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Modeling of the oxygen transfer in the respiratory process∗

Published online by Cambridge University Press:  13 June 2013

Sébastien Martin  and
Bertrand Maury
Sébastien Martin
Affiliation:
INRIA Paris Rocquencourt, REO project – BP 105, 78153 Le Chesnay cedex, France Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, 91405 Orsay cedex, France.. bertrand.maury@math.u-psud.fr
Bertrand Maury
Affiliation:
Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, 91405 Orsay cedex, France.. bertrand.maury@math.u-psud.fr
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Abstract

In this article, we propose an integrated model for oxygen transfer into the blood,coupled with a lumped mechanical model for the ventilation process. Objectives.We aim at investigating oxygen transfer into the blood at rest or exercise. Thefirst task consists in describing nonlinear effects of the oxygen transfer under normalconditions. We also include the possible diffusion limitation in oxygen transfer observedin extreme regimes involving parameters such as alveolar and venous blood oxygen partialpressures, capillary volume, diffusing capacity of the membrane, oxygen binding byhemoglobin and transit time of the red blood cells in the capillaries. The second taskconsists in discussing the oxygen concentration heterogeneity along the path length in theacinus. Method. A lumped mechanical model is considered: a double-balloonmodel is built upon physiological properties such as resistance of the branches connectingalveoli to the outside air, and elastic properties of the surrounding medium. Then, wefocus on oxygen transfer: while the classical [F.J. Roughton and R.E. Forster, J.Appl. Physiol. 11 (1957) 290–302]. approach accounts for thereaction rate with hemoglobin by means of an extra resistance between alveolar air andblood, we propose an alternate description. Under normal conditions, the Hill’s saturationcurve simply quantifies the net oxygen transfer during the time that venous blood stays inthe close neighborhood of alveoli (transit time). Under degraded and/or exerciseconditions (impaired alveolar-capillary membrane, reduced transit time, high altitude)diffusion limitation of oxygen transfer is accounted for by means of the nonlinearequation representing the evolution of oxygen partial pressure in the plasma during thetransit time. Finally, a one-dimensional model is proposed to investigate the effects oflongitudinal heterogeneity of oxygen concentration in the respiratory tract during theventilation cycle, including previous considerations on oxygen transfer. Results.This integrated approach allows us to recover the right orders of magnitudes interms of oxygen transfer, at rest or exercise, by using well-documented data, without anyparameter tuning or curve fitting procedure. The diffusing capacity of thealveolar-capillary membrane does not affect the oxygen transfer rate in the normal regimebut, as it decreases (e.g. because of emphysema) below a critical value,it becomes a significant parameter. The one-dimensional model allows to investigate thescreening phenomenon, i.e. the possibility that oxygen transfer might besignificantly affected by the fact that the exchange area in the peripheral acinus poorlyparticipates to oxygen transfer at rest, thereby providing a natural reserve of transfercapacity for exercise condition. We do not recover this effect: in particular we showthat, at rest, although the oxygen concentration is slightly smaller in terminal alveoli,transfer mainly occurs in the acinar periphery.

Keywords

Oxygen transferventilationlung diffusion capacityadvection-diffusion equation
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 4: Direct and inverse modeling of the cardiovascular and respiratory systems , July 2013 , pp. 935 - 960
Copyright
© EDP Sciences, SMAI, 2013

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