Multiphysics Approaches to Modelling Biological Systems Across Scales
We seek to build a unified framework for studying tissue mechanics and dynamics. From cellular processes to organ-level kinematics, it aims to uncover the principles that govern complex biological interactions through rigorous modelling and analysis. At its core, the research centres on the development of sophisticated mathematical models, the use of analytical techniques, and the implementation of tailored numerical methods to simulate complex multi-physics phenomena—particularly electro-chemo-mechanical couplings—that are essential to understanding biological function. These couplings appear in diverse contexts, such as tissue growth [1], fluid mechanics and dynamics [2,3,4], electrical signalling [5], biochemical processes [6], among others. While the emphasis is on mathematical modelling, we aim to go beyond equations to embrace interdisciplinary collaboration.
Figure 1: Schematic of the structural transformations that accompany the “visible” motion.
[1] Ramírez-Torres, A., Di Stefano, S. and Grillo, A. (2021) Influence of non-local diffusion in avascular tumour growth. Mathematics and Mechanics of Solids, 26(9):1264-1293
[2] Fulop, Z. B., Ramírez-Torres, A. and Penta, R. (2024) Multiscale modelling of fluid transport in vascular tumours subjected to electrophoresis anticancer therapies. Zeitschrift für Angewandte Mathematik und Physik, 75, 9