Fundamentals of the Diffusion Process

Diffusion of a gas is a process by which a net transfer of molecules takes place from a zone in which the gas exerts a high partial pressure to a zone in which it exerts a lower partial pressure. The mechanism of transfer is the random movement of molecules and the term excludes both active biological transport and transfer by mass movement of gas in response to a total pressure difference (i.e. gas flow as occurs during tidal ventilation). The partial pressure (or tension) of a gas in a gas mixture is the pressure which it would exert if it occupied the space alone (equal to total pressure multiplied by fractional concentration). Gas molecules pass in each direction but at a rate proportional to the partial pressure of the gas in the zone from which they are leaving. The net transfer of the gas is the difference in the number of molecules passing in each direction, and is thus proportional to the difference in partial pressure between the two zones. Typical examples of diffusion are shown in Figure 9.1.

Fig. 9.1 Three examples of diffusion of oxygen. In each case there is a net transfer of oxygen from left to right in accord with the partial pressure gradient. (A) Oxygen passes from one gaseous phase to another. (B) Oxygen passes from a gaseous phase to a liquid phase. (C) Oxygen passes from one liquid to another.

In each of the examples shown in Figure 9.1, there is a finite resistance to the transfer of the gas molecules. In Figure 9.1A, the resistance is concentrated at the restriction in the neck of the bottle. Clearly, the narrower the neck, the slower will be the process of equilibration with the outside air. In Figure 9.1B, the site of the resistance to diffusion is less circumscribed but includes gas diffusion within the alveolus, the alveolar/capillary membrane, the diffusion path through the plasma, and the delay in combination of oxygen with the reduced haemoglobin in the red blood cell (RBC). In Figure 9.1C, the resistance commences with the delay in the release of oxygen by haemoglobin, and includes all the interfaces between the RBC membrane and the site of oxygen consumption in the mitochondria. There may then be an additional component in the rate at which oxygen enters into chemical reactions.

In the living body oxygen is constantly being consumed, while carbon dioxide is being produced, so equilibrium cannot be attained as in the case of the open bottle of oxygen in Figure 9.1A. Instead, a dynamic equilibrium is attained with diffusion down a gradient between the alveolus and the mitochondria for oxygen and the reverse for carbon dioxide. The maintenance of these partial pressure gradients is, in fact, a characteristic of life.

In the case of gases that are not metabolised to any great extent, such as nitrogen and most inhalational anaesthetic agents, there is always a tendency towards a static equilibrium at which all tissue partial pressures become equal to the partial pressure of the particular gas in the inspired air. This occurs with nitrogen and would also be attained with an inhalational anaesthetic agent if it were administered for a very long time.

Quantification of Resistance to Diffusion

The propensity of a gas to diffuse as a result of a given pressure gradient is known as its diffusing capacity according to the equation:

The usual biological unit of diffusing capacity is ml.min⁻¹.mmHg⁻¹ or, in SI units, ml.min⁻¹.kPa⁻¹.

Small molecules diffuse more easily than large molecules. Graham’s law states that the rate of diffusion of a gas is inversely proportional to the square root of its density. In addition, gases also diffuse more readily at higher temperatures. Apart from these factors, inherent in the gas, the resistance to diffusion is related directly to the length of the diffusion path and inversely to the area of interface that is available for diffusion.

Diffusion of Gases in Solution

The partial pressure of a gas in solution in a liquid is defined as being equal to the partial pressure of the same gas in a gas mixture that is in equilibrium with the liquid. When a gas is diffusing into or through an aqueous phase, the solubility of the gas in water becomes an important factor, and the diffusing capacity under these circumstances is considered to be directly proportional to the solubility. Nitrous oxide would thus be expected to have about 20 times the diffusing capacity of oxygen in crossing a gas–water interface. High solubility does not confer an increased ‘agility’ of the gas in its negotiation of an aqueous barrier, but simply means that, for a given partial pressure, more molecules of the gas are present in the liquid.

Partial pressure versus concentration gradients. Non-gaseous substances in solution diffuse in response to concentration gradients. This is also true for gas mixtures at the same total pressure, when the partial pressure of any component gas is directly proportional to its concentration. This is not the case when a gas in solution in one liquid diffuses into a different liquid in which it has a different solubility coefficient. When gases are in solution, the partial pressure they exert is directly proportional to their concentration in the solvent but inversely to the solubility of the gas in the solvent. Thus, if water and oil have the same concentration of nitrous oxide dissolved in each, the partial pressure of nitrous oxide in the oil will be only one-third of the partial pressure in the water since the oil/water solubility ratio is about 3:1. If the two liquids are shaken up together, there will be a net transfer of nitrous oxide from the water to the oil until the tension in each phase is the same. At that time the concentration of nitrous oxide in the oil will be about three times the concentration in the water. There is thus a net transfer of nitrous oxide against the concentration gradient, but always with the partial pressure gradient. It is therefore useful to consider partial pressure rather than concentrations in relation to movement of gases and vapours from one compartment of the body to another. The same units of pressure may be used in gas, aqueous and lipid phases.

Diffusion of Oxygen in the Lungs

It is now widely accepted that oxygen passes from the alveoli into the pulmonary capillary blood by a passive process of diffusion according to physical laws, though for a while it was believed that oxygen was actively secreted into the blood (page 242). It is believed that diffusion equilibrium is very nearly achieved for oxygen during the normal pulmonary capillary transit time in the resting subject. Therefore, in these circumstances, the uptake of oxygen is limited by pulmonary blood flow and not by diffusing capacity. However, when exercising, while breathing gas mixtures deficient in oxygen or at reduced barometric pressure, the diffusing capacity becomes important and may limit oxygen uptake.

Components of the Alveolar/Capillary Diffusion Pathway

The gas space within the alveolus. At functional residual capacity, the diameter of the average human alveolus is of the order of 200 μm (page 20), and it is likely that mixing of normal alveolar gas is almost instantaneous over the small distance from the centre to the periphery. Precise calculations are impossible on account of the complex geometry of the alveolus, but the overall efficiency of gas exchange within the lungs suggests that mixing must be complete within less than 10 ms. Therefore, in practice it is usual to consider alveolar gas of normal composition as uniformly mixed.

This generalisation does not seem to hold when subjects inhale gases of widely different molecular weights. This was first demonstrated in normal subjects inhaling mixtures of sulphur hexafluoride (SF₆) and helium when the SF₆ concentration was found to be higher (relative to helium) earlier in the breath.² According to Graham’s law SF₆ (molecular weight 146), would diffuse six times less readily than helium (molecular weight 4) and would therefore tend to remain concentrated at the core of the alveolus. A similar problem is seen with inhaled anaesthetic agents, for example a large proportion of the end expiratory/arterial partial pressure gradient for the anaesthetic isoflurane (molecular weight 184.5) cannot be explained by alveolar dead space or shunt and may be due to failure to achieve uniformity within the alveolus.³ Nevertheless, it seems unlikely that non-uniformity within a single alveolus is an important factor limiting diffusing capacity under normal conditions with gases such as oxygen, nitrogen and carbon dioxide, which have molecular weights that are not greatly different.

Alveolar lining fluid. Alveoli contain a thin layer of surfactant rich fluid (page 218) through which respiratory gases must diffuse.⁴ The depth of this fluid layer, and therefore its impediment to diffusion, is very variable. There are ‘pools’ of fluid in alveolar corners (see Figure 2.8) and in the depressions between where the capillaries bulge into the alveolus, with only a very thin layer on the surface of the capillary bulges, thus providing the minimal diffusion barrier in the most vital area.

Tissue barrier. Electron microscopy reveals details of the actual path between alveolar gas and pulmonary capillary blood, shown in Figure 2.7. Each alveolus is lined with epithelium which, with its basement membrane, is about 0.2 μm thick, except where epithelial cell nuclei bulge into the alveolar lumen. Beyond the basement membrane is the interstitial space, which is very thin where it overlies the capillaries, particularly on the active side; elsewhere it is thicker and contains collagen and elastic fibres. The pulmonary capillaries are lined with endothelium, also with its own basement membrane, which is approximately the same thickness as the alveolar epithelium, except where it is expanded to enclose the endothelial cell nuclei. The total thickness of the active part of the tissue barrier is thus about 0.5 μm, containing two pairs of lipid bilayers separated by the interstitial space.

Plasma layer. Human pulmonary capillaries are estimated to have a mean diameter of 7 μm, similar to the diameter of a RBC, part of which is therefore forced into contact with the endothelial cell surface (see Figure 2.7). The diffusion path through plasma may therefore be very short indeed, but only a small proportion of the RBC surface will be in such close proximity with the endothelium, much of the RBC passing through the middle of the capillary, up to 3.5 μm from the endothelial cell. Furthermore, since the diameter of the capillary is about 14 times the thickness of the tissue barrier, it is clear that the diffusion path within the capillary is likely to be much longer than the path through the alveolar/capillary membrane. A complex pattern of diffusion gradients is therefore established within the plasma depending on the oxygen tension in the alveolus and the number of RBCs present.⁵ This is discussed in more detail below with respect to carbon monoxide.

Diffusion into and within the RBC.⁶ Confining haemoglobin within the RBC reduces the oxygen diffusing capacity by 40% in comparison with free haemoglobin solution.⁷ There are three possible explanations for this observation. First, there is evidence that the rapid uptake of O₂ and CO by RBCs causes depletion of gas in the plasma layer immediately surrounding the RBC.⁸ Referred to as the ‘unstirred layer’, this phenomenon is most likely to occur at low packed cell volume (PCV) when adjacent RBCs in the pulmonary capillary have more plasma between them.⁹ Secondly, oxygen must diffuse across the RBC membrane, though this is not normally believed to be a significant diffusion barrier. Thirdly, once in the cell, oxygen must diffuse through a varying amount of intracellular fluid before combining with haemoglobin, a process that is aided by mass movement of the haemoglobin molecules caused by the deformation of the RBC as it passes through the capillary bed, in effect ‘mixing’ the oxygen with the haemoglobin.

RBCs change shape as they pass through capillaries (both pulmonary and systemic) and this plays an important role in the uptake and release of oxygen.⁶ The dependence of diffusing capacity on RBC shape changes may result from reducing the unstirred layer by ‘mixing’ the plasma around the RBC, from changes in the cell membrane surface area to RBC volume ratio or from assisting the mass movement of haemoglobin within the cell. This has led to further studies in which the deformability of RBCs is reduced (using chlorpromazine) or increased (using sodium salicylate), which have demonstrated that diffusing capacity is increased with greater RBC deformability.⁹ Of more clinical significance is the effect of plasma cholesterol on RBC function.¹⁰ Elevated cholesterol concentration in the plasma causes increased cholesterol in the RBC membrane, a change that is known to make the membrane thicker and less deformable, both of which lead to reduced efficiency of diffusion across the membrane. Oxygen uptake by RBCs in the lung, and its release in the tissues, are both believed to be significantly impaired by hypercholesterolaemia, particularly in tissues with high oxygen extraction ratios such as the heart.

Uptake of oxygen by haemoglobin. The greater part of the oxygen that is taken up in the lungs enters into chemical combination with haemoglobin. This chemical reaction takes a finite time and forms an appreciable part of the total resistance to the transfer of oxygen.¹¹ This important discovery resulted in an extensive reappraisal of the whole concept of diffusing capacity. In particular, it became clear that measurements of ‘diffusing capacity’ did not necessarily give an indication of the degree of permeability of the alveolar/capillary membrane.

Quantification of the Diffusing Capacity for Oxygen

The diffusing capacity of oxygen is simply the oxygen uptake divided by the partial pressure gradient from alveolar gas to pulmonary capillary blood where the relevant tension is the mean pulmonary capillary Po₂:

The alveolar Po₂ can be derived with some degree of accuracy (page 140) but there are very serious problems in estimating the mean pulmonary capillary Po_2.

The mean pulmonary capillary Po_2. It is clearly impossible to make a direct measurement of the mean Po₂ of the pulmonary capillary blood, and therefore attempts have been made to derive this quantity indirectly from the presumed changes of Po₂ that occur as blood passes through the pulmonary capillaries.

The earliest analysis of the problem was made by Bohr in 1909.¹² He made the assumption that, at any point along the pulmonary capillary, the rate of diffusion of oxygen was proportional to the Po₂ difference between the alveolar gas and the pulmonary capillary blood at that point. Using this approach, and assuming a value for the alveolar/pulmonary end-capillary Po₂ gradient, it seemed possible to construct a graph of capillary Po₂, plotted against the time the blood had been in the pulmonary capillary. A typical curve drawn on this basis is shown as the broken line in Figure 9.2A. Once the curve has been drawn, it is relatively easy to derive the mean pulmonary capillary Po₂, which then permits calculation of the oxygen diffusing capacity. The validity of the assumption of the alveolar/pulmonary end-capillary Po₂ gradient is considered below.