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. The
first task consists in describing nonlinear effects of the oxygen transfer under normal
conditions. We also include the possible diffusion limitation in oxygen transfer observed
in extreme regimes involving parameters such as alveolar and venous blood oxygen partial
pressures, capillary volume, diffusing capacity of the membrane, oxygen binding by
hemoglobin and transit time of the red blood cells in the capillaries. The second task
consists in discussing the oxygen concentration heterogeneity along the path length in the
acinus. Method. A lumped mechanical model is considered: a double-balloon
model is built upon physiological properties such as resistance of the branches connecting
alveoli to the outside air, and elastic properties of the surrounding medium. Then, we
focus on oxygen transfer: while the classical [F.J. Roughton and R.E. Forster, J.
Appl. Physiol. 11 (1957) 290–302]. approach accounts for the
reaction rate with hemoglobin by means of an extra resistance between alveolar air and
blood, we propose an alternate description. Under normal conditions, the Hill’s saturation
curve simply quantifies the net oxygen transfer during the time that venous blood stays in
the close neighborhood of alveoli (transit time). Under degraded and/or exercise
conditions (impaired alveolar-capillary membrane, reduced transit time, high altitude)
diffusion limitation of oxygen transfer is accounted for by means of the nonlinear
equation representing the evolution of oxygen partial pressure in the plasma during the
transit time. Finally, a one-dimensional model is proposed to investigate the effects of
longitudinal heterogeneity of oxygen concentration in the respiratory tract during the
ventilation cycle, including previous considerations on oxygen transfer. Results.
This integrated approach allows us to recover the right orders of magnitudes in
terms of oxygen transfer, at rest or exercise, by using well-documented data, without any
parameter tuning or curve fitting procedure. The diffusing capacity of the
alveolar-capillary membrane does not affect the oxygen transfer rate in the normal regime
but, as it decreases (e.g. because of emphysema) below a critical value,
it becomes a significant parameter. The one-dimensional model allows to investigate the
screening phenomenon, i.e. the possibility that oxygen transfer might be
significantly affected by the fact that the exchange area in the peripheral acinus poorly
participates to oxygen transfer at rest, thereby providing a natural reserve of transfer
capacity for exercise condition. We do not recover this effect: in particular we show
that, at rest, although the oxygen concentration is slightly smaller in terminal alveoli,
transfer mainly occurs in the acinar periphery.