Identification of a spatially distributed diffusion model for simulation of temporal cellular growth

Abstract

This study introduces a spatially distributed diffusion model based on a Navier–Stokes formulation with a pseudo-velocity field, providing a framework for modelling cellular growth dynamics within diseased tissues. Five coupled partial differential equations describe diseased cell development within a two-dimensional spatial domain over time. A pseudo-velocity field mimics biomarker concentration increasing over time and space, influencing tumour growth dynamics. An $S$-shape coupling functions for individual equations were assumed to establish the mathematical relationship between parameters and variables. The parameters were identified in a minimisation procedure to validate the model’s efficacy based on limited clinical data. While the model draws inspiration from applications in oncology and could potentially be adopted for treatment planning and evaluation, it can also be helpful in applications from developmental biology to tissue engineering in clinical and experimental settings.