Cell adhesion and tumour growth: multi-scale modelling of biological systems

Salvatore Di Stefano (Polytechnic of Bari, Italy)

Tuesday 21st May 10:40-11:20 Lecture Theatre 116

Abstract

The main results of some studies devoted to address two different problems in Biomechanics are presented: cell adhesion and tumour growth [2, 3, 5]. In the first case, attention is put on focal adhesions, portrayed as biological systems consisting of an adhesion plaque and a portion of extra-cellular matrix (ECM), which interact with each other through a layer of integring receptors (a focal adhesion is briefly named FA-ECM system) [1, 2, 3]. In particular, the remodelling of focal adhesions is investigated, with the remodelling understood as the structural adaptation of the FA-ECM system in response to external stimuli [2]. In this respect, the time evolution of the FA-ECM system’s internal structure is described, with such a structural evolution manifesting itself as the re-distribution of the proteins in the adhesion plaque and as the occurrence of plastic-like strains within the ECM [2].

Secondly, the growth of a tumour is studied, as is the case of brain tumour. Growth is, in the present approach, explained in terms of mass variation and evolution of anelastic distortions [4], and represented by a growth law supported experimentally [5]. In particular, such growth law is re-written as a non-integrable and explicitly time-dependent constraint of the growth variable, which, in our framework, is meant to solve a dynamic equation [5, 6].

References
[1] X. Cao et al., A chemomechanical model of matrix and nuclear rigidity regulation of focal adhesion size, Biophysical Journal, 109(9) (2015), pp. 1807–1817.
[2] S. Di Stefano, E. Benvenuti, V. Coscia, On the role of friction and remodelling in cell–matrix interactions: A continuum mechanical model, International Journal of Non-Linear Mechanics, 142 (2022), pp. 103966.
[3] S. Di Stefano et al., On the role of elasticity in focal adhesion stability within the passive regime, International Journal of Non-Linear Mechanics, 146 (2022), pp. 104157.
[4] M. Epstein, G. A. Maugin, Thermomechanics of volumetric growth in uniform bodies, International Journal of Plasticity, 16(7-8) (2000), pp. 951-978.
[5] A. Grillo, S. Di Stefano, A formulation of volumetric growth as a mechanical problem subjected to non-holonomic and rheonomic constraint, Mathematics and Mechanics of Solids, 00(0) (2023), pp. 1–27.
[6] A. Grillo, S. Di Stefano, Addendum to “A formulation of volumetric growth as a mechanical problem subjected to non-holonomic and rheonomic constraint”, Mathematics and Mechanics of Solids, In production

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