The microvasculature plays a crucial role in the perfusion of blood through cerebral tissue. Current models of the cerebral microvasculature are discrete, and hence only able to model the perfusion over small voxel sizes before becoming computationally prohibitive. Larger models are required to provide comparisons and validation against imaging data. In this work, multi-scale homogenization methods were employed to develop continuum models of blood flow in a capillary network model of the human cortex. Homogenization of the local scale blood flow equations produced an averaged form of Darcy׳s law, with the permeability tensor encapsulating the capillary bed topology. A statistically accurate network model of the human cortex microvasculature was adapted to impose periodicity, and the elements of the permeability tensor calculated over a range of voxel sizes. The permeability tensor was found to converge to an effective permeability as voxel size increased. This converged permeability tensor was isotropic, reflecting the mesh-like structure of the cerebral microvasculature, with off-diagonal terms normally distributed about zero. A representative elementary volume of 375µm, with a standard deviation of 4.5% from the effective permeability, was determined. Using the converged permeability values, the cerebral blood flow was calculated to be around 55mLmin(-1)100g(-1), which is in very close agreement with experimental values. These results open up the possibility of future multi-scale modeling of the cerebral vascular network.

The advancement of ischaemic stroke treatment relies on resource-intensive experiments and clinical trials. In order to improve ischaemic stroke treatments, such as thrombolysis and thrombectomy, we target the development of computational tools for in silico trials which can partially replace these animal and human experiments with fast simulations. This study proposes a model that will serve as part of a predictive unit within an in silico clinical trial estimating patient outcome as a function of treatment. In particular, the present work aims at the development and evaluation of an organ-scale microcirculation model of the human brain for perfusion prediction. The model relies on a three-compartment porous continuum approach. Firstly, a fast and robust method is established to compute the anisotropic permeability tensors representing arterioles and venules. Secondly, vessel encoded arterial spin labelling magnetic resonance imaging and clustering are employed to create an anatomically accurate mapping between the microcirculation and large arteries by identifying superficial perfusion territories. Thirdly, the parameter space of the problem is reduced by analysing the governing equations and experimental data. Fourthly, a parameter optimization is conducted. Finally, simulations are performed with the tuned model to obtain perfusion maps corresponding to an open and an occluded (ischaemic stroke) scenario. The perfusion map in the occluded vessel scenario shows promising qualitative agreement with computed tomography images of a patient with ischaemic stroke caused by large vessel occlusion. The results highlight that in the case of vessel occlusion (i) identifying perfusion territories is essential to capture the location and extent of underperfused regions and (ii) anisotropic permeability tensors are required to give quantitatively realistic estimation of perfusion change. In the future, the model will be thoroughly validated against experiments.

An acute ischaemic stroke is due to the sudden blockage of an intracranial blood vessel by an embolized thrombus. In the context of setting up in silico trials for the treatment of acute ischaemic stroke, the effect of a stroke on perfusion and metabolism of brain tissue should be modelled to predict final infarcted brain tissue. This requires coupling of blood flow and tissue perfusion models. A one-dimensional intracranial blood flow model and a method to couple this to a brain tissue perfusion model for patient-specific simulations is presented. Image-based patient-specific data on the anatomy of the circle of Willis are combined with literature data and models for vessel anatomy not visible in the images, to create an extended model for each patient from the larger vessels down to the pial surface. The coupling between arterial blood flow and tissue perfusion occurs at the pial surface through the estimation of perfusion territories. The coupling method is able to accurately estimate perfusion territories. Finally, we argue that blood flow can be approximated as steady-state flow at the interface between arterial blood flow and tissue perfusion to reduce the cost of organ-scale simulations.

The effect of the microvasculature on observed clinical parameters, such as cerebral blood flow, is poorly understood. This is partly due to the gap between the vessels that can be individually imaged in humans and the microvasculature, meaning that mathematical models are required to understand the role of the microvasculature. As a result, a multi-scale model based on morphological data was developed here that is able to model large regions of the human microvasculature. From this model, a clear layering of flow (and 1-dimensional depth profiles) was observed within a voxel, with the flow in the microvasculature being driven predominantly by the geometry of the penetrating vessels. It also appears that the pressure and flow are decoupled, both in healthy vasculatures and in those where occlusions have occurred, again due to the topology of the penetrating vessels shunting flow between them. Occlusion of a penetrating arteriole resulted in a very high degree of overlap of blood pressure drop with experimentally observed cell death. However, drops in blood flow were far more widespread, providing additional support for the theory that pericyte controlled regulation on the capillary scale likely plays a large part in the perfusion of tissue post-occlusion.

Small CBF variations indicate that the topology of the penetrating vessels plays only a small part in the large regional variations of CBF seen in the brain. These results open up the possibility of efficient oxygen and blood flow simulations at MRI voxel scales which can be directly validated against MRI data.