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Gaseous diffusion in the lungs
Br. J. Dis. Chest (1980) 74, 99
Review Article GASEOUS
DIFFUSION
IN THE
LUNGS
KEITH HORSFIELD Midhurst Medical Research Institute, Midhurst, Sussex, England
The change in environment experienced by the vertebrates when they moved from the habitat of the sea to that of dry land brought with it some evolutionary changes in their respiratory mechanisms. Water can pass over the gills of a fish in a continuous flow bringing oxygen directly to them. In the land vertebrate, however, the need to conserve water which would be lost from an external gas exchange membrane has resulted in the development of an internal lung. The airways of mammals are a complex system of branching tubes open to the atmosphere at one end only and this necessitates reciprocating flow to achieve ventilation. But convective flow of inhaled fresh gas can not continue right up to the alveolar walls because these form blind endings in the airways. Some other mechanism must therefore move oxygen molecules up to the alveolar walls and carbon dioxide molecules away from them. This mechanism, by which gases in the respiratory airways become mixed, is molecular diffusion; without it mammalian lungs would be unable to exchange oxygen and carbon dioxide between air and blood. Inspired oxygen moves down the airways to the blood by three distinct physical processes: 1. Convective flow in the conducting airways. 2. Molecular diffusion in the gas phase in the respiratory airways. 3. Molecular diffusion in the tissue phase across the alveolar-capillary membrane. There is, of course, some overlap and interaction between (1) and (2), since diffusion also occurs in the conducting airways and convective flow in the respiratory airways. Each process, going down, is progressively less efficient at transporting gas, but this inefficiency is compensated for by the diminishing distance over which each operates and the rapid increase in the cross-sectional area of the airways distally, terminating in about 80 m ~ of alveolar surface area. These correlations between structure and function have been discussed in a previous article in this Journal (Horsfield 1974). The purpose of this article is to review the role of molecular diffusion in the respiratory processes of normal lungs, how diseases affect it and how pulmonary function tests attempt to measure it. Complex mathematical equations have been deliberately avoided in order to make the text more easily understandable, but a few simple equations have been included. Those who are interested in this aspect should be able to find their way into the subject from the references. MOLECULAR DIFFUSION
Molecules in a gas are in constant random motion, travelling in straight paths until colliding with other molecules or the walls of the container, when they bounce off in a
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Keith Horsfield
new direction. If two species of molecules are introduced into a closed container they will intermix by virtue of this motion. The process is more rapid at higher temperatures, which increase molecular movement, and slower at higher pressures, when the molecules are more crowded. o
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-1 Distance along tube from partition
Fig. 2. Time course of diffusive mixing in the cylinder shown in Fig. 1. to = time before removing partition, tx to t4= successive time intervals after removal of partition, too= infinite time (mixing complete)
Imagine a cylindrical container with a thin movable partition down the middle (Fig. IA) and a different gas in each half. At time zero the partition is instantly removed and the two gases diffuse into each other (Fig. 1B). At first mixing is rapid but as each gas becomes more evenly distributed between the two halves the rate of mixing diminishes (Fig. 2). The quantity of gas passing across a plane of section in a given time is
Gaseous Diffusion in the Lungs
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proportional to the concentration gradient, the cross-sectional area and the diffusivity of the gas. Diffusivity is expressed as the diffusion coefficient (D), the quantity of gas diffusing across unit area in unit time per unit gradient of concentration. This must be at a stated temperature and pressure. It has the basic units of cm 2 s -1 and is inversely proportional to the square root of the molecular weight of the gas, so that the larger the molecule the less easily it diffuses. When two gases mix by diffusion the behaviour of each is modified by the nature of the other. T h u s oxygen will diffuse into sulphur hexafluoride at a rate different from that at which it will diffuse into hydrogen. T h e diffusion coefficient must therefore be stated for two gases, for example oxygen and nitrogen diffusing into each other at 20°C, D = 0.22 cm z s -1 ; this is termed a binary diffusion coefficient. Table I gives the binary diffusion coefficients for some gases commonly used in respiratory work. Table I. Binary diffusion coefficients (D) in cm2/sec, at 37°C and 746 torr, dry Gases
D
Gases
D
02 in N2 CO2 in N2 CO2 in 02 CO in N2 CO in 02 CO in CO2
0.256 0.181 0.170 0.237 0.247 0.179
He in N2 He in CO2 02 in He SF6 in N2 SF6 in 02 SF6 in CO2
0.743 0.662 0.893 0.105 0.099 0.076
After Worth et al. (1978). In Fick's first equation of diffusion the driving force is stated in terms of the concentration gradient dQ dt -
aDdC dx
where Q is the quantity of gas, t is time, A is the area over which diffusion is occurring, c is the concentration of the gas species, D is the diffusion coefficient and x is linear distance. T h e equation simply says that the rate at which a substance diffuses, dQ/dt, is proportional to the area, the diffusion coefficient and the concentration gradient, dc/dx. T h e minus sign indicates that the direction of movement is down the concentration gradient. With gases in the gas phase, partial pressure is proportional to concentration and in respiratory work it is common to think of diffusion in terms of partial pressure. Strictly speaking, however, it is the activity (fugacity) of the gas which drives diffusion, which is similar to but not quite the same as partial pressure. When we come to consider diffusion in the blood and lung tissues another factor has to be taken into account, which is that the gas is soluble in serum and tissues. An example of the effect this has is as follows. Consider a two-phase system (Fig. 3) at 37°C with saline in one half equilibrated with oxygen at a partial pressure of 100 m m H g and olive
Keith Horsfield
102
oil in the other half equilibrated with oxygen at 40 mmHg, the two separated by a thin membrane. The concentration of oxygen is nearly twice as much in the oil, but oxygen will diffuse in the direction of the partial pressure gradient, that is against the concentration gradient, from the saline to the oil. In calculating the quantity of gas diffusing in a solvent, partial pressure must be used. If the solubility is e~ then concentration c = ~P, where P is the partial pressure, and Fick's equation becomes dQ dt -
dP AD C~dx
where dP/dx is the partial pressure gradient.
SALINE
OLIVE OIL
Oxygen content 0.0032 ml./rnt
0.0058 mt/m!. Oxygencontent
Partial pressure100 mm Hg
40 rnm Hg Portial pressure
Diffusion of oxygen T E
Fig. 3. Diffusion of oxygen in a two-phase liquid system. Although the oxygen content of the olive oil is greater the direction of diffusion is down the partial pressure gradient. The difference in content is due to the greater solubility of oxygen in olive oil TAYLOR DISPERSION The interaction between convective flow and simultaneous molecular diffusion in the airways, though not clinically important, is of considerable interest. The phenomenon was first investigated by Taylor (1953). If a gas, such as nitrogen, flows down a long straight tube at a velocity appropriate for laminar flow a parabolic velocity profile develops (Fig. 4A). Gas at the centre of the tube flows fastest and that at the edges slowest, and when fully developed the gas at the centre moves at twice the average velocity. Suppose now that a different gas, such as oxygen, is introduced into one end of the tube, starting off with a perfectly straight front between the two (Fig. 4B). As the oxygen flows down the tube displacing the nitrogen in front of it, the parabolic velocity profile causes the oxygen molecules in the centre of the tube to move faster and hence to progress further down the tube. A parabolic concentration profile would develop (Fig. 4c) if no mixing occurred between the two gases. However, diffusive mixing does occur, blurring the interface and changing the shape of the concentration profile. Although gas
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103
molecules move in all directions, it is convenient to think in terms of two components of their movement, axially along the tube and radially across it. Thus oxygen diffuses radially out of the central core and into the surrounding nitrogen and nitrogen in the reverse direction (Fig. 40). Those oxygen molecules which diffuse radially enter the slower-moving peripheral stream and are therefore transported more slowly than before. The higher the diffusion coefficient the more easily does radial diffusion occur, so that heavier gases tend to stay in the central core and be transported more rapidly. Comparing two gases in a mixture, say the light gas helium (He) and the heavy gas sulphur hexafluoride (SF6), in the circumstances just described, the front end of the concentration profile of the less diffusable gas SF6 arrives first at a given station S in the tube (Fig. 5A). Up to the point where the two concentration profiles cross, more SF6 than He passes S as the front flows through (Fig. 5B). Between this point and that where both gases reach maximum concentration, more He than SF6 passes S (Fig. 5c). Finally the gases pass in equal quantities when the concentration profile has passed S. !
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C D Fig. 4. Gas flow in a tube. A, Parabolic velocity profile when flow is laminar. B, A square wave of a second gas species is introduced. C, Parabolic concentration profile of the second gas. D, Radial diffusive mixing The forward movement of a gas front undergoing Taylor dispersion is equivalent to an apparent diffusion with an 'apparent diffusion coefficient', k, where r2v 2 k = D + 192D and r = radius of tube, v = maximum velocity of flow in the centre of the tube and D = diffusion coefficient (Aris 1956). This apparent diffusion is with respect to a plane across the tube moving at the average flow velocity. Of the two terms on the right-hand side of the equation, D represents the ordinary diffusion coefficient in the axial direction, and r2v2/192D represents the apparent diffusion coefficient due to Taylor dispersion. When D is very small compared with convective flow the concentration profile approximates to the parabolic form. If D increases relative to convection the second term becomes smaller and the concentration profile becomes shorter. When D is large relative to
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104
convection the second term becomes small, k approximates to D, forward flow is slow and axial diffusion predominates. Thus the concentration profile becomes flatter across the tube and the front lengthens. It can be seen that Taylor dispersion is maximally manifest in the intermediate situation. Furthermore, the value of the term r2v2/192D is inversely proportional to D, a mathematical expression of what has already been described, namely that a heavier gas disperses longitudinally more than a lighter one. It is obvious that Taylor dispersion, concerned as it is with the front between two fluids, can operate only while the front is passing down the tube. Once it has passed, as at station S in Fig. 5c, there can be no effect from this mechanism.
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Fig. 5. Partial separation at the front of a mixture of He and SF6 flowing in a tube. A, SF6 arrives at station S first. B, After the cross-over point more He than SF6 passes S. C, After the front has passed, both gases pass in equal concentrations DIFFUSION IN THE CONDUCTING AIRWAYS
Although the main function of the conducting airways is transport of gas by convective flow, molecular diffusion nevertheless occurs in them. The part played by simple diffusion in the forward (axial) transport of gas is necessarily small, because the quantity transported depends on cross-sectional area, which is relatively small, and on time in the airways, which is short. However, it seems likely that Taylor dispersion can occur in the conducting airways, at least in some of them in appropriate circumstances. In man at rest, breathing normally, tracheal flow is not high enough to cause turbulence, but turbulence does occur at the larynx and during inspiration this disturbed flow
Gaseous Diffusion in the Lungs
105
is carried down a few generations of airways, gradually dying out. Secondary vortices are generated at bifurcations (Schroter & Sudlow 1969) and eddy currents may also occur where the surface is not smooth or bends suddenly. Each of these will cause mixing of the gas front, tending to counteract Taylor dispersion. At high flows the tracheal flow regimen may approach turbulence. In this case the velocity profile, and hence the concentration profile of a second gas, are both flat, minimizing Taylor dispersion. In addition to these causes of mixing, convective flow in the upper conducting airways is high relative to diffusion, so that Taylor dispersion is minimal. Wilson and Lin (1970) were of the opinion that it does not occur to a significant degree and could be neglected, while Kvale et al. (1975) thought that it should be taken into account. Flow in the intermediate sized conducting airways is laminar, with flow velocities appropriate for Taylor dispersion to occur, but in exactly which airways depends on the diffusivity of the gas and the magnitude of the flow. Individual bronchi are too short to permit fully developed laminar flow with a parabolic profile, and this prevents Taylor dispersion from occurring maximally. In the small conducting airways, and more especially in the respiratory airways, forward flow velocity becomes low and radial diffusion rapidly obliterates radial gradients in airways of small calibre. Axial diffusion comes to dominate the formation of the longitudinal concentration gradient and is indeed the most important mechanism for moving gas in this region of the airways. The form of the concentration profile of a gas leaving an airway segment is at least partly determined by its form in the gas entering the segment. No mechanism has an isolated effect--the airways act sequentially in series so that at any point the end result is the sum of the effects of all the preceding airways. From the above discussion it can be seen that anything which changes flow and diffusivity will affect the mechanism of Taylor dispersion. Thus on exercise, when flow is increased, the region where it is maximal will move further down the airways. Test gases with widely differing diffusion coefficients will undergo maximal Taylor dispersion in different airways and to different degrees. Gases of the same diffusivity but of different viscosity might also behave differently because their flow regimens will differ. Diffusivity is related to the pressure of a gas; it will therefore be increased at altitude and diminished in compression chambers and in divers. The difficulty in calculating the effects of all these variables, and of defining detailed airway geometry, make it impossible at the present time to quantitate the effects of Taylor dispersion. In my opinion and that of Chang (1976) and Pack et al. (1977) it makes no significant contribution to normal respiration, but there is considerable evidence that it can be detected experimentally by using gases of widely differing diffusivity. EXPERIMENTALDEMONSTRATIONOF TAYLORDISPERSION Van Liew and Mazzone (1977) showed how the longitudinal concentration profile of SF6 flowing down a long straight tube is longer than the front of He, appearing in advance of the front of He but reaching full concentration later. A glass model of five generations of symmetrically branching tubes was used by Scherer et al. (1975) to demonstrate 11
106
Keith HorsfieM
enhancement of the effective diffusivity of benzone vapour in the main stem. A hollow cast of the airways of a pig lung was used by Horsfield et al. (1977) to show that when a mixture of gases was blown down the main bronchus the front of SF6 arrived distally in advance of that of either He or Argon (Ar). In dog lungs the transit time of carbon monoxide (CO) was observed by Wagner et al. (1969) to be less than half that expected for convective flow, a result they attributed to Taylor dispersion. Mazzone et al. (1976) found that He, when inhaled in a mixture of differing diffusivities, penetrated less deeply into the lung than expected, and this they attributed to radial diffusion of He. A similar result was obtained by Hogg et al. (1972). They showed that in dog lungs insuffiated with beads SF6 penetrated deeper than He, and this they attributed to Taylor dispersion. A different kind of experiment has been to use gases of differing diffusivities to transport 02 or CO into the lungs, and measure in some way their rate of arrival at the alveolarcapillary membrane. Johnson and Van Liew (1974) measured arterial blood Po2 when O2 was inspired in He and in N2. They found Pao2 rose more rapidly with the O2/N2 mixture. The uptake of CO, when inspired in He, N2 or SF6, plus 02, was measured by Kvale et al. (1975). It was greatest in SF6 and least in He. In both the above experiments the authors' interpretation was that the test gas is more effectively carried into the lung by the denser carrier gas which is more effectively dispersed longitudinally by Taylor dispersion. Whether pathological changes affect gaseous diffusion or Taylor dispersion in the conducting airways is not known. There remains the possibility, as yet unexplored, that the pattern of Taylor dispersion in diseased lungs might be used as a test of function or of structural change.
TERNARYDIFFUSION In respiratory experiments performed on living animals and man at least three gases are present in the lungs, and sometimes more. The presence of each gas affects the diffusion of the others and it is pertinent to enquire whether the binary diffusion coefficients commonly employed in calculations are adequate. If this problem is examined in detail it will be seen to be very complex indeed because during a respiratory manoeuvre the concentrations of the various gases at any point in the airways may change rapidly over a wide range. Worth et al. (1978) have determined diffusion coefficients for various gases in mixtures similar to alveolar gas. They found that the effective diffusion coefficients could be satisfactorily predicted by adding the reciprocals of the binary diffusion coefficients (diffusion resistances) weighted for the fractional concentration of the gases. The addition of more than one test gas, diffusing in the same or opposite directions, had no effect on diffusion provided that the concentrations were below 1%. At up to 10%, however, some interactions were observed. Water vapour was found to diminish D for light gases, have little effect with normal respiratory gases, and to increase D with heavy gases. Modell and Farhi (1976) investigated ternary diffusion using He, 02 and N2. Starting with 21% 02 in He at one end of a partitioned cylinder and 21% 02 in N2 at the other, when the central partition was removed the concentration of 02 at the N2 end fell, while it rose at the He end; it then returned to equilibrium concentrations. Between one and seven minutes in the experiment the concentration of oxygen mixing by ternary diffusion
Gaseous Diffusion in the Lungs
107
was actually increasing against a concentration gradient. The explanation for this is that He diffusing rapidly into the O2/N2 mixture caused the pressure to rise at that end of the cylinder, and hence produced convective flow in the direction of the 02/He mixture. There was thus a nett movement of 02 towards the He, producing an increase in 02 concentration. Thus when non-respiratory gases are inhaled for the purpose of physiological investigation one cannot be certain that a gas in the airways is always moving in the direction of the concentration gradient. A degree of caution in the interpretation of such experiments is therefore required. DIFFUSION IN THE AIRWAYS DISTAL TO THE TERMINAL BRONCHIOLES
Airways distal to the terminal bronchioles bear alveoli and are therefore termed respiratory, though Weibel (1963) termed the respiratory bronchioles transitional. Together the structures supplied by a terminal bronchiole constitute an acinus, which is usually pyramidal unless its shape is constrained by a pleural edge or a large adjacent structure. Both the airway and the artery enter at the apex. The airway then divides frequently so as to give throughout the lung a rapid increase in summed cross-sectional area, from about 80 cm 2 at the respiratory bronchioles to 104 cm 2 in the distal ducts, this occurring over a length of about 7 mm. Over 80% of the volume of a lung inflated to 75% of total lung capacity is made up of acinar air. With such a large cross-sectional area available molecular diffusion inevitably plays an important part in the movement of gas molecules in the respiratory airways. Because of the small size and inaccessibility of the structures concerned, investigation of diffusion in situ is difficult. The main efforts directed at this problem have been of two kinds: (1) study of the behaviour of gases of different diffusivities when respired, and (2) mathematical analysis of more or less complex models.
Behaviour of gases diffusing in the respiratory airways As has already been pointed out, oxygen is carried into the respiratory zone by convective flow and reaches distally-situated alveoli by molecular diffusion (Fig. 6). Similarly, carbon dioxide diffuses out in the reverse direction. There is thus a mixing of gases in the respiratory zone brought about by molecular diffusion, and this is the most important function of the airways at this level. It can be simply illustrated by the single breath test for nitrogen, in which a breath of 100% oxygen, usually 1000 ml, is inspired, and the concentration of nitrogen in the following expirate is measured and plotted against expired volume. If mixing within the respiratory airways were complete, but none at all occurred between the respiratory and the conducting airways, the expired nitrogen plot would be as in Fig. 7A, with no nitrogen in the first 150 ml or so, then a sudden upstroke in concentration, and finally a perfectly level plateau of alveolar nitrogen diluted with inspired oxygen. The 150 ml containing no nitrogen is the dead space, that is it represents that part of the airway in which no diffusive mixing has occurred (convective mixing on expiration being ignored). In reality the concentration curve is more sigmoid, with a less vertical upstroke and usually a gently rising plateau (Fig. 7B). The dead space can still be determined from this curve in terms of the volume of unmixed gas (Cumming et al. 1971) but the slope of the plateau has been the cause of much discussion. On the one hand it has been thought to represent regional variations in ventilation with oxygen,
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Keith Horsfield
followed by regional variations in rates of emptying, known as regional inhomogeneity. On the other hand, it has been thought to represent a failure of complete diffusive mixing in the respiratory airways. More rationally, it can be considered as the result of the interaction between regional factors, both anatomical and functional, and molecular diffusion (Pack et al. 1977). It is not the purpose of this paper to discuss the relative merits of these different interpretations, but rather to concentrate on the role of diffusive mixing. If we consider the process of getting oxygen up to the alveolar capillary membrane and carbon dioxide away from it, and also the maintenance of a flux of these gases through the membrane, it is a priori obvious that concentration gradients for these gases must exist, otherwise there would be no driving force for diffusion. The question is, then, not whether there is a gradient but rather what is its magnitude ? 100
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109
Gaseous Diffusion in the Lungs A
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ss Expired volume
Fig. 8. The appearance of SF6 and Ne in the expirate following inhalation of a mixture containing both gases
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Keith Horsfield
differences, the lapse of time permitting diffusive mixing to continue (possibly aided by cardiogenic mixing; see below).
Mathematical analysis of diffusion in the respiratory airways The study of diffusion in the airways by model analysis was started by Rauwerda (1946) who, using a simple model of the acinus, came to the conclusion that diffusive mixing was so rapid that no measurable gradient would be left after one second. Since then a considerable number of model analyses have been reported. Each of these has concentrated on one or two particular aspects of the problem and produced various conclusions. Those which conclude that mixing is effectively complete within the time of a normal respiration include La Force and Lewis (1970) and Paiva (1973). Those which suggest that mixing is not complete include Cumming et al. (1966, 1971) and Pack et al. (1977). These authors also make the point that regional differences, convection and diffusion interact so that consideration of any one without the others is meaningless. The variations of alveolar oxygen and carbon dioxide concentrations with time during the respiratory cycle have also been investigated using model analysis (Lin & Cumming 1973 ; Davidson & Fitz-Gerald 1974) as have the dead spaces for gases of different diffusivities (Cumming et al. 1971; Lacquet et al. 1975; Paiva et al. 1976; Sikand et al. 1976). Three good reviews of the general topic of model analysis of diffusion in the respiratory airways are those of Chang and Farhi (1973), Curnming (1974), and Pedley (1977). Of critical importance in model analyses are the boundary conditions employed. In most of the studies so far discussed the assumption has been made that there is no concentration gradient (dc/dx = 0) at the alveolar wall. Results from these studies suggest that gas mixing in the respiratory region is rapidly completed. Exceptions to this include Cumming et al. (1971), Butler (1974), Jones (1977), and Scrimshire et al. (1978), who assumed a no flux boundary condition at the alveolar wall. Their results suggest that gas mixing is incomplete. The problem of the correct choice of boundary condition is further discussed by Paiva et al. (1979) and is at present unresolved. Gomez (1965) pointed out how the movement of gas molecules by convection falls off rapidly as they enter the respiratory zone in the lung while movement by molecular diffusion rapidly increases. There is thus a cross-over point where the two are equal (Fig. 9) at about the level of the terminal bronchioles. Cumming et al. (1971) investigated the possible effects of this by a model analysis in which both diffusion and convective flow were represented. They showed the presence of a static front of nitrogen at about 250 ml down the model of the airways, independent of the volume of oxygen inspired (Fig. 10); this occurs because at that point nitrogen is diffusing up the airways at exactly the same rate as it is being convected down. Using a more sophisticated analysis Paiva (1973) came to the same general conclusion.
Explanation of the static front For a static concentration front to become established between a gas flowing down a tube and one diffusing up in the opposite direction the tube must have a trumpet-like shape. This the airways have if the cross-sectional areas at any given level are added together (Horsfield 1974). If oxygen, for example, is blown down the narrow end of such a tube into an atmosphere of nitrogen (Fig. 11) then nitrogen will diffuse up the wide end. Somewhere in the tube (flow and diffusivity being appropriate) a static nitrogen
Gaseous Diffusion in the Lungs
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front develops. Some molecules (Fig. llA), moving faster than average, will be further up the tube, but the further they get the higher is the velocity tending to sweep them down again. Other molecules (Fig. 11B), moving up the tube more slowly than average, will tend to be swept down, but the further down they go the slower is the velocity so that diffusion brings them back again. Although the nitrogen front is static oxygen continues to pass through it and out at the far end because there is a continuous flow of oxygen. In the lungs, where there is a closed elastic bag (the alveoli) distal to the tube, the OO
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Fig. 9. The relative velocity of molecular transfer in the airways by convective (bulk) flow and molecular diffusion (see text). (From Muir 1966) absolute concentration of nitrogen continues to fall during inspiration as it is diluted by the incoming oxygen, but the position of the front is nevertheless static if flow is constant (Fig. 12). Paiva et al. (1976) developed a simple mathematical relation between anatomy (the shape of the trumpet), diffusivity, and flow. Where the front is static dA dx
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where A = summed cross-sectional area, x = linear distance, I/= flow, and D = diffusion coefficient. In words, at the static point the rate of change of cross-sectional area with distance down the airways is equal to the flow divided by the diffusion coefficient. Thus,
Keith Horsfield
112
if the anatomy is known a plot of cross-sectional area against length can be drawn (Fig. 13) and a line of slope F/D constructed as a tangent to the graph. The point where the tangent meets the curve corresponds to the static point, which can be read off the abscissa in terms of length down the airways. When the calculations are made with values of D corresponding to hydrogen and sulphur hexafluoride, the static hydrogen front becomes established nearer the mouth than does the sulphur hexafluoride front, and thus the more diffusable gas has the lower dead space. 0.0
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Fig. 10. Calculated nitrogen concentration profiles in a lung model during the inspiration of 1 litre of oxygen over 1.5 seconds. Note the static front at about 250 ml The static front has been demonstrated in the airways of dogs by Engel et al. (1973) and Fukuchi et al. (1976). They also showed that in the living animal the position of the front oscillates back and forth with the heart beat and that this motion facilitates mixing between the gases on each side of it. Their data suggest that the effect of the heart beat on mixing is equivalent to increasing the diffusion coefficient within the airway by a factor of five.
Tests of mixing The position of the concentration front is obviously one factor determining tile magnitude of the 'anatomical' or 'series' dead space, which varies with lung volume (airway cross-section), the diffusion coefficient of the gas used, and the duration of any breath-holding period during which the interface will move up the airways by diffusion. The single-breath nitrogen test thus gives information on gas mixing with regard to both the slope of the plateau and the size of the dead space.
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The multi-breath test is carried out by the subject inhaling a gas containing no nitrogen, breathing normally for several minutes. A mixture of 79% argon and 21% oxygen is suitable for this, avoiding the effects on ventilation which occur when 100% oxygen is used. Nitrogen is progressively washed out of the lungs and its end expiratory concentration measured. Plotting concentration on a logarithmic scale against breath number gives a curve which in a perfect mixing system would be linear, in a normal lung is
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Distoncedowntube Fig. 11. Static front of nitrogen in a trumpet-shaped tube when oxygen is blown down at a constant flow. A, Molecules of N2 diffusing up quicker than average. B, Molecules of N2 diffusing up slower than average (see text) slightly curved, and in an abnormal lung is more or less markedly curved (Becklake 1952). This technique has been improved by Prowse and Cumming (1973) who measured the quantity of nitrogen remaining in the lung after each breath and plotted nitrogen decay curves (Fig. 14). The degree of divergence from perfect mixing is expressed as an inefficiency, which contains both regional and series mixing defects. Such inefficiencies are seen in airway obstruction of all kinds, since in these inspired gas cannot mix well with alveolar gas. In centrilobular emphysema the dilatation on the respiratory bronchioles forms a series mixing chamber (Fig. 15A) which impairs mixing between inspired
Keith Horsfield
114-
g
~
V|
vz
~. O
V3
g t)
0
Na
Distance down airways
Fig. 12. Behaviour of static front in lung when flow is constant but inspired volume (V) increases.
Va>Vs>V~
g .D
to
f
"dx D I I
Distance down airways
Fig. 13. Definition of the anatomical site of the static front. Th e curve is a plot of summed crosssectional area of the airways at any given level against distance down the airways to that level. If flow (V) and diffusion coefficient (D) are known, then the slope of the tangent dA/dx can be found. Th e point where the tangent touches the curve is the site of the static interface
and alveolar gas (Horsfield et al. 1973), while in panacinar emphysema mixing is slow in the distal dilatation (Fig. 15B). A series mixing problem of a different kind arises with blockage of peripheral airways with plugs of mucus, as in asthma. Collateral ventilation from adjacent acini can occur, but with a marked defect in mixing between the two (Fig. 15c).
Gaseous Diffusion in the Lungs
.~
115
810
c
~-"d ~ c o_= ="6 ~m = ~>
81
Perfec \ ~ ~ Normol mixing ~ ~'N~bjects Turnover of lung volume
Fig. 14. Lung nitrogen decay curves obtained by breathing a mixture of 79% Ar and 21% 02. One turnover of lung volume is when the sum of the tidal volumes equals the lung volume
A B C Fig. 15. Some lesions in airway disease causing serious mixing defects. A, Centrilobular emphysema. B, Panacinar emphysema. C, Airway blockage (asthma) with collateral ventilation of adjacent acini DIFFUSION ACROSS THEA LVEOLAR-CAPILLARY
M E M B R A N E
Anatomy T h e last part of the pathway taken by an oxygen molecule on its way to a red cell is the shortest but also the most complex--its passage through the alveolar wall. Four different tissues must be traversed before it reaches a haemoglobin molecule with which to combine (Weibel 1970/71). These are: 1. 2. 3. 4.
The The The The
surfactant layer. tissues of the alveolar wall. plasma in the capillary. red cell wall.
116
Keith Horsfield
The surface layer of surfactant is 5-20 nm thick; it consists of a basal layer and a phospholipid film 2-3 nm thick. It fills out crevices and acute angles, where it may be 1-3 Fm thick, thereby making the alveolar air space smoother and more rounded. Tissues of the alveolar-capillary membrane are basically two cells thick, the alveolar epithelial cell and the capillary endothelial cell, each with its basement membrane (Fig. 16). Thus an oxygen molecule must traverse the cell membrane, cytoplasm, cell membrane and basement membrane of the epithelial cell, the interstitial space, and the basement membrane, cell membrane, cytoplasm, and cell membrane of the endothelial cell. This is the minimum. But the interstitial space between the two basement membranes may contain ground substance, fibrous tissue, or liquid. Although the cytoplasmic extensions of the cells occupy most of the alveolar surface area, the cells do have nuclei, and where interstitium or nuclei are present the thickness may be 5 Fm or more. ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Cell membrane i ii!!!iiii!i i:i:i!iiii!iiiiiiiiiii fii !!iii!ii!iii ii fiiii i:!:!:i:i:i:i:i:!:!:!:i!iiiiiiiiiiiii!ii!i i ii!!i!iiii i i !:i:i:i:i:i:i:i:i:i:i:i:!:i:i:i:-Cy t 0 p la s m i!iiii!i!i!ii!i!iii•i•!i!::iii•i•i::!iiiiiiiiiii!i!iii!iiiii!!iiiiii•i•i•ii!•!i!ii•i•!iiiiiiii•i•ii!iiiii•!iiiiiiiiiii••!iii•••iiii•i• Cell membrane ~::~]~::~::~::~::::~::::~:~J::~JJ~::~]~[~::~:.~::~:J~::~::~::~::~:::::.~::~ B a s e m e n t membrane --Interstitial space ii!! !ii!!!!iii:i:!:!:i:i:i:!:i:i:i:i:i:!:i:: :i:!::::: ::: !!iii !ii i!!i!ii!iiiiiii!iiiiiiii!iiiiii !!!i !!ii i i!i i ii!!ii iii!ii!i!i!!"~ Ba se m ent membrane £:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::Cell membrane ii iiiii !!ii ::ili iiii iiiiiiiiiiiii:.ii!iiiiiii ::ii :: ii :::ii iiiiiiiiii!iiiiiii!iiiiiiiiiiii::i!iiiiii i i i i!ii!i!iiiiiiiiiiiiiiiiiii i if!i i- C y to p la s m iiiiii!i!iiiiiiiiiiiiiiiii!i!iiiiiiiiiiiiiiiiiiiiiiiiiiiiii!iiiii!i!iiii!iiii! i:.iiiii!ii!iiiiii!iiiiiiiiiii! iiiiii!iiii!iii!i!iiiiiii!iiiiiiiiiii!iiii!iiiiiiiii!iiiiiiiiiii!iiiil J C el I membrane
-[ r E p i t h eli u m J
q ) E n dot h eli u m
Fig. 16. Basic structure of the alveolar-capillary membrane
The plasma layer may be extremely thin, 5-10 nm, where the edge of a red cell appears to be in contact with the capillary wall, but in the centre of the capillary lumen oxygen may have to traverse half the capillary lumen in serum. Diffusion of oxygen into the red cell and its reaction kinetics with haemoglobin is a separate subject and will not be dealt with here. In a fully inflated lung the alveolar walls are probably flat, but at lower volumes the capillaries may bulge into the alveolar lumen. While the capillaries do not occupy the whole of the alveolar wall surface, if they are bulging into the lumen their surface area may not be much less than this. The red cells within the pulmonary capillaries have a total surface area which matches that of the alveoli, about 80 m g.
Diffusion in tissues When calculating the diffusion of gases through these structures the solubility of the gas in each is important. Table II (Weibel 1970/71) gives the diffusion coefficient, solubility, and permeation coefficient for oxygen in nitrogen, lung tissue, and plasma. Values for the surfactant layer are not known. Lung tissue and plasma are seen to have similar values which are markedly less than those for a gaseous medium.
Ternary membrane diffusion By the use of analytical methods Chang et al. (1975) showed that ternary mixtures diffusing across a membrane may behave in unexpected ways. Thus there may be no diffusion across the membrane in the presence of a partial pressure gradient, or transfer
Gaseous Diffusion in the Lungs
117
Table H. Solubility constant (~), diffusion coefficient (D), and permeation constant (K), where K = ~D, for oxygen in the lungs
Coefficient
in N~
in lung tissue
D K
-0.256 --
2.37 x 10-5 1.38 x 10-4 3.3 x 10-8
in plasma 2.8 x 10-5 ml/ml/mmHg 11.5 x 10-4 cm2/sec 3.2 x 10 -8 ml/ml/min/mmHg
where there is no gradient at all. The relevance of these findings to gas transfer in the lung is as yet unknown.
Factors affecting alveolar-capillary membrane diffusion For transfer across the membrane to occur, an oxygen molecule must first reach the alveolar wall, then go into solution in the tissues, diffuse through them, finally to combine with haemoglobin. This process can be affected by various factors. Exudate, oedema fluid or excess surfactant within the alveolar lumen will greatly slow down the rate of arrival of oxygen molecules at the alveolar wall. The alveolar epithelial cells or the capillary endothelial cells may be thickened, and between them fibrous tissue may increase or fluid accumulate. Within the capillary the diffusion distance may be increased with capillary dilatation. The total functional surface area puts an upper limit on the transfer of gases; it is that surface area which is ventilated with fresh gas and in contact with functioning capillaries. Exercise causes capillary recruitment as pulmonary blood flow increases and this helps to increase oxygen uptake. Surface area varies with lung size, increasing during growth and varying over a wide range between individuals. It increases with inspiration and is reduced in such conditions as emphysema, embolism and pneumonectomy.
Tests of alveolar-capillary membrane diffusion Diffusion across the alveolar-capillary membrane is usually estimated using carbon monoxide (CO). The method involves the inhalation of a small amount of CO, estimating its alveolar concentration, and calculating how much is taken up by the blood in a given time. From this the transfer factor for the lung for CO is calculated, usually as ml of CO per minute for each m m H g partial pressure difference. Capillary partial pressure of CO is taken to be zero because it combines so rapidly with haemoglobin. Hence the partial pressure difference is equal to the alveolar pressure. The test can be performed as a single breath with 10 seconds' breath-holding, or as a multi-breath method. Because CO molecules have to traverse the total pathway already described, their rate of uptake is limited by the series resistances offered by the conducting airways, diffusive mixing in the respiratory airways, diffusion across the membrane, plasma and red cell wall, and the reaction kinetics with haemoglobin. The result obtained from an estimation of TLCO is therefore dependent also on factors other than the alveolar-capillary membrane resistance, for example, on the imperfection of alveolar mixing. As we have already seen, this is probably the case even in normal lungs and is certainly the case in diseased lungs. Distribution of ventilation and perfusion may be mismatched so that CO going to unperfused areas will not be transferred to the blood. In such cases a low Tr~co, while
118
Keith Horsfield
measuring the ability of the lung to take up CO, is not necessarily a measure of the conductance of the alveolar-capillary membrane. The other important determinant of CO uptake is the blood itself. Even static red cells in the pulmonary capillaries will take up CO, and so long as the quantity of CO is small enough the blood may not be a limiting factor. The number of red cells in the capillaries and their haemoglobin content are important, so that TLco may be increased in polycythaemia and decreased in anaemia. The longer the time spent in a capillary by a red cell the more likely is it to become a limiting factor, and conversely faster flow may increase uptake. Finally, the balance between the formation of carboxyhaemoglobin and oxyhaemoglobin determine how much CO is actually taken up by the haemoglobin, and this is affected by the partial pressures of CO, oxygen, and carbon dioxide prevailing in the pulmonary capillaries, as well as pH, temperature, and red cell chemistry. In spite of the above problems the measurement of TLCO helps in the study of diseases affecting the alveolar wall. The significance of an abnormal result can be better interpreted from the above discussion.
IN CONCLUSION Molecular diffusion is an important mechanism during all phases of the movement of gas from the external air to the red cells. It is difficult to study in intact animals and difficult to model mathematically. Results of new model analyses, each more complex and comprehensive than the last, regularly appear in the literature; whether the results will be worth the effort expended in obtaining them remains to be seen. No better illustration of the interdependence of physiology, anatomy and basic sciences can be found than in the study of molecular diffusion in the lungs. REFERENCES Ares, R. (1956) On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. A 235, 67. BECKLAKE,M. R. (1952) A new index for the intrapulmonary mixing of inspired gas. Thorax 7, 111. BUTLER,J. P. (1974) Oxygen Transport in the Human Lung. PhD thesis, Harvard University, Cambridge, Mass., USA. CHANt, H.-K. (1976) Effect of Taylor dispersion on stratified inhomogeneity. Physiologist 19, 151. CHANG, H.-K. & FARHI, L. E. (1973) On mathematical analysis of gas transport in the lung. Resp. Physiol. 18, 370. CHANG, H.-K., TAI, R. C. & FARSI, H. E. (1975) Some implications of ternary diffusion in the lung. Resp. Physiol. 23, 109. CUMMING, G. (1967) Gas mixing efficiency in the human lung. Resp. Physiol. 2, 213. COMMINC, G. (1974) Alveolar ventilation: Recent model analysis. In: M T P International Review of Science: Respiratory Physiology, ed. J. G. Widdicombe, series 1, vol. 2, p. 139. London: Butterworths. CUMMINC, G., CRANK,J., HORSFmLD,K. & PARKER,I. (1966) Gaseous diffusion in the airways of the human lung. Resp. Physiol. 1, 58. CUMMING, G., HORSFIELD,K., JONES, J. G. & Mum, D. C. F. (1967) The influence of gaseous diffusion on the alveolar plateau at different lung volumes. Resp. Physiol. 2, 386. CUMMING,G., HORSFIELD,K. & PRESTON,S. B. (1971) Diffusion equilibrium in the lungs examined by nodal analysis. Resp. Physiol. 12, 329. DAVIDSON, M. R. & FiTz-GERALD,J. M. (1974) Transport of 02 along a model pathway through the respiratory region of the lung. Bull. Math. Biol. 36, 275. EN~EL, L. A., WOOD, L. D. H., UTZ, G. & MACKLEM,P. T. (1973) Gas mixing during inspiration. J. appl. Physiol. 35, 18.
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FUKUCHI, Y., Roussos, C. S., MACKLEM,P. T. & ENGEL,L. A. (1976) Convection, diffusion and cardiogenic mixing of inspired gas in the lung; an experimental approach. Reap. Physiol. 26, 77. GEORG, J., LASSEN,N. A., MELEMGAARD,K. & VINTHER,A. (1965) Diffusion in the gas phase of the lungs in normal and emphysematous subjects. Clin. Sci. 29, 525. GOMEZ, D. M. (1965) A physico-mathematical study of lung function in normal subjects and in patients with obstructive pulmonary diseases. Med. Thorac. 22, 275. HoGo, W., BRUNTON, J., KRYGER, M., BROWN, R. & MACKLEM,P. (1972) Gas diffusion across collateral channels. -7. appl. Physiol. 33, 568. HORSFIELD, K. (1974) The relation between structure and function in the airways of the lung. Dr. -7. Dis. Chest 68, 145. HORSHELD, K., DARER, D. H. & CUNNING, G. (1973) Centrilobular emphysema studied with a mathematical model. Scand. -7. resp. Dis. 54, 53. HORSFIELD, K., DAVIES, A. & CUMMING,G. (1977) The role of the conducting airways in the partial separation of inhaled gas mixtures. -7. appl. Physiol. d3, 391. JOHNSON, R. L. & VAN LIEW, H. D. (1974) Use of arterial Po2 to study convective and diffusive gas mixing in the lungs. J. appl. Physiol. 36, 91. JONES, T. J. (1977) Quantitative Analysis of Transport and Transfer in Human Lungs. PhD thesis, University of Aston, Birmingham. KVALE,P. A., DAVIS,J. & SCHROTER,R. C. (1975) Effect of gas density and ventilatory pattern on steady-state CO uptake by the lung. Resp. Physiol. 24, 385. LACQUET, L. M., VAN DER LINDEN, L. P. & PAIVA, M. (1975) Transport of H2 and SF6 in the lung. Resp. Physiol. 25, 157. LA FORCE,R. C. & LEWIS, B. M. (1970) Diffusional transport in the human lung. -7. appl. Physiol. 28, 291. LIN, K. H. & CUNNING, G. (1973) A time varying model of gas exchange. Resp. Physiol. 17, 93. MAZZONE,R. W., MODELL,H. I. & FARHI, L. E. (1976) Interaction of convection and diffusion in pulmonary gas transport. Resp. Physiol. 28, 217. MODELL,H. I. & FARHI,L. E. (1976) Ternary gas diffusion--in vitro studies. Resp. Physiol. 27, 65. MUIR, D. C. F. (1966) Bulk flow and diffusion in the airways of the lung. Br..7. Dis. Chest 60, 169. PACK,A., HOOPER,M. B., NIXON,W. & TAYLOR,J. C. (1977) A computational model of pulmonary gas transport incorporating effective diffusion. Resp. Physiol. 29, 101. PAIVA, M. (1973) Gas transport in the human lung. -7. appl. Physiol. 35, 401. PAIVA,M., ENGEL, L. A., CHANG,H. K. & SCHEID,P. (1979) On the boundary conditions used in calculations of gas mixing in alveolar lungs. Resp. Physiol. 37, 1. PAIVA, M., LACQUET,L. M. & VAN DER LINDEN, L. P. (1976) Gas transport in a model derived from Hansen-Ampaya anatomical data of the human lung..7, appl. Physiol. 41,115. PEDLEY, T. J. (1977) Pulmonary fluid dynamics. Ann. rev. Fluid Mech. 9, 229. POWER, G. (1969) Gaseous diffusion between airways and alveoli in the human lung. -7. appl. Physiol. 27, 701. PROWSE, K. & CUMMING,G. (1973) Effects of lung volume and disease on the lung nitrogen decay curve. -7. appl. Physiol. 34, 23. RAUWERDA,P. E. (1946) Unequal Ventilation of Different Parts of the Lung and Determination of Cardiac Output. MD thesis, Groningen University. SCHERER, P. W., SHENDALMAN,L. H., GREENE,N. M. & BOUHUYS,A. (1975) Measurement of axial diffusivities in a model of the bronchial airways. -7. appl. Physiol. 38, 719. SCHROTER, R. C. & SUDLOW,M. F. (1969) Flow patterns in models of human bronchial airways. Resp. Physiol. 7, 341. SCRIMSHIRE,D. A., LOUGHNANE,R. J. & JONES, T. J. (1978) A reappraisal of boundary conditions assumed in pulmonary gas transport models. Resp. Physiol. 35, 317. SIKAND, R. S., MAGNUSSEN,H., SCHEID, P. & PIIPER, J. (1976) Convective and diffusive gas mixing in human lungs: experiments and model analysis..7, appl. Physiol. 40, 362. TAYLOR, G. (1953) Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. A 219, 186. VAN LIEW, H. D. & MAZZONE,R. W. (1977) Mixing in flowing gas. Resp. Physiol. 30, 27.
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WAGNER,W. W., LATHAM,L. P., BRINKMAN,P. D. & FILLEY, G. F. (1969) Pulmonary gas transport time: larynx to alveolus. Science, N.Y. 163, 1210. WEIBEL, E. R. (1963) Morphometry of the Human Lung. Berlin: Springer Verlag. WEIBEL, E. R. (1970/71) Morphometric estimation of pulmonary diffusion capacity. I. Model and method. Resp. Physiol. 11, 54. WILSON, T. A. & LIN, K. H. (1970) Convection and diffusion in the airways and the design of the bronchial tree. In: Airway Dynamics, ed. A. Bouhuys. Springfield, Ill. : Charles C. Thomas. WORTH, H., NOSSE, W. ~ PIIPER, J. (1978) Determination of binary diffusion coefficients of various gas species used in respiratory physiology. Resp. Physiol. 32, 15. WORTH, H. & PIIPER, J. (1978) Diffusion of helium, carbon monoxide and sulphur hexafluoride in gas mixtures similar to alveolar gas. Resp. Physiol. 32, 155.
Review Article GASEOUS
DIFFUSION
IN THE
LUNGS
KEITH HORSFIELD Midhurst Medical Research Institute, Midhurst, Sussex, England
The change in environment experienced by the vertebrates when they moved from the habitat of the sea to that of dry land brought with it some evolutionary changes in their respiratory mechanisms. Water can pass over the gills of a fish in a continuous flow bringing oxygen directly to them. In the land vertebrate, however, the need to conserve water which would be lost from an external gas exchange membrane has resulted in the development of an internal lung. The airways of mammals are a complex system of branching tubes open to the atmosphere at one end only and this necessitates reciprocating flow to achieve ventilation. But convective flow of inhaled fresh gas can not continue right up to the alveolar walls because these form blind endings in the airways. Some other mechanism must therefore move oxygen molecules up to the alveolar walls and carbon dioxide molecules away from them. This mechanism, by which gases in the respiratory airways become mixed, is molecular diffusion; without it mammalian lungs would be unable to exchange oxygen and carbon dioxide between air and blood. Inspired oxygen moves down the airways to the blood by three distinct physical processes: 1. Convective flow in the conducting airways. 2. Molecular diffusion in the gas phase in the respiratory airways. 3. Molecular diffusion in the tissue phase across the alveolar-capillary membrane. There is, of course, some overlap and interaction between (1) and (2), since diffusion also occurs in the conducting airways and convective flow in the respiratory airways. Each process, going down, is progressively less efficient at transporting gas, but this inefficiency is compensated for by the diminishing distance over which each operates and the rapid increase in the cross-sectional area of the airways distally, terminating in about 80 m ~ of alveolar surface area. These correlations between structure and function have been discussed in a previous article in this Journal (Horsfield 1974). The purpose of this article is to review the role of molecular diffusion in the respiratory processes of normal lungs, how diseases affect it and how pulmonary function tests attempt to measure it. Complex mathematical equations have been deliberately avoided in order to make the text more easily understandable, but a few simple equations have been included. Those who are interested in this aspect should be able to find their way into the subject from the references. MOLECULAR DIFFUSION
Molecules in a gas are in constant random motion, travelling in straight paths until colliding with other molecules or the walls of the container, when they bounce off in a
1O0
Keith Horsfield
new direction. If two species of molecules are introduced into a closed container they will intermix by virtue of this motion. The process is more rapid at higher temperatures, which increase molecular movement, and slower at higher pressures, when the molecules are more crowded. o
o o
o
o o o
o o
o
0
o
o
o
•
o
A
gas X
•
•
gasY
•
0 0
• •
0
0
0
• 0
•
0
0 0
•
0
•
o •
o
o
o
o
Fig. 1. Molecular diffusion in a cylinder. A, Two gas species separated by a partition. B, On removal of the partition the two gases start intermixing +1 t1
g
E
E
too
~0 g P
LL
-1 Distance along tube from partition
Fig. 2. Time course of diffusive mixing in the cylinder shown in Fig. 1. to = time before removing partition, tx to t4= successive time intervals after removal of partition, too= infinite time (mixing complete)
Imagine a cylindrical container with a thin movable partition down the middle (Fig. IA) and a different gas in each half. At time zero the partition is instantly removed and the two gases diffuse into each other (Fig. 1B). At first mixing is rapid but as each gas becomes more evenly distributed between the two halves the rate of mixing diminishes (Fig. 2). The quantity of gas passing across a plane of section in a given time is
Gaseous Diffusion in the Lungs
101
proportional to the concentration gradient, the cross-sectional area and the diffusivity of the gas. Diffusivity is expressed as the diffusion coefficient (D), the quantity of gas diffusing across unit area in unit time per unit gradient of concentration. This must be at a stated temperature and pressure. It has the basic units of cm 2 s -1 and is inversely proportional to the square root of the molecular weight of the gas, so that the larger the molecule the less easily it diffuses. When two gases mix by diffusion the behaviour of each is modified by the nature of the other. T h u s oxygen will diffuse into sulphur hexafluoride at a rate different from that at which it will diffuse into hydrogen. T h e diffusion coefficient must therefore be stated for two gases, for example oxygen and nitrogen diffusing into each other at 20°C, D = 0.22 cm z s -1 ; this is termed a binary diffusion coefficient. Table I gives the binary diffusion coefficients for some gases commonly used in respiratory work. Table I. Binary diffusion coefficients (D) in cm2/sec, at 37°C and 746 torr, dry Gases
D
Gases
D
02 in N2 CO2 in N2 CO2 in 02 CO in N2 CO in 02 CO in CO2
0.256 0.181 0.170 0.237 0.247 0.179
He in N2 He in CO2 02 in He SF6 in N2 SF6 in 02 SF6 in CO2
0.743 0.662 0.893 0.105 0.099 0.076
After Worth et al. (1978). In Fick's first equation of diffusion the driving force is stated in terms of the concentration gradient dQ dt -
aDdC dx
where Q is the quantity of gas, t is time, A is the area over which diffusion is occurring, c is the concentration of the gas species, D is the diffusion coefficient and x is linear distance. T h e equation simply says that the rate at which a substance diffuses, dQ/dt, is proportional to the area, the diffusion coefficient and the concentration gradient, dc/dx. T h e minus sign indicates that the direction of movement is down the concentration gradient. With gases in the gas phase, partial pressure is proportional to concentration and in respiratory work it is common to think of diffusion in terms of partial pressure. Strictly speaking, however, it is the activity (fugacity) of the gas which drives diffusion, which is similar to but not quite the same as partial pressure. When we come to consider diffusion in the blood and lung tissues another factor has to be taken into account, which is that the gas is soluble in serum and tissues. An example of the effect this has is as follows. Consider a two-phase system (Fig. 3) at 37°C with saline in one half equilibrated with oxygen at a partial pressure of 100 m m H g and olive
Keith Horsfield
102
oil in the other half equilibrated with oxygen at 40 mmHg, the two separated by a thin membrane. The concentration of oxygen is nearly twice as much in the oil, but oxygen will diffuse in the direction of the partial pressure gradient, that is against the concentration gradient, from the saline to the oil. In calculating the quantity of gas diffusing in a solvent, partial pressure must be used. If the solubility is e~ then concentration c = ~P, where P is the partial pressure, and Fick's equation becomes dQ dt -
dP AD C~dx
where dP/dx is the partial pressure gradient.
SALINE
OLIVE OIL
Oxygen content 0.0032 ml./rnt
0.0058 mt/m!. Oxygencontent
Partial pressure100 mm Hg
40 rnm Hg Portial pressure
Diffusion of oxygen T E
Fig. 3. Diffusion of oxygen in a two-phase liquid system. Although the oxygen content of the olive oil is greater the direction of diffusion is down the partial pressure gradient. The difference in content is due to the greater solubility of oxygen in olive oil TAYLOR DISPERSION The interaction between convective flow and simultaneous molecular diffusion in the airways, though not clinically important, is of considerable interest. The phenomenon was first investigated by Taylor (1953). If a gas, such as nitrogen, flows down a long straight tube at a velocity appropriate for laminar flow a parabolic velocity profile develops (Fig. 4A). Gas at the centre of the tube flows fastest and that at the edges slowest, and when fully developed the gas at the centre moves at twice the average velocity. Suppose now that a different gas, such as oxygen, is introduced into one end of the tube, starting off with a perfectly straight front between the two (Fig. 4B). As the oxygen flows down the tube displacing the nitrogen in front of it, the parabolic velocity profile causes the oxygen molecules in the centre of the tube to move faster and hence to progress further down the tube. A parabolic concentration profile would develop (Fig. 4c) if no mixing occurred between the two gases. However, diffusive mixing does occur, blurring the interface and changing the shape of the concentration profile. Although gas
Gaseous Diffusion in the Lungs
103
molecules move in all directions, it is convenient to think in terms of two components of their movement, axially along the tube and radially across it. Thus oxygen diffuses radially out of the central core and into the surrounding nitrogen and nitrogen in the reverse direction (Fig. 40). Those oxygen molecules which diffuse radially enter the slower-moving peripheral stream and are therefore transported more slowly than before. The higher the diffusion coefficient the more easily does radial diffusion occur, so that heavier gases tend to stay in the central core and be transported more rapidly. Comparing two gases in a mixture, say the light gas helium (He) and the heavy gas sulphur hexafluoride (SF6), in the circumstances just described, the front end of the concentration profile of the less diffusable gas SF6 arrives first at a given station S in the tube (Fig. 5A). Up to the point where the two concentration profiles cross, more SF6 than He passes S as the front flows through (Fig. 5B). Between this point and that where both gases reach maximum concentration, more He than SF6 passes S (Fig. 5c). Finally the gases pass in equal quantities when the concentration profile has passed S. !
0
0 0
0
0
0
0
0
0
0
0
0 0
0
0
0
0
0
B
0
0
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•
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•
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•
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0 0
0
C D Fig. 4. Gas flow in a tube. A, Parabolic velocity profile when flow is laminar. B, A square wave of a second gas species is introduced. C, Parabolic concentration profile of the second gas. D, Radial diffusive mixing The forward movement of a gas front undergoing Taylor dispersion is equivalent to an apparent diffusion with an 'apparent diffusion coefficient', k, where r2v 2 k = D + 192D and r = radius of tube, v = maximum velocity of flow in the centre of the tube and D = diffusion coefficient (Aris 1956). This apparent diffusion is with respect to a plane across the tube moving at the average flow velocity. Of the two terms on the right-hand side of the equation, D represents the ordinary diffusion coefficient in the axial direction, and r2v2/192D represents the apparent diffusion coefficient due to Taylor dispersion. When D is very small compared with convective flow the concentration profile approximates to the parabolic form. If D increases relative to convection the second term becomes smaller and the concentration profile becomes shorter. When D is large relative to
Keith Horsfield
104
convection the second term becomes small, k approximates to D, forward flow is slow and axial diffusion predominates. Thus the concentration profile becomes flatter across the tube and the front lengthens. It can be seen that Taylor dispersion is maximally manifest in the intermediate situation. Furthermore, the value of the term r2v2/192D is inversely proportional to D, a mathematical expression of what has already been described, namely that a heavier gas disperses longitudinally more than a lighter one. It is obvious that Taylor dispersion, concerned as it is with the front between two fluids, can operate only while the front is passing down the tube. Once it has passed, as at station S in Fig. 5c, there can be no effect from this mechanism.
$
$
c
$
Fig. 5. Partial separation at the front of a mixture of He and SF6 flowing in a tube. A, SF6 arrives at station S first. B, After the cross-over point more He than SF6 passes S. C, After the front has passed, both gases pass in equal concentrations DIFFUSION IN THE CONDUCTING AIRWAYS
Although the main function of the conducting airways is transport of gas by convective flow, molecular diffusion nevertheless occurs in them. The part played by simple diffusion in the forward (axial) transport of gas is necessarily small, because the quantity transported depends on cross-sectional area, which is relatively small, and on time in the airways, which is short. However, it seems likely that Taylor dispersion can occur in the conducting airways, at least in some of them in appropriate circumstances. In man at rest, breathing normally, tracheal flow is not high enough to cause turbulence, but turbulence does occur at the larynx and during inspiration this disturbed flow
Gaseous Diffusion in the Lungs
105
is carried down a few generations of airways, gradually dying out. Secondary vortices are generated at bifurcations (Schroter & Sudlow 1969) and eddy currents may also occur where the surface is not smooth or bends suddenly. Each of these will cause mixing of the gas front, tending to counteract Taylor dispersion. At high flows the tracheal flow regimen may approach turbulence. In this case the velocity profile, and hence the concentration profile of a second gas, are both flat, minimizing Taylor dispersion. In addition to these causes of mixing, convective flow in the upper conducting airways is high relative to diffusion, so that Taylor dispersion is minimal. Wilson and Lin (1970) were of the opinion that it does not occur to a significant degree and could be neglected, while Kvale et al. (1975) thought that it should be taken into account. Flow in the intermediate sized conducting airways is laminar, with flow velocities appropriate for Taylor dispersion to occur, but in exactly which airways depends on the diffusivity of the gas and the magnitude of the flow. Individual bronchi are too short to permit fully developed laminar flow with a parabolic profile, and this prevents Taylor dispersion from occurring maximally. In the small conducting airways, and more especially in the respiratory airways, forward flow velocity becomes low and radial diffusion rapidly obliterates radial gradients in airways of small calibre. Axial diffusion comes to dominate the formation of the longitudinal concentration gradient and is indeed the most important mechanism for moving gas in this region of the airways. The form of the concentration profile of a gas leaving an airway segment is at least partly determined by its form in the gas entering the segment. No mechanism has an isolated effect--the airways act sequentially in series so that at any point the end result is the sum of the effects of all the preceding airways. From the above discussion it can be seen that anything which changes flow and diffusivity will affect the mechanism of Taylor dispersion. Thus on exercise, when flow is increased, the region where it is maximal will move further down the airways. Test gases with widely differing diffusion coefficients will undergo maximal Taylor dispersion in different airways and to different degrees. Gases of the same diffusivity but of different viscosity might also behave differently because their flow regimens will differ. Diffusivity is related to the pressure of a gas; it will therefore be increased at altitude and diminished in compression chambers and in divers. The difficulty in calculating the effects of all these variables, and of defining detailed airway geometry, make it impossible at the present time to quantitate the effects of Taylor dispersion. In my opinion and that of Chang (1976) and Pack et al. (1977) it makes no significant contribution to normal respiration, but there is considerable evidence that it can be detected experimentally by using gases of widely differing diffusivity. EXPERIMENTALDEMONSTRATIONOF TAYLORDISPERSION Van Liew and Mazzone (1977) showed how the longitudinal concentration profile of SF6 flowing down a long straight tube is longer than the front of He, appearing in advance of the front of He but reaching full concentration later. A glass model of five generations of symmetrically branching tubes was used by Scherer et al. (1975) to demonstrate 11
106
Keith HorsfieM
enhancement of the effective diffusivity of benzone vapour in the main stem. A hollow cast of the airways of a pig lung was used by Horsfield et al. (1977) to show that when a mixture of gases was blown down the main bronchus the front of SF6 arrived distally in advance of that of either He or Argon (Ar). In dog lungs the transit time of carbon monoxide (CO) was observed by Wagner et al. (1969) to be less than half that expected for convective flow, a result they attributed to Taylor dispersion. Mazzone et al. (1976) found that He, when inhaled in a mixture of differing diffusivities, penetrated less deeply into the lung than expected, and this they attributed to radial diffusion of He. A similar result was obtained by Hogg et al. (1972). They showed that in dog lungs insuffiated with beads SF6 penetrated deeper than He, and this they attributed to Taylor dispersion. A different kind of experiment has been to use gases of differing diffusivities to transport 02 or CO into the lungs, and measure in some way their rate of arrival at the alveolarcapillary membrane. Johnson and Van Liew (1974) measured arterial blood Po2 when O2 was inspired in He and in N2. They found Pao2 rose more rapidly with the O2/N2 mixture. The uptake of CO, when inspired in He, N2 or SF6, plus 02, was measured by Kvale et al. (1975). It was greatest in SF6 and least in He. In both the above experiments the authors' interpretation was that the test gas is more effectively carried into the lung by the denser carrier gas which is more effectively dispersed longitudinally by Taylor dispersion. Whether pathological changes affect gaseous diffusion or Taylor dispersion in the conducting airways is not known. There remains the possibility, as yet unexplored, that the pattern of Taylor dispersion in diseased lungs might be used as a test of function or of structural change.
TERNARYDIFFUSION In respiratory experiments performed on living animals and man at least three gases are present in the lungs, and sometimes more. The presence of each gas affects the diffusion of the others and it is pertinent to enquire whether the binary diffusion coefficients commonly employed in calculations are adequate. If this problem is examined in detail it will be seen to be very complex indeed because during a respiratory manoeuvre the concentrations of the various gases at any point in the airways may change rapidly over a wide range. Worth et al. (1978) have determined diffusion coefficients for various gases in mixtures similar to alveolar gas. They found that the effective diffusion coefficients could be satisfactorily predicted by adding the reciprocals of the binary diffusion coefficients (diffusion resistances) weighted for the fractional concentration of the gases. The addition of more than one test gas, diffusing in the same or opposite directions, had no effect on diffusion provided that the concentrations were below 1%. At up to 10%, however, some interactions were observed. Water vapour was found to diminish D for light gases, have little effect with normal respiratory gases, and to increase D with heavy gases. Modell and Farhi (1976) investigated ternary diffusion using He, 02 and N2. Starting with 21% 02 in He at one end of a partitioned cylinder and 21% 02 in N2 at the other, when the central partition was removed the concentration of 02 at the N2 end fell, while it rose at the He end; it then returned to equilibrium concentrations. Between one and seven minutes in the experiment the concentration of oxygen mixing by ternary diffusion
Gaseous Diffusion in the Lungs
107
was actually increasing against a concentration gradient. The explanation for this is that He diffusing rapidly into the O2/N2 mixture caused the pressure to rise at that end of the cylinder, and hence produced convective flow in the direction of the 02/He mixture. There was thus a nett movement of 02 towards the He, producing an increase in 02 concentration. Thus when non-respiratory gases are inhaled for the purpose of physiological investigation one cannot be certain that a gas in the airways is always moving in the direction of the concentration gradient. A degree of caution in the interpretation of such experiments is therefore required. DIFFUSION IN THE AIRWAYS DISTAL TO THE TERMINAL BRONCHIOLES
Airways distal to the terminal bronchioles bear alveoli and are therefore termed respiratory, though Weibel (1963) termed the respiratory bronchioles transitional. Together the structures supplied by a terminal bronchiole constitute an acinus, which is usually pyramidal unless its shape is constrained by a pleural edge or a large adjacent structure. Both the airway and the artery enter at the apex. The airway then divides frequently so as to give throughout the lung a rapid increase in summed cross-sectional area, from about 80 cm 2 at the respiratory bronchioles to 104 cm 2 in the distal ducts, this occurring over a length of about 7 mm. Over 80% of the volume of a lung inflated to 75% of total lung capacity is made up of acinar air. With such a large cross-sectional area available molecular diffusion inevitably plays an important part in the movement of gas molecules in the respiratory airways. Because of the small size and inaccessibility of the structures concerned, investigation of diffusion in situ is difficult. The main efforts directed at this problem have been of two kinds: (1) study of the behaviour of gases of different diffusivities when respired, and (2) mathematical analysis of more or less complex models.
Behaviour of gases diffusing in the respiratory airways As has already been pointed out, oxygen is carried into the respiratory zone by convective flow and reaches distally-situated alveoli by molecular diffusion (Fig. 6). Similarly, carbon dioxide diffuses out in the reverse direction. There is thus a mixing of gases in the respiratory zone brought about by molecular diffusion, and this is the most important function of the airways at this level. It can be simply illustrated by the single breath test for nitrogen, in which a breath of 100% oxygen, usually 1000 ml, is inspired, and the concentration of nitrogen in the following expirate is measured and plotted against expired volume. If mixing within the respiratory airways were complete, but none at all occurred between the respiratory and the conducting airways, the expired nitrogen plot would be as in Fig. 7A, with no nitrogen in the first 150 ml or so, then a sudden upstroke in concentration, and finally a perfectly level plateau of alveolar nitrogen diluted with inspired oxygen. The 150 ml containing no nitrogen is the dead space, that is it represents that part of the airway in which no diffusive mixing has occurred (convective mixing on expiration being ignored). In reality the concentration curve is more sigmoid, with a less vertical upstroke and usually a gently rising plateau (Fig. 7B). The dead space can still be determined from this curve in terms of the volume of unmixed gas (Cumming et al. 1971) but the slope of the plateau has been the cause of much discussion. On the one hand it has been thought to represent regional variations in ventilation with oxygen,
108
Keith Horsfield
followed by regional variations in rates of emptying, known as regional inhomogeneity. On the other hand, it has been thought to represent a failure of complete diffusive mixing in the respiratory airways. More rationally, it can be considered as the result of the interaction between regional factors, both anatomical and functional, and molecular diffusion (Pack et al. 1977). It is not the purpose of this paper to discuss the relative merits of these different interpretations, but rather to concentrate on the role of diffusive mixing. If we consider the process of getting oxygen up to the alveolar capillary membrane and carbon dioxide away from it, and also the maintenance of a flux of these gases through the membrane, it is a priori obvious that concentration gradients for these gases must exist, otherwise there would be no driving force for diffusion. The question is, then, not whether there is a gradient but rather what is its magnitude ? 100
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1500
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Fig. 6. Concentration-expired volume plots of a non-diffusing aerosol and an insoluble gas such as helium after inspiring 600 ml of each. None of the aerosol, which moves mainly by convective flow, has reached distally, whereas the He has mixed relatively well by molecular diffusion. The difference between the two curves illustrates the importance of diffusive mixing. (From Muir 1966) Investigation Of diffusive mixing has been carried out using gases each of different molecular weight, commonly helium, neon and sulphur hexafluoride. Thus if a mixture containing these gases is inspired and expired, then after the dead space the early part of the expirate contains more sulphur hexafluoride and the later part more helium, as shown in Fig. 8 (Georg et al. 1965; Cumming et al. 1967; Power 1969; Hogg et al. 1972; Sikand et al. 1976). Similar findings were obtained by Mazzone et al. (1976), except that in their experiments less helium than expected mixed peripherally, a result attributed to the effects of Taylor dispersion reducing its penetration. These demonstrations that the components of a gas mixture may partially separate in the airways cannot be explained simply by regional differences in ventilation since the gases were inhaled together; they must therefore result from molecular diffusion and possibly the interaction of diffusion with convection. A period of breath-holding between the inspiration of the gas mixture and its subsequent expiration results in a diminution of the concentration
109
Gaseous Diffusion in the Lungs A
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Fig. 7. Single-breath nitrogen test (see text), A, The theoretical square wave of nitrogen concentration which would result from perfect alveolar mixing and no conducting airway mixing. B, In reality alveolar mixing is imperfect (upsloping plateau) and mixing occurs in the conducting airways (sloping upstroke)
ss Expired volume
Fig. 8. The appearance of SF6 and Ne in the expirate following inhalation of a mixture containing both gases
110
Keith Horsfield
differences, the lapse of time permitting diffusive mixing to continue (possibly aided by cardiogenic mixing; see below).
Mathematical analysis of diffusion in the respiratory airways The study of diffusion in the airways by model analysis was started by Rauwerda (1946) who, using a simple model of the acinus, came to the conclusion that diffusive mixing was so rapid that no measurable gradient would be left after one second. Since then a considerable number of model analyses have been reported. Each of these has concentrated on one or two particular aspects of the problem and produced various conclusions. Those which conclude that mixing is effectively complete within the time of a normal respiration include La Force and Lewis (1970) and Paiva (1973). Those which suggest that mixing is not complete include Cumming et al. (1966, 1971) and Pack et al. (1977). These authors also make the point that regional differences, convection and diffusion interact so that consideration of any one without the others is meaningless. The variations of alveolar oxygen and carbon dioxide concentrations with time during the respiratory cycle have also been investigated using model analysis (Lin & Cumming 1973 ; Davidson & Fitz-Gerald 1974) as have the dead spaces for gases of different diffusivities (Cumming et al. 1971; Lacquet et al. 1975; Paiva et al. 1976; Sikand et al. 1976). Three good reviews of the general topic of model analysis of diffusion in the respiratory airways are those of Chang and Farhi (1973), Curnming (1974), and Pedley (1977). Of critical importance in model analyses are the boundary conditions employed. In most of the studies so far discussed the assumption has been made that there is no concentration gradient (dc/dx = 0) at the alveolar wall. Results from these studies suggest that gas mixing in the respiratory region is rapidly completed. Exceptions to this include Cumming et al. (1971), Butler (1974), Jones (1977), and Scrimshire et al. (1978), who assumed a no flux boundary condition at the alveolar wall. Their results suggest that gas mixing is incomplete. The problem of the correct choice of boundary condition is further discussed by Paiva et al. (1979) and is at present unresolved. Gomez (1965) pointed out how the movement of gas molecules by convection falls off rapidly as they enter the respiratory zone in the lung while movement by molecular diffusion rapidly increases. There is thus a cross-over point where the two are equal (Fig. 9) at about the level of the terminal bronchioles. Cumming et al. (1971) investigated the possible effects of this by a model analysis in which both diffusion and convective flow were represented. They showed the presence of a static front of nitrogen at about 250 ml down the model of the airways, independent of the volume of oxygen inspired (Fig. 10); this occurs because at that point nitrogen is diffusing up the airways at exactly the same rate as it is being convected down. Using a more sophisticated analysis Paiva (1973) came to the same general conclusion.
Explanation of the static front For a static concentration front to become established between a gas flowing down a tube and one diffusing up in the opposite direction the tube must have a trumpet-like shape. This the airways have if the cross-sectional areas at any given level are added together (Horsfield 1974). If oxygen, for example, is blown down the narrow end of such a tube into an atmosphere of nitrogen (Fig. 11) then nitrogen will diffuse up the wide end. Somewhere in the tube (flow and diffusivity being appropriate) a static nitrogen
Gaseous Diffusion in the Lungs
111
front develops. Some molecules (Fig. llA), moving faster than average, will be further up the tube, but the further they get the higher is the velocity tending to sweep them down again. Other molecules (Fig. 11B), moving up the tube more slowly than average, will tend to be swept down, but the further down they go the slower is the velocity so that diffusion brings them back again. Although the nitrogen front is static oxygen continues to pass through it and out at the far end because there is a continuous flow of oxygen. In the lungs, where there is a closed elastic bag (the alveoli) distal to the tube, the OO
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Fig. 9. The relative velocity of molecular transfer in the airways by convective (bulk) flow and molecular diffusion (see text). (From Muir 1966) absolute concentration of nitrogen continues to fall during inspiration as it is diluted by the incoming oxygen, but the position of the front is nevertheless static if flow is constant (Fig. 12). Paiva et al. (1976) developed a simple mathematical relation between anatomy (the shape of the trumpet), diffusivity, and flow. Where the front is static dA dx
IY D
where A = summed cross-sectional area, x = linear distance, I/= flow, and D = diffusion coefficient. In words, at the static point the rate of change of cross-sectional area with distance down the airways is equal to the flow divided by the diffusion coefficient. Thus,
Keith Horsfield
112
if the anatomy is known a plot of cross-sectional area against length can be drawn (Fig. 13) and a line of slope F/D constructed as a tangent to the graph. The point where the tangent meets the curve corresponds to the static point, which can be read off the abscissa in terms of length down the airways. When the calculations are made with values of D corresponding to hydrogen and sulphur hexafluoride, the static hydrogen front becomes established nearer the mouth than does the sulphur hexafluoride front, and thus the more diffusable gas has the lower dead space. 0.0
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Tests of mixing The position of the concentration front is obviously one factor determining tile magnitude of the 'anatomical' or 'series' dead space, which varies with lung volume (airway cross-section), the diffusion coefficient of the gas used, and the duration of any breath-holding period during which the interface will move up the airways by diffusion. The single-breath nitrogen test thus gives information on gas mixing with regard to both the slope of the plateau and the size of the dead space.
Gaseous Diffusion in the Lungs
113
The multi-breath test is carried out by the subject inhaling a gas containing no nitrogen, breathing normally for several minutes. A mixture of 79% argon and 21% oxygen is suitable for this, avoiding the effects on ventilation which occur when 100% oxygen is used. Nitrogen is progressively washed out of the lungs and its end expiratory concentration measured. Plotting concentration on a logarithmic scale against breath number gives a curve which in a perfect mixing system would be linear, in a normal lung is
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Keith Horsfield
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and alveolar gas (Horsfield et al. 1973), while in panacinar emphysema mixing is slow in the distal dilatation (Fig. 15B). A series mixing problem of a different kind arises with blockage of peripheral airways with plugs of mucus, as in asthma. Collateral ventilation from adjacent acini can occur, but with a marked defect in mixing between the two (Fig. 15c).
Gaseous Diffusion in the Lungs
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A B C Fig. 15. Some lesions in airway disease causing serious mixing defects. A, Centrilobular emphysema. B, Panacinar emphysema. C, Airway blockage (asthma) with collateral ventilation of adjacent acini DIFFUSION ACROSS THEA LVEOLAR-CAPILLARY
M E M B R A N E
Anatomy T h e last part of the pathway taken by an oxygen molecule on its way to a red cell is the shortest but also the most complex--its passage through the alveolar wall. Four different tissues must be traversed before it reaches a haemoglobin molecule with which to combine (Weibel 1970/71). These are: 1. 2. 3. 4.
The The The The
surfactant layer. tissues of the alveolar wall. plasma in the capillary. red cell wall.
116
Keith Horsfield
The surface layer of surfactant is 5-20 nm thick; it consists of a basal layer and a phospholipid film 2-3 nm thick. It fills out crevices and acute angles, where it may be 1-3 Fm thick, thereby making the alveolar air space smoother and more rounded. Tissues of the alveolar-capillary membrane are basically two cells thick, the alveolar epithelial cell and the capillary endothelial cell, each with its basement membrane (Fig. 16). Thus an oxygen molecule must traverse the cell membrane, cytoplasm, cell membrane and basement membrane of the epithelial cell, the interstitial space, and the basement membrane, cell membrane, cytoplasm, and cell membrane of the endothelial cell. This is the minimum. But the interstitial space between the two basement membranes may contain ground substance, fibrous tissue, or liquid. Although the cytoplasmic extensions of the cells occupy most of the alveolar surface area, the cells do have nuclei, and where interstitium or nuclei are present the thickness may be 5 Fm or more. ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Cell membrane i ii!!!iiii!i i:i:i!iiii!iiiiiiiiiii fii !!iii!ii!iii ii fiiii i:!:!:i:i:i:i:i:!:!:!:i!iiiiiiiiiiiii!ii!i i ii!!i!iiii i i !:i:i:i:i:i:i:i:i:i:i:i:!:i:i:i:-Cy t 0 p la s m i!iiii!i!i!ii!i!iii•i•!i!::iii•i•i::!iiiiiiiiiii!i!iii!iiiii!!iiiiii•i•i•ii!•!i!ii•i•!iiiiiiii•i•ii!iiiii•!iiiiiiiiiii••!iii•••iiii•i• Cell membrane ~::~]~::~::~::~::::~::::~:~J::~JJ~::~]~[~::~:.~::~:J~::~::~::~::~:::::.~::~ B a s e m e n t membrane --Interstitial space ii!! !ii!!!!iii:i:!:!:i:i:i:!:i:i:i:i:i:!:i:: :i:!::::: ::: !!iii !ii i!!i!ii!iiiiiii!iiiiiiii!iiiiii !!!i !!ii i i!i i ii!!ii iii!ii!i!i!!"~ Ba se m ent membrane £:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::Cell membrane ii iiiii !!ii ::ili iiii iiiiiiiiiiiii:.ii!iiiiiii ::ii :: ii :::ii iiiiiiiiii!iiiiiii!iiiiiiiiiiii::i!iiiiii i i i i!ii!i!iiiiiiiiiiiiiiiiiii i if!i i- C y to p la s m iiiiii!i!iiiiiiiiiiiiiiiii!i!iiiiiiiiiiiiiiiiiiiiiiiiiiiiii!iiiii!i!iiii!iiii! i:.iiiii!ii!iiiiii!iiiiiiiiiii! iiiiii!iiii!iii!i!iiiiiii!iiiiiiiiiii!iiii!iiiiiiiii!iiiiiiiiiii!iiiil J C el I membrane
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Fig. 16. Basic structure of the alveolar-capillary membrane
The plasma layer may be extremely thin, 5-10 nm, where the edge of a red cell appears to be in contact with the capillary wall, but in the centre of the capillary lumen oxygen may have to traverse half the capillary lumen in serum. Diffusion of oxygen into the red cell and its reaction kinetics with haemoglobin is a separate subject and will not be dealt with here. In a fully inflated lung the alveolar walls are probably flat, but at lower volumes the capillaries may bulge into the alveolar lumen. While the capillaries do not occupy the whole of the alveolar wall surface, if they are bulging into the lumen their surface area may not be much less than this. The red cells within the pulmonary capillaries have a total surface area which matches that of the alveoli, about 80 m g.
Diffusion in tissues When calculating the diffusion of gases through these structures the solubility of the gas in each is important. Table II (Weibel 1970/71) gives the diffusion coefficient, solubility, and permeation coefficient for oxygen in nitrogen, lung tissue, and plasma. Values for the surfactant layer are not known. Lung tissue and plasma are seen to have similar values which are markedly less than those for a gaseous medium.
Ternary membrane diffusion By the use of analytical methods Chang et al. (1975) showed that ternary mixtures diffusing across a membrane may behave in unexpected ways. Thus there may be no diffusion across the membrane in the presence of a partial pressure gradient, or transfer
Gaseous Diffusion in the Lungs
117
Table H. Solubility constant (~), diffusion coefficient (D), and permeation constant (K), where K = ~D, for oxygen in the lungs
Coefficient
in N~
in lung tissue
D K
-0.256 --
2.37 x 10-5 1.38 x 10-4 3.3 x 10-8
in plasma 2.8 x 10-5 ml/ml/mmHg 11.5 x 10-4 cm2/sec 3.2 x 10 -8 ml/ml/min/mmHg
where there is no gradient at all. The relevance of these findings to gas transfer in the lung is as yet unknown.
Factors affecting alveolar-capillary membrane diffusion For transfer across the membrane to occur, an oxygen molecule must first reach the alveolar wall, then go into solution in the tissues, diffuse through them, finally to combine with haemoglobin. This process can be affected by various factors. Exudate, oedema fluid or excess surfactant within the alveolar lumen will greatly slow down the rate of arrival of oxygen molecules at the alveolar wall. The alveolar epithelial cells or the capillary endothelial cells may be thickened, and between them fibrous tissue may increase or fluid accumulate. Within the capillary the diffusion distance may be increased with capillary dilatation. The total functional surface area puts an upper limit on the transfer of gases; it is that surface area which is ventilated with fresh gas and in contact with functioning capillaries. Exercise causes capillary recruitment as pulmonary blood flow increases and this helps to increase oxygen uptake. Surface area varies with lung size, increasing during growth and varying over a wide range between individuals. It increases with inspiration and is reduced in such conditions as emphysema, embolism and pneumonectomy.
Tests of alveolar-capillary membrane diffusion Diffusion across the alveolar-capillary membrane is usually estimated using carbon monoxide (CO). The method involves the inhalation of a small amount of CO, estimating its alveolar concentration, and calculating how much is taken up by the blood in a given time. From this the transfer factor for the lung for CO is calculated, usually as ml of CO per minute for each m m H g partial pressure difference. Capillary partial pressure of CO is taken to be zero because it combines so rapidly with haemoglobin. Hence the partial pressure difference is equal to the alveolar pressure. The test can be performed as a single breath with 10 seconds' breath-holding, or as a multi-breath method. Because CO molecules have to traverse the total pathway already described, their rate of uptake is limited by the series resistances offered by the conducting airways, diffusive mixing in the respiratory airways, diffusion across the membrane, plasma and red cell wall, and the reaction kinetics with haemoglobin. The result obtained from an estimation of TLCO is therefore dependent also on factors other than the alveolar-capillary membrane resistance, for example, on the imperfection of alveolar mixing. As we have already seen, this is probably the case even in normal lungs and is certainly the case in diseased lungs. Distribution of ventilation and perfusion may be mismatched so that CO going to unperfused areas will not be transferred to the blood. In such cases a low Tr~co, while
118
Keith Horsfield
measuring the ability of the lung to take up CO, is not necessarily a measure of the conductance of the alveolar-capillary membrane. The other important determinant of CO uptake is the blood itself. Even static red cells in the pulmonary capillaries will take up CO, and so long as the quantity of CO is small enough the blood may not be a limiting factor. The number of red cells in the capillaries and their haemoglobin content are important, so that TLco may be increased in polycythaemia and decreased in anaemia. The longer the time spent in a capillary by a red cell the more likely is it to become a limiting factor, and conversely faster flow may increase uptake. Finally, the balance between the formation of carboxyhaemoglobin and oxyhaemoglobin determine how much CO is actually taken up by the haemoglobin, and this is affected by the partial pressures of CO, oxygen, and carbon dioxide prevailing in the pulmonary capillaries, as well as pH, temperature, and red cell chemistry. In spite of the above problems the measurement of TLCO helps in the study of diseases affecting the alveolar wall. The significance of an abnormal result can be better interpreted from the above discussion.
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