Mathematical and Computational Modelling of Arterial Mechanobiology: Application to Cerebral Vasospasm

Cerebral vasospasm is a prolonged acute constriction of a cerebral artery and an aftermath of subarachnoid haemorrhage. It is the leading cause of death in patients who survive hospitalisation due to the decrease in blood, and therefore oxygen, supply to the brain. Despite its prevalence, its complex multifactorial pathophysiology make it a still poorly understood disease. Recent results concerning the treatment strategy, i.e. the success of stent retrievers in some cases, has challenged the current understanding of the disease. Stents represent a safer option compared to the traditional treatment via balloon angioplasty and thus there is motivation to further understand the disease with the aim of personalising the treatment strategy for individual patients. A novel hypothesis is formulated on the pathophysiology of cerebral vasospasm and tested in a mathematical model. The artery is represented as a non-linearly elastic cylindrical membrane and a constrained mixture approach is adopted which includes elastin, collagen and vascular smooth muscle cells. The key interest is in the study of how the pressure-diameter curve changes from health to vasospasm and predict the magnitude of pressure that an interventional device should apply in order to resolve the disease. The success criterion for a device is a strain-based damage criterion for the smooth muscle cells. The predictions of the model are consistent with published clinical observations. The membrane model assumes a uniform strain-field across the arterial wall thickness: this is reasonable for a healthy vessel but likely to no longer be true in moderate to severe cases of vasospasm. The model is therefore integrated into a finite element framework which has been successfully used to model aneurysm growth and remodelling with anisotropic volumetric growth. The framework is extended to accommodate a more realistic material model of collagen to include a fibre waviness distribution and remodeling, a material model for vascular smooth muscle cells with contractile active response and remodelling, and a damage model. Analogously to the mathematical model, the evolution of the pressure-diameter curves is studied and predictions of the magnitude of pressure required for effective treatment are obtained and compared to the mathematical model. A sophistication is finally included to account for the effect of the growth and remodelling of collagen on the development of vasospasm and its treatment, which had initially be assumed negligible. The results suggest that collagen growth and remodelling can play a significant role and should be included in models that aim at providing clinical support in the treatment decision. The work presented in this thesis is an illustration of how mathematical and computational modelling can be a useful tool for hypothesis testing in problems of clinical relevance. There is still however a lack of experimental data to inform the model: this holds not only for cerebral vasospasm in particular, but also for general knowledge of cell mechanobiology, i.e. the interaction between the mechanical environment of the cell and its biological function. The hope is that computational modelling motivates further research into these topics and offers suggestions regarding which research questions to address.