularly important role within the invasion processes, leading to dramatic changes in tumour morphology and influencing the overall pattern of cancer spread. Building on the multiscale moving boundary framework proposed in Trucu et al. (Multiscale Model. Simul 11(1): 309-335), in this work we propose a new formulation of this process involving a novel derivation of the macro-scale boundary movement law based on micro-dynamics, involving a transport equation combined with the level-set method. This is explored numerically in a novel finite element macro-micro framework based on cut-cells.