The non-Newtonian properties of blood, i.e., shear thinning and viscoelasticity, can have a significant influence on the distribution of Cerebral Blood Flow (CBF) in the human brain. The aim of this work is to quantify the role played by the non-Newtonian nature of blood. Under normal conditions, CBF is autoregulated to maintain baseline levels of flow and oxygen to the brain. However, in patients suffering from heart failure (HF), Stroke, or Arteriovenous malformation (AVM), the pressure in afferent vessels varies from the normal range within which the regulatory mechanisms can ensure a constant cerebral flow rate, leading to impaired cerebration in patients. It has been reported that the change in the flow rate is more significant in certain regions of the brain than others, and that this might be relevant to the pathophysiological symptoms exhibited in these patients. We have developed mathematical models of CBF under normal and the above disease conditions 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 relatively more severely under these conditions.
A one-dimensional model of viscous blood flow in an elastic vessel
