Eur J Appl Physiol (1991) 63:135-139
,our..,'u'°Ao,p p l i e d Physiology and Occupational Physiology © Springer-Verlag 1991
The validation of backward extrapolation of submaximal oxygen consumption from the oxygen recovery curve Gordon Sleivert and Laurel Traegar Mackinnon Department of Human Movement Studies, The University of Queensland, St. Lucia, Qld, Australia, 4067 Accepted April 8, 1991
Summary. The purpose of this study was to determine the validity and practicality of exponential vs linear backward extrapolation of the Oz recovery curve for prediction of exercise oxygen consumption (1702). Eight men and women, age 20.1, 0.9 years, body mass 66.0, 2.5 kg (mean, SEM), completed seven bouts of cycle ergometer exercise at submaximal power outputs ranging from 50 to 175 W. Respiratory gases were collected from each subject during exercise and recovery. The monoexponential extrapolation of five recovery samples (r2=0.85) and linear extrapolation of one recovery sample taken during the first 20-s of recovery (r 2= 0.83) accounted for similar amounts of variance in predicting exercise 1202. The linear regression equation was the most practical predictor, as only one recovery gas sample was necessary and it did not require the complicated mathematical techniques used in exponential regression. Key words: Oxygen consumption - Oxygen recovery curve - Submaximal work - Cycle ergometer - Backward extrapolation
Introduction Oxygen consumption (1702) is frequently measured at submaximal loads to calculate the energy cost of a certain task or examine efficiency of movement (Kearney and Van Handel 1989). To measure 1702 directly, respiratory gases must be collected during exercise. This is practical only in a laboratory setting and only for certain modes of exercise that allow easy collection of gas samples. In some sports, such as swimming or alpine skiing, the environment is not optimal for direct meas-
Offprint requests to: G. G. Sleivert, School of Physical Education, The University of Victoria, P.O. Box 3015, Victoria, B.C. Canada, V8W 3P1
urement of 1202 (D1?O2); however, exercise-specific testing is desirable, since a number of studies indicate that aerobic adaptation and the assessment of maximum oxygen consumption (1202max) are dependent upon the mode of exercise (Gleser et al. 1974; Magel et al. 1974; Montpetit et al. 1981; Roberts and Alspaugh 1972; Secher et al. 1974) and lack of exercise specificity may reduce the validity of 1202 measurement. Moreover, the attachment of cumbersome gas analysis equipment (e.g., mouthpiece) may actually interfere with accurate measurement by hindering the gross mechanical efficiency or specificity of movement (Leger et al. 1980). To circumvent problems associated with direct measurement of I202 in these situations, various methods have been used for indirect V02 estimation. One example, which was used to estimate the energy cost of speed skating (DiPrampero et al. 1976) is the backward extrapolation technique which estimates 1202 through exponential least-squares regression of the oxygen recovery curve (ORC). Although the initial investigation used only two subjects and four observations to validate this technique, the reliability and validity have been confirmed using both maximal and submaximal workloads (Costill et al. 1985; Leger et al. 1980, 1983; Lemon et al. 1980; Montpetit et al. 1981). Both monoexponential (Leger et al. 1980; Montpetit et al. 1981) and linear (Costill et al. 1985) regression of the first four 20-s recovery VO.2 values have been used for accurate prediction of VO2max (r>0.9). While monoexponential regression consistently underestimated submaximal VO2 by a constant amount (therefore correctable), linear regression did not, and one recovery sample provided as much prediction power as four. It is not clear whether the exponential or linear regression technique is superior, since investigators utilizing these methods have not compared the two techniques directly (Costill et al. 1985; Lavoie et al. 1983; Leger et al. 1980, 1983; Montpetit et al. 1981). Therefore, the purpose of this study was to compare these
136 techniques for practicality a n d validity in predicting s u b m a x i m a l VO2 at various exercise intensities.
Methods Eight physically active men and women age 20.1, 0.9 years, body mass 66.0, 2.5 kg (mean, SEM), were familiarized with the testing procedures, equipment and nature of the study prior to signing informed consent and agreeing to participate. All subjects completed two exercise sessions separated by 48 h. Each exercise session consisted of three bouts of 7-min cycling at three constant loads. For session 1, the three loads chosen were 50, 100, and 150 W and for session 2, the three workloads were 75, 125 and 175 W. In all cases, 25-min recovery periods separated each workload in order to minimize fatigue. Respiratory gas was collected in foil balloons every 20-s during the last minute of each exercise workload. Respiratory gases were also collected during recovery so that estimations of exercise 1702 obtained from recovery values could be compared with D 1702. There was a time lag of 2-4 s between the cessation of exercise and the beginning of recovery gas collection in order to simulate the field conditions of inserting a mouthpiece after exercise. Subjects breathed normally during this time lag. During recovery, 11 collection periods between 13 and 17 s in duration were used and the beginning and end of each gas collection period coincided with the same phase of the respiratory cycle. For all gas samples the %02 and %CO2 were determined using gas analyzers (Applied Electrochemistry S-3A/1 and CD-3A). The volume of expired air was measured using a Tissot tank and corrected from ATPS to STPD. Exercise I202 was directly calculated for each load by taking the mean of the three VO2 values measured during the last minute of exercise. For comparison with D 1702, the exercise 1702 values were estimated using exponential and linear regression of recovery 1702. Three exponential regression techniques were used: (1) monoexponential regression of the first four recovery 1702 values; (2) monoexponential regression of six recovery 1702 values determined from an exponential curve smoothed to fit the first five recove.ry 1702 values; and (3) biexponential regression of all recovery VO2 values. The equation for a one-component exponential recovery curve (RC) is: Y = Y 0 + K l e -alt
(1)
Thus, for monoexponential regression, three variables had to be estimated: (1) Yo=baseline VO2, (2) K I = Y intercept of the first "fast" component of the ORC and, (3) a 1t = slope for the fast component of the RC. For a two-component exponential RC the equation is: Y = Y o + K t e - a l t + K 2 e -a2t
(2)
Thus, for biexponential regression, five variables had to be estimated. For the first component the same variables as the one component model were required. In addition, two variables for the slow component of the curve required estimation of: (1) K 2 = Y intercept of the second "slow" component of the ORC and (2) a2t=slope for the slow component of the RC. These variables were initially estimated for each workload by a logarithmic plot of the difference between recovery PO~ and baseline VO2 vs time. For these calculations baseline I,'O2 was the lowest 1702 recorded during recovery. Accurate variable estimations are essential in the construction of a valid PC; therefore, the initial variable estimates were adjusted using a computer-based grid minimization technique developed to minimize the error between the estimated recovery 1702 values (calculated via the estimated variables) and the observed recovery 1702 values. From these new variable estimates an exponential.curve of best fit for the recovery data was plotted and exercise VO2 estimated.
The linear regression techniques used for 1;'O2 estimation were: (1) regression of the first recovery I702, (2) regression of the second recovery VO2, and (3) regression of the first two, first three and first four recovery VO2 values. The variations of the exponential and linear regression I702 predictor techniques were compared with D1702 to determine which of the techniques were the best predictors. This was achieved in two steps. Firstly, in order to determine the effects of the independent variables, workload and measurement technique, on the dependent variable, I202, a two-way analysis of variance (ANOVA) for repeated measures was utilized. Secondly, to determine the power of each measurement technique in predicting D1702, Pearson Product Moment correlations were calculated between D1702and predicted I202 values for each technique.
Results A t w o - w a y . A N O V A s h o w e d no significant difference between D VO2, VO2 estimated by any o f the e x p o n e n tial regression techniques, a n d VO2 estimated by linear regression o f the first recovery sample. A m a i n effect o f w o r k l o a d was f o u n d ( P < 0.05); significant interaction was also f o u n d b e t w e n w o r k l o a d a n d VO2 measurem e n t technique ( P < 0.05). A N e u m a n n - K e u l s post h o c test o n residual errors was then used to c o m p a r e D 1702 a n d 1202 estimation using, m o n o e x p o n e n t i a l regression o f the first f o u r recovery VO2 values. This analysis was p e r f o r m e d since graphically (Fig. 1) the latter t e c h n i q u e differentiated itself f r o m other techniques at the highest w o r k l o a d . ( 1 7 5 W). A significant difference ( P < 0 . 0 5 ) b e t w e e n VO2 estimated by m o n o e x p o n e n t i a l regression at 175 W a n d all other VO2 values estimated using the other techniques was found. Table 1 presents the correlations b e t w e e n D 1702 a n d the various extrapolation techniques used to estimate 1702. O f the exponential techniques, the s m o o t h e d m o n o e x p o n e n t i a l technique a c c o u n t e d for the m o s t variance in predicting D VO2 (Fig. 2A). Linear regression o f r e c o v e r y samples 1 (Fig. 2B), 1 a n d 2, 1 to 3, a n d 1 to 4 all yielded identical correlations a n d a c c o u n t e d for only slightly less variance than the s m o o t h e d m o n o exponential regression technique. Linear regression o f the second, third, and fourth recovery samples yielded consistently decreasing r values.
Discussion O f the regression p r o c e d u r e s used in this study to estim a t e D VO2, linear regression o f the first recovery I702 s a m p l e m a y be the technique o f choice since it has identical prediction p o w e r to linear regression o f two or m o r e samples (r=0.91), has only marginally less prediction p o w e r t h a n the best o f the exponential regression p r o c e d u r e s ( s m o o t h e d m o n o e x p o n e n t i a l regression: r = 0.92) a n d is simple in terms o f gas collection a n d analysis. Lavoie et al. (1983) f o u n d a similar correlation coefficient o f r = 0 . 9 2 b e t w e e n 1702 m e a s u r e d using D o u glas bags during a s u p r a m a x i m a l 400 m swim a n d 1702 m e a s u r e d d u r i n g the first 20-s o f recovery. Costill et al.
137 3.5-
3.0
2.5
2.0 e" E
. n
="
1.5
1.0
ii
0.5
0.0
50
0
75
100
125
150
175
Power output (W) Fig. 1. Oxygen consumption (1202) as measured or estimated at different power outputs using five different techniques: D 1202, Direct exercise VO2 measurement; El1202, VO2 estimated via m.onoexponential regression of 4 recovery VO2 values; SE11202, VO2 estimated via smoothed monoexponential regression of 5 re-
covery 1202 values; E21202, 1202 estimated via biexponential regression of 11 recovery I702 values; LR~ 1202, VO2 estimated via linear regression of 1 recovery I702 values, m D1202; ~ El1202; ~ SE~ VO2; ~ E21202; ~ LR11202
Table 1. Correlations of direct exercise oxygen consumption (1202) measurement with 1202 extrapolation technique measurements
(.1985) found that linear regression of one 20-s recovery VO2 sample accurately predicted D 1202 ( r = 0.98), and that no further power was gained by adding more sample points, although correlations were not reported. These investigators did not include a 2- to 4-s time delay between cessation of exercise and recovery 1202 collection, which m a y account for the higher correlations found in comparison to those reported in the present study. Although beginning recovery gas collection immediately u p o n cessation o f exercise m a y yield more accurate data using backward extrapolation, a delay in gas collection of several seconds m a y be more applicable to the field situation, since practically several seconds are required after the cessation of exercise to initiate gas collection. In this study the variance accounted for in predicting D 1202 decreased from recovery sample one to sample four which was consistent with previously reported research (Costill et al. 1985). This suggests that recovery samples should be collected as close to the cessation of exercise as possible. It m a y also be argued that shorter collection periods would provide better prediction power, since the overall gas collection would be com-
Extrapolation technique E1 Clu r CI1
SE1
E2
LR1
LR2
LR3
LR4
LR2-4
0 . 9 2 0 . 9 5 0 . 8 8 0 . 9 5 0.91 0 . 9 1 0 . 8 9 0.95 0.86 0 . 9 2 0 . 7 9 0.91 0 . 8 5 0 . 8 4 0 . 8 0 0.91 0.76 0 . 8 6 0 . 6 5 0 . 8 4 0 . 7 5 0 . 7 3 0 . 6 7 0.84
All data significant at P
,our..,'u'°Ao,p p l i e d Physiology and Occupational Physiology © Springer-Verlag 1991
The validation of backward extrapolation of submaximal oxygen consumption from the oxygen recovery curve Gordon Sleivert and Laurel Traegar Mackinnon Department of Human Movement Studies, The University of Queensland, St. Lucia, Qld, Australia, 4067 Accepted April 8, 1991
Summary. The purpose of this study was to determine the validity and practicality of exponential vs linear backward extrapolation of the Oz recovery curve for prediction of exercise oxygen consumption (1702). Eight men and women, age 20.1, 0.9 years, body mass 66.0, 2.5 kg (mean, SEM), completed seven bouts of cycle ergometer exercise at submaximal power outputs ranging from 50 to 175 W. Respiratory gases were collected from each subject during exercise and recovery. The monoexponential extrapolation of five recovery samples (r2=0.85) and linear extrapolation of one recovery sample taken during the first 20-s of recovery (r 2= 0.83) accounted for similar amounts of variance in predicting exercise 1202. The linear regression equation was the most practical predictor, as only one recovery gas sample was necessary and it did not require the complicated mathematical techniques used in exponential regression. Key words: Oxygen consumption - Oxygen recovery curve - Submaximal work - Cycle ergometer - Backward extrapolation
Introduction Oxygen consumption (1702) is frequently measured at submaximal loads to calculate the energy cost of a certain task or examine efficiency of movement (Kearney and Van Handel 1989). To measure 1702 directly, respiratory gases must be collected during exercise. This is practical only in a laboratory setting and only for certain modes of exercise that allow easy collection of gas samples. In some sports, such as swimming or alpine skiing, the environment is not optimal for direct meas-
Offprint requests to: G. G. Sleivert, School of Physical Education, The University of Victoria, P.O. Box 3015, Victoria, B.C. Canada, V8W 3P1
urement of 1202 (D1?O2); however, exercise-specific testing is desirable, since a number of studies indicate that aerobic adaptation and the assessment of maximum oxygen consumption (1202max) are dependent upon the mode of exercise (Gleser et al. 1974; Magel et al. 1974; Montpetit et al. 1981; Roberts and Alspaugh 1972; Secher et al. 1974) and lack of exercise specificity may reduce the validity of 1202 measurement. Moreover, the attachment of cumbersome gas analysis equipment (e.g., mouthpiece) may actually interfere with accurate measurement by hindering the gross mechanical efficiency or specificity of movement (Leger et al. 1980). To circumvent problems associated with direct measurement of I202 in these situations, various methods have been used for indirect V02 estimation. One example, which was used to estimate the energy cost of speed skating (DiPrampero et al. 1976) is the backward extrapolation technique which estimates 1202 through exponential least-squares regression of the oxygen recovery curve (ORC). Although the initial investigation used only two subjects and four observations to validate this technique, the reliability and validity have been confirmed using both maximal and submaximal workloads (Costill et al. 1985; Leger et al. 1980, 1983; Lemon et al. 1980; Montpetit et al. 1981). Both monoexponential (Leger et al. 1980; Montpetit et al. 1981) and linear (Costill et al. 1985) regression of the first four 20-s recovery VO.2 values have been used for accurate prediction of VO2max (r>0.9). While monoexponential regression consistently underestimated submaximal VO2 by a constant amount (therefore correctable), linear regression did not, and one recovery sample provided as much prediction power as four. It is not clear whether the exponential or linear regression technique is superior, since investigators utilizing these methods have not compared the two techniques directly (Costill et al. 1985; Lavoie et al. 1983; Leger et al. 1980, 1983; Montpetit et al. 1981). Therefore, the purpose of this study was to compare these
136 techniques for practicality a n d validity in predicting s u b m a x i m a l VO2 at various exercise intensities.
Methods Eight physically active men and women age 20.1, 0.9 years, body mass 66.0, 2.5 kg (mean, SEM), were familiarized with the testing procedures, equipment and nature of the study prior to signing informed consent and agreeing to participate. All subjects completed two exercise sessions separated by 48 h. Each exercise session consisted of three bouts of 7-min cycling at three constant loads. For session 1, the three loads chosen were 50, 100, and 150 W and for session 2, the three workloads were 75, 125 and 175 W. In all cases, 25-min recovery periods separated each workload in order to minimize fatigue. Respiratory gas was collected in foil balloons every 20-s during the last minute of each exercise workload. Respiratory gases were also collected during recovery so that estimations of exercise 1702 obtained from recovery values could be compared with D 1702. There was a time lag of 2-4 s between the cessation of exercise and the beginning of recovery gas collection in order to simulate the field conditions of inserting a mouthpiece after exercise. Subjects breathed normally during this time lag. During recovery, 11 collection periods between 13 and 17 s in duration were used and the beginning and end of each gas collection period coincided with the same phase of the respiratory cycle. For all gas samples the %02 and %CO2 were determined using gas analyzers (Applied Electrochemistry S-3A/1 and CD-3A). The volume of expired air was measured using a Tissot tank and corrected from ATPS to STPD. Exercise I202 was directly calculated for each load by taking the mean of the three VO2 values measured during the last minute of exercise. For comparison with D 1702, the exercise 1702 values were estimated using exponential and linear regression of recovery 1702. Three exponential regression techniques were used: (1) monoexponential regression of the first four recovery 1702 values; (2) monoexponential regression of six recovery 1702 values determined from an exponential curve smoothed to fit the first five recove.ry 1702 values; and (3) biexponential regression of all recovery VO2 values. The equation for a one-component exponential recovery curve (RC) is: Y = Y 0 + K l e -alt
(1)
Thus, for monoexponential regression, three variables had to be estimated: (1) Yo=baseline VO2, (2) K I = Y intercept of the first "fast" component of the ORC and, (3) a 1t = slope for the fast component of the RC. For a two-component exponential RC the equation is: Y = Y o + K t e - a l t + K 2 e -a2t
(2)
Thus, for biexponential regression, five variables had to be estimated. For the first component the same variables as the one component model were required. In addition, two variables for the slow component of the curve required estimation of: (1) K 2 = Y intercept of the second "slow" component of the ORC and (2) a2t=slope for the slow component of the RC. These variables were initially estimated for each workload by a logarithmic plot of the difference between recovery PO~ and baseline VO2 vs time. For these calculations baseline I,'O2 was the lowest 1702 recorded during recovery. Accurate variable estimations are essential in the construction of a valid PC; therefore, the initial variable estimates were adjusted using a computer-based grid minimization technique developed to minimize the error between the estimated recovery 1702 values (calculated via the estimated variables) and the observed recovery 1702 values. From these new variable estimates an exponential.curve of best fit for the recovery data was plotted and exercise VO2 estimated.
The linear regression techniques used for 1;'O2 estimation were: (1) regression of the first recovery I702, (2) regression of the second recovery VO2, and (3) regression of the first two, first three and first four recovery VO2 values. The variations of the exponential and linear regression I702 predictor techniques were compared with D1702 to determine which of the techniques were the best predictors. This was achieved in two steps. Firstly, in order to determine the effects of the independent variables, workload and measurement technique, on the dependent variable, I202, a two-way analysis of variance (ANOVA) for repeated measures was utilized. Secondly, to determine the power of each measurement technique in predicting D1702, Pearson Product Moment correlations were calculated between D1702and predicted I202 values for each technique.
Results A t w o - w a y . A N O V A s h o w e d no significant difference between D VO2, VO2 estimated by any o f the e x p o n e n tial regression techniques, a n d VO2 estimated by linear regression o f the first recovery sample. A m a i n effect o f w o r k l o a d was f o u n d ( P < 0.05); significant interaction was also f o u n d b e t w e n w o r k l o a d a n d VO2 measurem e n t technique ( P < 0.05). A N e u m a n n - K e u l s post h o c test o n residual errors was then used to c o m p a r e D 1702 a n d 1202 estimation using, m o n o e x p o n e n t i a l regression o f the first f o u r recovery VO2 values. This analysis was p e r f o r m e d since graphically (Fig. 1) the latter t e c h n i q u e differentiated itself f r o m other techniques at the highest w o r k l o a d . ( 1 7 5 W). A significant difference ( P < 0 . 0 5 ) b e t w e e n VO2 estimated by m o n o e x p o n e n t i a l regression at 175 W a n d all other VO2 values estimated using the other techniques was found. Table 1 presents the correlations b e t w e e n D 1702 a n d the various extrapolation techniques used to estimate 1702. O f the exponential techniques, the s m o o t h e d m o n o e x p o n e n t i a l technique a c c o u n t e d for the m o s t variance in predicting D VO2 (Fig. 2A). Linear regression o f r e c o v e r y samples 1 (Fig. 2B), 1 a n d 2, 1 to 3, a n d 1 to 4 all yielded identical correlations a n d a c c o u n t e d for only slightly less variance than the s m o o t h e d m o n o exponential regression technique. Linear regression o f the second, third, and fourth recovery samples yielded consistently decreasing r values.
Discussion O f the regression p r o c e d u r e s used in this study to estim a t e D VO2, linear regression o f the first recovery I702 s a m p l e m a y be the technique o f choice since it has identical prediction p o w e r to linear regression o f two or m o r e samples (r=0.91), has only marginally less prediction p o w e r t h a n the best o f the exponential regression p r o c e d u r e s ( s m o o t h e d m o n o e x p o n e n t i a l regression: r = 0.92) a n d is simple in terms o f gas collection a n d analysis. Lavoie et al. (1983) f o u n d a similar correlation coefficient o f r = 0 . 9 2 b e t w e e n 1702 m e a s u r e d using D o u glas bags during a s u p r a m a x i m a l 400 m swim a n d 1702 m e a s u r e d d u r i n g the first 20-s o f recovery. Costill et al.
137 3.5-
3.0
2.5
2.0 e" E
. n
="
1.5
1.0
ii
0.5
0.0
50
0
75
100
125
150
175
Power output (W) Fig. 1. Oxygen consumption (1202) as measured or estimated at different power outputs using five different techniques: D 1202, Direct exercise VO2 measurement; El1202, VO2 estimated via m.onoexponential regression of 4 recovery VO2 values; SE11202, VO2 estimated via smoothed monoexponential regression of 5 re-
covery 1202 values; E21202, 1202 estimated via biexponential regression of 11 recovery I702 values; LR~ 1202, VO2 estimated via linear regression of 1 recovery I702 values, m D1202; ~ El1202; ~ SE~ VO2; ~ E21202; ~ LR11202
Table 1. Correlations of direct exercise oxygen consumption (1202) measurement with 1202 extrapolation technique measurements
(.1985) found that linear regression of one 20-s recovery VO2 sample accurately predicted D 1202 ( r = 0.98), and that no further power was gained by adding more sample points, although correlations were not reported. These investigators did not include a 2- to 4-s time delay between cessation of exercise and recovery 1202 collection, which m a y account for the higher correlations found in comparison to those reported in the present study. Although beginning recovery gas collection immediately u p o n cessation o f exercise m a y yield more accurate data using backward extrapolation, a delay in gas collection of several seconds m a y be more applicable to the field situation, since practically several seconds are required after the cessation of exercise to initiate gas collection. In this study the variance accounted for in predicting D 1202 decreased from recovery sample one to sample four which was consistent with previously reported research (Costill et al. 1985). This suggests that recovery samples should be collected as close to the cessation of exercise as possible. It m a y also be argued that shorter collection periods would provide better prediction power, since the overall gas collection would be com-
Extrapolation technique E1 Clu r CI1
SE1
E2
LR1
LR2
LR3
LR4
LR2-4
0 . 9 2 0 . 9 5 0 . 8 8 0 . 9 5 0.91 0 . 9 1 0 . 8 9 0.95 0.86 0 . 9 2 0 . 7 9 0.91 0 . 8 5 0 . 8 4 0 . 8 0 0.91 0.76 0 . 8 6 0 . 6 5 0 . 8 4 0 . 7 5 0 . 7 3 0 . 6 7 0.84
All data significant at P
