Singh M P, Sharan M, Sud I
Centre for Atmospheric & Fluid Sciences, Indian Institute of Technology, New Delhi.
IMA J Math Appl Med Biol. 1988;5(4):281-301. doi: 10.1093/imammb/5.4.281.
A mathematical model is proposed to deal with the simultaneous transport of oxygen (O2) and carbon dioxide (CO2) in systemic capillaries and the surrounding tissue in a hyperbaric environment. The transport in the capillary region depends on molecular diffusion (radial as well as axial), the convective effect of the blood, and the saturation of haemoglobin with O2 and CO2. The corresponding equation in the tissue region describes the transport of the species due to radial and axial diffusion in the tissue and consumption of O2 in the metabolic process. The production of CO2 inside the tissue is incorporated through the respiratory quotient. The saturation of blood with O2 and CO2 have been approximated by linear functions to simulate the conditions of the hyperbaric environment. The resulting system of governing equations with the physiologically relevant boundary conditions is solved analytically. The concentration of O2 is shown to decrease from the core of the capillary to the tissue periphery, whereas the concentration of CO2 increases. It is shown that very little of the CO2 is transported radially. The location of the vulnerable point from the point of view of CO2 accumulation is found to be the corner (x = R2, z = L) situated at the periphery of the tissue near the venous end of the capillary. The accumulation of O2 and CO2 in the tissue is discussed in terms of various dimensionless parameters. It is found that the accumulation of CO2 increases whereas that of O2 decreases in the hyperbaric environment. Finally, it is surmised that one of the major causes of discomfort among divers could be excessive accumulation of CO2 in the tissue.
提出了一个数学模型，用于处理高压环境下全身毛细血管及周围组织中氧气（O₂）和二氧化碳（CO₂）的同时传输。毛细血管区域内的传输取决于分子扩散（径向和轴向）、血液的对流效应以及血红蛋白与O₂和CO₂的饱和度。组织区域内的相应方程描述了由于组织中的径向和轴向扩散以及代谢过程中O₂的消耗而导致的物质传输。组织内CO₂的产生通过呼吸商来体现。血液与O₂和CO₂的饱和度已通过线性函数进行近似，以模拟高压环境的条件。对所得的具有生理相关边界条件的控制方程组进行了解析求解。结果表明，O₂的浓度从毛细血管核心向组织周边降低，而CO₂的浓度则升高。结果显示，极少的CO₂进行径向传输。从CO₂积累的角度来看，易损点位于毛细血管静脉端附近组织周边的角落（x = R₂，z = L）。根据各种无量纲参数讨论了组织中O₂和CO₂的积累情况。研究发现，在高压环境下，CO₂的积累增加，而O₂的积累减少。最后推测，潜水员不适的主要原因之一可能是组织中CO₂的过度积累。
