A One-Dimensional Shear Thinning Model For Cerebral Blood Flow

Samuel Lieber, Cell Biology & Molecular Medicine, University of Medicine & Dentistry of New Jersey

Cerebral blood flow (CBF) is normally autoregulated to preserve baseline levels of flow and oxygen to the brain. However, under disease conditions CBF can be compromised, leading to impaired cerebration in patients. Accordingly, there is considerable interest and need for identifying methods by which CBF can be regulated under disease conditions. Previous work has shown that simple one-dimensional mathematical models are capable of explaining CBF auto regulation. These one-dimensional models assume that the blood is Newtonian and that the blood’s viscosity is constant, and disregard shear thinning effects. However, shear thinning effects are critical in disease conditions where low flow rates cause the blood viscosity to change with the shear rate. We derive an improved one-dimensional model of CBF using a viscoelastic shear thinning model. This modification promises to predict and explain CBF auto regulation under both normal and diseased conditions.