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

Maithili Sharan, Aleksander S. Popel

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)1181
Number of pages1
JournalMathematical and Computer Modelling
Volume12
Issue number9
DOIs
StatePublished - 1989

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computer Science Applications

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