Mathematical modelling of the restenosis process after stent implantation

Abstract

<jats:p>The stenting procedure has evolved to become a highly successful technique for the clinical treatment of advanced atherosclerotic lesions in arteries. However, the development of in-stent restenosis remains a key problem. In this work, a novel two-dimensional continuum mathematical model is proposed to describe the complex restenosis process following the insertion of a stent into a coronary artery. The biological species considered to play a key role in restenosis development are growth factors, matrix metalloproteinases, extracellular matrix, smooth muscle cells and endothelial cells. Diffusion–reaction equations are used for modelling the mass balance between species in the arterial wall. Experimental data from the literature have been used in order to estimate model parameters. Moreover, a sensitivity analysis has been performed to study the impact of varying the parameters of the model on the evolution of the biological species. The results demonstrate that this computational model qualitatively captures the key characteristics of the lesion growth and the healing process within an artery subjected to non-physiological mechanical forces. Our results suggest that the arterial wall response is driven by the damage area, smooth muscle cell proliferation and the collagen turnover among other factors.</jats:p>

Effect of Rivaroxaban and Clopidogrel Combination Therapy on In-Stent Responses After Everolimus-Eluting Stent Implantation in a Porcine Coronary Model

“…Neointimal areas were measured around the stent and above the inner membrane 20) , and a morphometric analysis of the smooth muscle cells (SMCs) was performed. Neointimal SMCs were divided into two subtypes: SMCs with contractile features and SMCs with synthetic features [21][22][23] . Both subtypes were distinguished according to cell morphology, surrounding extracellular matrix (ECM), and their role in the formation of in-stent restenosis.…”

“…The high proportion of layered patterns in the AR and CR groups at 1 month might reflect a clearer boundary between SMCs with contractile and synthetic features. SMC heterogeneity has been described in atherosclerotic lesions and restenosis after angioplasty or stenting [21][22][23] . Consistent with previous studies, two types of SMCs were distinguished in the neointima atherosclerosis; therefore, the reaction to antiplatelet drugs and anticoagulants may be different in actual atherosclerotic lesions.…”

Mechanistic evaluation of long-term in-stent restenosis based on models of tissue damage and growth

“…The model was able to quantify the volume of neointima hyperplasia and give a quantitative comparison between different stents. Escuer et al ( 2019 ) developed another damage-related volumetric growth model, in terms of densities/concentrations of important species such as growth factors, matrix metalloproteinases, extracellular matrix and contractile and synthetic SMCs. This model was used to simulate the development of ISR, and the results suggested that the arterial wall response was driven by the damage area, proliferation of SMCs and the collagen turnover.…”

Computational model of damage-induced growth in soft biological tissues considering the mechanobiology of healing

“…From the mechanical perspective, the key players in their framework are collagen and a noncollagenous matrix, together forming the ECM. Another model on continuum scale has been published by Escuer et al (2019). The authors address the problem of restenosis, which is the pathological renarrowing of arteries after angioplasty.…”

“…At the continuum scale, the concentration of MMPs and GFs is coupled with a homogenized constrained mixture model, motivated by Cyron et al (2016), to describe the change in tissue volume as a gross effect caused by mechanisms on molecular and cellular scale. With respect to a number of existing approaches (Buganza Tepole and Kuhl 2016;Escuer et al 2019;Li et al 2019;Nolan and Lally 2018), the proposed framework includes a consistent continuum-based biomechanical description and coupling of damage evolution, biological events and tissue growth and remodeling. Damage is not simply considered as an internal variable independent from mechanics, but it is initiated by overloads and determines tissue softening and permanent deformations.…”