630

J. Physiol. (I956) I34, 630-649

ASSESSMENT OF VENTILATORY EFFICIENCY BY THESINGLE-BREATH TECHNIQUE

BY R. J. SHEPHARD*From the R.A.F. Institute of Aviation Medicine, Farnborough, Hants

(Received 5 July 1956)

The introduction of apparatus for the continuous metering of nitrogen concen-tration and respiratory gas flow (Lilly, 1946, 1950a) has permitted a study ofgas distribution in the lungs following the inhalation of a single breath ofoxygen. Of the many parameters that may be estimated, interest has focusedon the respiratory dead space, the uniformity of alveolar nitrogen concentra-tion, and the functional residual volume. The accuracy of individual measure-ments with the single breath technique is rather less than can be claimed formore complex procedures (Lanphier, 1953), but since observations can berepeated very rapidly, the probability of obtaining satisfactory results frompatients who are not experienced respiratory subjects is increased.

Previous work on the respiratory dead space has recently been reviewed byRossier & Biihlmann (1955). The uniformity of alveolar nitrogen concentrationhas been reported as 2-64+0.8% (Fowler, 1948b). Detailed study of theliterature relating to both topics (Shephard, 1956) reveals that small alterationsof technique-particularly changes of tidal volume, rate of gas flow and periodof breath-holding-have a considerable effect on the results obtained. Thisfact assumes some importance when dealing with clinical cases, for somepatients find difficulty in adhering to a standard routine despite many pre-liminary 'conditioning' runs. In order to interpret results in such circumstancesthere is clearly a need to determine the main variables and to prepare normalcurves showing their effect on the parameters of ventilatory efficiency. Thepresent work was initiated in order to meet this need. Normal curves fordead space, alveolar uniformity and functional residual volume have beenestablished by repeated observations on a group of healthy adult subjects, andfurther information has been obtained on more fundamental problems relatingto gas mixing within normal human lungs.

* Present address: Department of Preventative Medicine, University of Cincinnati, Cincinnati,Ohio, U.S.A.

VENTILATORY EFFICIENCY 631

METHODS

General description of technique. By operation of a large-bore three-way cock the subject couldbreathe either atmospheric air or oxygen drawn from a spirometer. Gas from this cock was led inturn through a gauze-mesh pneumotachograph and a short metal pipe carrying the needle samplingvalve of the nitrogen meter. A short rubber mouthpiece covered the upper end of the metal pipe.Measurements were made with subjects in the standing position (the observations of Fowler

(1950) and Brown (1952) have emphasized the large effect of posture on dead space). A fewseconds' recording of normal respiration was obtained. At the end of a normal expiration thesubject momentarily held his breath, and operating the three-way cock next took a single con-trolled breath of oxygen (normally 600-700 ml.). The oxygen was held in the lungs for j-30 sec,and then the cock was turned back to room air. The subject completed the test by giving amaximal expiration lasting approximately 2 sec.

The pneumotachographSome practical problems in the use of the standard pneumotachograph (Lilly, 1950 b) have been

discussed elsewhere (Shephard, 1955 a). In the present experiments, flow rates rarely exceeded150 1./min, so that back-pressure effects and non-linearity of calibration were not importantsources of error. The amount of water vapour exhaled was also relatively small, and there was noevidence of significant condensation effects over the short course of a given test. Between tests,the spirometer was refilled with oxygen, and the apparatus from the three-way cock to the mouth-piece blown through with compressed air until the nitrogen-meter again indicated 79-1% nitrogen.This routine ensured the removal of oxygen and excess water vapour from the pneumotachographand its connexions.

The nitrogen analyserPerformance characteristics of the Lundin-Akeson nitrogen analyser used in this laboratory

have been described previously (Shephard, 1955 b). However, certain problems specific to themeasurement of respiratory dead space remain to be discussed.

Carbon dioxide. This gas is known to influence the total discharge intensity, although its effectrelative to nitrogen is small. In normal healthy subjects the carbon dioxide and nitrogen deadspaces are closely similar, so that after a single breath of oxygen the expired carbon dioxide andnitrogen concentrations will rise pari passu, and no error should be introduced into the calculateddead-space value. Further, if the specified operating conditions (2500 ,u& Hg vacuum pressure,4 0 mA discharge current) are maintained, the total contribution of carbon dioxide to the indicatednitrogen content of alveolar gas is less than 0-1 % (Shephard, 1955 b), so that variations of carbondioxide concentration can have no measurable effect on the slope of the alveolar nitrogen plateau.

Water vapour. It is not yet fully decided whether water vapour affects the discharge intensityby physical dilution of the gas sample (Shephard, 1955 b) or by chemical combination with nitrogen(Luft, 1956, personal communication), but it is clear that a large change in saturation is necessaryto produce a 1 % change in the indicated nitrogen concentration. The present apparatus isarranged in such a way that fluctuations of water-vapour tension in the sampling chamber areminimized. Inspired gas is saturated by storage in the spirometer, and condensation of expiredwater vapour is prevented by flushing the sampling chamber with compressed air between eachobservation.

Phase lag. There is a considerable phase lag between the pneumotachograph and the nitrogenanalyser, due largely to the time required for gas to be pumped from the needle valve to thedischarge tube. This may be examined quantitatively by noting the response to a high-velocitystream of oxygen (10 I./sec) directed into the apparatus from below. The instrumental dead spacebelow the needle valve is quite large (about 180 ml.), but assuming a 'square' wave-front ofoxygen is maintained under the conditions of turbulent flow, this should reach the needle valve in18 msec. The nitrogen meter fails to respond for a further 402 msec.

632 R. J. SHEPHARDIf correction is made for this phase lag, dead space may be calculated by the standard plani-

metric technique (Fig. 1). Measuring areas a,, bl, v%, and v2 the basic expression for total deadspace (subject and apparatus), is

dead space =v + (a: b) v2 (Brown, 1954).

This simple equation neglects the response time of the nitrogen meter and pneumotachograph.The true course of both curves probably lies a few milliseconds to the left, as indicated by thedotted lines. Small areas xl, x2, x3 are involved, the correct value for total dead space being givenby the expression

dead space = (v1 +X2) + (V2 + X3) ( .1)

-o-0, 60

0 ~~~~~~~~0~

Fig. 1. Diagram to show method used in calculating dead space;

dead space = (V1 + X2) + (v2 + X3) (a +b).-

In practice it is difficult to obtain a 'pure' square wave, and the magnitude of areas xl, x2 and x8cannot be determined with any precision. However, it can be stated that x2 is negligible, and xland X3 are approximately equal, so that the residual error is small, and probably does not differgreatly from one subject to another.

Non-linearity of calibration. Ideally, an apparatus with a linear calibration curve is required.In practice, the nitrogen meter seems to give satisfactory results, although it has been shownrepeatedly (Lundgren, White &; Boothby, 1954; Balke, 1954) that the calibration chart has aslight concavity. The effect is a displacement of the observed nitrogen concentration curve to theright, particularly during the early phases of expiration. Some gain of absolute accuracy might beachieved by a laborious replotting of the curve, but since the displacement is similar in all subjects,it seems preferable to accept it as a small systematic error in the dead-space values. For thecalculation of functional residual volume, absolute accuracy is more important and observednitrogen readings must be corrected by an appropriate calibration chart (Fig. 2).

Methods of calculationRespiratory dead.space. The method of determining total dead space has been detailed above.

The respiratory dead space is obtained by subtracting the instrumental dead space between mouthand needie valve (54 ml.).

VENTILATORY EFFICIENCY 633Uniformity of alveolar nitrogen concentration. The alveolar nitrogen concentration has been

measured at the commencement of the alveolar plateau (alvo), and 1 sec later (alv,). The volume ofgas expired during 1 sec (v1-0) has also been determined, and the slope of the alveolar plateauexpressed in terms of the ratio

av a x 1000 (%/1000 mI.).v'-0

80

70-

60

c500

.40

° 30

' 20

10

20 40 60 80True nitrogen (%)

Fig. 2. Calibration chart for nitrogen meter. Observed scale readimgs plottedagainst absolute values determined by Haldane gas analysis.

In most subjects the slope ofthe plateau was reasonably uniform during the first second, and a gasvolume of 1000-1500 ml. was expired at a fairly steady rate. An undulatory tracing (Fowler,1948 b) was noted in one or two instances; these undulations appeared to be synchronous with thestroke of the pump (frequency about 120/min), and may therefore have been caused by fluctuationsin the vacuum pressure. The selected vacuum pressure (2500 jt Hg) minimized this difficulty.Tracings with a negative slope were never observed except in one or two instances where thesubject made an error of technique.

Functional residual volume. In each experiment, values are available for the volume of oxygeninspired (VO2), the respiratory dead space (VDI), the instrumental dead space (VDE); the expiratoryalveolar nitrogen concentration (alvN2) has been taken as the mean of alvo and alvL, correspondingwith a point rather more than half-way through expiration. If an initial alveolar nitrogenconcentration of 80% be assumed, it is then simple to calculate an approximate value for thefunctional residual volume, FRV:

80 (FRV + VDE) = alVN2 (FRV + V02 - VD,)

FRV= alvN2 (V°2 - VDI) -80 (VDE)FRY- ~80 - alvN2

Subjects and experimental conditionsThe subjects were all healthy young men, members of the staff of the R.A.F. Institute of

Aviation Medicine. Their ages and physical characteristics are summarized in Table 1. Most hadsome previous experience of respiratory work. Measurements were made in the resting state.At least 2-3 min elapsed between individual experiments; this time interval was found sufficientto restore the normal nitrogen content of the lungs.

634 R. J. SHEPHARD

TABLE 1. Age and physical characteristics of subjects

PreviousHeight Weight experience as

Subject Age A - Body surface respiratory(male) (yr) ft. in. cm* lb. kg.* (m2) subjectsR.J.S. 26 6 0 183 159 72 1.91 ConsiderableM. B. 22 5 11 182 155 70 1.89 SlightD. PI. 22 5 8 173 151 68 1-81 FairP. B. 43 5 8 173 167 76 1-88 FairP. R. 22 5 8 173 127 57 1-68 NoneW. E. 26 5 7i 172 160 72 1-85 SlightK.Fg. 37 5 71 172 141 64 1F75 FairF. G. 41 5 8j 174 139 63 1*76 ConsiderableD.Py. 26 5 7 170 138 62 1-72 Considerable

* To nearest unit.

RESULTS

Principal variables with the single-breath techniqueThe period of breath-holding after oxygen is accepted by most authors as themain variable. The normal subjects deliberately varied the extent of breath-holding, so that information regarding the natural variation of this period andalso of the critical expiratory phase has been derived from 100 consecutiveobservations made on a group of twenty-seven patients seen after limitedsegmental resections. The actual times achieved by this group often differedquite widely from the intended 2 sec:

CriticalBreath-holding time expiratory phase

(sec) (sec)Mean time (100 expts.) 2-60±0-20 3-38±0-20S.D. for single observation ± 200 ±2-00Range 0-08-15-10 0-39-15-80

The influence of these variables on the dead space, alveolar nitrogen uni-formity, and functional residual gas volume must now be considered.

Respiratory dead spaceBreath-holding and critical expiratory phase. Preliminary analysis suggested

that dead-space values were related to time by a function of exponential type.The highest correlations were obtained between dead space and e-t, where t isthe breathing-holding time or critical expiratory phase in seconds. The criticalexpiratory phase is theoretically the more important value (Roos, Dahlstrom,& Murphy, 1955), and this alone has been analysed in detail.

Fitting a linear regression of the formDead space =a+ be-t

to the available data (251 observations from nine subjects), a graph of theform shown in Fig. 3 is obtained. In this figure dead-space values have alsobeen grouped according to critical expiratory phase, the mean and S.E. being

VENTILATORY EFFICIENCY

calculated for each group. It will be noted that the exponential curve satisfiesthese mean points quite reasonably over the entire experimental range (criticalexpiratory phase 0 75-30 sec.).

,,3000-

o 200U < ~~~~~~~~~~D=131-7+ 324e-I

"I 100_+0~

o

5 10 15 20 25Critical expiratory phase t (sec)

Fig. 3. Relationships between respiratory dead space and critical expiratory phase. 251 ob-servations from nine normal subjects. The curve 'dead space =a + be-t' has been fitted by themethod of least squares. The mean and S.E. of grouped observations are also shown.

Inspired gas volume. To assess the effect of this variable, subject M. B.deliberately varied the volume of oxygen inspired over the range 500-3000 ml.Knowing the critical expiratory phase for each experiment, individual dead-space readings have been expressed as a percentage of the expected values.Observations can be divided into two groups, according to the length of thecritical expiratory phase. Where this is less than 2-5 sec, there is a significantpositive correlation between the dead space and the volume of oxygen inspired(slope of linear regression 3-70+0410%/100 ml. BTPS). However, if thecritical expiratory phase exceeds 2-5 sec, there is no longer a significant cor-relation (slope - 0 8 + 0 9 0//100 ml. BTPS). The difference between the twogroups of observations is highly significant (t55= 3-16, P <0001).

Expiratory gas flow. Data from the nine normal subjects have been stan-dardized to a critical expiratory phase of 2-5 sec and an inspired gas volume of750 ml. by means of the curves referred to in the previous paragraph. Group-ing values according to the rate of expiratory gas flow, a graph of ratherunusual form has been obtained (Fig. 4). At very low rates of flow, the deadspace is quite large; as the rate of flow increases, the dead space reaches aminimum at 60-70 1./min, and then gradually increases again to approach alimiting value of 170 ml. at a flow rate of 150 1./min.

Inspiratory gas flow. Dead-space data standardized for critical expiratoryphase, inspired gas volume, and expiratory gas flow show no significantvariation with inspiratory flow rates ranging from 10 to 80 1./min.

Intersubject variation. Standardization of the data in the manner indicatedabove effects a considerable reduction of the intersubject variation (Table 2);

635

the individual variation is also reduced, particularly in the subject showingthe widest range of techniques (M. B.).

Differences of body-surface area are rather small, but over this limitedrange no decrease of intersubject variation is achieved by expressing results interms of a standard surface area of 1-80 n2. A slight improvement can beobtained if dead-space values are expressed per inch of standing height.

200

V~

XL Mean

a.t _I S.E.

1.50 r _CL

40)

soX0 50 100 150 200

Peak rate of expiratory gas flow (I./mmn BTPS)

Fig. 4. Relationships between respiratory dead space and expiratory gas flow. Data from ninenormal subjects, standardized for critical expiratory phase and inspired gas volume.

Uniformity of alveolar nitrogen concentrationExpiratory gas flow. Preliminary correlation tests suggested that the most

important factor affecting alveolar uniformity readings was the rate ofexpiratory gas flow. Grouped data from the nine normal subjects are presentedin Fig. 5. The slope of the alveolar gas plateau decreases rapidly over the flowrange 30-60 1./min, and thereafter shows little change. Two subjects have aparticularly large number of observations in the low-velocity range, and bothshow significant linear correlations between expiratory flow and alveolaruniformity (in W.E., t18=4 49, P <0-001).

Critical expiratory phase. Omitting the sixty observations where the ex-piratory gas flow is less than 60 l./min, 199 values remain. If these are groupedto show the relationship between critical expiratory phase and alveolaruniformity, a rather irregular curve is obtained (Fig. 6), but there is someevidence of a peak at approximately 2 sec, followed by a decline that isvirtually complete within 10 sec.

Other variables. If the uniformity readings are standardized for criticalexpiratory phase, intersubject and in most cases also the individual variation,is reduced. The standardized values are not affected by changing inspiratorygas flow (over the range 10-80 l./min). Nor are they influenced by differences

R. J. SHEPHARD636

VENTILATOR Y EFFICIENCY

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637

638 R. J. SHEPHARD

of inspired gas volume (over the range 500-3000 ml.). The range of ages is notvery wide, but it may be significant that the highest values are observed inP. B., who is the oldest subject, and has the largest residual gas volume.

30 F

Cuhoo 'i-

0 -0 2-0" 'CL, 2LUELcx

1-4

1§ i-

C-I"

Meant*S.E.

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50 100 150 200Peak rate of gas flow (1./min BTPS)

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201- 'A

I-

V

Mean*S.E.

i_

5 10 15

Critical expiratory phase (sec)20 25

Fig. 6. Relationships between uniformity of alveolar nitrogen concentration and critical ex-

piratory phase. Grouped data from nine normal subjects, omitting observations where theexpiratory gas flow is less than 60 l./mi.

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VENTILATORY EFFICIENCY 639

Functional residual gas volumeThe principal factor that affects the calculated functional residual gas

volume is the amount of oxygen inspired. If this exceeds the total dead space(apparatus+ subject) by 400 ml., relatively constant values are obtained(Fig. 7), although there is some further increase of functional residual volume(200-300 ml.) if even larger breaths are taken. Individual values for each ofthe nine normal subjects are given in Table 3. The average S.D. of a singleobservation is 29x2 %, so that if six observations are made on any one subject

s _<L -- sM~~~~~~~~~~~~~~~eanc-E

I 3000E'uE

, 2000

0C

.2

1000_

u

U

100 200 300 400 *500 600 700 800 900 1000 1100 1200Inspired volume less dead space volume (ml. BTPS)

Fig. 7. Effect of volume of oxygen inspired on the calculated value for functional residual gasvolume. Note that a relatively constant value is obtained if the inspired volume exceeds thetotal dead space by more than 400 ml.

(the usual clinical routine), a S.E. of 11 9% ( 300 ml.) would be expected. Insix subjects values are available for the remaining subdivisions of total lungcapacity. Subject P. B. has a residual volume that is much larger than the restof the group. He was older, and had a rather barrel-shaped chest, but showedno other manifestations of respiratory disease.

DISCUSSION

The observations presented above cover a sufficiently wide variation inindividual procedures to meet the primary requirement of interpreting thenormality of data obtained from clinical material. It now remains to considerthe physiological significance of the results, and their relevance to problems ofgas mixing in the human lungs.

640

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VENTILATORY EFFICIENCY

The dead space measured by the nitrogen-meter technique has generallybeen accepted as a physiological entity. Fowler (1948a) defines it as 'thevolume of the conducting airway down to the location at which a large changein gas composition occurs'. Theoretically a small component related to well-ventilated, poorly perfused alveoli (the 'parallel' dead space of Folkow &Pappenheimer, 1955) is ignored. In practice this does not seem important, atleast in normal subjects, since there is no systematic difference between resultsobtained by the nitrogen meter and by blood-gas methods (Rossier & Biihl-mann, 1955). While Fowler's gas-boundary concept is physically correct, itis obvious that the volume measured is changing continuously with time. Ifthe results are to have clinical and pathological significance, it seems necessaryto relate dead-space values to something more tangible than the location of agas boundary. Consider what happens when a single breath of oxygen isdrawn quietly into the lungs. The advancing wave front tends to a conicalform. Henderson, Chillingworth & Whitney (1915) were the first to drawattention to this practical consequence of axial flow, and recent experimentsby Briscoe, Forster & Comroe (1954) have demonstrated that it must occur atleast with the inspiration of small gas volumes. The coniform wave front wouldclearly be destroyed if flow became turbulent, but a number of considerationssuggest that this is unlikely during a normal quiet inspiration (see Appendix).Thus it may be assumed that the initial volume of the oxygen dead space isequal to the inspired gas volume, distributed through the conducting airwaysin a coniform pattern.The early observations of Henderson et al. (1915) on the behaviour of

tobacco smoke in a glass tube demonstrated the rapidity with which the gasboundary disappears when flow stops; if a breath is checked in the lungs, theboundary may disappear even more rapidly, since the process of diffusion isaided to some extent by the massaging action of the heart. It is convenient toconsider subsequent changes of gas composition as proceeding in two distinctzones-alveolar and bronchial-although in practice these inevitably overlap.

Alveolar zone. A conical wave front of oxygen projects initially into arelatively large volume of alveolar gas. The mean diffusion path is short, anda homogeneous gas composition is rapidly attained. The shape and location ofthe gaseous interface are continuously changing, but to a first approximationit may be shown (Shephard, 1956) that the effective volume of 'dead' oxygenAt remaining in the alveolar zone at any time t is an exponential function ofthe initial oxygen volume AO:

At =AOe-kt.Bronchial zone. An axial stream of oxygen initially fills a large part of the

airway. When gas flow stops, diffusion rapidly obliterates the difference ofconcentration between axis and periphery at any cross-section of the airway.

41 PHYSIO. CXXXIV

641

642 R .SEHR

This change has no effect on the calculated dead-space value. However, thevolume of 'dead' oxygen in the bronchial zone is reduced by a diffusionalinterchange between alveolar and bronchial gas. This causes a gradual retreatof the gaseous interface up the smaller bronchioles. Finally the process ishalted by the decreasing total cross-section of the airway and the increasinglength of the mean diffusion path. It can be shown that to a first approxima-tion the volume of dead space in the bronchial zone is represented by anexponential function of the type

Bo (I + e-k2t) + C,

where Bo is half the volume of the airway from the alveolar zone to the limitinglevel, and C is the volume of the airway above this level.

Thus the total equation for the dead space measured by the nitrogen metertechnique becomes

Volume of dead space at time t =Aoe-klt+Bo (1+ ekst) + C.

It is now necessary to consider the relative magnitudes of the constants tothis equation. Fig. 3 is of some help in this respect. The form of this curve canbe accepted with some confidence, since it agrees well with more limitedobservations by Roos et al. (1955) (using the nitrogen meter) and Brown (1954)(using infra-red analysis of carbon dioxide). The coefficient C amounts toapproximately 130 ml. This corresponds quite closely with classical estimatesof the anatomical dead space, measured to the level of the intralobularbronchi. It seems equally clear from Fig. 3 that with a critical expiratoryphase in the range 0-5-10-0 sec dead-space values are well satisfied by a singleexponential function. It is most improbable that the constants k1 and k2 are ofthe same order, and it must therefore be presumed that the alveolar process(described by the term Aoe-klt) is largely completed within 0-5 sec. This is inaccord with the work of Rauwerda (1946), who calculated that the meandiffusion path in the alveolar zone was such that concentration differencesmust be obliterated within a small fraction of a second.

There remains a change of 150-200 ml. in the volume of 'dead' oxygen,occupying a period of about 2 sec, and occurring somewhere between thealveoli and the interlobular bronchi. Anatomical estimates (Rohrer, 1915)suggest that the total volume of the intralobular bronchi and bronchioles doesnot exceed 20 ml. in the collapsed lung, and it is evident that if a volume of150 ml. of oxygen is to be accommodated, considerable expansion must occurduring inspiration. Haldane & Priestly (1935) reached a similar conclusion ondifferent grounds, and commenting on the anatomical and histological studiesof Miller (1934) suggested that the most likely sites for expansion were therelatively unsupported alveolar ducts and atria. On the basis of broncho-graphic and bronchoscopic observations, Huizinga (1937) also concluded that

642 R. J. SHEPHARD

VENTILATORY EFFICIENCY

the main change of diameter occurred in the air passages with a diameter ofless than 1-2 mm. The crucial question is whether oxygen can remain 'dead'within this zone for a period of 2 sec. Rauwerda (1946) claimed that con-centration differences throughout Miller's primary lobule were reduced to16% of their original value within 0-38 sec. However, his calculation restsentirely on the assumption that dimensions remain unchanged throughoutinspiration. In fact there may well be an eightfold increase of volume, leadingto a twofold increase in length of the alveolar ducts. In these circumstancesapplication of Rauwerda's diffusion equations shows that the concentrationgradient will not be reduced to 16% of its original value for at least 1-6 sec, atime relationship that is in agreement with the present experimental results.

The atrial expansion concept gains further support from experiments wherethe inspired gas volume was varied. The additional dead space produced by adeep inspiration was largely obliterated within 2-5 sec, so that the expansiblepart of the conducting airway must lie in close proximity to the alveolar zone.The absolute increase of dead space produced by an increase of tidal volume isnot large. The present estimate (7 ml./100 ml. BTPS) may be compared witha recent estimate by the carbon dioxide method (Brown, 1954: 15-20 ml./100 ml.over the range 450-1000 ml., and thereafter 1-4-3 ml./1000 ml.). The data ofboth Brown and the present author show too wide a scatter to permit commenton details of the curves, but on the whole the present figures do not supportthe view that enlargement of the dead space is less marked at volumes inexcess of 1 1.The effect of rate of gas flow on the calculated dead-space volume does not

appear to have been examined before. The present results suggest that in-spiratory flow rates are unimportant over the range normally encountered, butthat changes of expiratory flow rates can seriously influence the dead-spacefigures. An explanation may be sought in patterns of gas flow. The relativelystraight course of the trachea seems particularly favourable to axial flow, andduring expiration an increase of flow causes an increasing proportion of thedead-space oxygen to cling to the tracheal walls; this oxygen subsequentlycontributes to the slope of the alveolar plateau. However, if the criticalvelocity is exceeded, the oxygen in the upper airway is washed out by a muchsmaller volume of alveolar gas, and the calculated dead space increases to alimiting value determined by the anatomical size of the air passages.For clinical purposes it seems desirable to express the dead space as the

volume that would be observed in a given patient under standard conditions,and the curves presented above enable this calculation to be carried out. Theselected critical expiratory phase (2.5 sec) is roughly comparable with thatobserved during quiet breathing (rate 12-14 breaths/min); if this value of tbe used one obtains a volume which corresponds with an anatomical entity(the conducting airway to the level of the intralobular bronchi), and slight

41-2

643

alterations in timing do not produce an undue scatter of the results. It is con-ceivable that in emphysema and related disorders pathological enlargement ofthe alveolar ducts may also occur; diffusion rates should still be adequate toovercome this change during quiet respiration, but with more rapid breathingrates a stratified non-homogeneity of the type postulated by Krogh & Lindhard(1917) and Haldane & Priestley (1935) could develop. A qualitative index ofthis change could be obtained by repeating the readings with a criticalexpiratory phase of 1 sec. The selected tidal volume (750 ml.) needs littlecomment. The selected gas flow (150 1./min) represents the upper recordinglimit of many pneumotachographs, and seems adequate to prevent distortionof dead-space values by axial flow during the course of expiration.

Previous workers have differed in their interpretation of the slope of thealveolar plateau. Armitage & Arnott (1949) dismissed it as an artifact causedby incomplete washing out of the dead space, but it would appear that in theequation on which their argument depends, a constant value of 175 ml. hasbeen assumed for the dead space of subject and apparatus. Clearly, if thedead space exceeded this figure, a mid-expiratory rather than end-expiratoryalveolar sample might satisfy their equation. Fowler (1948b) took an oppositeview, claiming that dead-space gas played no part in producing the slope of thealveolar plateau. He contended that (1) 400 ml. of oxygen would be needed toproduce the observed slope (most of the present results could be explained by200 ml.) and (2) if serial measurements were made at any point on successiveplateaus, extrapolation back to zero time gave a value for alveolar nitrogen(78.5-81 %) that was theoretically acceptable and corresponded with measure-ments made at any other point on the same series of plateaux. However, thevalidity of extrapolation is questionable, since the nitrogen clearance curvedoes not follow a single-constant pattern (Roos et al. 1955). The first argumentcarries greater weight, but even this does not eliminate the possibility thatpart of the slope is due to dead-space effects. A number of authors have notedthat the slope of the plateau is decreased by a rise of expiratory flow (Fowler,1948b; Lanphier, 1953; Roos et al. 1955), but this has been attributed to analteration in the sequence of pulmonary emptying. The present results showthat flow changes produce little effect at rates greater than 60 1./min. Ittherefore seems tempting to suggest that during normal quiet breathing, partof the slope of the plateau is attributable to axial flow, and that this effect isabolished if the gas flow is increased sufficiently to produce generalizedturbulence.The increase in non-uniformity of gas distribution with short periods of

breath-holding (critical expiratory phase 0-2 5 sec) is probably related to theincreasing amount of oxygen that reaches the alveolar zone over this period.The present results do not suggest that uniformity is increased by deeperrespirations, at least over the range 500-2500 ml. Fowler (1948b) has pre-

644 R. J. SHEPHARD

VENTILATORY EFFICIENCY

viously reported some increase, but it is difficult to dissociate the slightchanges that were noted from concomitant variations of expiratory flow.For clinical purposes it is clearly desirable to encourage the patient to

achieve an expiratory flow that is sufficient to produce turbulence in the mainairways (i.e. > 60-70 1./min). It is also convenient to standardize for variationsof critical expiratory phase. Two times are of particular interest. The non-uniformity at 2'5 sec represents the peak encountered during normal breathing-much of this non-homogeneity exists at a local (lobular) level, since it is readilyabolished by diffusion; further measurements at 10 sec serve to distinguishresidual (lobar) differences. It will be appreciated that the single-breathtechnique offers different and in some respects fiuller information than con-ventional serial breath analysis methods. Many of the latter either ignore thedead space, or make debatable assumptions regarding its volume (Gilson &Hugh-Jones, 1955). Theoretically the single-breath method only indicates thefull extent of uneven ventilation if expiration is a mirror image of inspiration(Fowler, 1948a). However, in practice, the indicated non-uniformity ofventilation (10-15% in normal subjects) is of a similar order to that found byserial methods (Gilson & Hugh-Jones, 1955).The values for functional residual gas volume require little comment. The

need for a large inspired gas volume is readily explained by the occurrence oflaminar flow through the pneumotachograph and its connexions. The use ofmid-expiratory alveolar nitrogen concentrations is at variance with Fowler,who suggested the 'least ventilated gas'. Lanphier (1953) also used end-expiratory concentrations, but was forced to the conclusion that 'the con-centration of the terminal sample, although readily identified, does notconsistently approximate the mean value required'. It did not prove possibleto check the present results against closed-circuit determinations of residualvolume, but their general order of magnitude suggests that the use of a mid-expiratory nitrogen concentration avoids a systematic bias of the results. Thevariance of a single observation is rather large (partly owing to true minute-to-minute variations of the functional residual volume), but since measurementscan be carried out very rapidly, the confidence limit for a given subject canreadily be improved by repeating the experiment. Finally, as Comroe (1951)has pointed out, clinical significance can only be attached to large changes ofresidual volume.

SUMMARY

1. Respiratory dead space, alveolar gas uniformity, and functional residualgas volume have been measured by the single-breath (nitrogen meter) techniqueof Fowler (1948 a). Factors contributing to the variance ofthese measurementshave been defined, and standard curves prepared to allow the interpretation ofdata obtained from clinical subjects.

645

2. The respiratory dead space decreases exponentially with time; over theperiod 0-5-10 0 sec the curve is satisfied by a single exponential constant.Evidence suggesting that the decrease of volume occurred largely withinMiller's 'primary lobule' is presented. Larger tidal volumes produce anincrease of dead space (7 ml./100 ml.); this effect is abolished by shortperiods of breath-holding, and is therefore related to the primary lobule.The rate of expiratory flow also affects the calculated dead-space value,apparently by a transition from laminar to turbulent flow. Conditions in thetrachea seem such that generalized turbulence would develop at a flow of60-70 1./min.

3. At low flow rates the slope of the alveolar plateau on the expired nitrogenconcentration curve is partly an artifact attributable to incomplete washingout of the respiratory dead space. At higher rates of flow two true causes ofnon-uniformity may be distinguished. One is rapidly abolished by diffusionand must be presumed lobular in origin; the other persists with breath-holdingand is therefore of lobar origin.

4. Erroneously small values for the functional residual gas volume may becaused by laminarity of gas flow during inspiration. This difficulty can beovercome by increasing the volume of oxygen inspired. Single measurementsof functional residual volume have a rather large variance, but since thetechnique is rapid, a precision of + 300 ml. can readily be obtained by repeatedmeasurements.

The author is indebted to the statistics section for their help in fitting the exponential curveto Fig. 3.

REFERENCESARMITAGE, G. H. & ARNOTT, W. M. (1949). Air distribution in the lungs during hyperventilation.

J. Phy8iol. 109, 70-80.BALKE, B. (1954). Continuous determination of nitrogen concentrations during the respiratory

cycle. U.S.A.F. School of Aviat. Med., Proj. 21-1201-0014 Rep. no. 5.BRIscox, W. A., FORSTER, R. E. & ComRoE, J. H. (1954). Alveolar ventilation at very low tidal

volumes. J. appl. Phy8iol. 7, 27-30.BROwN, E. S. (1952). Application of infra-red C02 analysis to lung compartment estimation.

Fed. Proc. 11, 18.BROwN, E. S. (1954). Measurement of physiological dead space and alveolar ventilation with

rapid CO2 and flow analysis. U.S.A.F. School of Aviat. Med., unnumbered report.CoMRoE, J. H., Jr. (1951). Interpretation of commonly used pulmonary function tests. Amer. J.

Med. 10, 356-374.FENN, W. 0. (1951). Mechanics of respiration. Amer. Forces Tech. Rep. no. 6528, pp. 156-169.FOLKOW, B. & PAPPENHEIMER, J. R. (1955). Components of the respiratory dead space and

their variation with pressure breathing and with bronchioactive drugs. J. appl. Phy8iol. 8,102-110.

FOWLER, W. S. (1948 a). Lung function studies. II. The respiratory dead space. Amer. J. Phy8iol.154, 405-416.

FOwLER, W. S. (1948b). Lung function studies. III. Uneven pulmonary ventilation in normalsubjects and in patients with pulmonary disease. J. appl. Phy8iol. 2, 283-299.

FowLzu, W. S. (1950). Lung function studies. IV. Postural changes in respiratory dead spaceand functional residual capacity. J. clin. Inve8t. 29, 1437-1438.

646 R. J. SHEPHARD

VENTILATORY EFFICIENCY 647GmLSON. J. C. & HUGH JONES, P. (1955). Lung function in coal workers' pneumoconiosis. Spec.

Rep. Ser. med. Res. Coun., Lond., 290, 1-266.HALDANE, J. S. & PRIESTLEY, J. G. (1935). Respiration, 2nd ed. Oxford: The Clarendon Press.HENDERSON, Y., CHILLINGWORTH, F. P. & WHITNEY, J. L. (1915). The respiratory dead space.

Amer. J. Physiol. 38, 1-19.HUIZINGA, E. (1937). tYber die Physiologie des Bronchialbaumes. Pflug. Arch. ges. Physiol. 238,

767-779.KROGH, A. & LiNDHARD, J. (1917). The volume of the dead space in breathing and the mixing of

gases in the lungs of man. J. Physiol. 51, 59-90.LANPHIER, E. H. (1953). Determination of residual volume and residual volume/total capacity

ratio by single breath technics. J. appl. Physiol. 5, 361-366.LILLY, J. C. (1946). Studies on the mixing of gases within the respiratory system with a new type

of nitrogen meter. Fed. Proc. 5, 64.LILLY, J. C. (1950a). Mixing of gases within respiratory system studied with a new type nitrogen

meter. Amer. J. Physiol. 161, 342-351.LiLLY, J. C. (1950b). Pulmonary function tests. In Methods in Medical Research, Vol. 2, Sec-

tion II. Ed. COMROE, J. H. Chicago: Year Book Publishers.LuNDGREN, N. P. V., WHITE, C. S. & BOOTHBY, W. M. (1954). Calibration of the Lilly-Anderson-

Harvey nitrogen meter. With special reference to the influence of water vapour and carbondioxide. U.S.A.F. School of Aviat. Med. Proj. 21-1201-0007.

MLLER, W. S. (1934). The Lung. Balli6re, Tindal & Cox. London.OTIS, A. B. & BEMBOwER, W. C. (1949). The effect of gas density on resistance to respiratory gas

flow in man. J. appl. Physiol. 2, 300-306.OTIS, A. B. & PROCTOR, D. F. (1948). Measurement of alveolar pressure in human subjects.

Amer. J. Physiol. 152, 106-112.RAIUWERDA, P. E. (1946). Unequal ventilation of different parts of the lung, and the determina-

tion of cardiac output. Thesis, Groningen University.ROHRER, F. (1915). Der Str6mungswiderstand in den menschlichen Atemwegen und der Einfluss

der unregelmassigen Verzweigung des Bronchialsystems auf den Atmungsverlauf in ver-schiedenen Lungenbezirken. Pflug. Arch. ges. Physiol. 162, 225-299.

Roos, A., DAHLSTROM, H. & MuIRPHY, J. P. (1955). Distribution of inspired air in the lungs.J. appl. Physiol. 7, 645-659.

RoSSIER, P. H. & BtHLMANN, A. (1955). The respiratory dead space. Physiol. Rev. 35, 860-876.SHEPHARD, R. J. (1955 a). The place of the pneumotachograph in the measurement of breathing

capacity; Air Ministry Flying Personnel Research Committee Rep. F.P.R.C. 916, 1-19.SHEPHARD, R. J. (1955 b). Performance characteristics of the nitrogen meter, with particular

reference to the effect of carbon dioxide. Air Ministry Flying Personnel Research CommitteeRep. F.P.R.C. 936, 1-14.

SHEPHARD, R. J. (1956). Assessment of ventilatory efficiency by a single breath technique. AirMinistry Flying Personnel Research Committee Rep. F.P.R.C. 972.

YOUNG, A. C. (1955). Dead space at rest and during exercise. J. appl. Physiol. 8, 91-94.

APPENDIX

The pattern of gas flow through the respiratory tract and needle valveBefore considering problems of gas mixing in the human respiratory tract, it is essential to deter-mine whether gas flow is laminar or turbulent. Evidence bearing on this question can be obtainedfrom at least five sources:

Noise level. During normal breathing there is little noise, suggesting that turbulence is localizedto a few special sites. On the other hand, deep breathing produces considerable noise, either in thechest (rales and rhonchi) or in the larynx (phonation, and the stridor of laryngeal stenosis).

Calculatione of Reynolds' number. Under normal conditions, turbulent flow may develop whenthe Reynolds' number exceeds 1500 c.g.s./units. The critical velocity Vc is given by

Vc =250 cm/sec,dy d

648 R. J. SHEPHARDwhere 71 is the viscosity of air (190 x 10-6 c.g.s. units), d is the diameter of the airway in cm, and y isthe density of air relative to water (114 x 10-5 c.g.s. units). Dimensional errors have invalidatedprevious estimates for the human trachea (Rohrer, 1915; Fenn, 1951). Assuming a diameter of2-5 cm, the critical velocity is approximately 30 1./min, and it would be surprising if turbulencedid not develop at twice this velocity.

Use of models. The pattern of gas flow may be examined directly in a translucent model of theairway, using cigarette smoke (Henderson et al. 1915) or ammonium chloride vapour (Rohrer,1915). A more refined technique, now being applied to physiological work, is the photography ofbirefringent suspensions in polarized light (Shephard & Spels, unpublished). No accurate modelsof the respiratory tract have yet been studied by these techniques.

Pressure measurements. The resistance to laminar gas flow is directly proportional to velocity;the resistance to turbulent flow varies as Vn, where n has a positive value between 1-7 and 2-0.This technique has been used by Otis and his colleagues (Otis & Proctor, 1948; Otis & Bembower,1949). Although their curves have been fitted on the basis of Rohrer's calculations (which assumethat turbulence never develops except as a localized phenomenon where the airway branches orchanges its dimensions), the experimental values are valid; they show a flow resistance that islinear to approximately 50-60 I./min breathing air, and 150 l./min breathing a helium/oxygenmixture.

Gas sampling methods. With laminar flow, changes of gas composition proceed more rapidly atthe axis of the airway. With turbulent flow, no systematic concentration gradient is establishedacross the airway, and mixing at an existing gas boundary is greatly accelerated.Roos et al. (1955) examined the shape of the expired N2 curve after a single breath of oxygen,

sampling simultaneously at the level of the trachea (tracheotomy), and at the mouth. The twocurves were of similar form, suggesting that little mixing occurred between the two sites; ap-parently the experiment was performed during normal quiet respiration, although the velocity ofgas flow is not indicated.

It can be seen from the above summary that information concerning the flow pattern in thehuman respiratory tract is meagre, but is not incompatible with the theoretical expectation thattransition from laminar flow to generalized turbulence will occur during a forcible expiration.

The needle valveDespite the quite widespread use of sampling valves in respiratory physiology, little considera-

tion has been given to the problem of gas-flow patterns in the vicinity of the sampling device. Onerecent author (Young, 1955) concludes that involved analysis of dead-space data is not justifiedbecause so little is known about the pattern of flow during the standard test procedure. Hedevelops detailed equations describing laminar and turbulent flow in the airway leading to aninfra-red analyser, but does not hazard any guess as to when turbulence develops. However, hisexperimental results using an added dead space are best satisfied by the 'laminar' equation over aflow range 10-50 I./min.The sampling valve of the Lundin-Akeson nitrogen meter comprises a smooth-walled metal

tube of 2-0cm diameter and approximately 11 cm in length. At its midpoint, this tube is traversedby a fenestrated cylinder some 10 mm in diameter that serves to protect the needle valve. Theexperiments now to be described suggest that there is localized turbulence around the fenestrationsat quite low velocities, and that more generalized turbulence develops at a flow of 40-50 l./min.

Noise level. There is some noise even at low rates of flow (10l./min), but there is a considerableincrease of noise at flow rates in excess of 40-50 I./min.

Calculation of Reynolds' number. The complex structure of the tube precludes an accurate cal-culation. Assuming a Reynolds' number of 1500, the critical flow for the main tube is 24 I./min.

Models. No models have yet been prepared.Pressure measurements. The main component of the resistance to gas flow is attributable to the

fenestrated region. A linear relationship was found between back pressure and the square of gasflow, suggesting that turbulence develops in this region at very low velocities.

VENTILATORY EFFICIENCY 649Ga8 8amplitng method8. A weighted spirometer was used to introduce a 'square' wave front of

oxygen into the apparatus from below. In the first series of experiments, the standard needlevalve was used. Differing rates of gas flow were achieved by varying the weighting of the spiro-meter. If a turbulent (square) wave front was maintained at all rates of flow, variations in thephase lag between the pneumotachograph and the nitrogen meter should be determined simply bythe time taken for the wave front to traverse the 180 ml. of airway connecting the spirometer withthe needle valve. This seems true over the range from 180 to 70 l./min, but at lower flow ratesoxygen reached the needle valve much earlier and it must be presumed that laminar (coniform)flow occurred.

In the second group of experiments, the mouthpiece was replaced by a 100 cm length of smooth-walled 2 in. diameter hose-pipe, and gas samples were obtained by means of a fine needle piercingthe wall of the hose-pipe immediately above the sampling tube. Recordings were made with theneedle inserted to different depths. At low rates of gas flow (25-30 I./min), both the initial phaselag and the full response time were greater at the periphery of the gas stream, but this differencewas not observed with high rates of gas flow (170-180 l./min). It must therefore be presumed thatat the low flow rate, gas flow reverts to a laminar form beyond the immediate vicinity of theneedle valve.