Title: Select topics of mathematical modelling in Cell, Cancer, and Cardiovascular Biomechanics

Abstract

Current interdisciplinary approaches in the investigation of mechanobiological phenomena spanning several length- and time-scales present a substantial spectrum of views, each joining the discussion with a unique perspective. In this discussion, mathematical modelling provides a concrete framework to facilitate the understanding of physical processes. In the context of the present talk three such method and modelling frameworks are presented, negotiating: (i) the cytoskeletal reorganization and cellular realignment in response to substrate stretching; (ii) the cell-collagen fibre mechanical interaction and its implication on intratumoural solid stress build-up and tumour growth; and (iii) the automated, accurate and objective geometric quantification of the ascending aorta, and aneurysm growth thereof, from longitudinal patient studies. Where available, frameworks were informed by experimental or examination data, and due to their inherent versatility, they were able to test hypotheses beyond the reach of contemporary laboratory methods. The developed methods and models were able to capture salient features of the underlying mechanobiology, and their findings were either in agreement with experimental data reported in literature, or were validated in further series of experiments motivated, partly or fully, by model predictions.