A chemo-mechano-biological formulation for the effects of biochemical alterations on arterial mechanics: the role of molecular transport and multiscale tissue remodelling

Abstract

This paper presents a chemo-mechano-biological framework for arterial physiopathology. The model accounts for the fine remodelling in the multiscale hierarchical arrangement of tissue constituents and for the diffusion of molecular species involved in cell-cell signalling pathways. Effects in terms of alterations in arterial compliance are obtained. A simple instructive example is introduced. Although oversimplified with respect to realistic case studies, the proposed application mimics the biochemical activity of matrix metalloproteinases, transforming growth factors beta and interleukins on tissue remodelling. Effects of macrophage infiltration, of intimal thickening and of a healing phase are investigated, highlighting the corresponding influence on arterial compliance. The obtained results show that the present approach is able to capture changes in arterial mechanics as a consequence of the alterations in tissue biochemical environment and cellular activity, as well as to incorporate the protective role of both autoimmune responses and pharmacological treatments.

Mathematical modelling of the restenosis process after stent implantation

“…Other continuum mathematical biological models typically comprise a series of coupled diffusion-reaction equations for describing the biological interaction between several species. Such models have been developed to describe phenomena such as neointimal hyperplasia formation [32], atherosclerotic plaque formation [33][34][35][36], fibrotic tissue formation surrounding medical implants [37,38] and, more recently, ISR [39] and arterial physiopathology [40]. In contrast to discrete models where cell behaviour is usually described by a set of rules, continuum models offer a mechanistic description, featuring physical parameters which may in principle be measured.…”

Cell signaling model for arterial mechanobiology

“…As noted above, both kinetic and logic-based models offer considerable promise in this regard. Some models coupling tissue mechanics to cell signaling have been developed using kinetic formulations [4,79], and provide illustrative examples through parameter studies. Biochemical species-primarily growth factors and proteases-were modeled using either a system of ODEs [4,80] or reaction-diffusion PDEs [79].…”

“…Some models coupling tissue mechanics to cell signaling have been developed using kinetic formulations [ 4 , 79 ], and provide illustrative examples through parameter studies. Biochemical species—primarily growth factors and proteases—were modeled using either a system of ODEs [ 4 , 80 ] or reaction–diffusion PDEs [ 79 ]. Yet, with time-course data for these species lacking, parameterization and quantitative verification remains a challenge, particularly if more detailed signaling is to be considered in the future.…”

A framework for incorporating 3D hyperelastic vascular wall models in 1D blood flow simulations

“…Some studies have characterized the axial and circumferential residual stress in aorta and carotid arteries by using measurable quantities, such as the opening angle, and the circumferential and axial curvatures (Delfino et al 1997;Holzapfel et al 2007;Sommer et al 2010;Sommer and Holzapfel 2012). Despite the intrinsic complexity of the system, several advanced computational models have been recently proposed for the study of pathological conditions involving the dysfunction of arterial wall components and potential therapies (Marino et al 2017;Ferruzzi et al 2018;Gültekin et al 2019;Niestrawska et al 2019;Heusinkveld et al 2018;Hemmler et al 2018). In most of the cases, the onset and progression of the vascular disease may depend on both systemic and local haemodynamic conditions.…”