Both exercise economy and maximum oxygen uptake (V˙O2) influence endurance performance (5,21). Somewhat counterintuitively, an inverse relationship between V˙O2max and exercise economy has been demonstrated for cycling (7,14,16,22) and running (19,23). In studies of running, steady-state V˙O2 at a single speed typically has been used as a measure of economy (5,9,19,23). In contrast, for cycling, the linear relationship between V˙O2 and power output has been used to assess exercise efficiency (i.e., ΔV˙O2/Δwork rate, with the inverse of this relationship used to define cycling efficiency) (4,7,10,14,16,18,20). A positive correlation between ΔV˙O2/Δwork rate and V˙O2max has been reported (7,14,16). The reason for the inverse relationship between ΔV˙O2/Δwork rate and V˙O2max in cycling remains unclear, although muscle fiber type and mitochondrial factors may play a role (3,4,12,18). Noakes and Tucker (22) proposed that among competitive endurance athletes with similar performance characteristics, the relationship between V˙O2max and running/cycling economy will always be inverse, that is, competitors with low V˙O2max compensating with higher movement economy to achieve the same performance (19,22). Thus, it is the peak work rate (or running speed) reached during a maximal exercise stress test that is the best predictor of endurance performance, with the V˙O2max achieved on the test being dependent on both peak work rate (or running speed) achieved and exercise economy of the performer (21,22). However, an inverse relationship between V˙O2max and ΔV˙O2/Δwork rate in cycling also has been reported for untrained persons (7,16).
For walking, Hunter et al. (12) reported an inverse relationship between V˙O2max and walking economy in sedentary women. In that study, walking economy was assessed at one speed, 3.0 mph. We are unaware of any published data that examine whether the slope of the V˙O2-walking/running relationship is related to V˙O2max. Figures from previously published work indicate that the slope of the V˙O2-walking/running relationship may vary considerably among individuals (5,8,17,21). However, in these studies, the relationships between V˙O2-treadmill speed slope and V˙O2max were not reported.
Therefore, we examined the relationship between V˙O2peak and submaximal exercise V˙O2 elicited during a walking/running protocol in men and women heterogeneous for cardiorespiratory fitness. Because the slope of the V˙O2-walking speed relationship is nonlinear (8,17,24), we analyzed data with a polynomial random coefficient regression (PRCR) model. We hypothesized that V˙O2peak would correlate positively with both linear and quadratic coefficients of the model.
Fifty-two subjects (29 women and 23 men) between the ages of 19 and 40 yr enrolled in the study. Subjects were generally physically active, and none of the subjects was a competitive runner or race walker. Written informed consent was obtained from each subject, and the University of Virginia's institutional review board approved the study. A preparticipation medical history and examination was completed on each subject to ensure good health. Because of exclusions from exercise test data (see below), 21 women and 19 men were used for data analysis (Table 1).
Each subject reported to the exercise physiology laboratory on three occasions, each separated by at least 48 h. On one occasion, body fat percentage was determined by air displacement plethysmography (6), and incremental walking protocol was administered to assess V˙O2peak. On each of the two other occasions, subjects performed a routine involving walking and running (2). These two protocols were identical in nature and for a given subject were performed at the same time of day on each occasion. Subjects were instructed to come to the laboratory at least 2 h postabsorptive, to not perform any exercise before the session on the day of the test, and to not engage in strenuous exercise on the day before the test.
Incremental treadmill walking protocol.
A modified Balke protocol was performed on a motorized treadmill for determination of V˙O2peak. Subjects began walking at 3.3 mph (88 m·min−1), 0% grade for the first minute. The grade was increased to 2% for 1 min and then increased by 1% every minute thereafter. If a 25% grade was reached, treadmill speed was increased by 0.5 mph (13.4 m·min−1) every minute. The test was terminated at the point of volitional exhaustion. During the test, verbal encouragement was given to all subjects. Subjects were not permitted to hold on to handrail supports at any time during the test. Pulmonary ventilation and gas exchange were measured breath-by-breath with the VmaxST portable metabolic measurement system (VIASYS, Yorba Linda, CA). We previously reported that this system provides reliable measurements of V˙O2 during walking and running (2). Time to exhaustion averaged 24.5 min (SD = 4.1 min). V˙O2peak was taken as the highest 30-s average during the test. To be included in the data analysis, subjects had to have either a peak respiratory exchange ratio (R) ≥ 1.10 or a peak heart rate ≥ 90% of age-predicted maximum. Three subjects were excluded by these criteria. At exhaustion, heart rate averaged 187 beats·min−1 (SD = 11 beats·min−1; 97.4% ± 6.1% of age-predicted maximum) and R averaged 1.14 (SD = 0.09).
Upon arrival to the laboratory, subjects were fitted with the VmaxST system. After a 5-min period of seated rest, subjects then walked on a motor-driven treadmill at 2.0 mph (53.6 m·min−1), 3.0 mph (80.5 m·min−1), and 4.0 mph (107.3 m·min−1) and ran at 6.0 mph (160.9 m·min−1). Subjects exercised for 5 min at each speed, with 3 min of rest (standing) between each exercise period. Ventilation and gas exchange were measured breath-by-breath during each minute of each exercise bout, and V˙O2 was averaged over the last 2 min of exercise. This walk/run protocol was repeated for each subject (for purposes of assessing reliability of the VmaxST system, published previously ), and the average of the two trials was used in the statistical analysis. Nine subjects were excluded from the data analysis because of failure to achieve a steady-state V˙O2 during the run at 6.0 mph (steady-state defined as a <100-mL·min−1 increase in V˙O2 during the last 2 min of the test).
The relationship between V˙O2 and walking/running speed was examined by way of polynomial random coefficient regression (PRCR). The V˙O2 (mL·kg−1·min−1) measurements at walking speeds of 2.0, 3.0, and 4.0 mph and at the running speed of 6.0 mph represented the response measurements in the PRCR analysis. Separate analyses were performed using all speeds in the same regression model (i.e., walking and running bouts combined) and for walking speeds only. Walking and running speed represented the predictor of V˙O2 in the PRCR analysis, with a second-order curve-linear polynomial model specification that included linear and quadratic terms. We also performed the same analyses with time to exhaustion included in the model as a predictor of V˙O2. Marginal PRCR coefficient estimates (i.e., average) and subject-specific intercepts and linear and quadratic coefficient best linear unbiased predictions were derived by way of restricted maximum likelihood. Statistical inferences with respect to the marginal regression PRCR coefficients were based on type III F-tests. A P < 0.05 decision rule was used as the criterion for rejecting the null hypothesis that the PRCR marginal coefficient was equal to 0.
The correlations between V˙O2peak and the PRCR subject-specific linear and quadratic coefficient best linear unbiased predictions were assessed by way of the univariate Pearson correlation coefficients. A P < 0.05 decision rule was used as the criterion for rejecting the null hypothesis of zero correlation.
The SAS PROC MIXED and PROC CORR procedures of SAS version 9.1.3 (SAS Institute Inc., Cary, NC) were used to conduct the PRCR analysis and the Pearson univariate analyses, respectively.
As expected, the relationship between V˙O2 and walking speed was curve-linear (Fig. 1), with a significant quadratic coefficient (P < 0.0001) and a marginally significant linear coefficient (P = 0.0549) (Table 2). Both linear (r = 0.36, P = 0.023) and quadratic (r = 0.54, P < 0.001) coefficients were significantly correlated with V˙O2peak (Fig. 2). Including treadmill time to exhaustion to the random coefficient regression model did not improve predictions (P = 0.763).
When the PRCR analysis was restricted to only the walking speeds, both linear and quadratic coefficients were significant (Table 2), and both linear (r = 0.31, P = 0.053) and quadratic (r = 0.35, P = 0.029) coefficients were correlated with V˙O2peak (Fig. 3). There were no differences between men and women concerning PRCR coefficients.
Steady-state V˙O2 at each speed was also positively correlated with V˙O2peak, with the strongest correlation at the running speed of 6 mph (Fig. 4).
Our finding of a positive relationship between V˙O2peak and the regression coefficients of the V˙O2-walking speed relationship confirms our hypothesis and suggests that what has been reported for cycling (4,7,10,14,16,18,20) also applies to walking. The higher the V˙O2peak of the subject, the greater is the increase in V˙O2 when speed is increased throughout a range of walking speeds from slow (2.0 mph) to brisk (4.0 mph). Because we obtained data on only one running speed, additional experiments are necessary to confirm that our findings extend to running.
The reason for including only one running speed was because the original design of this study was to evaluate the reliability of a portable metabolic measurement system, and we focused primarily on walking speeds that would ensure steady-state V˙O2 (2). Nevertheless, the results for the two PRCR analyses (i.e., with and without the running speed in the analysis) yielded similar results (Table 2), and the correlations between the V˙O2peak and the linear and quadratic regression coefficients from the models with and without the one running speed included in the analysis were qualitatively similar (Figs. 2 and 3).
The results of our regression analyses are consistent with the findings of others who reported positive relationships between V˙O2max and steady-state V˙O2 in walking (12) and running (19,23). Hunter et al. (12) reported a correlation of 0.28 between V˙O2 walking at 3.0 mph and V˙O2max in sedentary women, which is very close to the correlation of 0.30 that we found for our subjects (Fig. 4). For running, Pate et al. (23) reported a correlation of 0.26 between V˙O2max and V˙O2 while running at 6.0 mph in 188 male and female distance runners. This is lower than the correlation of 0.48 that we observed for our subjects (Fig. 4). Compared with our subjects, the subjects of Pate et al. (23) had higher V˙O2max values (50.3 vs 40-45 mL·kg−1·min−1) and slightly higher V˙O2 values for running at 6.0 mph (33.9 vs ∼32.8 mL·kg−1·min−1; Table 1). The approximately 3% higher V˙O2 at 6.0 mph in the subjects studied by Pate et al. (23) is consistent with the notion that higher V˙O2max values are associated with lower economy (22).
Why increases in walking speed (or cycling power output) elicit greater increases in V˙O2 in subjects with higher V˙O2peak is not well understood. Muscular factors may be involved in cycling efficiency and exercise economy (3,4,12,18). Buemann et al. (3) reported that cycling efficiency was reduced in subjects with a specific polymorphism of the uncoupling protein 2 gene. Similarly, Mogensen et al. (18) reported that cycling efficiency was inversely correlated with muscle uncoupling protein 3 and positively correlated with type I fiber percentage. This latter observation is similar to that of Coyle et al. (4), who reported that cycling efficiency in experienced cyclists was correlated with type I muscle fiber percentage. In contrast, Mallory et al. (16) found that cycling efficiency was unrelated to type I muscle fiber percentage (r = 0.11) and to citrate synthase activity (r = 0.21) but was significantly inversely correlated with V˙O2peak (r = −51).
With respect to treadmill exercise, Hunter et al. (12) found that V˙O2 walking at 3.0 mph was positively correlated with type IIa muscle fiber percentage in gastrocnemius muscle of sedentary women and that both of these variables were positively correlated with V˙O2max. Hunter et al. (12) suggested that individuals with a high proportion of energetically inefficient type IIa muscle fibers will tend to be both less economical and have a greater oxidative capacity, with the greater "capacity" being a consequence of the higher O2 demand of the inefficient type IIa fibers. If true and if recruitment of type II fibers is influenced by both the percentage of muscle comprised of type II fibers and the exercise intensity, it could help explain why the correlations between the V˙O2peak and the linear and quadratic regression coefficients were higher when the running speed of 6.0 mph was included in the analysis (Figs. 2 and 3). It also may help explain why the correlation between V˙O2peak and steady-state V˙O2 was highest for the running speed (Fig. 4).
In contrast to the discussion above, Layec et al. (13) recently reported that the energy cost of muscle contraction was not different in trained and untrained subjects differing markedly in V˙O2max (67.1 vs 42.3 mL·kg−1·min−1). Muscle fiber characteristics of subjects were not obtained. Nevertheless, this study, in combination with some of the inconsistent findings described above, suggests that there may be factors other than skeletal muscle morphology and oxidative capacity that influence the slope of the relationship between V˙O2 and increases in work rate.
Several anthropometric variables have been hypothesized to contribute to economy during walking and/or running, including leg length, stride characteristics and other biomechanical characteristics, body mass, and weight distribution between the trunk and the limbs (1,12,15,23). We have no data to contribute to the discussion of this issue. Selected exercise intensity (walking/running speed) could also affect assessment of economy. In the study by Pate et al. (23), the running speed used to assess economy (6.0 mph; 10-min·mile−1 pace) was much slower than the typical training pace (∼8.4 min·mile−1) of their subjects, and this may have influenced their results. However, Morgan and Daniels (19) reported a significant correlation of 0.59 between V˙O2max and submaximal V˙O2 in elite distance runners running at speeds typically encountered in daily training.
For walking and running studies, determination of economy typically involves measurement of steady-state V˙O2 at one or more selected speeds, without analysis of the characteristics of the V˙O2-speed relationship (1,5,12,15,17,19,23). However, it is apparent that considerable between-individual variation in the slope of the V˙O2-speed relationship exists (5,19,21). Our results demonstrate that similar to several reports on cycling (7,14,16), the regression coefficients describing the curve-linear relationship between V˙O2 and walking speed are positively correlated with V˙O2peak.
A limitation of our study is that we only had three walking speeds. Our speeds, however, did encompass a range that is typically used for studies of energy expenditure during walking (1,8,12,15). Speeds slower than 2.0 mph are below freely chosen walking speeds for young healthy adults (17), and speeds above 4.0 mph typically approach a transition speed in which subjects "walk-jog," thus affecting gait. It is unlikely that inclusion of more speeds between 2.0 and 4.0 mph would have materially affected the PRCR analyses. Our subjects were asked to not eat or drink calorie- or caffeine-containing beverages for 2 h before the exercise sessions. Two hours postabsorptive does not reflect a true fasted state, and therefore metabolism may have been slightly affected by the subjects' previous meal. To control for this, we tested the subjects at the same time of day and asked them to eat and drink the same before each session. We also did not control for stage in the menstrual cycle for the female subjects.
On the other hand, a major strength of the study is that V˙O2 values used in the PRCR analyses represented the average of two identical trials of treadmill walking/running for each subject. As previously reported, the VmaxST system used in the present study produces reliable measurements of V˙O2, with coefficients of variation of 5.5%-7.5%, intraclass correlation coefficients of 0.77-0.90, and R 2 of 0.88-0.95 (2). Furthermore, we excluded subjects who appeared not to have achieved a V˙O2peak and who also appeared to have a significant slow component of V˙O2 at 6.0 mph (11).
In summary, we observed significant positive correlations between V˙O2peak and both linear and quadratic coefficients of the curve-linear relationship between V˙O2 and walking speed. These findings are similar to those reported for cycling (7,14,16) and are consistent with the inverse relationship between V˙O2peak and economy demonstrated for submaximal steady-state walking (12) and running (19,23). Because so much of the variance in the relationship is unexplained (Figs. 2 and 3), understanding the causal factors will be challenging.
This study was supported by National Institutes of Health grant No. RR00847 to the University of Virginia General Clinical Research Center and grant No. R21 CA112323.
Results of the present study do not constitute endorsement by the American College of Sports Medicine.
1. Allor KM, Pivarnik JM, Sam LJ, Perkins CD. Treadmill economy in girls and women matched for height and weight. J Appl Physiol
2. Blessinger J, Sawyer BJ, Davis C, Irving BA, Weltman A, Gaesser G. Reliability of the VmaxST portable metabolic measurement system. Int J Sports Med
3. Buemann B, Schierning B, Toubro S, et al. The association between the val/ala-55 polymorphism of the uncoupling protein 2 gene and exercise efficiency
. Int J Obes Relat Metab Disord
4. Coyle EF, Sidossis LS, Horowitz JF, Beltz JD. Cycling efficiency
is related to the percentage of type I muscle fibers. Med Sci Sports Exerc
5. Daniels J, Daniels N. Running economy of elite male and elite female runners. Med Sci Sports Exerc
6. Dempster P, Aitkens S. A new air displacement method for the determination of human body composition. Med Sci Sports Exerc
7. Drinkard BE, Hicks J, Danoff J, Rider LG. Fitness
as a determinant of the oxygen uptake/work rate slope in healthy children and children with inflammatory myopathy. Can J Appl Physiol
8. Falls HB, Humphrey LD. Energy cost of running and walking in young women. Med Sci Sports Exerc
9. Fletcher JR, Esau SP, MacIntosh BR. Economy of running: beyond the measurement of oxygen uptake. J Appl Physiol
10. Gaesser GA, Brooks GA. Muscular efficiency
during steady-rate exercise
: effects of speed and work rate. J Appl Physiol
11. Gaesser GA, Poole DC. The slow component of oxygen uptake kinetics in humans. Exerc Sport Sci Rev
12. Hunter GR, Bamman MM, Larson-Meyer DE, et al. Inverse relationship between exercise
economy and oxidative capacity in muscle. Eur J Appl Physiol
13. Layec G, Bringard A, Vilmen C, et al. Does oxidative capacity affect energy cost? An in vivo MR investigation of skeletal muscle energetic. Eur J Appl Physiol
14. Lucia A, Hoyos J, Perez M, Santalla A, Chicharro JL. Inverse relationship between V˙O2max
in world-class cyclists. Med Sci Sports Exerc
15. Malatesta D, Simar S, Dauvilliers Y, et al. Energy cost of walking and gait instability in healthy 65- and 80-yr-olds. J Appl Physiol
16. Mallory LA, Scheurmann BW, Hoelting BD, Weiss ML, McAllister RM, Barstow TJ. Influence of peak V˙O2
and muscle fiber type on the efficiency
of moderate exercise
. Med Sci Sports Exerc
17. Martin PE, Rothstein DE, Larish DD. Effects of age and physical activity status on the speed-aerobic demand relationship. J Appl Physiol
18. Mogensen M, Bagger M, Pedersen PK, Fernstrom M, Sahlin K. Cycling efficiency
in humans is related to low UCP3 content and to type I fibres but not to mitochondrial efficiency
. J Physiol
19. Morgan DW, Daniels JT. Relationship between V˙O2max
and the aerobic demand of running in elite distance runners. Int J Sports Med
20. Moseley L, Achten J, Martin JC, Jeukendrup AE. No differences in cycling efficiency
between world-class and recreational cyclists. Int J Sports Med
21. Noakes TD. Implications of exercise
testing for prediction of athletic performance-a contemporary perspective. Med Sci Sports Exerc
22. Noakes TD, Tucker R. Inverse relationship between V˙O2max
and economy in world-class cyclists. Med Sci Sports Exerc
23. Pate RR, Macera CA, Bailey SP, Bartoli WP, Powell KE. Physiological, anthropometric, and training correlates of running economy. Med Sci Sports Exerc
24. Willis WT, Ganley KJ, Herman RM. Fuel oxidation during human walking. Metabolism