Towards a large-scale simulation of blood flow in brain microcirculation

The human brain microcirculation has a multiscale architecture. At large scale, arteriolar and venular trees supply the cerebral cortex with blood carrying oxygen and nutrients, and drain the metabolic waste. At small scale, the capillary vessels constitute a mesh-like network that connects the larger trees. They are embedded in the cerebral tissue and control most of the mass transfer toward the neurons. For the last decades, network approaches have significantly advanced our understanding of blood flow, mass transport and regulation mechanisms. However, because of the huge number of capillaries, these approaches cannot be used in large cortical volumes, which are clinically relevant. Here, we develop a hybrid approach for modeling blood flow by replacing the dense and space-filling capillary bed by a porous medium, defined by effective properties (e.g. permeability) at coarser scale. The arteriolar and venular networks are still represented by a network approach because of their quasifractal structure. To couple both frameworks, we use an approach similar to Peaceman, SPE/AIME, 1978. This model is based on an analytical approximation describing the strong pressure gradients building up in the vicinity of the arterio- and venulo-capillary coupling points. Fig. 1 compares the results obtained from the present approach (black) with those from a standard network approach (orange), showing a very good agreement. In contrast, not taking into account the local pressure gradients, i.e. using a simple condition of pressure continuity at coupling points (gray) results in large errors. The hybrid approach also yields a huge gain in computation time (several orders of magnitude for the network in Fig. 1). It has further been implemented in a code designed for high performance computing. Assuming that sufficient skeletonized anatomical data (arterioles and venules) will be available in the future (Errico, Nature, 2015), this approach paves the way for simulating blood flow and mass transfers in the whole brain, with perspectives for absolute blood flow quantification in perfusion imaging.