Modeling NO Biotransport in Brain Using a Space-Fractional Reaction-Diffusion Equation

Abstract

Nitric oxide (NO) is a small gaseous molecule that is involved in some critical biochemical processes in the body such as the regulation of cerebral blood flow and pressure. Infection and inflammatory processes such as those caused by COVID-19 produce a disequilibrium in the NO bioavailability and/or a delay in the interactions of NO with other molecules contributing to the onset and evolution of cardiocerebrovascular diseases. A link between the SARS-CoV-2 virus and NO is introduced. Recent experimental observations of intracellular transport of metabolites in the brain and the NO trapping inside endothelial microparticles (EMPs) suggest the possibility of anomalous diffusion of NO, which may be enhanced by disease processes. A novel space-fractional reaction-diffusion equation to model NO biotransport in the brain is further proposed. The model incorporates the production of NO by synthesis in neurons and by mechanotransduction in the endothelial cells, and the loss of NO due to its reaction with superoxide and interaction with hemoglobin. The anomalous diffusion is modeled using a generalized Fick’s law that involves spatial fractional order derivatives. The predictive ability of the proposed model is investigated through numerical simulations. The implications of the methodology for COVID-19 outlined in the section “Discussion” are purely exploratory.