A homogenized constrained mixture model of restenosis and vascular remodelling after balloon angioplasty

Abstract

Restenosis is one of the main adverse effects of the treatment of atherosclerosis through balloon angioplasty or stenting. During the intervention, the arterial wall is overstretched, causing a cascade of cellular events and subsequent neointima formation. This mechanical stimulus and its mechanobiological effects can be reproduced in biomechanical simulations. The aim of these models is to predict the long-term outcome of these procedures, to help increase the understanding of restenosis formation and to allow for in silico optimization of the treatment. We propose a predictive finite-element model of restenosis, using the homogenized constrained mixture modelling framework designed to model growth and remodelling in soft tissues. We compare the results with clinical observations in human coronary arteries and experimental findings in non-human primate models. We also explore the model’s clinical relevance by testing its response to different balloon loads and to the use of drug-eluting balloons. The comparison of the results with experimental data shows the relevance of the model. We show its ability to predict both inward and outward remodelling as observed in vivo and we show the importance of an improved understanding of restenosis formation from a biomechanical point of view.

A predictive multiscale model of in-stent restenosis in femoral arteries: linking haemodynamics and gene expression with an agent-based model of cellular dynamics

“…Different modelling strategies, based on continuum (e.g. [7,8]) and/or discrete (e.g. [9]) approaches, have been adopted [6].…”

An intricate interplay between stent drug dose and release rate dictates arterial restenosis

“…Alternatively, a handful of continuum models also exist that utilise partial differential equations (PDEs), motivated through consideration of the underlying physics and biology [37][38][39]. Moreover, there are constrained mixture models that investigate long-term restenosis evolution, simulating the significance of initial vascular injury and subsequent tissue growth within a constitutive framework describing arterial kinematics [40][41][42][43].…”

Multiscale Computational Modeling of Vascular Adaptation: A Systems Biology Approach Using Agent-Based Models

“…Moreover, for a more exhaustive vision related to the modeling of vascular adaptation, the reader should be directed also to multiscale frameworks entirely based on continuum models (which are not the object of this review), implying that also the cell scale is represented through ODE/PDE systems. Examples can be found in models of atherosclerosis (e.g., Cilla et al (2014) , Di Tomaso et al (2015) , Thon et al (2018) and Pleouras et al (2020) ), ISR (e.g., Lally and Prendergast (2006) , Escuer et al (2019) and Maes et al (2021) ), vein graft remodeling (e.g., Budu-Grajdeanu et al (2008) and Casarin et al (2017) ) and other vascular applications (see Humphrey (2021) for an extensive review on constrained mixture models of tissue growth and remodeling). The difference of these works with those reviewed in Multiscale Agent-Based Modeling Frameworks of Vascular Pathophysiology mainly regarded the representation of the cell scale (through a ODE/PDE versus ABM approach), which thus determined the nature of the multiscale framework to be either hybrid (i.e., based on the combination of continuum models with an ABM) or fully-continuum.…”

“…Besides the works by Casarin et al (2017) and Maes et al (2021) , in which a set of ODEs was adopted to describe the temporal dynamics of tissue growth and remodeling, in all the other cited continuum-based studies PDE systems were implemented to capture the spatio-temporal evolution of the species of interest (e.g., growth factors, cells, ECM components, LDL), and thus the subsequent tissue remodeling, in response to fluid or mechanical stimuli. For example, in the patient-specific atherosclerosis model by Pleouras et al (2020) , CFD simulations were coupled with a PDE system describing mass transport of monocytes, LDL, and high-density lipoproteins, and inflammatory species’ dynamics in the arterial wall, ultimately leading to plaque growth over time ( Figure 11 ).…”