The influence of gaseous diffusion on the alveolar plateau at different lung volumes

Respiration Physiology (1967) 2, 386398; North-Holland Publishing Company, Amsterdam

THE INFLUENCE

OF GASEOUS

PLATEAU

DIFFUSION

AT DIFFERENT

LUNG

ON THE ALVEOLAR VOLUMES

G. CUMMING, K. HORSFIELD~, J. G. JONES AND D. C. F. MUIR* Dept. of Medicine, Queen Elizabeth Hospital, Edgbaston, Birmingham 15, England

Abstract. The effect of gaseous diffusion upon the alveolar plateau has been investigated using an aerosol which behaves as a gas with very low diffusivity (10-a), a poorly diffusible gas, Sulphur Hexafluoride (0.37), and a readily diffusible gas, Neon (1 .O). The mathematical solution of the diffusion equation in a model representing lung anatomy suggested that the expired curves after inspiring these gases should differ. Experiments conflrmed that the expired curves, within the same expirate, were different and that the manner of difference was such that it could be explained only on the basis of diffusion. Since the difference between the curves rapidly diminished with breath holding this again suggested a diffusion mechanism. Experiments at different lung volumes showed that different slopes of alveolar plateaux were produced. It is concluded that whilst regional inhomogeneity is undoubtedly present in the lung it is difficult to obtain information about it from a study of the alveolar plateau produced in the manner described, and that this plateau results in the main from stratified inhomogeneity. Alveolar gas Alveolar plateau Diffusion in the airways

Neon Pulmonary regional inhomogeneity Sulfur Hexafluoride

The concentration of nitrogen in the expired gas following the inspiration of a breath of oxygen shows a progressive rise. This observation has been utilised in the single breath test, in which a measured quantity of oxygen is inspired, the concentration of nitrogen in the expirate being measured and plotted against expired volume. The shape of the curve thus obtained may be described in three parts. Initially the expired gas comes from the anatomical dead space and consists only of oxygen, the concentration of nitrogen being zero. A rapid rise in nitrogen concentration then occurs as alveolar gas mixes with dead space gas. Finally there is a gradual rise as alveolar gas is expired, this part being described as the alveolar plateau. Accepted for publication 18 january 1967. This work was supported by the Aerospace Medical Laboratories under Contract AF 61(052)-775, through the European Office of Aerospace Research (OAR) United States Air Force. t In receipt of a grant from the British Heart Foundation. * Dept. of Physiology, London School of Hygiene, Keppel Street, London W.C.I., England. 386

INFLUENCE OF GASDIFFUSION ON THEALVEOLAR PLATEAU

387

A variety of methods have been used to measure the slope of the alveolar plateau (FOWLER,1949) and it has been generally agreed that the magnitude of this slope expresses information about the degree of inequality of ventilation. OTIS et al. (1956) have suggested that it is possible to explain the slope of the alveolar plateau on the basis of the mechanical properties of the lung and their hypothesis has been generally accepted. Thus different lung regions, by virtue of their compliance and the resistance of their supplying airways, receive different proportions of the inspired gas and reach differing concentration of nitrogen. The sequential emptying which results from such a model of lung behaviour produces the rising nitrogen concentration during expiration. Implicit in this argument is the assumption that gas mixing within the various lung regions is regarded as being instantaneous. Other mechanisms for the production of regional inhomogeneity have been put forward. FOWLERK. T. (1964) has shown that the filling pattern of the upper and lower lobes differs depending on the volume of the lungs at the beginning of inspiration, so that the bulk of inspiration at residual volume (RV) enters the upper lobe. This problem of regional inhomogeneity has been further clarified by the work of MILIC-EMILIet al. (1966). Using radioactive Xenon they have demonstrated that gas flow differs between upper, middle and lower zones, but was constant throughout the breath in any single zone, when breathing was at or above functional residual capacity (FRC). Below FRC a different pattern was observed, in that gas entered the upper zone preferentially at the beginning of inspiration. SIKAND,CERRETELLI and FARHI(1966) measured the total inert gas partial pressure during expiration following inspiration of a mixture containing argon. They concluded that whatever regional inhomogeneity existed in the lungs the proportion contributed by the various areas of the lung remained the same throughout the expiration, so that regional differences were not reflected in the alveolar plateau. Thus the evidence offered by Milic-Emili and by Sikand suggests that in breaths taken at or above F.R.C. the change in concentration of the expired gas is not a measure of regional inhomogeneity. The slope of the alveolar plateau must therefore be explained in some other way. The inspired gas is mixed with the residual gas by molecular diffusion. The rate of such diffusion upwards in the airways has been reported by many authors Roos, DAHLSTROMand MURPHY(1955), SHEPARDet al. (1957), and POWER and FORSTER (1965) who have shown a progressive mixing of alveolar gas with dead space gas on breath holding over several seconds. The rate of diffusion mixing downwards towards the alveolar sacs is not so well documented. RAUWERDA(1946) believed that 84% equilibration occurred in 380 msec, and this view appears to be supported by GOMEZ (1965) who indicates a time of 200 msec for gas transport between the respiratory bronchiole and the alveolar sacs in normal subjects. Thus no appreciable concentration gradient would exist during normal respiration between these limits, which represent 95 % of lung volume. It has been suggested however (CUMMINGet al., 1966) that the rate of diffusion mixing is less rapid than this, and that a concentration gradient due to the failure of complete mixing by diffusion would exist during normal

388

G. CUMMINGet al.

breathing. A similar conclusion has been drawn by SIKANDet al. (1966). Such a concentration gradient would produce a sloping alveolar plateau, the slope diminishing with breath holding. Such breath holding experiments have been reported by KJELLMEX,SANDQVIST and BERGLUND(1959) and by SIKANDet aZ. (1966) and these authors confirm the diminution of the slope of the alveolar plateau. Experimental investigation of the rate of diffusion equilibration has been offered by GEORGet al. (1965) using gases of different diffusivity. These authors inspired a mixture of Helium and Sulphur Hexafluoride so that mechanical differences in ventilation would be identical for the two gases, and any differences would reflect different diffusion rates only. In this paper we have made calculations from a mathematical model, compatible so far as possible with normal anatomical structure, for the diffusion behaviour of the two gases Neon (Ne) and Sulphur Hexafluoride (SF,). Experiments are then reported in subjects breathing these two gases to see how far the theoretical and experimental curves agree. In view of the reported different behaviour of the lung at different degrees of inflation referred to above, the experiments have been carried out at FRC, at RV and at total lung capacity (TLC) to define the effects of regional ventilation in breaths taken below FRC. It has been suggested by Georg et al. using evidence from an extrapolated graph, that a gas with an infinitely small diffusion coefficient would achieve a significant alveolar concentration during normal breathing. This conflicts with the evidence of ALTSCHIJLER et al. (19591, and we have used aerosols to study their effect on the alveolar plateau. Aerosol particles of about 0.5~ diameter behave in many respects like gases of very low diffusivity. The analogy is not perfect since in addition to a diffusion coefficient of 6.5 x lo-’ cm’.sec-‘, the particles have a settling velocity of 1 x 10W3 cm.sec-’ due to the force of gravity. Despite this, aerosols present the nearest approach to a non-diffusing gas that is available. Particles larger than 0.5~ diameter have a greater mobility due to an increasing settling velocity and particles smaller than this critical size diffuse in a manner similar to gases by means of Brownian movement. Methods Aerosols of di-2 ethylhexyl sebacate which is insoluble in water and of low vapour pressure, were prepared with a modified LAMERSINCLAIRgenerator (MUIR, 1965). The aerosols were of uniform size and 0.5~ diameter and no change in particle size occurred during breathing. The aerosol concentration was measured close to the mouth by an optical method in which an intense beam of light is focussed on the cloud and light scattered at 90” measured by means of a photomultiplier (MUIR and DAVIES,to be published). Measurements were carried out on three subjects, each inspired one litre of aerosol from the position of FRC and then exhaled to residual volume. Aerosol concentration and expired volume were recorded photographically, the traces being measured at 100 ml intervals, permitting a plot of aerosol concentration against expired volume. Calculation of the concentration gradient to be expected in the lungs following an

INFLUENCE OF GASDIFFUSION ON THEALVEOLAR PLATEAU

389

inspirate of Ne and SF, were made using a KDF 9 computer (L~QM~coN~-FERRANTI).The lung model upon which the calculations were based was Model No. 7 as described by CUMMINGet al. (1966). This model is a conical segment of a hollow sphere, the dimensions of which have been determined by the anatomical structure of the airways and by a physiological requirement. This requirement is, that if the model contains nitrogen and then expands by an amount compatible with a one litre inspirate of oxygen such that the oxygen/nitrogen interface is 2 mm from the alveolar sac, then no nitrogen would be lost by diffusion if the cone were open at its narrow end. Such a cone has a volume of airways above it of 80 ml, and has a length of side of 2.6 cm. Analysis of the process of diffusion in this model shows that no perceptible difference in concentration results if the cone is open or closed. Since the concentration at infinite time would be finite in the normal lung, its behaviour is more closely simulated by the closed cone, since the open cone would have zero concentration at infinite time. The diffusion coefficients used were Ne:N,=0.315;

SF,:N,

=O.l17cm*.sec-‘ .

Experimental observations of the behaviour of the two gases were made as follows. One litre of a gas mixture containing 40 % SF,, 20 % Ne, 20 % 0, and 20 % N, was inspired. This gas mixture was contained in one of the bags of the recording bag in a box spirometer (CUMMING,1966) so that the size of the inspirate could be predetermined and measured. The concentrations of SF, and Ne chosen were dictated by the characteristics of the measuring device, which was a mass spectrometer type MS 4 (Associated Electrical Industries Ltd.). Neon was measured at a mass/charge ratio of 20. The most convenient peak in the complex cracking pattern of SF, was that of fluorine at a mass charge ratio of 19 and an abundance of 8 %. The response time of the mass spectrometer was identical for both gases and both gases gave a linear concentration response. The discrimination between peaks was such that no detectable output of peak 19 was observed when peak 20 gave full scale deflection. The inspired and expired concentrations were measured with the mass spectrometer and recorded photographically (DR 8 recorder, Electronics for Medicine). The gain of the mass spectrometer was set so that the signals looking at Ne and SF, were superimposed whilst sampling air and whilst sampling the gas mixture. Studies were carried out on three normal subjects whose lung volumes and subdivisions are shown in table 1. Each subject inspired one litre of gas mixture as quickly as possible, breathing out to residual volume at a rate of about one litre per second. TABLE I Lung volumesof the subjects.

Subject 1 Subject 2 Subject 3

Ht. in cm

FRC

RV

TLC

175 185 187

3.03 3.66 5.58

1.95 1.82 2.94

6.67 8.01 8.95

390

G. CUMMING f?t al.

They breathed in from the position of quiet expiration (FRC) and three test breaths were recorded, sufficient time being allowed to wash out indicator gas between studies. Three test breaths were made without breath holding, three with 5 set and three with 30 set breath holding. This experimental plan was then repeated at residual volume, and at one litre below TLC. Prolonged breath holding in these latter studies was not possible. Gas concentration was measured at a variety of points on the expired curve between 250 ml and 2000 ml of expired volume. The concentration of the gases and of the aerosol were expressed as “fractional concentration”, that is, the ratio of expired to inspired concentrations, inspired concentration being designated as unity. Results from all three subjects obtained at FRC without breath holding were pooled. The arithmetic mean of the nine values for each of six points on the curve was found and the mean values were plotted against expired volume. A similar procedure was adopted for each lung volume and breath holding period. Results

A representative plot of the fractional concentration of aerosol against expired volume is shown in fig. 1 and it will be seen that no detectable amount of aerosol was found in the end expiratory sample. There was however, mixing between the inspired volume and the gas originally present and the average mixing was such that 150 ml of aerosol left the inspired volume. This value of 15% agrees with that reported by ALTSHULER et al. (1959). Solution of the diffusion equation for the chosen model yields a graph such as is

\“I. L__ . 0

1000 Expired

3000

2000 volume

(ml)

Fig. 1. A graph showing the fractional concentration of aerosol and volume of expired gas. This is from a single subject but was characteristic of all the records obtained.

shown in fig. 2, in which the fractional concentration is plotted against linear distance. However to be meaningful in physiological terms it should be plotted against volume, and to do this requires anatomical information. We have taken Model A as described by WEIBEL (1963) and plotted the summed volume of the airways and the alveoli at any given distance from that point in the airways corresponding to the narrow end of the model, and 2.6 cm from the alveolar sacs, with the results seen in fig. 3. Combina-

INFLUENCE OF GAS DIFFUSION ON THE ALVEOLARPLATEAU

391

1.0-

E ?I B

0.7 s J i L 0.60 5

I 0.5

I

I

1.5 1.0 Linear distance km)

I 2.0

b 2.5

Fig. 2. Computed fractional concentrations of Neon and SF6 in a model of the terminal airways. The graph shows the change of fractional concentration of the two gases with respect to linear distance.

Ii u

$’

B E

2 Q

3 I

OO

0.5

I 1.0 1.5 Linear distance km)

I 2.0

I 2.5

Fig. 3. Relation between summed volume and linear distance down the airways. The summed volume of the airways and alveoli (y axis) is plotted against linear distance down the terminal 2.6 cm of the airways.

tion of fig. 2 and fig. 3 permits the plotting of a concentration/volume graph, fig. 4, This shows that the fractional concentration of SF, lies above that of Ne early in the expirate, the two curves cross, and SF, lies below Ne for the latter part of the expirate. The slope of the latter part of the curve is different for each gas, that for SF, being steeper. After breath holding for 5 set as shown in fig. 5 the SF, curve still lies above the Ne curve early in expiration the fractional concentration of both are lower and the crossover point occurs earlier in expiration. In the latter part of the curve the fractional concentration of both is increased. The slope for both gases on breath holding diminishes and with increased times of breath holding the curves approximate. After 5 set the slopes are almost identical, but the fractional concentrations remain different.

392

G. CUMMING

et al.

1.0i \

\

2

s p.9-

s gEl0.8

-

$ :

uo.7 E E 5 8 I= 0.60

Ne

1 500 Expired

I I 1000 1500 volume (ml)

, 2000

Fig. 4. Computed fractional concentration of Ne and SF6 related to the volume of the airways. The graphs of fractional concentration in fig. 1 have been replotted with respect to volume, the linear distance being converted to volume by reference to fig. 2. On the y axis the fractional concentration is shown, and the expired volume is on the x axis. This plot assumes sequential emptying of the lung within a region, the gas from the more distal airways reaching the lips later in the expirate.

0.60600

Expired

volume (ml)

Fig. 5. Computed fractional concentrations

after 5 sec.

The “knee” of the curve becomes more angular and less rounded with breath holding, also appearing earlier in the expirate. If breath holding were prolonged infinitely the knee would intersect the ordinate and the curves would become superimposed horizontal lines, indicating complete diffusion equilibration throughout the lung. The results following inspiration of the gas mixture at various lung volumes and with different breath holding times are shown in table 2. The statistical significance in mean values for the two gases were determined by Student’s T test. The probabili-

INFLUENCE

OF GAS DIFFUSION

ON THE ALVEOLAR

TABLE Mean

Lung Volume

FRC

values

Breath holding time

Gas

0

5

393

PLATEAU

2

of fractional concentrations

of tracer gas in the expirate.

Expired volume (ml)

‘A difference 7X-1250

250

500

750

1000

1250

2000

SF6

0.301*

0.201

0.178

0.163*

0.150*

0.121*

2.8

Ne

0.246

0.197

0.183

0.169

0.161

0.136

2.2

SFe

0.221*

0.189*

0.181

0.179

0.172

0.151

0.9

Ne

0.209

0.194

0.183

0.181

0.176

0.155

0.7

SF6

0.199

0.190

0.186

0.181

0.177

0.164

0.9

Ne

0.199

0.190

0.186

0.183

0.179

0.165

0.7

0

SF6 Ne

0.381* 0.350

0.346’ 0.327

0.320* 0.307

0.287 0.290

-

-

-

5

SFs N0

0.347* 0.337

0.320* 0.312

0.342 0.309

0.301 0.301

-

-

2.9

30

0

5

SF6

-

0.193*

0.137*

0.121

0.108

0.091

Ne

-

0.157

0.130

0.119

0.113

0.095

1.3

SF6

-

0.151

0.136

0.129

0.122

0.114

1.3

Ne

-

0.146

0.137

0.133

0.127

0.118

1.0

* Indicates that the value for SF6 is significantly different from the value for Ne at a level of p =0.05.

0.

6 s.3 $ g lno.2 8 e .g g0.l t 1

500

x)00 Expired

1500

volume

(ml)

2000

Fig. 6. The experimental results obtained without breath holding. Each point on the curve is the mean of the experimental values for all the subjects. If it were possible to extrapolate the curves to include zero expired volume on one side and all the gas still remaining in the lungs at the end of expiration on the other, the areas under the two curves should be equal.

G. CUMMING et d.

394

ties of these differences being due to change are also shown in the table. This information is shown graphically in figs. 6, 7 and 8. As seen in these figures at 1 set and 5 set the SF, curve lies above that for Ne, the curves cross then SF6 lies below Ne. The slopes of the plateaux at all points in the expirate made without breath holding are different and the slope of SF, is steeper than that for Ne. After 5 set breath holding the relative positions of the curves are the same, but the fractional concentrations early in the expirate have increased, at the same time the curves are more nearly coincident. Further, the crossover point has moved progressively to the left with increased breath holding time. The crossover point after 30 set appears to lie at about 250 ml, but the difference between the two curves is not statistically significant, and this point must be treated with reserve. It has not been possible to represent the change in shape of the “knee” in an average manner, but inspection of the experimental rec.---.

SF,

-Neon RV

F.R.C. T. LC .-lo00

500

2000

1500 1000 Expired volume (ml)

Fig. 7. Experimental

results after 5 set breath holding.

30 sea e---o

breath

hc+WJ

SF,

-NS+l

x0.2“,,

0

\

-- .-___

500

loo0 Expired

Fig. 8. Experimental

----‘----______eFRC

1500 volume

2000 (ml)

results after 30 set breath holding.

INFLUENCE OF GAS DIFFUSION ON THE ALVEOLAR PLATEAU

395

ords indicates that the sharpening of the knee occurs in each case with breath holding. The movement of the knee to the left is seen on inspection of figs. 6-8. Inspection of fig. 8 shows that although the two curves are practically superimposed, a finite slope remains. The plots of aerosol, SF, and Ne against expired volume are shown superimposed in fig. 9.

E 1.0

3

2 t; 0.8 s ; 0.6 F 0.4 .P g 0.2 L lL 0 0

1000 Expired

2000 volume

3000 (ml)

Fig. 9. This shows the comparison in behaviour between aerosols, SFG and Neon in a single expirate.

Discussion

Fig. 1 shows the manner in which aerosol is distributed in the expired gas and suggests that the patterns of lung filling and of lung emptying are different, since if they were identical a square wave of aerosol would result. This may be due in part to some diffusion mixing, or mixing by other factors such as turbulence. In addition since the shape of the interface between the aerosol and lung gas is approximately exponential, this may be due to a washing out of the dead space. In this context dead space implies that volume of lung into which aerosol is drawn by mass movement. The resemblance between the computed diffusion gradients in figs. 4 and 5 and the alveolar plateaux obtained experimentally and shown in figs. 6,7 and 8 may be seen by comparing these figures. The qualitative similarity is evident but any attempt at quantitation fails since the fractional concentration reached in the model at equilibrium differs considerably from that seen in the subjects. This difference reflects the inadequacy of the model to represent lateral diffusion of gas from alveolar ducts to alveoli, a defect which overestimates the equilibrium concentration and underestimates the slope of the gradient. Considering the results obtained at FRC, at 0, 5, and 30 sec. Without breath holding the fractional gas concentrations are significantly different at all points apart from the crossover, and this must result from the different diffusivity of the two gases, indicating that diffusion equilibrium has not been attained. At 5 set the fractional concentrations after 500 ml of expiration do not differ significantly, in other words the alveolar plateaux for the two gases cannot be distinguished.

396

G. CUhfMING etd.

Were this the only evidence for continuing diffusion no conclusions could be drawn about the completeness or otherwise of the diffusion process. However, other evidence is available which permits of such a conclusion. Foremost is the fact that the slope of the expired curve for both gases changes between 5 set and 30 sec. This change is such that the curve pivots about the crossover point, that part to the left of it falling whilst that part to the right rises, and this occurs between zero and 5 set as well as between 5 set and 30 sec. Despite the lack of significant difference between the two fractional concentrations, it is noteworthy that in every instance their relative positions were preserved, suggesting that diffusion processes were still progressing. A third point which suggests continuing diffusion is that the “knee” of the curve moves to the left and becomes more acute with increasing breath holding time. Thus it will be seen that the actual slope of the alveolar plateau between 750 ml and 1250 ml is a poor determinant of the completeness of gaseous diffusion, but that the ancillary evidence suggests that diffusion continues up to at least 30 sec. The question then remains of the amount of the slope which results from diffusion, and the amount contributed by other causes. Considering the two curves made at FRC and after 30 set breath holding (fig. 8) it will be seen that they do not differ significantly, so that no evidence for incompleteness of mixing may be obtained from them. Nevertheless a sloping alveolar plateau remains, and it may be that this residual slope represents a contribution from factors other than diffusion. The slope of the alveolar plateau measured at FRC and between the volumes 750 ml and 1250 ml of expirate was 2.2 % without breath holding and 0.7 % after 30 sec. Thus two thirds of the slope reflects diffusion and the remaining third may be attributable to other factors. Since however it is not possible to say with certainly that mixing within the terminal airways is complete it may be that a greater proportion of the slope than this may be attributed to diffusion. It is relevant to discuss the nature of the mechanical factors which might contribute to the alveolar plateau. FOWLER K. T. (1964) has suggested that the mechanical hypothesis of OTIS et al. (1956) is not a valid explanation of the genesis of the plateau. Regional differences of ventilation as shown by MILK-EMILI et al. (1966) and others might be a reasonable explanation. However the experiments reported with 30 set breath holding were made at FRC when contributions from such a source between 750 ml and 1250 ml expired volume, are least likely. However, the evidence offered for regional inhomogeneity is largely derived from radioactive gas studies which measure distribution of the gases during inspiration. Our experiments report concentrations during expiration, and the assumption that expiration is a mirror image of inspiration is not valid. Consequently we conclude that the slope of the alveolar plateau may be explained in part by mechanical factors, probably regional in character and arising from the effects of gravity on the lungs. Turning now to the effects of preinspiratory lung volume on the alveolar plateau. With diminishing lung volume and inspiring the same volume of gas the fractional concentration increases, reflecting a lesser dilution. In addition the slope of the plateau

INFLUENCE OF GAS DIFFUSIONON THE ALVEOLAR PLATEAU

397

increases, so that over 500 ml of expirate the slope at RV is 3.7 %; at FRC is 2.2 % and at TLC is 1.3 %. Since breaths below FRC are likely to be affected by regional filling and emptying the increasing slope could be taken as evidence of an increasing contribution from regional inhomogeneity. Whilst this is possible explanation an alternative one is also possible. If it is assumed for the purposes of the argument that there is no regional inhomogeneity, then stratified inhomogeneity would result from the diffusion gradient, which would have at any instant a fixed anatomical distribution in terms of linear distance down the airways. A gradient of 10 % seen in an expirate of 2 1 would have half the slope when seen in an expirate of 4 1. Thus it is possible to explain an increasing slope with diminishing lung volume without invoking regional inhomogeneity, and the observation permits of no conclusion as to the presence or absence of such inhomogeneity. It does however illustrate the importance of defining preinspiratory lung volume in any test involving measurements of the alveolar plateau. As the preinspiratory lung volume increases, the “knee” of the expired curve is moved to the right, consequent on an increase in anatomical dead space. Thus the 750 ml point at large lung volumes may include a part of the rapid upstroke and produce a spuriously large value for the alveolar slope between 750 and 1250 ml. This may account in part for several reports (MILLS and HARRIS, 1965; KJELLMER et d. 1959) that the slope diminished with increasing lung volume initially, but then increases at TLC is approached. If the original concepts of FOWLER (1949) are used this difficulty does not arise. A second reason technical in nature may also contribute. If the delay and response time of the concentration detector and recorder exceeds about 100 msec this also moves the “knee” to the right and as reponse time increases so does the error in slope measurements. In our experiments the volume and concentration records have been electrically synchronised. In conclusion the experiments reported appear to support the hypothesis that the rate of diffusion equiIibrium within the terminal airways is slower than the quoted figure of less than 0.5 see, and may be as long as 30 sec. The stratified inhomogeneity thus produced contributes to the slope of the alveolar plateau and from the evidence offered it seems likely that at least two thirds of the slope arises from this cause. References ALTSCHULER,B., E. D. PALMES,L. YARMUSand N. NELSON(1959). Intrapulmonary mixing of gases studied with aerosols. J. Appf. Physiol. 14: 321-327. GUMMING,G. (1966). A recording bag-in-a-box spirometer. J. Appl. Physiof. 21: 291-292. CUMMING,G., J. CRANK, K. HORSFIELDand I. PARKER(1966). Gaseous diffusion in the airways of the human lung. Respir. Physiol. 1: 58-74. FOWLER,K, T. (1964). Relative complianoes of well and poorly ventilated spaces in the normaI human lung. J. Appl. Physiol. I9 : 937-945. FOWLERW. S. (1949). Lung function studies. III. Uneven pulmonary ventilation in normal subjects and in patients with pulmonary disease. J. Appl. Physiol. 2: 283-299. GEORGJ., N. A. LASSEN,K. MELLEMGAARD and A. VINTHER(1965). Diffusion in the gas phase of the lungs in normal and emphysematous subjects. C&z. Sci. 29: 525-532. GOMEZ, D. M. (196.5). A physico-mathematical study of lung function in normal subjects and in patients with obstructive pulmonary diseases. Med. Thorac. 22: 275-294.

G. CUMMING

398

et d.

KJELLMER,I., L. SANDQVISTand E. BERGLUND(1959). “Alveolar plateau” of the single breath nitrogen elimination curve in normal subjects. J. Appl. Physiol. 14: 105-108. MILIC-EMILI, J., J. A. M. HENDERSON,M. B. DOLOVICH,D. TROP and K. KANEKO (1966). Regional distribution of inspired gas in the lung. J. Appl. Physiol. 21: 749-759. MILLS, R. J. and P. HARRIS (1965). Factors influencing the concentration

of expired nitrogen after a

breath of oxygen. J. Appl. Physiol. 20: 103-109. MUIR, D. C. F. (1965). The production

of monodisperse

aerosols by a LaMer - Sinclair generator.

Ann. Occup. Hyg. 8: 233-238. OTIS, A. B., C. B. MCKERROW, R. A. BARTLETT,J. MEAD, M. B. MCILROY, N. J. SELVER~TONE and E. P. RADFORD JR. (1956). Mechanical factors in distribution of pulmonary ventilation. J. Appl.

Physiol. 8: 427-443. POWER G. G. and R. E. FORSTER(1965). Gas diffusion between dead space and alveoli. Federation

Proc. 24: 396. RAUWERDA, P. E. (1946). Unequal ventilation of different parts of the lung and determination

of

cardiac output. Groningen University, Groningen. Roos, A., H. DAHLSTROMand J. P. MURPHY (1955). Distribution

of inspired air in the lungs. J. Appl.

Physiol. 7: 645-659. SHEPARD,R. H., E. J. M. CAMPBELL,H. B. MARTIN and T. ENNS (1957). Factors affecting the pulmonary dead space as determined by single breath analysis. J. Appl. Physiol. 11: 241-244. SIKAND, R., P. CERRETELLIand L. E. FARHI (1966). Effects of VA and VA/Q distribution and of time on the alveolar plateau. J. Appl. Physiol. 21: 1331-1337. WEIBEL,E. (1963). Morphometry

of the human lung. Springer-Verlag, Berlin.