Diffusion of gases through the alveolar membrane

This chapter is vaguely relevant to Section F7(iii) from the 2017 CICM Primary Syllabus, which expects the exam candidates to be able to "explain perfusion-limited and diffusion-limited transfer of gases". Before one can approach that explanation (in another chapter), some fundamental aspects need to be discussed first in order for it to make sense. The college had shown some mild interest in this subject in Question 20 from the first paper of 2012 and Question 22 from the second paper of 2016. The examiners' comments were unusually instructive as to what was expected, and were used to fashion this set of notes.

In summary:

There is no single reference available which might cover this entire subject matter, other than the relevant chapter of textbooks which CICM candidates should probably already own. The characteristic feature of this topic seems to be the large number of numerical values which, upon closer examination, are not particularly well supported by references, or which originate in ancient papers from the 1940s. Most textbooks are quite happy to plagiarise from one another and by some intergenerational cut-and-pasting these values have been transmitted unchanged to the modern-day. The savvy exam candidate is advised to regurgitate these numbers without questioning their origin. 

Diffusion in general

Without revisiting content from the chapter concerned with the movement of substances across membranes, it will suffice to restate the definition of passive diffusion from Guyton & Hall (Ch.4):

"[passive diffusion is] kinetic movement of molecules or ions [which] occurs through a membrane opening or through intermolecular spaces without any interaction with carrier proteins in the membrane."

That certainly describes the movement of gas molecules across cell boundaries, but is not particularly specific to the setting of respiratory gases.  Nunn's gives an alternative which one might uphold as the definitive statement on diffusion for the CICM primary:

"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."

 It is quite quick. One can quantify this quickness using a "permeability coefficient",  a  measure of how fast the molecule moves across the membrane substance (in units of distance per second). Gases like molecular oxygen and carbon dioxide have excellent permeability coefficients, and diffuse across a lipid bilayer membrane at a rate of 2-3 mm/sec, approximately one hundred times as quickly as water. Given that the blood-gas barrier is approximately 300 nanometres, the first gas molecules across the finish line should record a time of about 0.1 milliseconds.

Diffusion everywhere, including the alveolar membrane, is described by Graham's law and by Fick's law of diffusion. The latter states:

 "The molar flux due to diffusion is proportional to the concentration gradient"

which, in the form of a formula, looks like:

where

• J is "diffusive flux", the magnitude and direction of the flow of a substance from one compartment to another
• dφ is the concentration difference 
• dx is the distance for diffusion (or the thickness of the membrane)
• D is a diffusion coefficient 

...Or, one can sometimes see it like this:

where

• ΔN/Δt is the amount of gas transferred over time
• dφ is still the concentration difference 
• dx is still the distance for diffusion (or the thickness of the membrane)
• A is the surface area of the membrane
• K is  Krogh's diffusion coefficient, which is basically the diffusion coefficient (D) multiplied by the solubility (a) of a gas in the fluid through which the gas diffuses. 

As one can see, variants on this formula do exist, which is fine, and CICM trainees who rearrange the formula are unlikely to meet with any arguments from the examiners, so long as their understanding of the law meets some sort of standards for internal logical consistency. The fundamental things to remember would be:

• Diffusion rate is proportional to:
  • Diffusion coefficient, or Krogh's coefficient 
  • Partial pressure gradient
  • Surface area of the  gas exchange surface
• Diffusion rate is inversely proportional to:
  • Molecule size
  • Gas density
  • Membrane thickness

Graham's Law is often forgotten in the discussion of alveolar gas transfer. It states that the rate of diffusion for a gas is inversely proportional to the square root of its molar mass. In essence, the denser the gas, the slower the diffusion rate. This is perfectly relevant from the viewpoint of a physicist, but for medicine it may be sidelined somewhat, as usually the gases we insufflate our patients with have a fairly predictable density. It's always going to be oxygen, or some combination of oxygen and nitrogen, with occasional fruity-smelling sedative impurities. Sure, on those rare occasions one might have to give a patient some sort of helium-oxygen mixture, but in those scenarios, one would not ever be interested in the absorption of the helium into the blood, because though it might get in there, once in there it does nothing interesting.  And of course, at the higher range of densities, there are no representatives whatsoever. As far as the author is aware, there is no peacetime medical application for tungsten hexafluoride. In short, CICM exam candidates need to be aware of Graham's law for the duration of the exam, and not beyond.

The factors which affect the diffusion of gases across the alveolar membrane must therefore be:

• Diffusion coefficient of the gas, which is influenced by:
  • size of the molecules (predictable, for O₂ and CO₂)
  • the viscosity of the fluid (probably also quite stable)
  • solution temperature (probably a stable 37ºC)
• Surface area of the pulmonary gas exchange surface, which is influenced by:
  • Age
  • Disease (eg. emphysema)
  • Degree of pulmonary capillary recruitment
  • Degree of pulmonary alveolar recruitment (i.e. all factors which influence atelectasis, including posture, FRC volume, closing capacity, etc)
• Partial pressure gradient between the capillary and the alveolus,
  which is influenced by:
  • Alveolar gas mixture
  • Mixed venous blood gas content
  • Haemoglobin concentration
  • Affinity of haemoglobin for oxygen
  • Solubility of the gas in water and lipid
• Blood-gas barrier thickness, which is influenced by:
  • Age
  • Disease (eg. pulmonary fibrosis)
• Additionally, capillary transit time (i.e. duration of exposure of blood to the gas exchange surface) is a factor, as the blood in the pulmonary capillaries is constantly moving. 

If one were to abbreviate this massive list for the purposes of an exam answer, one could probably (safely) stick to the first order bullet points. If, however, one were to throw brevity to the wind, one could continue reading the rest of this chapter.

Diffusion coefficient of respiratory gases

By a completely nonbiologically-centred Fickian definition of this term, the Diffusion Coefficient (D) is a proportionality factor which describes the movement of a mass of substance (over a time interval) through a surface of a certain area, along a certain concentration gradient. As such, it is usually represented in terms of square metres or centimetres per second. And judging from that definition, one might come to the conclusion that it is probably something quite unique to every combination of gas molecule and membrane structure. This would be a correct assumption. Generally, diffusion coefficients are measured experimentally.  Factors which influence the diffusion coefficient for any combination of gas and membrane include some membrane and medium-specific factors, for example the viscosity of the fluid through which the gas is diffusing, as well as the temperature of the fluid (which roughly represents the vigourousness of molecular movement; higher temperatures generally lead to faster diffusion). As one can see, as far as pulmonary physiology is concerned,  most of the factors which influence gas diffusion are relatively fixed. The temperature of the respiratory structures and viscosity of the alveolar cytosol is probably not going to vary massively from person to person. 

So, what are the diffusion coefficients for respiratory gases trying to negotiate the blood-gas barrier? 

• For oxygen, 2.40 × 10^-5 cm²/s  (Frank et al, 2009)
• For carbon dioxide, 1.85 × 10^-5 cm²/s (Sharan & Singh, 1985)

Those numbers might look scientific, but the author soberly confesses that they really are not. Both values come from papers which were published as experiments in mathematical modelling of pulmonary gas transfer, where the diffusion coefficients were incorporated into the model. Both groups of authors offer the same numbers, which seems encouraging, but neither group offers any references as to where they got them from. In short, the coefficients are quoted here without any experimental data to support them. 

What do these numbers mean? Where do they fit in the grand scheme of such numbers, how do they compare to other diffusion coefficients? Well. To create contrast, the diffusion of gases through gases could be mentioned here, reluctantly, in a temporary excursion away from exam-relevant material.  Worth et al (1978) did actually measure the diffusion coefficients of various respiratorily important gases as they diffused through other gases, and presented their data in the form of a table which is reproduced below for some uncertain educational benefit:

If one is somewhat bewildered as to what one ought to take away from this, it is that the diffusion coefficient for respiratory gas mixtures varies substantially from the alveolus (where gas only needs to diffuse through gas) to the physical blood-gas barrier bilayer (where the diffusion coefficient jumps by five or six orders of magnitude, as seen in the section above). 

Surface area of the pulmonary gas exchange surface

The "gas exchange surface area" is a fairly elastic parameter which incorporates several factors. One  is the crude surface area of the alveolar membrane which is available for gas to exchange across.  The other is the capillary surface area, which changes according to pulmonary blood flow variation and capillary recruitment. 

Popular folklore holds that the surface of the lungs is approximately 140m², or roughly the same area as a tennis court. Whenever one sees this figure, it is usually without any supporting reference, but digging deeper one finds that it is in fact all coming from a 1978 article by Gehr et al, where eight average-sized cadaveric human lungs were fixed in glutaraldehyde and carefully scrutinised using transmission electron microscopy. From these data, Gehr et al concluded that the average lung has an alveolar surface area of 143 m², and a capillary surface area of around 125 m². Obviously, every author will report a slightly different number, because the surface area of the lung is something quite variable between different humans, and even within the same person over the course of their lifespan. For instance, Sprung et al (2006) found that the total gas exchange surface area decreases from 75 m² at age 30 to 60 m² at age 70.

The concentration and partial pressure gradient

As discussed in the chapter on partial pressure and gas solubility, when it comes to the diffusion of gas through solutions, the most important factor is not concentration but partial pressure. This is because different gases have different solubilities in different solvents (water, fat, etc). In a scenario where a gas comes into contact with two solvents where it happens to be much more soluble in one, the gas will equilibrate such that the partial pressure will be the same between the two solutions, but the gas content (moles per L) will be much greater in the better solvent. At risk of saturating this site with beaker diagrams:

Observe: though there is a significant concentration gradient between these two compartments, there would be no mass movement of  gas because the partial pressures are in equilibrium

This nerdy digression aside, the partial pressure gradients at the alveolar-capillary interface should usually look something like this: 

The partial pressure gradient for CO₂ is a relatively unpredictable thing. Alveolar capillary PCO₂ at the beginning of such a capillary is approximately the same as the mixed venous PCO₂, which is about 46 mmHg. Alveolar pCO₂ could theoretically be the same as atmospheric (0.3 mmHg in these difficult times), but realistically CO₂ invades the alveolus so rapidly that the alveolar CO₂ is better described by the alveolar gas equation (PaCO₂ × 1.25), and though it could theoretically be anything, for the diagram 40mmHg was chosen.  The magnitude of the CO₂ gradient should therefore be close to 6mmHg.  The partial pressure gradient for oxygen is from about 100 mmHg in the alveolus to about 40 mmHg in the capillary, corresponding to the PO₂ of mixed venous blood (sats of around 75%). From these various statements, one can come to the conclusion that the partial pressure gradients here would be influenced by the following factors:

• Mixed venous gas content
  • Oxygen extraction ratio
  • Metabolic rate
  • Cardiac output
  • Multiple other possible influences
• Alveolar gas mixture
  • Total atmospheric pressure
  • FiO2 
  • Alveolar ventilation (i.e whether CO₂ is being cleared from the alveolus with each breath)

Influence of gas-protein interactions

The raw partial pressure gradient is not necessarily the only determinant of gas movement into the capillary, or out of it. Consider especially the case of oxygen:

• Oxygen enters into the capillary blood along a partial pressure gradient
• In the capillary, the oxygen binds to haemoglobin
• Bound oxygen does not exert a partial pressure
• Thus, partial pressure drops
• This maintains the partial pressure gradient between alveolar gas and capillary blood, as all the oxygen which has crossed the barrier keeps disappearing into the bottomless haemoglobin sinkhole

Apart from this aspect, one also needs to consider that the act of binding haemoglobin takes time. This nonzero time interval needs to be factored into the influence of capillary transit time, which is discussed below. 

Thickness of the blood-gas barrier

In general, if we were to really overanalyse this, there is a huge and very heterogeneous series of hurdles which respiratory gases need to negotiate on their way to the bloodstream:

• Diffusion of one gas through another, in the alveolar gas mixture
• Diffusion though aqueous compartments
  • Alveolar surfactant water
  • Cytosol of the alveolar lining cells, capillary endothelium and erythrocytes
  • Plasma
• Diffusion through lipid compartments
  • Cell membranes
  • Surfactant layer lipids
• Diffusion though protein layers
  • Alveolar basement membrane
  • Protein contents of surfactant layer and the cell cytosol

To put it into a sequential order, the barriers to diffusion can be depicted in the following manner:

In short, it is a complicated field to cross. There's at least five lipid bilayers and three lakes of cytosol to cross, not to mention a whole ocean of unpredictably swirling plasma. Åberg et al (2010) treat this complex subject with the sort of patient granularity that could potentially drive a person insane. The CICM trainee probably does not need to know how the cholesterol content of surfactant affects its gas permeability characteristics. For First Part Exam purposes, it will suffice to say that the barrier consists of multiple cellular lipid bilayers, solid tissue, and water.  

The diffusion of gases through gases should be mentioned here,  reluctantly, in a temporary excursion away from exam-relevant material.  This takes place in the airways and is generally safely ignored. For completeness, this apocryphal matter will be included here purely so that trainees can recognise it in the future, and give it no further thought. Worth et al (1978) did actually measure the diffusion coefficients of various respiratorily important gases as they diffused through other gases, and presented their data in the form of a table which is reproduced below for some uncertain educational benefit:

If one is somewhat bewildered as to what one ought to take away from this, it is that the diffusion coefficient for respiratory gas mixtures varies substantially from the alveolus (where gas only needs to diffuse through gas) to the physical blood-gas barrier bilayer (where the diffusion coefficient jumps by five or six orders of magnitude, as seen in the section above). 

Capillary transit time

Because oxygen and carbon dioxide do not exchange between the alveolus and capillary instantaneously, the duration spent by blood at the gas exchange surface is obviously an important aspect of the diffusion process. Each capillary is clearly going to have some individual and different flow rate and each erythrocyte will have a slightly different transit time, but wherever you look, you see people quote "0.75 seconds" as the normal time it takes for a red cell to traverse an alveolar capillary.  

This figure is repeated by many authoritative voice organs. Specifically, 0.75 seconds seems to be very popular with the authors of textbooks.  For instance, West's (p.30 of the 10th edition) and Levitzky (p. 232 of the 7th edition) both give a transit time of 0.75 seconds, and according to Nunn's you get 0.8 seconds when you divide the total pulmonary capillary blood volume by the total pulmonary blood flow.

Where did this figure come from? Wherever it appears, there are usually no references, but with a little detective work one can determine that the origin of this figure were some early studies which calculated the transit time on the basis of diffusing capacity and an estimated pulmonary capillary blood volume. These were works by  Johnson et al (1960) who got 0.79 seconds, or Roughton (1945) who got 0.73 seconds. The latter appears to be the very first time anybody published on this topic: Roughton remarks that "no data, to my knowledge, existed heretofore as to the magnitude of this physiologically important yime interval".

Nowadays, of course, we have plenty of data which is measured directly rather than calculated. For example, one may see a piece of original reseach by Presson et al (1995), who actually did measure capillary transit times in a single subpleural capillary network which they had isolated in the lung of a dog. In-vivo fluorescent videomicroscopy was used to record and measure the transit times of the RBCs and plasma in the lung (as an aside, one interesting finding from this paper was that red cells were faster than plasma). Across the capillary network there was a bell-curve distribution of transit times, which were 3-4 seconds on average, with a resting heart rate. By increasing the cardiac output of the dog with isoprenaline, the investigators were able to decrease both the transit time and the distribution of times across capillaries, such that all the capillaries became rapid transit capillaries.  The original investigators' data is reproduced here, because honestly there is no better way to represent the same information:

This is similar to the data acquired by Klocke et al (1995), who found a mean transit time of around 1.7 seconds in isolated rabbit lungs, and Capen et al (1990), who got 2.0 seconds at rest and 0.8 seconds with vigorous exercise. Zavorsky et al (2002) got 2.5 seconds in a healthy human lung with maximum exercise;  Stan Linstedt (1984) gave a figure of 2.0 seconds, with a minimum of around 0.5 seconds, and besides that produced a table comparing different measured values among various species of mammal.

However, whatever the findings of later studies, many major publications tend to stick to quoting these numbers from 19945-1960.  CICM trainees should probably assume that their examiners will have used those textbooks to create exam questions and viva stations.  The correct exam answer is therefore the 1960s value.

So, that aside, what are the implications of capillary transit time for gas exchange? The answer requires a brief exploration of the patterns of gas diffusion along a capillary. 

Radial and axial diffusion of O₂ and CO₂

If one were to consider the pulmonary capillary as a roughly tubular structure, one would expect that there should be two important directions for gas diffusion. Firstly, there would be the diffusion of the gas into the blood through the wall of the capillary, roughly along a direction from the periphery of the capillary towards its centre. Let's call that the "radial" direction for diffusion. Additionally, as blood moves along the capillary and gains (or loses) more and more gas, there should be some change in diffusion along the longitudinal axis of the capillary. Let's call this the "axial" direction. 

The direction of greatest interest here will probably be the axial direction, as this is the change in concentration gradient which occurs along the same direction as the direction of blood flow. Using a mathematical model, Sharan & Singh (1985) were able to create this representation of partial pressures along the length of an average capillary. Presented here on the same coordinate scale, below one can see a slightly mutated version of the same data. The partial pressure numbers refer to the PO₂ and PCO₂ inside the capillary. The graph only covers the first 20 μm of a capillary, which may be up to 600 μm long (Staub et al, 1968).

Note that the authors assumed alveolar CO₂ will be around 40mmHg, which had narrowed that gradient somewhat. Even if they did not, one would be easily able to conclude that:

• CO₂ equilibrates with alveolar gas over a very short capillary distance
• O₂ takes longer to equilibrate with alveolar gas
• By the end of a capillary, the blood is 100% oxygenated

Thus; if the capillary blood is traversing this capillary distance over the supposed average capillary transit time of 0.75 seconds, then after spending about zero seconds in the capillary the blood is already fully oxygenated. However, as you increase the capillary transit speed, the capillary transit time shortens. At some stage, you will meet a scenario where blood is whistling through the capillaries with such speed that by the end of the capillary those erythrocytes still have not had enough time to fully oxygenate. Hypoxia will be the result. Moreover, the "slow" capillaries will not be able to compensate for this hypoxia, as the blood in them is already maximally oxygenated. 

So, what transit time would be too fast to achieve complete oxygenation of capillary blood? Or, to rephrase the question, how long does it take for capillary blood to achieve maximum oxygen saturation?

Minimum transit time required to oxygenate capillary blood

As one might imagine,  no direct measurement of this is available for discussion, but there are plenty of models. Nunn's  references  Staub (1963), which was a theoretical paper using all contemporary data to generate predictions of red cell oxygen uptake in flowing capillary blood. The stolen image, lightly Photoshopped, is offered below:

As one can see from this relationship,  the minimum capillary transit time is about 0.25 seconds (1/3rd of the usual transit time). The other arrows indicate fractions of this usual transit time to indicate what might happen if capillary transit time were to decrease. From this graph, it would appear that, at a transit time of 0.075 seconds (one-tenth of the normal), the erythrocytes would only end up with a PaO₂ of about 80 mmHg, which would still produce sats of around 96-97%.  Conceivably, a transit time which is even shorter would produce the abovementioned scenario where blood is whooshing through those capillaries so fast that there is no time for the erythrocytes to pick up any oxygen whatsoever. 

Realistically, how low does transit time go in the real world? In a study which returned plausible and familiar-sounding number, Warren et al (1991)  looked at the mean capillary transit time in healthy athletic humans.  Their transit times were around 1.05 seconds at rest. With some moderate exercise, that value dropped to 0.46 seconds, and stayed there even as the intensity of the exercise increased. The A-a gradients of these athletes increased (not by much -  only up to 22.3 mmHg), but the authors were forced to conclude that this could not have possibly been the consequence of a short capillary transit time.

However, that's a group of individuals who were picked because their routine habits included running more than 64 km cycling over 240 km per week. Things are significantly different if the patient has a pathology which decreases the diffusion coefficient of their blood-gas barrier. As they exert themselves and their cardiac output increases, the capillary transit time becomes shortened to the point where hypoxia becomes a serious problem. This has been demonstrated in vivo.  Jernudd-Wilhelmsson (1986) concluded that "a limitation on diffusion across the alveolar-capillary membrane developed during exercise, contributing approximately 30% to P(A-a)O₂" in such patients, on the basis of an A-a gradient which had doubled in spite of  MIGET data which demonstrated a completely unchanged V/Q pattern.

Protein-gas binding rate 

When the capillary transit time was first being contemplated by the early pioneers, the calculation to determine a rate of oxygen diffusion across the membrane yielded numbers which were implausibly slow because they used just the raw partial pressure difference between the alveolus and the capillary, treating capillary blood as a relatively inert recipient fluid (this was the so-called "Bohr integration:, by Christian Bohr, 1911). Of course, it is not inert- the haemoglobin molecules in blood hungrily gobble up all the oxygen molecules as soon as they cross the barrier, and the partial pressure of oxygen does not get a chance to increase until haemoglobin is well-saturated (and the rate of the oxygen-haemoglobin reaction diminishes). When you incorporate the effects of this haemoglobin sinkhole, the rate of oxygen uptake into the capillary is increased from Bohrian values. Staub et al (1962) discuss this in great detail, and one particularly illustrative diagram from their article is reproduced below after being misappropriated and altered:

As one can see, with the oxygen-scavenging effects of haemoglobin taken into account, the diffusion rate is much faster. The exam candidate may not need to know about this in any great detail, but should probably maintain some dim awareness of the fact that the oxygen partial pressure gradient between the capillary and the alveolus is not the only factor driving its diffusion. Moreover, some other gases similarly have their alveolar uptake accelerated by binding to proteins or other substances. An excellent (though slightly veterinary) exploration of anaesthetic drug solubility by Soares et al (2012) notes that inhaled anaesthetics bind avidly to both albumin and triglycerides, which would surely influence their uptake from the capillary.