Modeling of blood flow in the human brain

Under normal conditions, Cerebral Blood Flow (CBF) is related to the metabolism of the cerebral tissue. Three factors that contribute significantly to the regulation of CBF include the carbon dioxide and hydrogen ion concentration, oxygen deficiency and the level of cerebral activity. These regulatory mechanisms ensure a constant CBF of 50 to 55 ml per 100g of brain per minute for mean arterial blood pressure between 60 - 180 mm Hg. Under severe conditions when the autoregulatory mechanism fails to compensate, sympathetic nervous system constricts the large and intermediate sized arteries and prevents very high pressure from ever reaching the smaller blood vessels, preventing the occurrence of vascular hemorrhage. Several invasive and non-invasive techniques such as pressure and thermoelectric effect sensors to Positron Emission Tomography (PET) and magnetic resonance imaging (MRI) based profusion techniques have been used to quantify CBF. However, the effects of the non-Newtonian properties of blood, i.e., shear thinning and viscoelasticity, can have a significant influence on the distribution of CBF in the human brain and are poorly understood. The aim of this work is to quantify the role played by the non-Newtonian nature of blood on CBF. We have developed mathematical models of CBF that use direct numerical simulations (DNS) for the individual capillaries along with the experimental data in a one-dimensional model to determine the flow rate and the methods for regulating CBF. The model also allows us to determine which regions of the brain would be affected more severely under these conditions.