Abstract
This chapter addresses the question of oxygen transfer from air to blood. Section 5.1 gives a general overview of the phenomena on which transfer relies: diffusion through various barriers, and capturing of oxygen by hemoglobin. The notion of Diffusing Capacity is introduced. The next Section 5.2 presents a global model with a minimal set of variables: volume V (ventilation model in the spirit of Chapter 2), mean instantaneous oxygen concentration in the lungs, and oxygen partial pressure in the plasma. To account for heterogeneities of oxygen concentration, a one-dimensional model is proposed in Section 5.3: the longitudinal position, i.e. distance from the root of the tree (entrance of the trachea) is introduced as a space parameter, and an advection–diffusion equation is written. Section 5.4 is devoted to mathematical developments on the notion of diffusion capacity, which allow to perform fine investigations on the influence of geometrical parameters on this capacity. The concluding Section 5.5 discusses the different approaches that have been proposed to account for gas transfer, in particular the Forster and Roughton framework.
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Notes
- 1.
Most part of oxygen molecules are indeed captured by hemoglobin, but some will continue to flow freely in the plasma.
- 2.
This concentration scales like a number of units per unit volume, e.g. mol m–3, or mass per unit volume (kg m−3). Depending of this choice, the flux will be in number of units per unit area per second, i.e. mol m−2 s−1, or in mass per unit area per second, kg m−2 s−1. Note that, in the context of lung modeling, quantities of oxygen are often expressed as volumes. The volume associated to an amount of gas corresponds to the volume occupied by this amount of gas at Standard Temperature and Pressure (STP), even if the gas is diluted in a liquid. Thus, concentrations may happen in the literature to be scaled like volumes per unit volume (i.e. dimensionless quantities), and fluxes like m3 m−2 s−1 = m s−1, although a flux has nothing to do with a speed!
- 3.
Variations in time of this quantity will be considered later on, but at a much larger scale than τ b .
- 4.
Indeed, the concentration of oxygen potentially captured by hemoglobin is about 4 × 2.2 ≃ 9mmol L- 1, whereas the concentration in the plasma which balances alveolar partial pressure is 104σ mmHg = 0.15 mmol L-1 (about 60 times smaller).
- 5.
Note that they are not direct measurement, and they rely on an auxiliary variable 9 whose physiological significance is not clear.
- 6.
It may be due to a local impairment of the membrane itself, or to a bad perfusion of the corresponding area.
- 7.
It is mainly dedicated to polymers, but it is known to give reasonable values for single molecules.
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Maury, B. (2013). Gas exchanges. In: The Respiratory System in Equations. MS&A — Modeling, Simulation and Applications. Springer, Milano. https://doi.org/10.1007/978-88-470-5214-7_5
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DOI: https://doi.org/10.1007/978-88-470-5214-7_5
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