TY - GEN

T1 - Mathematical Modeling of the Steady-State Behavior of Nitric Oxide in Brain

AU - Drapaca, Corina S.

AU - Tamis, Andrew

N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-030-63591-6_47

DO - 10.1007/978-3-030-63591-6_47

M3 - Conference contribution

AN - SCOPUS:85115138309

SN - 9783030635909

T3 - Springer Proceedings in Mathematics and Statistics

SP - 511

EP - 520

BT - Recent Developments in Mathematical, Statistical and Computational Sciences - The V AMMCS International Conference, 2019

A2 - Kilgour, D. Marc

A2 - Kunze, Herb

A2 - Makarov, Roman

A2 - Melnik, Roderick

A2 - Wang, Xu

PB - Springer

T2 - International Conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2019

Y2 - 18 August 2019 through 23 August 2019

ER -