Modelling Growth, Remodelling and Damage of a Thick-walled Fibre-reinforced Artery with Active Response: Application to Cerebral Vasospasm and Treatment

TL;DR

This work develops a novel 3D rate-based constrained mixture model that captures VSMC active contraction, remodeling, and damage in a thick-walled artery to simulate cerebral vasospasm and its mechanical treatment with stent-retrievers. Implemented in a finite element framework, the model integrates elastin, collagen, and VSMCs with homeostasis-driven remodeling, and introduces a Gaussian spatial pattern of VSMC activity to reproduce vasospasm. The results show that mechanical treatment can mechanically resolve vasospasm in arteries up to about $3$ mm in diameter, with wall thickness significantly modulating the required pressure, and predict that thicker walls demand higher pressures for complete VSMC damage. This in silico tool aligns with clinical observations and offers a platform for patient-specific predictions and stent-design optimization, potentially guiding clinical decisions and device development for vasospasm therapy.

Abstract

Cerebral vasospasm, a prolonged constriction of cerebral arteries, is the first cause of morbidity and mortality for patients who survive hospitalisation after aneurysmal subarachnoid haemorrhage. The recent finding that stent-retrievers can successfully treat the disease has challenged the viewpoint that damage to the extracellular matrix is necessary. We apply a 3D finite element rate-based constrained mixture model (rb-CMM) to simulate vasospasm, remodelling and treatment with stents. The artery is modelled as a thick-walled fibre-reinforced constrained mixture subject to physiological pressure and axial stretch. The model accounts for distributions of collagen fibre homeostatic stretches, VSMC active response, remodelling and damage. After simulating vasospasm and subsequent remodelling of the artery to a new homeostatic state, we simulate treatment with commonly available stent-retrievers. We perform a parameter study to examine how arterial diameter and thickness affect the success of stent treatment. The model predictions on the pressure required to mechanically resolve the constriction are consistent with stent-retrievers. In agreement with clinical observations, our model predicts that stent-retrievers tend to be effective in arteries of up to 3mm diameter, but fail in larger ones. Variations in arterial wall thickness significantly affect stent pressure requirements. We have developed a novel rb-CMM that accounts for VSMC active response, remodelling and damage. Consistently with clinical observations, simulations predict that stent-retrievers can mechanically resolve vasospasm. Moreover, accounting for a patient's arterial properties is important for predicting likelihood of stent success. This in silico tool has the potential to support clinical decision-making and guide the development and evaluation of dedicated stents for personalised treatment of vasospasm.

Figures (10)

• Figure 1: Split of deformation gradient $\mathbf{F}$ into growth ($\mathbf{F^g}$) and elastic ($\mathbf{F^e}$ ) parts, and corresponding states of constituent stretches in reference, intermediate and loaded configurations. *Collagen stretch is actually a distribution of values, but is shown here as a single value for simplicity.
• Figure 2: Active component of the stress response of vascular smooth muscle cells as a function of their stretch (solid curve). The dashed line corresponds to VSMC homeostatic stretch: $\lambda_{M}=\lambda_{M}^{h}=1.15$.
• Figure 3: Axial and radial views of VSMC stretch $\lambda_M$ distribution at three representative stages of the simulation: unloaded geometry, pre-vasospasm and vasospasm. Following loading from the stress-free configuration, VSMCs remodel until their stretch equals the homeostatic value uniformly across the geometry. Since remodelling to maintain homeostatic stretch continues during vasospasm, the uniform strain field remains in this phase as well.
• Figure 4: Axial and radial views of VSMC recruitment stretch $\lambda_M^R$ distribution at three representative stages of the simulation: unloaded geometry, pre-vasospasm state and vasospasm. Following loading, VSMCs remodel until their stretch equals the homeostatic value uniformly across the geometry, resulting in a radial gradient of the recruitment stretch. Following vasospasm, the new geometry requires a recruitment stretch distribution that varies both radially and axially.
• Figure 5: Identification of representative locations on vessel geometry for interpretation of results.