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A mathematical model for the process of gas exchange in lung capillaries using nth order one-step kinetics of oxygen uptake by haemoglobin

Published online by Cambridge University Press:  17 February 2009

Maithili Sharan ,
M. P. Singh  and
Balbir Singh
Maithili Sharan
Affiliation:
Department of Mathematics, Indian Institute of Technology, New Delhi-110016, India.
M. P. Singh
Affiliation:
Department of Mathematics, Indian Institute of Technology, New Delhi-110016, India.
Balbir Singh
Affiliation:
Department of Mathematics, Indian Institute of Technology, New Delhi-110016, India.
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Abstract

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A mathematical model is developed for the process of gas exchange in lung capillaries, taking into account the transport mechanisms of molecular diffusion and the facilitated diffusion of the species due to haemoglobin. We have assumed here equilibrium conditions which enable us to neglect advection effects. The nth order one-step kinetics of oxygen uptake by haemoglobin, proposed by Sharan and Singh [8], have been incorporated. The solution of this coupled nonlinear facilitated diffusion-reaction problem together with the physiologically-relevant boundary conditions is obtained in the closed form.

It is found that about 97.15% of total haemoglobin has combined with oxygen and 2.85% free pigment is left, which is present as carbaminohaemoglobin, met haemoglobin, carboxy haemoglobin etc. It is also shown that the percentage of free haemoglobin at a given PO2 and PCO2 is independent of total haemoglobin content present in the blood.

The well-known Hill's empirical relation is deduced from our solution. The results obtained from our model, based on physical formulation, are in good agreement with the documented data [6] and those computed from the Kelman [3] empirical relation.

Type
Research Article
Information
The ANZIAM Journal , Volume 30 , Issue 2 , October 1988 , pp. 203 - 213
Copyright
Copyright © Australian Mathematical Society 1988

References

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