Patient specific cerebral arterial blood flow modelling

Abstract

Many cerebrovascular diseases are complex and treatment is often based on experience and relatively small studies. A mathematical blood flow model might aid in better treatment decisions and might lead to more personalised healthcare. In this thesis we set out to develop a clinical applicable cerebrovascular blood flow model. Initially we developed a complex 3D blood flow model which was tested in two retrospective patients treated by proximal and distal occlusion for complex cerebral aneurysms. Results matched well with follow-up data. This pilot study confirms the potential of a complex 3D model. However, it also showed the complexity in these 3D models which limits clinical applicability. Hence, we set out to develop a simplified model. In a narrative literature survey, we identified important causes that might hamper development of such a model and presented possible solutions. One of such difficulties lies in distal boundary conditions (peripheral resistance). One solution to estimate distal boundary conditions is the usage of branching patterns to generate structured arterial trees which can serve as replacing resistances. However, data on branching patterns in the cerebral circulation were scarce. Hence, we validated and used a method based on 7T MRI and 9.4T MRI scanning of plastic cerebral arterial casts to acquire cerebrovascular branching patterns. Additionally, manual measurements were used. The branching patterns showed a broad distribution. Further, it was confirmed that on average the cerebral arterial tree complies to the principle of minimum work as defined in Murray’s Law. A simplified mathematical blood flow model of the cerebral arterial circulation was produced based on linear Hagen-Poiseuille equations. Blood pressure cuff measurement served as a simple accessible proximal boundary condition. A semi-automatic method was used to generate patient-specific morphology of the larger cerebral arteries based on MRI data. Distal boundary conditions were based on branching patterns combined with a simplified autoregulatory model. Calculated flow values were compared to phase-contrast MRI based measurements acquired using the Noninvasive Optimal Vessel Analysis (NOVA) software. Data of 10 healthy subjects was used to optimize parameters of distal boundary conditions. Data of 20 additional healthy subjects were used to compare calculated and NOVA measured flow to validate the model. The model showed to be accurate in a range that might proof feasible for clinical use. For some specific purposes more complex 3D models are likely required, especially when information on flow patterns and wall stresses are needed. However, based on the current thesis and literature, simplified models show great potential. Hence, studies developing a patient-specific blood flow model for a specific clinical question should whenever possible first consider the usage of such a simplified model.