A mathematical model of countercurrent exchange of oxygen between paired arterioles and venules (Q1105501)

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 \(P_{O_ 2}\) 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 \(P_{O_ 2}\) are found to be small. Examples are presented where the model predicts significant gradients of venular \(P_{O_ 2}\) when the blood flow rate in the venule is several times smaller than that in the arteriole.