A mathematical model of countercurrent exchange of oxygen between paired arterioles and venules

Maithili Sharan; Aleksander S. Popel

doi:10.1016/0025-5564(88)90022-3

A mathematical model of countercurrent exchange of oxygen between paired arterioles and venules

Maithili Sharan, Aleksander S. Popel

School of Medicine

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

A mathematical model is formulated for diffusive countercurrent exchange of oxygen between paired arterioles and venules. A closed form solution of the problem is obtained by linearizing the nonlinear oxyhemoglobin dissociation curve at the inlet P_O₂ in the vessel. The closed form solution is compared with the corresponding numerical solution of the nonlinear problem. Under normal conditions, longitudinal gradients of venular P_O₂ are found to be small. Examples are presented where the model predicts significant gradients of Venular P_O₂ when the blood flow rate in the venule is several times smaller than that in the arteriole.

Original language	English (US)
Pages (from-to)	17-34
Number of pages	18
Journal	Mathematical Biosciences
Volume	91
Issue number	1
DOIs	https://doi.org/10.1016/0025-5564(88)90022-3
State	Published - Sep 1988

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Biochemistry, Genetics and Molecular Biology(all)
Immunology and Microbiology(all)
Agricultural and Biological Sciences(all)
Applied Mathematics

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10.1016/0025-5564(88)90022-3

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abstract = "A mathematical model is formulated for diffusive countercurrent exchange of oxygen between paired arterioles and venules. A closed form solution of the problem is obtained by linearizing the nonlinear oxyhemoglobin dissociation curve at the inlet PO2 in the vessel. The closed form solution is compared with the corresponding numerical solution of the nonlinear problem. Under normal conditions, longitudinal gradients of venular PO2 are found to be small. Examples are presented where the model predicts significant gradients of Venular PO2 when the blood flow rate in the venule is several times smaller than that in the arteriole.",

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AB - A mathematical model is formulated for diffusive countercurrent exchange of oxygen between paired arterioles and venules. A closed form solution of the problem is obtained by linearizing the nonlinear oxyhemoglobin dissociation curve at the inlet PO2 in the vessel. The closed form solution is compared with the corresponding numerical solution of the nonlinear problem. Under normal conditions, longitudinal gradients of venular PO2 are found to be small. Examples are presented where the model predicts significant gradients of Venular PO2 when the blood flow rate in the venule is several times smaller than that in the arteriole.

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A mathematical model of countercurrent exchange of oxygen between paired arterioles and venules

Abstract

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