Mathematical Modeling of the Steady-State Behavior of Nitric Oxide in Brain

Nitric oxide (NO) is a small diffusible molecule that plays an important role in brain’s signalling processes and regulation of cerebral blood flow and pressure. While most of the NO production is achieved through various chemical reactions taking place in the neurons, endothelial cells, and red blood cells, only the endothelial NO is activated by the shear stress at the blood-endothelium interface. NO is removed from the brain by blood’s hemoglobin and through diffusion and other chemical processes. Given its relevance to brain functions, numerous studies on NO exist in the literature. The majority of the mathematical models of NO biotransport are diffusion-reaction equations predicting the spatio-temporal distribution of NO concentration either inside or outside the blood vessels, and do not account for the endothelial NO production through mechanotrasduction. In this paper we propose a mathematical model of the steady-state behavior of NO in the brain that links the NO synthesis and inactivation from inside and outside a cerebral arteriole and the blood flow. The blood flow is assumed to be a Poiseuille flow, and we use two models of blood: viscous Newtonian and non-local non-Newtonian fluids. The model is used to study through numerical simulations the effects of the cerebral blood pressure on the NO concentration.