Estimation of energy expenditure from expired air Medica Statistics Branch, Nationa Coa Board, London., Engand LIDDELL, F. D. K. Estimation of energy expenditure from expired air. J. App. Physio. 18(1): 25-29. Ig63.-Short cut methods of estimating energy expenditure from pumonary ventiation are examined. Athough for any one subject carrying out a particuar task, the reationship between his energy expenditure and his ventiation is approximatey inear, the equation of the regression ine differs from task to task and, for any particuar task, from subject to subject. Thus, the estimation of energy expenditure, for the generaity of subjects and tasks, from pumonary ventiation aone, by appication of a singe simpe formua, is seen to be unacceptabe as the estimates coud be subject to serious error. Anaysis of expired air cannot, therefore, be dispensed with but the cacuations for estimating energy expenditure in terms of ventiation and the anaysis of the expired air, aready simpified by Weir, are shown to be even further reducibe. A nomogram by which they can be carried out with negigibe error is presented. T HE TRADITIONAL METHOD Of estimating energy expenditure, indirect caorimetry, is carried out by I) measuring the quantity of air expired by the subject (pumonary ventiation) and its temperature, 2) anayzing a sampe of the expired air to obtain the oxygen and carbon dioxide content, 3) carrying out a compex cacuation of the kca/iter of expired air, and 4) mutipying the pumonary ventiation, adjusted to STPD, by the kca/iter of air, to obtain energy expenditure, expressed as kiocaories per unit time. Weir (I) has shown that the cacuations of stage 3 can be greaty simpified, but even more radica is the suggestion (2, 3) to omit the anaysis of expired air and appy instead a simpe equation to estimate energy expenditure directy from pumonary ventiation. This paper examines these methods in the ight of data obtained in underground surveys of miners performing varied tasks. Athough it is shown that the anaysis of expired air cannot in genera be dispensed with, a further important simpification of the cacuation is introduced. A. Data. The data were obtained in a survey (4) of the energy expenditure of miners performing norma mining tasks: shoveing and hewing in various postures; waking, upright and stooped, on the eve and up and down gradients. The information avaiabe in each of 335 cases consisted of the pumonary ventiation, adjusted to STPD, and the temperature of the sampe, together with the percentages of oxygen and carbon dioxide in Received for pubication I March I 962. the sampe of expired air, as determined. There were aso avaiabe daiy readings of barometric pressure both at pit bottom and at pit head. B. Reationship between energy expenditure and pumonary ventiation. An approximatey inear reationship between a subject s energy expenditure and his pumonary ventiation has been noted since eary in the 2th century and so at first sight it woud seem that energy expenditure coud be predicted from ventiation by means of a inear equation. The best equation for such prediction is the regression ine, fitted by the method of east squares. Figure I shows energy expenditure and pumonary ventiation of men performing waking tasks. The regression ines for individua subjects were found to differ significanty, in a statistica sense, one from another. However, the fu ine is the regression ine fitted irrespective of subject; the broken ine is the corresponding ine for mining tasks. The difference between these two ines shows that the reationship between energv expenditure and ventiation depends, to a arge exte&, on the task being performed or on differences in the environmenta conditions in which the different tasks were carried out. Certain subjects had performed both waking and mining tasks, and their reationships were found to differ from task to task in the same way as they did for the whoe group of subjects. Tabe I reates the resuts of the present survey with those from certain previous studies (2, 3, 5-1) ; the differences are seen to be marked. In those sets of resuts for which the information is avaiabe, the variation about the fitted ines is found to be of simiar order, and quite insufficient to account for the differences arising from the different prediction equations themseves. Possibe causes of the differences between the various regression equations incude : differences, incuding those in ages, between subjects; differences in the type of work performed; and differences in experimenta technique, particuary in the use of face masks. The resuts for individua subjects undoubtedy differ markedy; so much so indeed that Durnin and Edwards (2) advocated fitting a separate ine for each subject.. Type of work is aso an important cause of differences in the observed reationships, for, as can be seen from Tabe I, in a Adjustment has been made to these figures to take account of impurities in the inspired air (i.e., differences in the anaysis of inspired air from 2.937~ oxygen and.3% carbon dioxide) ; it can be shown by simpe agebra that these adjustments were justifiabe.
/ 26 IO 9 8 7 b 4 3 KU3LE I. Estimates of energy expenditure at certain rates of ventiation according to various authorities, kca/min Ventiation, Ventiation, Authority I iters/min 4 iters/min (STPD) (STPD) Margaria (6) 2. 9-4 Assmussen and Neisen (7) 2.8 [2.3] 1.5 [8.8] Grodins (8) 2.3 8.4 Durnin and Edwards (2) 2.6t [2.1]$ 1*4t [8*41$ Sartorei (5) 2.2 9.7 Durnin and Mikuicic (9) 3.2 c2.41 9.5 [g-o1 Ford and Heerstein (3) I.6 8. Bobbert (IO) 2.4 [2.] 9*6 [8*51 Humphreys and Lind (4) -3 b-71 8.3 L7.11 Estimates for tasks invoving major arm movements are in brackets. Estimates are averages, irrespective of subject, obtained (for iustrative purposes ony) from the quoted reationships often ony graphica and in some cases invoving considerabe extrapoation beyond the range of ventiations over which the authority quotes resuts. t Estimate for cerks and students. $ Estimate for miners. 2 VENTILATION (itedmn S.T. P.D.) A 1 1 I I IO 2 3 4 5 FIG. I. Energy expenditure and ventiation of a subjects performing waking tasks. Fu ine is the regression ine for waking tasks, irrespective of subject. Broken ine is the regression ine for mining tasks, irrespective of subject. the enquiries where resuts have been given separatey for tasks requiring major arm movements across the chest-cranking, shoveing, hewing, and the ike-the energy expended for a given ventiation has been ess for these tasks than for the tasks more commony examined, particuary treadmi waking. Ford and Heerstein (3) have suggested that the considerabe differences between their average resuts and those of Sartorei (5) were due mainy to differences in the dead space of the face masks. Humphreys and Lind (4) used simiar face masks and their ine for waking tasks agrees cosey with that of Ford and Heerstein (3), with both a itte apart from the others. From the avaiabe evidence, we draw the foowing concusions, athough eaving a discussion of the errors of prediction to section F: a) a prediction ine obtained in previous work may be quite inappicabe to a new survey; b) the use of a singe ine, irrespective of subject, for a particuar task woud ead to considerabe errors, due to differences between subjects, even were the technique of coecting expired air to remain the same; c) even the use of a ine specific to an individua subject, but estimated from one task, woud not necessariy be appropriate for the same subject carrying out other tasks, even of a simiar nature; and d) as it is necessary to caibrate each subject on each task, or at east to check that a particuar ine is appicabe, most if not a assessments of energy expenditure must be based on the resuts of anaysis of expired air. C. Cacuating kca/iter of expired air. The estimation of kca/iter of expired air is considered in terms of the foowing symbos for the components of the inspired and expired air: % 2 % co2 % N2 In inspired air Oi Ci Ni = 1 - Oi - Ci In expired air, CC? N, = IOO -, - C, The traditiona method of cacuation (I I) starts by determining the true oxygen consumption ( ), aowing for the change in voume of expired air as compared with inspired air, as = Oi(Ne/Ni) -, Then, the respiratory quotient (RQ) is found as RQ = (C, - Ci)/O whie the kca/iter of oxygen (6) is obtained from one of severa reationships avaiabe, a of the form = a + b*rq where a and b are constants, which depend on the particuar reationship used. Finay, the kca/iter of air (K) is estimated as K = 6( /1) Substituting from these equations successivey for 8, RQ, and, it can be seen by eementary agebra that K= (I/Ioo)*[Ioo*aOi/Ni - b*ci] - (r/roo)*a*[oi/ni + 1]*, + (I/IOO)*[~ - a*oi/ni]*c, where, for any given a and b and any given Oi and Ci, the coefficients of, and C, are constants. We obtain their vaues by taking a = 3.9 and b = I.I (i.e., using the reationship of Weir (I) incuding the protein correction ) and Oi = 2.93 and Ci =.3 (i.e., assum- 2 Weir pointed out that the numerica vaues used in the cacuations depend upon the fundamenta data reating to metaboism of anima fat, etc. We use his reationship which is based on data by Zuntz and Schumburg, with an estimated protein correction. The use either of his reationship without the protein correction or
ENERGY EXPENDITURE FROM EXPIRED AIR 27 4-3.5 - c5 2s xi 3-o - 2@5 - ~ I 15-5 16- b*5 17 17*5 18 a I&5 FIG. 2. Oxygen and carbon dioxide percentages in expired air (as recorded: a subjects). ing that pure air is inspired). Then the kca/iter of air can be obtained from the anaysis of expired air (as determined ) as K = I.324 -.49327, +.673 c, The use of this formua introduces no inaccuracy that is not inherent in the method. This formua can be simpified further by making use of the cose reationship between the oxygen percentage and carbon dioxide percentage (as determined) in the expired air, which arises in practice. Figure 2 has been prepared from the data aready described which consist of 335 sets of observations on 14 subjects, performing varied tasks. Not ony is the reationship between C, and, cose, but the resuts for each subject separatey foow the genera pattern very we. The equation of the prediction (regression) ine is: C, = 15.6 -.751, and the standard deviation of an estimate of C, for a particuar vaue of, is o. 15. Substituting for C, in the equation reating K to, and C, eads to the formua K = I.opg -.498, which is very simiar to formua 2 obtained by Weir (I) and so justifies the approximations he had to make. The standard deviation of an estimate based on this formua (due to the substitution for C,) is (.673) X (.15) =.1 kca/iter of air, so that the error introduced is ess than.1 % and competey negigibe in practice.3 of that given by Dougas and Priestey (I I ) makes very itte difference; the deviations associated with the particuar choice of reationship are much smaer than those due to experimenta error. 3 Because, in the anaysis of expired air, the carbon dioxide percentage is determined first, it is tempting to estimate kca/iter of expired air from this percentage aone; it can be shown that this is possibe but that the error is unacceptaby arge. Quick, accurate cacuation by nomogram is discussed in sectzon E. D. AaYjustment of pumonary ventiation to standard con& tions of temperature and pressure. The adjustment of pumona ry ventiation to standard temperature and pressure, dry, is of considerabe importance, but corrections to individua voumes of expired air are normay unnecessary. In the present series of resuts, which were obtained over 5 separate days, spread from eary June to the foowing February, barometric pressure at the working pace underground varied from 732 mm Hg to 767 mm Hg whie the temperature varied between 12-23 C. The extremes of the factors for correcting the voume as determined to STPD vaue thus varied ony between.888~.94. If an average correcting factor, obtained as the mean of the two extremes, i.e.,.914, had been used afterward to adjust a the voumes, the maximum error introduced into the determination of energy expenditure woud have been ess than 3 % with a standard deviation of about 1.5 %. The effect of using an average correcting factor woud have been very simiar if the experiments had been carried out in a surface aboratory, for the barometric pressure on the surface, athough naturay rather ower on average, showed about the same amount of variation (7 I 1-749 mm Hg) and it might be expected that, in aboratory conditions, temperatures woud have been rather more constant. E. Nomogram for compete cacuation. The whoe cacuation of energy expenditure can be competed by use of one simpe nomogram, which is presented in Figure 3. It requires ony the pumonary ventiation (as determined), the factor for correcting ventiation to STPD, and the oxygen percentage (as determined) in the expired air. First, seect the point in the centra grid corresponding to the ventiation (in iters/min, as determined) and the particuar factor for correcting ventiation to STPD, i.e., the intersection of the appropriate soping and
, the are ). 28 16-O-- 1 (O/o) 17.5-17*-- itps*- I&3-- s*s-- I*.,.,,I,,..,.,,.1.8.9 I- Foctor for corrcctinq ventiation to S.T.? D. 6 n ss $ * so z.- FIG. 3. Nomogram for determining energy expenditure from oxygen percentage in expired air and pumonary ventiation, correcting to stpd. See section E for instructions on use. vertica ines. Second, ook horizontay to the bod right hand scae of the centra grid; the point of intersection indicates the ventiation corrected to STPD. Third, join this point to that on the eft hand scae corresponding to the percentage of oxygen in the expired air (as determined) with a straight ine, which wi cut the scae on the right hand side of the nomogram at a point indicating the energy expenditure (in kca/ min). We have vaidated the use of the nomogram, enarged, by comparing estimates obtained from it with those obtained by cacuation using the fu process? The maximum error introduced was.5 kca/ min, and the standard deviation.2 kcajmin. F. Errors introduced by short-cut methods. In considering the errors introduced by approximate methods, it must be borne in mind a) that the assessed amount of energy expended by a particuar subject performing the same task under nominay identica conditions wi vary to some extent from one occasion to another, in other 4 Copies of the nomogram, 24 X 16 in., wi be suppied at a nomina cost on appication to the author. 4s: words that there is an inherent error, and b) that the standard deviations of the errors from various sources are not additive; given independence the standard deviation (SD) of a combined error from a number of sources is the root sum square of the SD S of the individua errors; i.e., if ~1, ~2, s3, SD S of errors from sources I, 2, 3, SD of the error from a sources combined is -\/ (s12 + sz2 + ss2 + Thus, if the errors introduced by approximate methods have SD rather smaer than the SD of the inherent error, the over-a error wi be increased ony sighty. For exampe, if the SD of the inherent error is taken as IOO units and the additiona errors have SD = 5 units, the combined error has SD I I 2 units; if the SD of the additiona errors is 2 units, the combined error has SD 12 units. In our data, the standard deviation of an individua assessment was.6 kca/min. This compares favoraby with the estimate from the data of Garry et a. (I 2); the rather higher vaue deduced from their resuts is probaby because of differences in the rate of work on dupicate runs on nominay the same task. It is ikey that in aboratory experimentation, where contro of conditions can be more cosey exercised, this error can be reduced somewhat, but it cannot be eiminated. In the foowing paragraphs, we discuss how the various approximate methods affect these errors. The errors invoved in predicting energy expenditure from pumonary ventiation, without anayzing the expired air, are not easy to assess except when using the ine, fitted to the resuts for a particuar subject carrying out a particuar task, to obtain further assessments of energy expenditure by the same subject carrying out the same task. In these very restricted circumstances, an average energy expenditure based on two measurements of ventiation woud be just about as accurate as a singe assessment making use of the resuts of anaysis of expired air. In other cases the errors introduced are arger and incude an indeterminate systematic component. This is because the regression ines differ from subject to subject, even when they are performing the same task, and differ from task to task, even for the same subject. Thus any particuar ine determined from previous experimentation wi not be strictv. appicabe to any future situation, and, if the ine is in fact inappropriate, the systematic errors introduced cannot be reduced by increasing the number of readings. The order of the errors invoved is perhaps best indicated by Tabe I of Durnin and Edwards (2); their vaues of a, the energy expenditure per unit pumonary ventiation, vary from.178 to.31. At a ventiation of 3 itersimin, in the midde of the range for which their resuts are appicabe, this impies a range of energy expenditure from 5.3 to 9. kca/min. Thus the method of estimating energy expenditure from pumonary ventiation, without anaysis of the expired air, must be considered of doubtfu vaue, except in certain restricted circumstances. The use of a singe factor for adjusting a pumonary ventiations to STPD introduces an error whose standard deviation, in the particuar case examined, is I.5 7,
ENERGY EXPENDITURE FROM EXPIRED AIR 29 eading to a simiar percentage error in the determination of energy expenditure. Over a range of tasks, simiar to those in the present survey, we might therefore expect the standard deviation to be of the order of.1 kca/min and its effect is ony to increase the tota error from.6 kca/min to.61. If an unfortunate choice of the singe factor is made, a sma systematic error wi be introduced into the resuts, but it is unikey that this woud be greater than about I or 2 %. The sight oss of precision appears to be more than compensated by the considerabe gain in time. If, however, the inherent error in aboratory experimentation were as ow as, say, o. I kca/min, the effect of using a singe correcting factor woud be much arger, increasing the over-a error to o. 14 kca/min. In such a case, the correcting factor specific to each ventiation shoud be determined and aowed for in using the nomogram. Again, if the conditions in which the experiments are carried out differ more markedy than in the present series, separate corrections may be necessary. The nomogram is based on the formua of section C, which differs sighty from that obtained by Weir (I) and from those which arise from the different reationships assumed between kca/iter of oxygen and respiratory quotient. However, the greatest deviation between estimates obtained from the various formuas is just over I %. The use of the nomogram (instead of cacuation) introduces an error with standard deviation.2 kca/min. This is competey negigibe when compared with an inherent error with SD.6 kca/min, which is probaby as ow as can be achieved in fied work. Even if the inherent error coud be reduced so that its SD is o. I kca/min, the use of the nomogram woud ony increase the standard deviation to O. I 2. CONCLUSIONS The most radicai of the suggested short cuts in the estimation of energy expenditure from expired air is to make use of the observed inear reationships between energy expenditure and pumonary ventiation and to estimate energy expenditure in further cases directy from the ventiation, omitting anaysis of the expired air. However, the reationship has been found to differ markedy from subject to subject carrying out the same task and, even for a particuar subject, from task to task. Therefore, in situations other than the very restricted one in which a specific ine reating energy expenditure to ventiation is used to estimate the energy expended by the same subject repeating the same task, the errors introduced by this method may be arge and, more important, may incude an indeterminate systematic component, with biases of up to =t25 %, which cannot be eiminated by increasing the number of readings, and which can be highy miseading. AS this approach requires very much ess experimenta abor it remains an attractive prospect, were it possibe to determine simpy the appropriate prediction ine to use in any particuar case. This suggests the need for coser examination, probaby in terms of aboratory experimentation, of the reasons for the differences between the observed reationships for varying tasks and conditions. Unti then, most assessments of energy expenditure must be based on the resuts of anaysis of expired air. However, the compet e cacuation can be made with negigibe error by using the nomogram of Figure 3. Finay, in a series of experiments where the ambient temperature and pressure remain within reasonabe imits throughout, a singe vaue of a factor for adjusting the voume of expired air to standard temperature pressure, dry, can be used to reduce cacuating time. There wi remain a number of cases where the corrections of ventiatory voumes to STPD have to be made individuay; this can sti be done by the use of the nomogram. The author thanks, most sincerey, Mr. P. W. Humphreys for his very great hep, given with unfaiing patience, and Dr. A. R. Lind and Dr. J. S. McLintock for many hepfu discussions. The views expressed are, of course, my own and shoud not be taken to commit any of the above mentioned in any way. REFERENCES I. WEIR, J. B. DE V. J. Physio., London 19 : I, I gag. 2. DURNIN, J. V. G. A., AND R. G. EDWARDS. Quart. J. ExptZ. Physio. 4: 37, 1955. 3. FORD, A. B., AND H. K. HELLERSTEIN. J. AppZ. Physio. 14: 891, I959. 4. HUMPHREYS, P. W., AND A. R. LIND. hit. J. Ind. Med. Ig : 264, 1962. 5. SARTORELLI, E. Med. Lavoro 47 : 35, I 956. 6. MARGARIA, R. Atti ReaZe Accad. Nat. dei Lincei. 7 : 299, I 938. 7. ASMUSSEN, E., AND M. NEILSEN. Acta Physio. Stand. I 2 : I 7 I, 1946. 8. GRODINS, F. S. Physio. Rev. 3 : 22, I 95. g. DURNIN, J. V. G. 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