A two layer model for the blood oxygenation in pulmonary capillaries is proposed. The model consists of a core of erythrocytes surrounded by a symmetrically placed plasma layer. The governing equations in the core describe the free molecular diffusion, convection, and facilitated diffusion due to the presence of haemoglobin. The corresponding equations in the plasma layer are based on the free molecular diffusion and the convective effect of the blood. According to the axial train model for the blood flow proposed by Whitmore (1967), the core will move with a uniform velocity whereas flow in the plasma layer will be fully developed. The resulting system of nonlinear partial differential equations is solved numerically. A fixed point iterative technique is used to deal with the nonlinearities. The distance traversed by the blood before getting fully oxygenated is computed. It is shown that the concentration of O2 increases continuously along the length of the capillary for a given ratio of core radius to capillary radius. It is found that the rate of oxygenation increases as the core to capillary ratio decreases. The equilibration length increases with a heterogeneous model in comparison to that in a homogeneous model. The effect of capillary diameters and core radii on the rate of oxygenation has also been examined.
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November 1990
Research Papers
A Numerical Model for Studying the Effect of Plasma Layer on the Process of Blood Oxygenation in the Pulmonary Capillaries
Maithili Sharan,
Maithili Sharan
Centre for Atmospheric Sciences, Indian Institute of Technology, Delhi, India, Hauz Khas, New Delhi-110016
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M. P. Singh,
M. P. Singh
Centre for Atmospheric Sciences, Indian Institute of Technology, Delhi, India, Hauz Khas, New Delhi-110016
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A. Aminataei
A. Aminataei
Centre for Atmospheric Sciences, Indian Institute of Technology, Delhi, India, Hauz Khas, New Delhi-110016
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Maithili Sharan
Centre for Atmospheric Sciences, Indian Institute of Technology, Delhi, India, Hauz Khas, New Delhi-110016
M. P. Singh
Centre for Atmospheric Sciences, Indian Institute of Technology, Delhi, India, Hauz Khas, New Delhi-110016
A. Aminataei
Centre for Atmospheric Sciences, Indian Institute of Technology, Delhi, India, Hauz Khas, New Delhi-110016
J Biomech Eng. Nov 1990, 112(4): 457-463 (7 pages)
Published Online: November 1, 1990
Article history
Received:
March 9, 1989
Revised:
May 20, 1990
Online:
March 17, 2008
Citation
Sharan, M., Singh, M. P., and Aminataei, A. (November 1, 1990). "A Numerical Model for Studying the Effect of Plasma Layer on the Process of Blood Oxygenation in the Pulmonary Capillaries." ASME. J Biomech Eng. November 1990; 112(4): 457–463. https://doi.org/10.1115/1.2891211
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