Physiological Model of the Cerebrovascular System based on Supply and Demand Relationship between Arteries and Tissues

Image-based blood flow simulations have been studied over decades and are increasingly utilized in clinical practice to diagnose cardiovascular disease. Blood flow simulations, however, require physiological boundary conditions to simulate realistic blood flow and pressure. Traditionally, Murray's law has been used to assign boundary conditions for the cerebrovascular system but it is highly sensitive to the segmented geometry as flow is nonlinearly dependent on vessel caliber. We developed a physiological model of the cerebrovascular system by utilizing a supply-demand relationship between arteries and tissues. Perfusion territories and flows of major cerebral arteries are computed using a Voronoi tessellation of segmented arteries in proximity to the tissues. The model was validated with 40 healthy patients under the age of 50 and cerebral blood flow and perfusion territories of major cerebral arteries were compared against the PC-MRI data of similar age groups from literature. The model estimates blood flows and perfusion territories realistically and is more robust to the changes in vessel caliber compared to Murray's law. The model will be validated against actual patient measurements and utilized as a boundary condition of the cerebrovascular system to diagnose cerebrovascular disease.