A dynamic multiscale model of cerebral blood flow and autoregulation in the microvasculature

Abstract

Models of the micro-circulatory blood flow in the brain can play a key role in understanding the variety of cerebrovascular diseases that occur in the microvasculature. These conditions are often linked to structural modifications in the vessel network, alterations in the blood flow patterns, as well as impairment in the autoregulatory response, all of which are pathological changes that the model should be able to address if it were to have any clinical value. Furthermore, if the model results were to be validated against clinical MRI data, the model simulations need to be computationally feasible when used on networks on the scale of an MRI voxel. This requires some form of an upscaling approach that bypasses the need for an explicit architectural representation of the whole network while maintaining the relevant anatomical connections. To this end, we developed a hybrid multiscale model of blood flow and autoregulation that traces the dynamic changes in blood flow, volume, and pressure in the cortical microvasculature, where the discrete topology of the penetrating vessels is preserved, and these are then appropriately coupled to the homogenised capillary bed by a spatially distributing support function in the terminal endings. In contrast to the other multiscale models, the model developed here accounts for the dynamic physiological phenomena of the blood flow and the autoregulation processes in the microvessels. We show how the adaptive meshing scheme for the capillary bed developed in this study can be employed to ensure a scale-invariant coupling formulation and numerically accurate simulations, all without compromising the computational feasibility of the model. A statistically accurate cortical network on the scale of an MRI voxel is generated, and the model parameter values are calibrated using a Monte Carlo Filtering analysis to ensure that the model results are physiologically informed. The model is found to be able to capture the steep pressure gradients that have been reported to occur at coupling interfaces. Furthermore, in response to an upstream pressure drop, the network is found to be able to recover cerebral blood flow while exhibiting the characteristic autoregulatory behaviour in terms of changes in vessel calibre and the biphasic flow response. Overall, the model developed here offers a high-quality characterisation of dynamic flow and autoregulation in the microvasculature at improved computational efficiency and lays the ground for whole-brain dynamic simulations.