成对小动脉与小静脉之间氧气逆流交换的数学模型。
A Mathematical Model of Countercurrent Exchange of Oxygen Between Paired Arterioles and Venules.
作者信息
Sharan Maithili, Popel Aleksander S
机构信息
Department of Biomedical Engineering, The Johns Hopkins University, School of Medicine, Baltimore, Maryland 21205.
出版信息
Math Biosci. 1988 Sep;91(1):17-34. doi: 10.1016/0025-5564(88)90022-3.
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 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 are found to be small. Examples are presented where the model predicts significant gradients of venular when the blood flow rate in the venule is several times smaller than that in the arteriole.
摘要
建立了一个数学模型，用于描述成对的小动脉和小静脉之间氧气的扩散逆流交换。通过在血管入口处将非线性氧合血红蛋白解离曲线线性化，得到了该问题的闭式解。将闭式解与非线性问题的相应数值解进行了比较。在正常情况下，发现小静脉的纵向梯度很小。给出了一些例子，当小静脉中的血流速度比小动脉中的血流速度小几倍时，该模型预测小静脉会有显著的梯度。
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