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

Corina S. Drapaca, Andrew Tamis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publicationRecent Developments in Mathematical, Statistical and Computational Sciences - The V AMMCS International Conference, 2019
EditorsD. Marc Kilgour, Herb Kunze, Roman Makarov, Roderick Melnik, Xu Wang
PublisherSpringer
Pages511-520
Number of pages10
ISBN (Print)9783030635909
DOIs
StatePublished - 2021
EventInternational Conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2019 - Waterloo, Canada
Duration: Aug 18 2019Aug 23 2019

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume343
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2019
Country/TerritoryCanada
CityWaterloo
Period8/18/198/23/19

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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