A Theoretical Investigation of the Impact of Blood-Endothelium Mechanical Interactions on the Cerebral Nitric Oxide Biotransport

Abstract

Cerebral nitric oxide (NO), a small diffusive molecule, plays a critical role in brain’s functionality. More precisely, NO acts as a neuro-glial-vascular messenger that aids various chemo-mechanical communications among brain cells, blood, and cerebral vasculature. A disequilibrium in the NO bioavailability and/or a delay in (or lack of) interactions of NO with other molecules due to, for instance, inflammation can lead to the onset and progression of cerebrovascular diseases. Mathematical models of cerebral NO biotransport can provide essential insights into mechanisms of cerebrovascular diseases that may lead to the development of better preventive, diagnostic, and therapeutic methods. In this chapter, a two-dimensional space-fractional reaction-diffusion equation is proposed to model cerebral NO biotransport. The equation uses spatial fractional order derivatives to describe NO anomalous diffusion caused by the experimentally observed entrapping of NO in circulating endothelial microparticles. Cerebrovascular diseases cause an increase in the amount of endothelial microparticles and thus may lead to an enhanced anomalous diffusion of NO. The model includes the NO production by synthesis in neurons and by shear-induced mechanotransduction in the endothelial cells, and the loss of NO due to its interactions with superoxide and hemoglobin. The blood-endothelium mechanical interactions contribute to the shear-induced production of NO. Perturbation series solutions for the coupled blood-endothelium mechanics are adapted from literature for two cases: impermeable and permeable endothelium. Thus, the viscous dissipation at the blood-endothelium interface can be calculated analytically. The model generalizes a published one-dimensional model of cerebral NO anomalous diffusion in which the blood flow effect on the vascular wall was modeled as a mere oscillatory boundary condition. Numerical simulations suggest that for NO anomalous diffusion of fractional order 0.85 and in the presence of endothelial permeability and blood flow, the NO concentration at the endothelium increases in time which agrees with studies of stroke.