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. © 1989.
Sharan, M., & Popel, A. S. (1989). A mathematical model of countercurrent exchange of oxygen between paired arterioles and venules. Mathematical and Computer Modelling, 12(9), 1181. https://doi.org/10.1016/0895-7177(89)90254-9