Multi-scale modelling of the microvasculature in the human cerebral cortex

Cerebrovascular diseases are by far the largest causes of death in the UK, as well as one of the leading causes of adult disability. The brain’s healthy function depends on a steady supply of oxygen, delivered through the microvasculature. Cerebrovascular diseases, such as stroke and dementia, can interrupt the transport of blood (and hence oxygen) rapidly, or over a prolonged period of time. An interruption in flow can lead to ischaemia, with prolonged interruptions leading to tissue death and eventual brain damage. The microvasculature plays a key role in the transport of oxygen and nutrients to brain tissue; however, its role in diseases such as dementia is poorly understood, primarily due to the inability of current clinical imaging techniques to resolve microvessels, and due to the complexity of the underlying microvasculature. Therefore, in order to understand cerebrovascular diseases, it is necessary to be able to resolve and understand the microvasculature. In particular, generating large-scale models of the human microvasculature that can be linked back to contemporary clinical imaging is important in helping plug the current imaging gap that exists. A novel statistical model is proposed here that generates such large-scale models efficiently. Homogenization theory is used to generate a porous continuum capillary bed (characterised by its permeability) that allows for the efficient scaling up of the microvasculature. A novel order-based density-filling algorithm is then developed which generates morphologically accurate penetrating arterioles and venules, also demonstrating that the topology of the vessels only has a minor influence on CBF compared to diameter. Finally, the capillary bed and penetrating vessels are coupled into a large voxel-sized model of the microvasculature from which pressure and flux variations through the voxel can be analysed. A decoupling of the pressure and flux, as well as a layering of flow, was observed within the voxel, driven by the topology of the penetrating vessels. Micro-infarctions were also simulated, demonstrating the large local effects they have on the pressure and flux, whilst only causing a minor drop in CBF within the voxel.