Intracranial aneurysm disease: novel modelling of inception and the microstructural adaption of collagen fabric
Keywords: elastin
intracranial aneurysm
collagen
cerebral aneurysm
strain
mathematical modelling
haemodynamics
stress

An intracranial aneurysm (IA) is a balloon-like focal lesion on the cerebral arterial wall. IAs are poorly understood, but are commonly considered to be a disease caused by multiple factors. Current interventional treatments are accompanied with risks. Given the low incidence of rupture, it would be ideal to only treat aneurysms identified with rupture risk. Numerical models of aneurysm development may provide insight into the disease mechanisms, and contribute to the prediction of disease progression. Better understanding of the disease aetiology will also guide clinical decision making.
Different hypotheses have been proposed on the influence of haemodynamic stimuli on IA inception. We investigate this influence by examining the haemodynamic stimuli of the 'pre-aneurysmal' vasculature in the locations of IA formation in 22 clinical cases. The 'pre aneurysmal' geometries are obtained by applying a novel numerical vessel reconstruction method on the aneurysmal geometries. This automated reconstruction method propagates a closed curve along the vessel skeleton using the local Frenet frames to smoothly morph the upstream boundary into the downstream boundary. We observe that locally elevated wall shear stress (WSS) and gradient oscillatory number (GON) are highly correlated with regions susceptible to sidewall IA formation, whilst haemodynamic indices associated with the oscillation of the WSS vectors have much lower correlations.
A common assumption made in the literature on arterial growth and remodelling (G&R;) is that the 'state of stretch' (denoted as the attachment stretch) at which collagen fibres are configured in the extracellular matrix (ECM) is assumed to be constant. This will lead to an unrealistically thickened arterial wall in modelling aneurysm evolution. We propose a novel 1D mathematical model of collagen microstructural adaption during IA evolution. We assume new collagen fibres are configured into the ECM in a state of attachment stretch distribution which can be temporally adaptive. We explicitly define the functional form of this distribution and model its temporal adaption during IA evolution. This model is then implemented into two 3D models of IA evolution: a solid structural model and Fluid-Solid-Growth (FSG) model. In the solid structural model, the artery is modelled as a two-layer, nonlinear elastic cylindrical membrane using a physiologically realistic constitutive model. The development of the aneurysm is considered as a consequence of the growth and remodelling of its material constituents: elastinous constituents are prescribed to degrade in a localised circular patch; collagen concentration and recruitment variables enable the growth and remodelling of collagen fabric to be simulated; adaption of the attachment stretch distribution is confined locally within the region of aneurysm evolution. The sophisticated solid model predicts stabilised saccular IAs with realistic sizes and wall thicknesses. The FSG model simulates the IA development on patient-specific vasculature: the updated 3D solid structural model is integrated into a patient-specific geometry of the vasculature and the growth and remodelling of the constituents is now linked to the local haemodynamic stimuli obtained from a rigid-wall computational fluid dynamics analysis. Adaption of the attachment stretch distribution is also confined locally in the region where the constituents degrade. An illustrative case of IA development on patient specific geometry is provided.
Based on our study, we conclude that incorporating the adaption of attachment stretch distribution is necessary to simulate IA evolution with physiological evolving wall thicknesses. However, how vascular cells confine this adaption heterogeneously needs further investigation. Improved understanding and modelling of the biology of the arterial wall is needed for more sophisticated models of aneurysm evolution. It will in turn assist in understanding the aetiology of IA formation. Ultimately we hope to have a patient-specific growth model that could have the potential be used to assist diagnostic decisions.