Department of Mathematics, University of Kashmir, Srinagar, India.
Comput Methods Biomech Biomed Engin. 2023 Feb;26(2):199-208. doi: 10.1080/10255842.2022.2053115. Epub 2022 Mar 24.
Human body has a great ability to maintain homeostasis and the respiratory system plays a pivotal role in physiological processes. In this paper, a mathematical model of oxygen and carbon dioxide transport in the human body through capillary and tissue system has been formulated. The model is given by four ordinary differential equations for the oxygen and carbon dioxide transport, two equations for the capillary and other two for the tissue. An analytic approach based on Taylor's series method has been presented in this paper to obtain a computable approximate solution of the differential equation to model the oxygen and carbon dioxide diffusion in a spherical tissue. The concentration profiles at the capillary and tissue regions has been estimated in relation with partial pressure as the main driving force. The results are in agreement with the literature data those arrived at by Whiteley et al. (2005). The results obtained may help bio-medical sciences to deal with hypoxia and other respiratory ailments faced by the people living at high altitudes. Moreover, facilitated diffusion due to haemoglobin has been presented.
人体具有维持内稳态的巨大能力，呼吸系统在生理过程中起着关键作用。本文通过毛细管和组织系统建立了一个人体氧气和二氧化碳传输的数学模型。该模型由四个描述氧气和二氧化碳传输的常微分方程组成，两个描述毛细管的方程和另外两个描述组织的方程。本文提出了一种基于泰勒级数法的解析方法，以获得可计算的微分方程近似解，从而对球形组织中的氧气和二氧化碳扩散进行建模。根据主要驱动力分压，估算了在毛细管和组织区域的浓度分布。结果与文献数据（Whiteley 等人，2005 年）一致。所得到的结果可能有助于生物医学科学应对生活在高海拔地区的人们面临的缺氧和其他呼吸疾病。此外，还介绍了由于血红蛋白而促进的扩散。
