Real-world walking economy: can laboratory equations predict field energy expenditure?

Portable calorimeter measures were corrected for a consistent measurement-range offset of +13.8 ± 1.8% versus a well-validated laboratory system (Parvomedics TrueOne).

“Portable calorimeter measures were corrected for a consistent measurement-range offset (+13.8 ± 1.8%, means ± SD) versus a well-validated laboratory system (Parvomedics TrueOne).”

• Also stated in: § RESULTS · plain

  “At each speed, the offset fell within a range from 11.4% to 16.5% (means ± SD: 13.8 ± 1.8%).”

The Looney equation overpredicted unloaded field total energy expenditure by +20% (predicted 1,176 ± 24 mL O2/kg).

“The mean energy expenditure total measured for the unloaded field trials (981 ± 91 mL O2/kg) was overpredicted by +4%, +13%, +17%, and +20% by the Minimum Mechanics, ACSM, Pandolf, and Looney equations, respectively (corresponding predicted totals: 1,018 ± 19, 1,108 ± 26, 1,145 ± 37, and 1,176 ± 24 mL O2/kg).”

• AssumptionRests on an assumption: The terrain/treadmill factors (asphalt = 1.0, grass = 1.08) determined from level overground walking apply to the graded portions of the field course.

Computational comparisons for hypothetical trials at different constant speeds (0.6-1.8 m/s) on variable-gradient loop courses revealed between-equation prediction differences from 0% to 37%.

“Computational comparisons for hypothetical trials at different constant speeds (range: 0.6–1.8 m/s) on variable-gradient loop courses revealed between-equation prediction differences from 0% to 37%.”

• AssumptionRests on an assumption: The terrain/treadmill factors (asphalt = 1.0, grass = 1.08) determined from level overground walking apply to the graded portions of the field course.

The overground walking speed subjects selected on initial flat portion during loaded trials was nearly identical to unloaded speed (1.34 vs. 1.35 m/s).

“The overground walking speed subjects selected on the initial flat portion of the course during the loaded trials (larger open triangles, Fig. 3) was nearly identical to the unloaded speed (1.34 vs. 1.35 m/s).”

Mean rates of oxygen uptake measured by portable calorimeter during unloaded and loaded overground walking on initial flat concrete portion of field course exceeded those measured by TrueOne laboratory system during treadmill walking at similar speeds.

“The mean rates of oxygen uptake measured by the portable calorimeter during unloaded and loaded overground walking on the initial flat, concrete portion of the field course (smaller open triangles, Fig. 3) also exceeded those measured by the TrueOne laboratory system during treadmill walking at similar speeds.”

The disagreement between methods on individual subject basis only exceeded 1.0 mL O2/kg·min in six of 45 total observations.

“The disagreement between methods, when considered on an individual subject basis, only exceeded 1.0 mL O2/kg·min in six of the 45 total observations made (15 subjects × 3 speeds).”

The Pandolf equation overpredicted unloaded field total energy expenditure by +17% (predicted 1,145 ± 37 mL O2/kg).

“The mean energy expenditure total measured for the unloaded field trials (981 ± 91 mL O2/kg) was overpredicted by +4%, +13%, +17%, and +20% by the Minimum Mechanics, ACSM, Pandolf, and Looney equations, respectively (corresponding predicted totals: 1,018 ± 19, 1,108 ± 26, 1,145 ± 37, and 1,176 ± 24 mL O2/kg).”

• AssumptionRests on an assumption: The terrain/treadmill factors (asphalt = 1.0, grass = 1.08) determined from level overground walking apply to the graded portions of the field course.

When expressed per kg total (body + load), mean rate of oxygen uptake during both unloaded (1.35 m/s) and loaded (1.34 m/s) level overground walking was 13.0 mL O2/kg·min for both load conditions.

“When expressed on a per kg total basis (body + load), the mean rate of oxygen uptake during both unloaded (1.35 m/s) and loaded (1.34 m/s) level overground walking was 13.0 mL O2/kg·min for both load conditions.”

The Minimum Mechanics equation overpredicted unloaded field total energy expenditure by +4% (predicted 1,018 ± 19 mL O2/kg).

“The mean energy expenditure total measured for the unloaded field trials (981 ± 91 mL O2/kg) was overpredicted by +4%, +13%, +17%, and +20% by the Minimum Mechanics, ACSM, Pandolf, and Looney equations, respectively (corresponding predicted totals: 1,018 ± 19, 1,108 ± 26, 1,145 ± 37, and 1,176 ± 24 mL O2/kg).”

• AssumptionRests on an assumption: The terrain/treadmill factors (asphalt = 1.0, grass = 1.08) determined from level overground walking apply to the graded portions of the field course.

Mean absolute differences between measurement methods for 15 individual subjects at each speed ranged from 0.32 ± 0.44 to 0.87 ± 0.53 mL O2/kg·min.

“The mean absolute differences observed between measurement methods for the 15 individual subjects at each of the respective speeds ranged from: 0.32 ± 0.44 to 0.87 ± 0.53 mL O2/kg·min, respectively.”

The percentage offset between mean standing oxygen uptake measured by portable calorimeter at outset of unloaded field trials and laboratory calorimeter during first 5-min standing was +14.3% (4.22 ± 0.47 vs. 3.69 ± 0.42 mL O2/kg·min).

“Similarly, the percentage offset between the mean standing rate of oxygen uptake measured by the portable calorimeter at the 5-min stand at outset of the unloaded field trials and that measured by the laboratory calorimeter during the first 5-min of standing in the laboratory test was +14.3% (4.22 ± 0.47 vs. 3.69 ± 0.42 mL O2/kg·min; see Y-intercept, Fig. 3).”

The overall mean values acquired with two techniques for 15 participating subjects differed by ≤0.3 mL O2/kg·min at each of three protocol speeds.

“The overall mean values acquired with two techniques for the 15 participating subjects differed by ≤ 0.3 mL O2/kg·min at each of the three protocol speeds.”

The ACSM equation overpredicted unloaded field total energy expenditure by +13% (predicted 1,108 ± 26 mL O2/kg).

“The mean energy expenditure total measured for the unloaded field trials (981 ± 91 mL O2/kg) was overpredicted by +4%, +13%, +17%, and +20% by the Minimum Mechanics, ACSM, Pandolf, and Looney equations, respectively (corresponding predicted totals: 1,018 ± 19, 1,108 ± 26, 1,145 ± 37, and 1,176 ± 24 mL O2/kg).”

• AssumptionRests on an assumption: The terrain/treadmill factors (asphalt = 1.0, grass = 1.08) determined from level overground walking apply to the graded portions of the field course.

For unloaded field trials, mean measured total energy expenditure was 981 ± 91 mL O2/kg.

“The mean energy expenditure total measured for the unloaded field trials (981 ± 91 mL O2/kg) was overpredicted by +4%, +13%, +17%, and +20% by the Minimum Mechanics, ACSM, Pandolf, and Looney equations, respectively”

The minimum error observed for field predictions by any of the other three equations was +12%.

“By comparison, the minimum error observed for field predictions by any of the other three equations was +12%.”

The Pandolf/Santee equation predicts totals that vary little across slow and intermediate speeds but become slightly greater at the faster speeds examined.

“The Pandolf/Santee equation predicts totals that vary little across the slow and intermediate speeds but become slightly greater at the faster speeds examined.”

The Minimum Mechanics equation predicted unloaded total oxygen uptake 4% greater than measured (1,018 ± 19 mL O2/kg).

“The values predicted from the Minimum Mechanics equation were 4% greater than those measured (1,018 ± 19 mL O2/kg);”

The Pandolf/Santee equation predicted unloaded total oxygen uptake 17% greater than measured (1,145 ± 37 mL O2/kg).

“those predicted with the ACSM (1,108 ± 26 mL O2/kg) and Pandolf/Santee (1,145 ± 37) equations were 13% and 17% greater than the measured mean, respectively,”

Compared with each of the other three equations, the Minimum Mechanics equation predicted rates of walking energy expenditure that were somewhat lower across all portions of the course.

“Compared with each of the other three equations, the Minimum Mechanics equation predicted rates of walking energy expenditure that were somewhat lower across all portions of the course (Fig. 7).”

Group mean total oxygen uptake for the seven subjects from their unloaded trials was 981 ± 91 mL O2/kg.

“Group mean total oxygen uptake values (981 ± 91 mL O2/kg) obtained for the seven subjects from their unloaded trials are shown in Fig. 6 (black dashed horizontal line, left portion of the panel).”

The measured mean respiratory exchange ratio from the field trials was 0.83 ± 0.04 for the loaded trials.

“The measured mean respiratory exchange ratio (V̇co2/V̇o2) from the field trials was 0.82 ± 0.03 for the unloaded trials, and 0.83 ± 0.04 for the loaded trials.”

Standard errors of estimate for loaded trials were 176 and 241 mL O2/kg for the Minimum Mechanics and Pandolf/Santee equations, respectively.

“Standard errors of estimate (SEE) for each equation for the unloaded trials were: 107, 207, 186, and 248 mL O2/kg for the Minimum Mechanics, Pandolf/Santee, ACSM, and Looney equations, respectively; loaded trials SEE values were 176 and 241 mL O2/kg for the Minimum Mechanics and Pandolf/Santee equations, respectively.”

The between-calorimeter offset observed for the standing trials was +14.3%.

“The between-calorimeter offset observed for the standing trials we administered was similar at +14.3%.”

For six subjects completing both load conditions, total oxygen taken up for loaded trials exceeded unloaded by factor 1.35 (1,310 ± 153 vs. 972 ± 95 mL O2/kg).

“For the six subjects completing both load conditions, the total oxygen taken up for the loaded trials exceeded those for the unloaded trial condition by a factor of 1.35 (1,310 ± 153 vs. 972 ± 95 mL O2/kg).”

The Minimum Mechanics equation predicted loaded total oxygen uptake of 1,289 ± 22 mL O2/kg, which was −2% below the measured total.

“The totals predicted by the Minimum Mechanics equation of 1,289 ± 22 mL O2/kg agreed closely, being −2% below the measured total whereas the Pandolf/Santee predicted mean of 1,463 ± 32 mL O2/kg was 12% greater than the measured value.”

Implementing the simple downhill coefficient of 0.73 times the walking portion of the body's metabolic rate on level gradients reduced the overprediction of the ACSM equation by 5%.

“We eliminated this limitation by implementing the simple downhill coefficient validated in an earlier study (14) of 0.73 times the walking portion of the body’s metabolic rate (i.e., total V̇o2 minus resting V̇o2) on level gradients. This lone adjustment reduced the overprediction of the ACSM equation by 5%.”

• cites [14] sourceNot checked yet

The measured mean respiratory exchange ratio from the field trials was 0.82 ± 0.03 for the unloaded trials.

“The measured mean respiratory exchange ratio (V̇co2/V̇o2) from the field trials was 0.82 ± 0.03 for the unloaded trials, and 0.83 ± 0.04 for the loaded trials.”

In contrast to the null outcome hypothesized, predictions for both load conditions differed appreciably across equation.

“In contrast to the null outcome hypothesized, predictions for both load conditions differed appreciably across equation (Fig. 6).”

The largest between-equation differences for the loaded trial are present on the downhill portions of the course.

“The largest between-equation differences are present on the downhill portions of the course.”

The ACSM and Pandolf/Santee equations predict oxygen uptake rates that are in between Minimum Mechanics and Looney equations for the unloaded trial.

“The ACSM (red line) and Pandolf/Santee (green) equations predict oxygen uptake rates that are in between Minimum Mechanics and Looney equations.”

The ACSM equation predicted unloaded total oxygen uptake 13% greater than measured (1,108 ± 26 mL O2/kg).

“those predicted with the ACSM (1,108 ± 26 mL O2/kg) and Pandolf/Santee (1,145 ± 37) equations were 13% and 17% greater than the measured mean, respectively,”

For the large majority of speeds and grades considered, the Looney et al. equation predicted totals that were greater than those of the other three equations.

“For the large majority of speeds and grades considered, the Looney et al. equation predicted totals that were greater than those of the other three equations.”

The overall mean respiratory exchange ratio of 0.83 ± 0.04 corresponds to a non-protein energetic equivalent of 20.2 Joules per mL of O2.

“The overall mean from both load conditions of 0.83 ± 0.04 corresponds to a non-protein energetic equivalent of 20.2 Joules per mL of O2 that closely matched the 20.1 value selected a priori based on the expected sources of substrate oxidation for walking.”

The loaded field mean total oxygen uptake was 34% greater than the unloaded trial measured mean.

“The mean total obtained from the field for the loaded condition of 1,310 ± 153 mL O2/kg was 34% greater than that from the unloaded trial measured mean.”

The non-protein energetic equivalent of 20.2 J/mL O2 closely matched the 20.1 value selected a priori based on expected sources of substrate oxidation for walking.

“The overall mean from both load conditions of 0.83 ± 0.04 corresponds to a non-protein energetic equivalent of 20.2 Joules per mL of O2 that closely matched the 20.1 value selected a priori based on the expected sources of substrate oxidation for walking.”

The level walking values acquired from the portable calorimeter at the outset of the field trials exhibited essentially the same positive offset versus the laboratory system treadmill values.

“In addition, the level walking values acquired from the portable calorimeter at the outset of the field trials also exhibited essentially the same positive offset versus the laboratory system treadmill values (open triangles, Fig. 3).”

The overall mean respiratory exchange ratio from both load conditions was 0.83 ± 0.04.

“The overall mean from both load conditions of 0.83 ± 0.04 corresponds to a non-protein energetic equivalent of 20.2 Joules per mL of O2 that closely matched the 20.1 value selected a priori based on the expected sources of substrate oxidation for walking.”

The Looney et al. equation prediction totals varied the most across speed, exhibiting differences of up to 37% across the analysis range of speeds.

“The Looney et al. equation prediction totals varied the most across speed, exhibiting differences of up to 37% across the analysis range of speeds.”

Across the slower portion of the speed range examined from 0.6 to 1.0 m/s, between-equation differences between the Pandolf/Santee and Looney equations consistently exceeded 20% and averaged roughly 30% regardless of the gradient profile of the course.

“Across the slower portion of the speed range examined from 0.6 to 1.0 m/s, between-equation differences between the Pandolf/Santee and Looney equations consistently exceeded 20% and averaged roughly 30% regardless of the gradient profile of the course (Fig. 8).”

For a loaded trial, oxygen uptake rates predicted by the Minimum Mechanics equation are slightly to moderately lower than those of the Pandolf/Santee equation throughout the trial.

“Throughout this trial, the oxygen uptake rates predicted by the Minimum Mechanics equation are slightly to moderately lower than those of the Pandolf/Santee equation.”

Between-equation differences for computational comparisons that spanned a much broader range of speed and gradient conditions reached a maximum of 37%.

“Between-equation differences for our computational comparisons that spanned a much broader range of speed and gradient conditions were, in some cases, approximately twice as large, reaching a maximum of 37%.”

The Minimum Mechanics and Pandolf/Santee oxygen uptake totals differed from one another for loaded trials (P < 0.001; ANOVA F = 66.7, df = 2).

“The Minimum Mechanics and Pandolf/Santee oxygen uptake totals did not differ statistically from the measured values (P > 0.99 and P = 0.115, respectively), but did differ from one another (P < 0.001; ANOVA F = 66.7, df = 2].”

The Looney et al. equation predicted unloaded total oxygen uptake 20% greater than measured (1,176 ± 24 mL O2/kg).

“and those from the Looney et al. equation prediction were 20% greater (1,176 ± 24 mL O2/kg).”

The totals predicted by the Minimum Mechanics equation decrease with speed, with decreases of roughly 15% from the slowest to the fastest speed in the range examined.

“The totals predicted by the Minimum Mechanics equation exhibit a somewhat similar tendency to decrease with speed but do so to a lesser extent, with decreases of roughly 15% from the slowest to the fastest speed in the range examined.”

When both downhill and load carriage modifications were implemented for the loaded field trials, the ACSM predicted total exceeded the measured field mean by only +8%.

“When both modifications were implemented to generate predictions for the loaded field trials here, the predicted total exceeded the measured field mean by only +8%.”

The agreement between the mean field value from the portable calorimeter for the field trials and the totals predicted by the laboratory equations varied [ANOVA: F = 3,794.6, df = 4].

“The agreement between the mean field value obtained from the portable calorimeter for the field trials and the totals predicted by the laboratory equations varied [ANOVA: F = 3,794.6, df = 4].”

For the two shallower grade courses, ACSM, Minimum Mechanics, and Pandolf/Santee equations predict similar total oxygen uptake at intermediate walking speeds from 1.1 to 1.4 m/s, whereas the Looney et al. equation predicts appreciably greater totals.

“For the two shallower grade courses, there is a general tendency for the values predicted by the ACSM, Minimum Mechanics, and Pandolf/Santee equations to be similar in the intermediate walking speeds from 1.1 to 1.4 m/s, whereas the Looney et al. equation predicts appreciably greater totals.”

Group mean total oxygen uptake from field trials for the six subjects completing loaded trials was 1,310 ± 153 mL O2/kg.

“The mean total obtained from the field for the loaded condition of 1,310 ± 153 mL O2/kg was 34% greater than that from the unloaded trial measured mean.”

Under unloaded and loaded field trial conditions, the Minimum Mechanics equation predicted the energy expended in the field to within +4% and −2% of the respective measured means.

“Under unloaded and loaded field trial conditions, the Minimum Mechanics equation predicted the energy expended in the field to within +4% and −2% of the respective measured means (Fig. 6).”

The Pandolf/Santee equation provided slightly more accurate predictions under loaded versus unloaded conditions in the field.

“In keeping with our prior laboratory testing results, the Pandolf/Santee equation provided slightly more accurate predictions under loaded versus unloaded conditions in the field.”

Direct comparison of the laboratory system against the gold standard Douglas bag technique during same-condition treadmill walking trials produced virtually identical values at each of three walking speeds.

“First, our direct comparison of our laboratory system against the gold standard Douglas bag technique during same-condition treadmill walking trials produced virtually identical values at each of three walking speeds (Fig. 5).”

Compared with the Parvomedics TrueOne laboratory system, the Cosmed K4b2 unit had a consistent positive bias during walking of +13.8 ± 1.8% (range: +11.4% to +16.5%).

“Compared with our Parvomedics TrueOne laboratory system quantified a consistent positive bias in the middle of the literature-reported range for our Cosmed K4b2 unit during walking (Fig. 3) of +13.8 ± 1.8% (means ± SD, range: +11.4% to +16.5%).”

Standard errors of estimate for unloaded trials were 107, 207, 186, and 248 mL O2/kg for the Minimum Mechanics, Pandolf/Santee, ACSM, and Looney equations, respectively.

“Standard errors of estimate (SEE) for each equation for the unloaded trials were: 107, 207, 186, and 248 mL O2/kg for the Minimum Mechanics, Pandolf/Santee, ACSM, and Looney equations, respectively; loaded trials SEE values were 176 and 241 mL O2/kg for the Minimum Mechanics and Pandolf/Santee equations, respectively.”

The use of a single coefficient of 0.73 times level values for downhill walking appeared to be relatively accurate on the −3% gradients on the course.

“The use of a single coefficient of 0.73 times level values for downhill walking also appeared to be relatively accurate on the −3% gradients on our course.”

Mean walking rates of oxygen uptake at each of three test speeds were nearly identical when measured with Parvomedics TrueOne laboratory metabolic system versus Douglas bag method.

“Mean walking rates of oxygen uptake at each of the three test speeds were nearly identical when measured with the Parvomedics TrueOne laboratory metabolic system versus the Douglas bag method (Fig. 4).”

Only one of four predictive equations tested met the hypothesized expectation well.

“We found that that only one of four predictive equations tested met our hypothesized expectation well.”

The ACSM equation field overestimation of +13% is at least somewhat attributable to the absence of negative gradient, or downhill, capabilities.

“The ACSM equation field overestimation of +13% is clearly at least somewhat attributable to the absence of negative gradient, or downhill, capabilities.”

Numerous factors appear to have contributed to the accuracy of the unloaded and loaded field means predicted using the Minimum Mechanics equation.

“Numerous factors appear to have contributed to the accuracy of the unloaded and loaded field means predicted here using this equation.”

The maximum error present on the postcorrection walking energy expenditure field means was likely ±2.6% or less.

“Thus, our collective experimental results suggest that the maximum error present on our postcorrection walking energy expenditure field means was likely ±2.6% or less.”

The extent to which the energy expenditure predictions of the four laboratory equations tested were not similar was unexpected.

“The unexpected outcome was the extent to which the energy expenditure predictions of the four laboratory equations tested were not similar.”

The maximum potential error introduced by conversion between the energy units in the Pandolf/Santee and Looney equations into oxygen units in the ACSM and Minimum Mechanics equations was less than 1.0%.

“These field data indicate the maximum potential error introduced by conversion between the energy units in the Pandolf/Santee and Looney equations into oxygen units in the ACSM and Minimum Mechanics equations was less than 1.0%.”

The linear treatment of the V̇o2 versus speed relationship, which is well-known to be curvilinear, compromises predictive accuracy somewhat across speed, but to a relatively small degree.

“The linear treatment of a relationship well-known to be curvilinear (14, 36–38) does compromise predictive accuracy somewhat across speed, but to a relatively small degree (36, Fig. 4C).”

• cites [14] sourceNot checked yet
• cites [36]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [37] Margaria R, 1938, Atti Accademia Nazionale dei LinceiNot checked yet
• cites [38] sourceNot checked — no full text of the source

The study analyzed equation accuracy only of group mean data, not individual subjects.

“One important analytic note regarding our results is that we only analyzed equation accuracy of the group mean data acquired.”

Free-walking field energy expenditure can indeed be accurately predicted from a laboratory treadmill-based equation.

“The finding that one equation agreed to within an average of 3% across load conditions with appreciably different energetic requirements leads us to conclude that free-walking field energy expenditure can indeed be accurately predicted from a laboratory treadmill-based equation.”

Prior validation of the laboratory system with precision infusions of N2-CO2 gas indicated an oxygen uptake measurement accuracy of ±2.9% within the relevant measurement range for walking.

“Second, our prior validation of our laboratory system with precision infusions of N2-CO2 gas indicated an oxygen uptake measurement accuracy of ±2.9% within the relevant measurement range for walking (33).”

• cites [33] sourceNot checked — no full text of the source

Accuracy metrics for individuals could misrepresent equation predictive accuracy because the measurement variability of the portable calorimeter would be present to an unknown extent.

“Equally important, accuracy metrics for individuals could misrepresent equation predictive accuracy because the measurement variability of the portable calorimeter (22–28, Fig. 3) would be present to an unknown extent.”

• cites [22] sourceNot checked — no full text of the source
• cites [23] Eisenmann JC, 2003, J Sports Med Phys FitnessNot checked — no full text of the source
• cites [24] sourceNot checked — no full text of the source
• cites [25] sourceNot checked — no full text of the source
• cites [26] sourceNot checked — no full text of the source
• cites [27] McNaughton LR, 2005, J Sports Med Phys FitnessNot checked — no full text of the source
• cites [28] sourceNot checked — no full text of the source

The correction factor implemented for the portable calorimeter could only be as valid as the laboratory calorimeter used to quantify it.

“Of course, we recognized that the correction factor implemented for the portable calorimeter could only be as valid as the laboratory calorimeter used to quantify it.”

Rigorous validation of the Parvomedics TrueOne system by several groups of investigators indicated the accuracy of this system all but equals that of the gold standard Douglas bag method.

“Third, the rigorous validation of the Parvomedics TrueOne system by several groups of investigators indicated the accuracy of this system all but equals that of the gold standard Douglas bag method (34, 35) in keeping with our original data here.”

• cites [34] sourceNot checked — no full text of the source
• cites [35] sourceNot checked — no full text of the source

The lower Pandolf/Santee rates on declined portions are attributable to the ACSM equation predicting similar rates of oxygen uptake for level and declined portions due to the absence of a declined term and consequent need to treat downhill gradients as level surfaces.

“The latter observation is attributable to the ACSM equation predicting similar rates of oxygen uptake for the level and declined portions of the field course due to the absence of a declined term and consequent need to treat downhill gradients as level surfaces for predictive purposes.”

Significant elevations in walking metabolism above treadmill values on loose and slippery terrain are well documented.

“In the last case, significant elevations in walking metabolism above treadmill values on loose and slippery terrain are well documented (6, 16), but asphalt-treadmill comparisons have been inconsistent (17, 18) and consideration of other relevant surfaces, like grass, have been limited.”

• cites [6] sourceNot checked — no full text of the source
• cites [16] sourceNot checked — no full text of the source

Differences in the bases of the predictive equations tested, whether formulaic or due to dataset bias, or both, can result in substantial differences in the walking energetic costs predicted from identical inputs.

“Clearly, differences in the bases of the predictive equations tested, whether formulaic or due to dataset bias, or both, can result in substantial differences in the walking energetic costs predicted from identical inputs.”

The oxygen uptake totals acquired over roughly 70-min walking trials provide valid measures of total energy expended.

“Given the submaximal nature of the nonsteady-state exercise intensities involved, the oxygen uptake totals acquired over the roughly 70-min walking trials provide valid measures of the total energy expended (29, 30).”

• cites [29] sourceCheck pending
• cites [30] sourceCheck pending

Despite a somewhat limited empirical basis for negative gradients, the full Pandolf/Santee equation performs relatively accurately under laboratory conditions, particularly across speed on the declines tested.

“Nonetheless, and despite a somewhat limited empirical basis for negative gradients, the full equation performs relatively accurately under laboratory conditions, particularly across speed on the declines tested (14, Fig. 4E and Fig. 5E).”

• cites [14] sourceNot checked yet

The expectation that laboratory equations could accurately predict the energy expended during free walking in the field across variable gradients and terrain was well-supported, but less fully than expected.

“Our expectation that laboratory equations could accurately predict the energy expended during free walking in the field across variable gradients and terrain was well-supported, but less fully than expected.”

The speed, grade, and body weight inputs into the four equations were identical.

“This was the case even though the speed, grade, and body weight inputs into the four equations were identical, and as noted, all four predictive equations were formulated using indirect calorimetry data obtained during constant-speed laboratory walking trials.”

The remaining +8% predictive error of the ACSM equation seems most likely attributable to consistent overpredictions observed across all positive grades under treadmill conditions.

“The remaining +8% predictive error seems most likely attributable to consistent overpredictions observed across all positive grades under treadmill conditions (14, Fig. 4C).”

• cites [14] sourceNot checked yet

Asphalt-treadmill comparisons have been inconsistent.

“In the last case, significant elevations in walking metabolism above treadmill values on loose and slippery terrain are well documented (6, 16), but asphalt-treadmill comparisons have been inconsistent (17, 18) and consideration of other relevant surfaces, like grass, have been limited.”

• cites [17] Daniels F, Vanderbie JH, Winsmann FR. Energy Cost of Treadmill Walking Compared to Road Walking. Report No. 220. Natick, MA: Quartermaster Research and Engineering Command, 1953.Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [18] sourceNot checked — no full text of the source

The calorimeter model in question consistently exceeds well-validated laboratory systems under similar conditions by magnitudes ranging from 2% to 25%.

“The calorimeter model in question consistently exceeds well-validated laboratory systems under similar conditions by magnitudes ranging from 2% to 25% (22–28).”

• cites [22] sourceNot checked — no full text of the source
• cites [23] Eisenmann JC, 2003, J Sports Med Phys FitnessNot checked — no full text of the source
• cites [24] sourceNot checked — no full text of the source
• cites [25] sourceNot checked — no full text of the source
• cites [26] sourceNot checked — no full text of the source
• cites [27] McNaughton LR, 2005, J Sports Med Phys FitnessNot checked — no full text of the source
• cites [28] sourceNot checked — no full text of the source

The overestimates of +17% and +12% for the unloaded and loaded field trials of the Pandolf/Santee equation resulted predominantly from moderate overpredictions on all portions of the field course in the range of relatively fast walking speeds subjects chose.

“The respective overestimates of +17% and +12% for the unloaded and loaded field trials of the Pandolf/Santee equation in the field here resulted predominantly from moderate overpredictions on all portions of the field course (negative, level, and positive grades) in the range of relatively fast walking speeds subjects chose.”

At speeds above 1.4 m/s, both Pandolf/Santee and Looney equations appear to have positive bias.

“At speeds above 1.4 m/s, both Pandolf/Santee and Looney equations appear to have positive bias.”

The choice of existing equations, due to derivation and formulation constraints, can have a large impact on the validity of the predictions generated, even when using identical inputs.

“Second, the choice of existing equations, due to derivation and formulation constraints, can have a large impact on the validity of the predictions generated, even when using identical inputs.”

The relatively steep slope of the Pandolf/Santee equation overpredicts the increase in the energy expenditure totals over the faster two-thirds of this speed range.

“In contrast, the relatively steep slope of the Pandolf/Santee equation overpredicts the increase in the energy expenditure totals over the faster two-thirds of this speed range.”

The Looney and ACSM equations both appear to have appreciable positive bias at and below 1.0 m/s.

“The Looney and ACSM equations both appear to have appreciable positive bias at and below 1.0 m/s.”

At walking speeds of less than 0.6 m/s, the Pandolf/Santee equation is likely the most accurate of the four evaluated.

“Third, at walking speeds of less than 0.6 m/s, the Pandolf/Santee equation is likely the most accurate of the four evaluated.”

The linear treatment of the V̇o2-speed relationship added to a constant resting baseline value in the case of the ACSM equation results in near-linear decreases in total energy required to cover the 4-mile course at faster speeds.

“The linear treatment of the V̇o2-speed relationship added to a constant resting baseline value in the case of the ACSM equation results in near-linear decreases in total energy required to cover the 4-mile course at faster speeds.”

The accuracy obtained when using laboratory-based equations in the field is significantly equation-dependent.

“Thus, the accuracy obtained when using laboratory-based equations in the field is significantly equation-dependent.”

The results support the long-standing assumption that the energy cost of free walking in the field can be accurately inferred from constant-speed, laboratory-treadmill measurements.

“Finally, on a more basic level our results support the long-standing assumption that the energy cost of free walking in the field can be accurately inferred from constant-speed, laboratory-treadmill measurements.”

The equation chosen for field applications, particularly for hikes and marches at slower speeds, is more than large enough to be of practical consequence.

“Accordingly, the equation chosen for field applications, particularly for hikes and marches at slower speeds are more than large enough to be of practical consequence.”