Walking economy is predictably determined by speed, grade, and gravitational load.

Relatively smaller muscle volumes are activated during the relatively high-force eccentric contractions that simultaneously support and lower the body on negative grades.

“Relatively smaller muscle volumes are activated during the relatively high-force eccentric contractions that simultaneously support and lower the body on negative grades (24,61).”

• cites [24] sourcePartly supported

  In “Muscle work output during incline and decline running” (page unavailable), the paper reports greater force during muscle lengthening and increased energy absorption on declines. “Strategies for changing whole body work output” describes examples of muscles that are less active on declines, but the paper does not measure or establish that a smaller total muscle volume is activated to support and lower the body. (LLM, conf=0.84)

  Experimental — accuracy not yet measured
• cites [61] sourceNot checked — no full text of the source

This interpretation is fully consistent with the neuromuscular activation data available from the tissue level under different load conditions.

“This interpretation is fully consistent with the neuromuscular activation data available from the tissue level under different load conditions (52,66).”

• cites [52] sourceSupported
• cites [66] sourceNot checked — no full text of the source

The walking portion of the body's gross metabolic rate increased in direct proportion to load.

“As theorized, the walking portion (V ˙O2-walk ϭ V ˙O2-gross -V ˙O2-supine-rest) of the body's gross metabolic rate increased in direct proportion to load and largely in accordance with support force requirements across both speed and grade.”

The addition of either 18 or 31% of the body's weight resulted in proportional increases in walking metabolic rates regardless of the speed or grade of the walking trial.

“The addition of either 18 or 31% of the body's weight resulted in proportional increases in walking metabolic rates regardless of the speed or grade of the walking trial (Fig. 1).”

When walking metabolic rates were determined by subtracting supine resting rates from the gross rates measured, load-induced increases in walking metabolism were a close function of the load added regardless of speed, grade, and gross metabolic rate elicited by the trial.

“When walking metabolic rates were determined by subtracting supine resting rates from the gross rates measured (i.e., V ˙O2-walk ϭ V ˙O2-gross Ϫ V ˙O2-rest ), load-induced increases in walking metabolism were a close function of the load added regardless of the speed, grade, and gross metabolic rate elicited by the trial”

The mean overall ratio for the heavier load from these 20 speeds and grades was 1.35 ± 0.006.

“The mean overall ratio for the heavier load from these 20 speeds and grades was 1.35 Ϯ 0.006.”

The grade-induced differences present at any speed were an approximately linear function of grade across positive grades from 0 to 9°.

“The grade-induced differences present at any speed were an approximately linear function of grade across positive grades from 0 to 9°.”

The mean measured standing metabolic rate was 3.51 ± 0.08 ml O2·kg−1·min−1 (range: 2.62-4.55).

“whereas the mean measured standing rate was 3.51 Ϯ 0.08 ml O 2 •kg Ϫ1 •min Ϫ1 (range: 2.62-4.55 ml O 2 •kg Ϫ1 •min Ϫ1 ).”

There was no discernable trend across the gross metabolic rates measured under either load condition.

“There was no discernable trend across the gross metabolic rates measured under either load condition.”

Across the 90 different trial conditions, individual walking metabolic rates spanned a nearly 10-fold range from a minimum of 4.8 to a maximum of 45.4 ml O2·kg-body−1·min−1.

“Across these 90 different trial conditions, individual walking metabolic rates spanned a nearly 10-fold range from a minimum of 4.8 ml O 2 •kg -body Ϫ1 •min Ϫ1 to a maximum of 45.4 ml O 2 •kg -body Ϫ1 •min Ϫ1 .”

For both the +18 and +31% added load conditions, the ratios observed were greatest at low metabolic rates and least at the highest ones.

“For both the ϩ18 and ϩ31% added load conditions, the ratios observed were greatest at low metabolic rates and least at the highest ones.”

Individual variability in walking economy was limited, with the mean standard deviation from each of the 90 different trial conditions averaging <0.8 ml O2·kg-body−1·min−1.

“Individual variability in walking economy was limited, with the mean standard deviation from each of the 90 different trial conditions averaging Ͻ0.8 ml O 2 •kg -body Ϫ1 •min Ϫ1 .”

Because of the close relationship between increases in mass-specific metabolic rates and added gravitational loads relative to body weight, the accuracy of the minimum mechanics model under loaded conditions was almost the same as under unloaded conditions.

“Because of the close relationship between increases in mass-specific metabolic rates and added gravitational loads relative to body weight, the accuracy of the minimum mechanics model under loaded conditions was almost the same as under unloaded conditions (Fig. 5, A and B).”

Metabolic rates spanned a 14-fold range from supine rest to the greatest single-trial walking mean (3.1 ± 0.1 to 43.3 ± 0.5 ml O2·kg-body−1·min−1).

“Metabolic rates spanned a 14-fold range from supine rest to the greatest single-trial walking mean (3.1 Ϯ 0.1 to 43.3 Ϯ 0.5 ml O 2•kg-body Ϫ1 •min Ϫ1 , respectively).”

At any given speed in the protocol, walking metabolic rates spanned a minimum range of fourfold and as much as sevenfold from the −6 to +9° grade conditions examined.

“At any given speed in the protocol, walking metabolic rates spanned a minimum range of fourfold and as much as sevenfold range from the Ϫ6 to ϩ9° grade conditions examined.”

The mean ratio of V̇O2-L to V̇O2-UL across the 20 common speeds and grades with the lighter load was 1.17 ± 0.004.

“The mean value for the ratio of V ˙O2-L to V ˙O2-UL across the 20 common speeds and grades administered with the lighter load was 1.17 Ϯ 0.004.”

The opposite pattern was observed when the literature standing value of 4.5 ml O2·kg−1·min−1 was subtracted from the V̇O2-gross values measured.

“The opposite pattern was observed when the literature standing value of 4.5 ml O 2 •kg Ϫ1 •min Ϫ1 was subtracted from the V ˙O2-gross values measured (where V ˙O2-walk ϭ V ˙O2-gross Ϫ V ˙O2-stand ; Fig. 3, green open triangles and curve fits).”

Subtraction of the literature standing values from measured rates resulted in ratios of loaded to unloaded walking metabolic rates that were appreciably greater than the respective relative increase in load for both conditions.

“Subtraction of the literature standing values from measured rates resulted in ratios of loaded to unloaded walking metabolic rates (V ˙O2-L /V ˙O2-UL ) that were appreciably greater than the respective relative increase in load for both conditions.”

The influence of grade on walking economy was larger than that of speed.

“The influence of grade on walking economy was larger than that of speed (Figs. 1 and 2).”

When no baseline quantity was subtracted, the ratio of loaded to unloaded walking metabolic rates was appreciably less than the relative increase in load.

“When no baseline quantity was subtracted (Fig. 3, red open squares and curve fits), the ratio of loaded to unloaded walking metabolic rates (V ˙O2-L /V ˙O2-UL ) was appreciably less than the relative increase in load.”

For both the +18 and +31% added load conditions, ratios were lowest at low metabolic rates and greatest at the highest ones.

“For both the ϩ18 and ϩ31% added load conditions, ratios were lowest at low metabolic rates and greatest at the highest ones.”

The derivation/validation data set includes steady-state loaded and unloaded walking trials (n = 3,414) that span a fourfold range of walking speeds on each of six different surface gradients (−6 to +9°).

“The derivation/validation data set includes steadystate loaded and unloaded walking trials (n ϭ 3,414) that span a fourfold range of walking speeds on each of six different surface gradients (Ϫ6 to ϩ9°).”

There was no effect of load condition on walking economy per kilogram total load (ANOVA, α = 0.05).

“There was no effect of load condition on walking economy per kilogram total load (ml O 2 •kg -total Ϫ1 •min Ϫ1 ; ANOVA, ϰ ϭ 0.05).”

When load-induced increases in mass-specific walking metabolic rates were expressed per kg-total, there were no discernable differences across any of the 20 speed and grade conditions for which each of the three load conditions were administered.

“Consequently, when the load-induced increases in the body's mass-specific (i.e., per kg -body ) walking metabolic rates were expressed in relation to the total load carried, or per kg -total , there were no discernable differences across any of the 20 speed and grade conditions for which each of the three load conditions were administered (Fig. 2).”

The proportion of total variance in the 297 measured metabolic rates for validation group subjects accounted for by the minimum-mechanics model was >98%.

“The proportion of the total variance in the 297 measured metabolic rates for the validation group subjects accounted for by the minimum-mechanics model was Ͼ98%.”

At all grades, speed-induced increases in walking metabolic rates were slightly curvilinear.

“At all grades, speed-induced increases in walking metabolic rates were slightly curvilinear.”

Coefficient of variation values tended to be greater for trials eliciting lower metabolic rates.

“In general, coefficient of variation values tended to be greater for trials eliciting lower metabolic rates.”

The mean sitting metabolic rate was 3.16 ± 0.08 ml O2·kg−1·min−1 (range: 2.22-4.24).

“The corresponding mean for sitting metabolic rates was 3.16 Ϯ 0.08 ml O 2 •kg Ϫ1 •min Ϫ1 (range: 2.22-4.24ml O 2 •kg Ϫ1 •min Ϫ1 )”

The supine resting values predicted for all 32 subjects using the population equations of Schofield et al. (3.21 ± 0.05 ml O2·kg−1·min−1) agreed to within <0.1 ml O2·kg−1·min−1 of the mean measured value.

“The supine resting values predicted for all 32 subjects using the population equations of Schofield et al. (64) based on height, weight, and sex of 3.21 Ϯ 0.05 ml O 2 •kg Ϫ1 •min Ϫ1 agreed to within Ͻ0.1 ml O 2 •kg Ϫ1 •min Ϫ1 of the mean measured value provided above.”

• cites Schofield et al. [64] Schofield WN, 1985, Hum Nutr Clin NutrNot checked yet

When individual variability was quantified as coefficient of variation, values ranged from 0.034 to 0.122.

“When individual variability was quantified in relation to each trial mean as a coefficient of variation (ϭ standard deviation/trial mean), values ranged from a minimum of 0.034 to a maximum of 0.122.”

A single minimum-mechanics equation was derived from the data of 10 unloaded-condition subjects to predict the pooled mass-specific economy of all remaining loaded and unloaded trials combined (n = 1,412 trials from 90 speed/grade/load conditions).

“Consequently, a single minimum-mechanics equation was derived from the data of 10 unloaded-condition subjects to predict the pooled mass-specific economy (V ˙O2-gross, ml O2•kg-body ϩ load Ϫ1 •min Ϫ1 ) of all the remaining loaded and unloaded trials combined (n ϭ 1,412 trials from 90 speed/grade/load conditions).”

• AssumptionThe authors state this as an assumption: Elevations in the body's metabolic rate above supine resting rates due to walking result entirely from the activity of skeletal muscle.
• AssumptionThe authors state this as an assumption: Elevations in metabolic rate above supine resting due to walking are attributable primarily to the activity of the limb muscles to support the weight of the body, or body plus load, against gravity.
• AssumptionThe authors state this as an assumption: Elevations in metabolic rate above supine resting due to walking vary across grade in accordance with muscular contractions that elevate, maintain, or lower the body's center of mass during each step.
• AssumptionThe authors state this as an assumption: Each kilogram of added torso weight incurs an equal metabolic cost to each kilogram of body weight.

The mean measured supine resting metabolic rate for all 32 subjects was 3.13 ± 0.07 ml O2·kg−1·min−1 (range: 2.34-3.82).

“The mean measured supine resting metabolic rate for all 32 subjects was 3.13 Ϯ 0.07 ml O 2 •kg Ϫ1 •min Ϫ1 (range: 2.34 -3.82 ml O 2 •kg Ϫ1 •min Ϫ1 ).”

Both alternative data treatments of the gross metabolic rates measured during walking were signal size dependent.

“Both alternative data treatments of the gross metabolic rates measured during walking were signal size dependent.”

The minimum-mechanics equation predicted pooled mass-specific walking economy with r2 = 0.99 and SEE = 1.06 ml O2·kg−1·min−1.

“The accuracy of prediction achieved (r 2 ϭ 0.99, SEE ϭ 1.06 ml O2•kg Ϫ1 •min Ϫ1 )”

• AssumptionThe authors state this as an assumption: Elevations in the body's metabolic rate above supine resting rates due to walking result entirely from the activity of skeletal muscle.
• AssumptionThe authors state this as an assumption: Elevations in metabolic rate above supine resting due to walking are attributable primarily to the activity of the limb muscles to support the weight of the body, or body plus load, against gravity.
• AssumptionThe authors state this as an assumption: Elevations in metabolic rate above supine resting due to walking vary across grade in accordance with muscular contractions that elevate, maintain, or lower the body's center of mass during each step.
• AssumptionThe authors state this as an assumption: Each kilogram of added torso weight incurs an equal metabolic cost to each kilogram of body weight.

In both cases, the ratios progressively decreased toward a value proportional to the relative load added as the measured gross metabolic rates increased.

“In both cases, the ratios progressively decreased toward a value proportional to the relative load added as the measured gross metabolic rates increased.”

For both load conditions, the ratios progressively approached a value directly proportional to the relative load added as the measured gross metabolic rates increased.

“For both load conditions, the ratios progressively approached a value directly proportional to the relative load added as the measured gross metabolic rates increased.”

Grade-induced differences in walking metabolic rates from 0 to −6° were not linear.

“In contrast, gradeinduced differences in walking metabolic rates from 0 to Ϫ6° were not linear.”

The mean standing metabolic rate measured under postabsorptive conditions in this study was 3.53 ± 0.08 ml O2·kg−1·min−1.

“The mean standing metabolic rate we measured under postabsorptive conditions here of 3.53 Ϯ 0.08 ml O2•kg Ϫ1 •min Ϫ1 is representative of this difference.”

The accuracy of our walking predictions here approached that of Astrand and Rhyming's cycling predictions.

“The accuracy of our walking predictions here approached that of Astrand and Rhyming's (5) cycling predictions.”

• cites Astrand and Rhyming [5] sourceNot checked — no full text of the source

The average literature value of 4.5 ml O2·kg−1·min−1 in Table 3 exceeds the supine resting values measured for our subjects here (mean = 3.1 ml O2·kgbody−1·min−1; n = 32) by 1.4 ml O2·kg−1·min−1.

“The average literature value of 4.5 ml O 2•kg Ϫ1 •min Ϫ1 in Table 3 exceeds the supine resting values measured for our subjects here (mean ϭ 3.1 ml O2•kgbody Ϫ1 •min Ϫ1 ; n ϭ 32) by 1.4 ml O2•kg Ϫ1 •min Ϫ1 .”

63% of our unloaded level and inclined walking trials fell within the ±6.0% standard.

“Here, 63% of our unloaded level and inclined walking trials fell within the Ϯ6.0% standard.”

The grade- and signal size-dependent predictive bias patterns of the loaded conditions were similar to those in the unloaded trials in part I.

“The grade-and signal size-dependent predictive bias patterns of the loaded conditions were similar to those in the unloaded trials in part I.”

The relative agreement between model-predicted and measured values across nearly 300 speed and grade values in part I and across >1,100 speed, grade, and load values in part II was >98% in each case.

“The relative agreement between the model-predicted and measured values across nearly 300 speed and grade values in part I and across Ͼ1,100 speed, grade, and load values in part II was Ͼ98% in each case (Figs.4B and 5B).”

In each case, economy ratios progressively approached the condition weight ratios as the body's gross metabolic rates increased.

“In each case, economy ratios progressively approached the condition weight ratios as the body's gross metabolic rates increased.”

The Pandolf et al. (56) model equation had slightly better overall performance than the ACSM model equation.

“The greater conditional breadth of the Pandolf et al. (56) model equation resulted in slightly better overall performance (Figs. 4, E and F, 5, E and F, and 6, E and F) vs. the ACSM model equation.”

• cites Pandolf et al. [56] Pandolf KB, 1977, J Appl Physiol Respir Environ Exerc Physiol sourceNot checked — no full text of the source

The postabsorptive sitting metabolic rates of our subjects were essentially identical to their supine resting rates (3.13 ± 0.07 vs. 3.16 ± 0.08 ml O2·kg−1·min−1, n=32).

“The postabsorptive sitting metabolic rates of our subjects were essentially identical to their supine resting rates (3.13 Ϯ 0.07 vs. 3.16 Ϯ 0.08 ml O 2•kg Ϫ1 •min Ϫ1 , respectively; n ϭ 32).”

For our level walking economy data, the resulting underestimations of walking metabolic rates range from a maximum of 33.9% at 0.4 m/s to a minimum of 12.0% at 1.6 m/s.

“For our level walking economy data illustrated in Fig. 7, the resulting underestimations of walking metabolic rates range from a maximum of 33.9% at 0.4 m/s to a minimum of 12.0% at 1.6 m/s.”

Nearly all the zero-subtraction economy ratios from 40 different load condition trials administered were lower than the ratio of loaded to unloaded walking weight.

“Indeed, this is precisely what we observed, as nearly all the zero-subtraction economy ratios from 40 different load condition trials administered were lower than the ratio of loaded to unloaded walking weight (Fig. 3, A and B, red squares and line fits).”

Our 738 individual loaded walking trials spanning a 2.5-fold range of speeds on six different grades consistently supported the alternative conclusion that each kilogram of body and load mass incurs the same metabolic cost.

“However, our 738 individual loaded walking trials spanning a 2.5-fold range of speeds on six different grades consistently supported the alternative conclusion that each kilogram of body and load mass incurs the same metabolic cost (Figs. 2 and 3 and Table 5).”

In many cases, the literature standing subtraction eliminates most of the originally measured metabolic signal.

“As Fig. 7 illustrates, in many of these cases, the literature standing subtraction eliminates most of the originally measured metabolic signal.”

Preexercise standing metabolic rates in Table 3 are substantially greater on average than values reported in literature from studies where measuring standing metabolic rate was a primary rather than a secondary objective.

“These measures are substantially greater on average than the values reported in the literature from those studies for which measuring standing metabolic rate was a primary rather than a secondary objective.”

Predictive error for the Pandolf et al. equation was most pronounced across slower speeds and at lower metabolic rates.

“Predictive error was most pronounced across slower speeds and at lower metabolic rates for two reasons.”

The two-component modeling approach ultimately provided highly accurate descriptions of the two- to fourfold increases in walking metabolic rates observed across the fourfold range of speeds investigated on the six different grades.

“This approach, although more mathematically descriptive than physiologically mechanistic, ultimately provided highly accurate descriptions of the two-to fourfold increases in walking metabolic rates observed across the fourfold range of speeds investigated on the six different grades (Figs. 2, 3, 4, and 5).”

At the greatest metabolic rates, the economy ratios from all three subtraction methods converged at or very near the values of the weight ratios from the respective conditions: 1.18 for the lighter load and 1.31 for the heavier one.

“At the greatest metabolic rates for which the resting subtraction quantities have the least influence, the economy ratios from all three subtraction methods converged at or very near the values of the weight ratios from the respective conditions: 1.18 for the lighter load and 1.31 for the heavier one (Figs.3A and 3B, respectively).”

The overall error of individual prediction of our minimum mechanics model was roughly one-half that of the ACSM and Pandolf et al. equations on average when evaluated with the SEE statistic.

“The overall error of individual prediction of our minimum mechanics model was roughly one-half that of the ACSM and Pandolf et al. equations on average when evaluated with the SEE statistic.”

Across more than 1,400 individual values from 90 different speed, grade, and load trial conditions and gross metabolic rates ranging from two to 14 times the body's resting rate, the model predicted measured rates with a standard error of estimate of just >1.0 ml O2·kg−1·min−1 out of an overall mean nearly 14 times larger (14.6 ± 0.2 ml O2·kg-body−1·min−1; n = 1,412).

“Across more than 1,400 individual values from 90 different speed, grade, and load trial conditions and gross metabolic rates that ranged from two to 14 times the body's resting rate, our model predicted the rates we measured with a standard error of estimate of just Ͼ1.0 ml O 2 •kg Ϫ1 •min Ϫ1 out of an overall mean nearly 14 times larger (14.6 Ϯ 0.2 ml O 2 •kg -body Ϫ1 •min Ϫ1 ; n ϭ 1,412).”

Long periods of ground force application to support the body's weight and conservative, pendulum-like gait mechanics constrain gait-induced elevations in whole body metabolism to two to four times the body's supine resting rate across the level walking speeds typically used.

“However, long periods of ground force application to support the body's weight (12,36) and conservative, pendulum-like gait mechanics that minimize muscular work (11,12) constrain gaitinduced elevations in whole body metabolism two to four times the body's supine resting rate across the level walking speeds typically used.”

• cites [12] sourceNot checked — no full text of the source
• cites [36] sourceNot checked — no full text of the source
• cites [11] sourceNot checked — no full text of the source

The Pandolf et al. and ACSM equations generally underpredict walking metabolic rates under predominantly level conditions.

“However, both were formulated using very small sample sizes, have somewhat unclear scientific foundations, do not include declined conditions, and generally underpredict walking metabolic rates under the predominantly level conditions under which they have been thus far evaluated (46).”

• cites [46] sourceNot checked — no full text of the source

The Pandolf et al. and ACSM equations were formulated using very small sample sizes.

“However, both were formulated using very small sample sizes, have somewhat unclear scientific foundations, do not include declined conditions, and generally underpredict walking metabolic rates under the predominantly level conditions under which they have been thus far evaluated (46).”

• cites [46] sourceNot checked — no full text of the source

The two predictive equations with greatest conditional breadth, those of Pandolf et al. and the American College of Sports Medicine (ACSM), are the most widely used.

“The two predictive equations with greatest conditional breadth, those of Pandolf et al. (56) and the American College of Sports Medicine (ACSM) (3), are the most widely used.”

• cites Pandolf et al. [56] Pandolf KB, 1977, J Appl Physiol Respir Environ Exerc Physiol sourceNot checked — no full text of the source
• cites American College of Sports Medicine (ACSM) (3)Not matched

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

The accuracy of the minimum mechanics model (r2 = 0.99; SEE = 1.06 ml O2·kg−1·min−1) appreciably exceeds that of currently used standards.

“The accuracy of our minimum mechanics model (r 2 ϭ 0.99; SEE ϭ 1.06 ml O2•kg Ϫ1 •min Ϫ1 ) appreciably exceeds that of currently used standards.”

• AssumptionThe authors state this as an assumption: Elevations in the body's metabolic rate above supine resting rates due to walking result entirely from the activity of skeletal muscle.
• AssumptionThe authors state this as an assumption: Elevations in metabolic rate above supine resting due to walking are attributable primarily to the activity of the limb muscles to support the weight of the body, or body plus load, against gravity.
• AssumptionThe authors state this as an assumption: Elevations in metabolic rate above supine resting due to walking vary across grade in accordance with muscular contractions that elevate, maintain, or lower the body's center of mass during each step.
• AssumptionThe authors state this as an assumption: Each kilogram of added torso weight incurs an equal metabolic cost to each kilogram of body weight.

The Pandolf et al. and ACSM equations do not include declined conditions.

“However, both were formulated using very small sample sizes, have somewhat unclear scientific foundations, do not include declined conditions, and generally underpredict walking metabolic rates under the predominantly level conditions under which they have been thus far evaluated (46).”

• cites [46] sourceNot checked — no full text of the source

The walking portion of the body's gross metabolic rate largely followed support force requirements across both speed and grade.

“As theorized, the walking portion (V ˙O2-walk ϭ V ˙O2-gross -V ˙O2-supine-rest) of the body's gross metabolic rate increased in direct proportion to load and largely in accordance with support force requirements across both speed and grade.”

The rationale for standing metabolic rate subtractions is unclear because standing, like walking, includes a nonresting metabolic cost of supporting the body's weight against gravity.

“The rationale for standing metabolic rate subtractions is unclear because standing, like walking, includes a nonresting metabolic cost of supporting the body's weight against gravity (75).”

• cites [75] sourceNot checked — no full text of the source

Scores of predictive equations have been developed, but the vast majority have been limited to level surface conditions.

“Scores of predictive equations have been developed, but the vast majority have been limited to level surface conditions (10,46,59,71,73,77).”

• cites [10] Bubb W, 1985, J Cardiopulm Rehabil sourceNot checked — no full text of the source
• cites [46] sourceNot checked — no full text of the source
• cites [59] Ralston HJ, 1958, Int Z Angew Physiol sourceNot checked — no full text of the source
• cites [71] sourceNot checked — no full text of the source
• cites [73] sourceNot checked — no full text of the source
• cites [77] sourceNot checked — no full text of the source

A generalized understanding of walking metabolism across the full range of conditions humans typically walk remains unavailable.

“Despite extensive and ongoing scientific attention, a generalized understanding of walking metabolism across the full range of conditions humans typically walk remains unavailable.”

A minimum mechanics model predicts human walking economy across a broad range of conditions from only three variables: speed, surface grade, and body-plus-load mass.

“Introduced is a “minimum mechanics” model that predicts human walking economy across a broad range of conditions from only three variables: speed, surface grade, and bodyplus-load mass.”

• AssumptionThe authors state this as an assumption: Elevations in the body's metabolic rate above supine resting rates due to walking result entirely from the activity of skeletal muscle.
• AssumptionThe authors state this as an assumption: Elevations in metabolic rate above supine resting due to walking are attributable primarily to the activity of the limb muscles to support the weight of the body, or body plus load, against gravity.
• AssumptionThe authors state this as an assumption: Elevations in metabolic rate above supine resting due to walking vary across grade in accordance with muscular contractions that elevate, maintain, or lower the body's center of mass during each step.
• AssumptionThe authors state this as an assumption: Each kilogram of added torso weight incurs an equal metabolic cost to each kilogram of body weight.

Human walking economy is predictably determined by the minimum mechanical requirements present across a broad range of conditions.

“The accuracy of prediction achieved (r 2 ϭ 0.99, SEE ϭ 1.06 ml O2•kg Ϫ1 •min Ϫ1 ) leads us to conclude that human walking economy is predictably determined by the minimum mechanical requirements present across a broad range of conditions.”

• AssumptionThe authors state this as an assumption: Elevations in the body's metabolic rate above supine resting rates due to walking result entirely from the activity of skeletal muscle.
• AssumptionThe authors state this as an assumption: Elevations in metabolic rate above supine resting due to walking are attributable primarily to the activity of the limb muscles to support the weight of the body, or body plus load, against gravity.
• AssumptionThe authors state this as an assumption: Elevations in metabolic rate above supine resting due to walking vary across grade in accordance with muscular contractions that elevate, maintain, or lower the body's center of mass during each step.
• AssumptionThe authors state this as an assumption: Each kilogram of added torso weight incurs an equal metabolic cost to each kilogram of body weight.

Deviation from economy ratios specified a priori on the basis of load weight can be used to detect resting baseline under- and oversubtractions.

“Specifically, deviation from economy ratios specified a priori on the basis of load weight can be used to detect resting baseline under-and oversubtractions.”

Not removing any contribution of resting to the gross metabolic rate signal measured during walking disproportionately inflates the metabolic requirements of walking in the unloaded condition.

“Not removing any contribution of resting to the gross metabolic rate signal measured during walking disproportionately inflates the metabolic requirements of walking in the unloaded condition.”

Across-speed analyses and other scientific assessments are directly affected and potentially confounded by the baseline quantity subtracted.

“Accordingly, across-speed analyses and other scientific assessments are directly affected and potentially confounded by the baseline quantity subtracted.”

For conditions and interventions that elicit relatively low walking metabolic rates, such as walking downhill, in simulated reduced gravity, and with assistive pulling, the specific value of the baseline quantity subtracted will most heavily influence the effects.

“Potential effects for those conditions and interventions that elicit relatively low walking metabolic rates, such as walking downhill, in simulated reduced gravity, and with assistive pulling, will be most heavily influenced by the specific value of the baseline quantity subtracted.”

The alternative suggestions that significant metabolic requirements exist for factors other than supporting and displacing the body's mass, such as repositioning the limbs between steps and the trailing and leading limbs pushing against one another during double support, do not explain our results.

“The alternative suggestions that significant metabolic requirements exist for factors other than supporting and displacing the body's mass, such as repositioning the limbs between steps (18,27) and the trailing and leading limbs pushing against one another during double support (19,43), do not explain our results.”

• cites [18] sourceNot checked — no full text of the source
• cites [27] sourceNot checked — no full text of the source
• cites [19] Donelan JM, 2002, J Exp Biol sourceNot checked — no full text of the source
• cites [43] sourceNot checked — no full text of the source

The extensively validated population equations of Schofield et al. provide accurate resting metabolic rate estimates from only sex, height, and weight.

“First, the extensively validated population equations of Schofield et al. (64) provide accurate resting metabolic rate estimates from only sex, height, and weight.”

• cites [64] Schofield WN, 1985, Hum Nutr Clin NutrNot checked yet

The majority of the fivefold range in walking economy values observed across grade is explained by the different per-fiber muscular forces generated under the different grade conditions.

“However, the majority is explained by the different perfiber muscular forces generated under the different grade conditions.”

Astrand and Rhyming reported being able to predict cycling metabolic rates with an accuracy of ±6.0% for 67% of their cycling trials.

“In their original work, these authors reported being able to do so with an accuracy of Ϯ6.0% for 67% of their cycling trials.”

• cites Astrand and Rhyming [5] sourceNot checked — no full text of the source

The constant metabolic rates per total kilogram supported across three load conditions on all six inclines investigated here reveal that Margaria's support and displacement conclusions from unloaded walking on very steep positive and negative grades also apply to the moderate and intermediate grades examined here.

“The constant metabolic rates per total kilogram supported across three load conditions on all six inclines (Fig. 2B) investigated here reveal that Margaria's support and displacement conclusions from unloaded walking on very steep positive and negative grades also apply to the moderate and intermediate grades we examined here.”

The inability of skeletal muscle to convert lost gravitational potential energy into accumulated chemical energy reveals the physiologically unsound foundation of this prevailing approach.

“The inability of skeletal muscle to convert lost gravitational potential energy into accumulated chemical energy reveals the physiologically unsound foundation of this prevailing approach (3,8,17,25,56,78).”

• cites [3] American College of Sports Medicine, 2013Not checked yet
• cites [8] sourceNot checked — no full text of the source
• cites [17] sourceNot checked — no full text of the source
• cites [25] sourceNot checked — no full text of the source
• cites [56] Pandolf KB, 1977, J Appl Physiol Respir Environ Exerc Physiol sourceNot checked — no full text of the source
• cites [78] sourceNot checked — no full text of the source

The constant ratios for each load condition allow us to infer that the measured supine resting rates we subtracted (3.1 ± 0.1 ml O2·kg-body−1·min−1) from the gross bodily rates measured during walking accurately isolated the non-resting fraction of bodily metabolism for which walking was responsible.

“Accordingly, the constant ratios for each load condition allow us to infer that the measured supine resting rates we subtracted (3.1 Ϯ 0.1 ml O 2 •kg -body Ϫ1 •min Ϫ1 ) from the gross bodily rates measured during walking (i.e., V ˙O2-gross -V ˙O2-rest ) accurately isolated the non-resting fraction of bodily metabolism for which walking was responsible.”

Walking economy can be predicted accurately across a broad range of conditions from only three mechanical variables: speed, grade, and the total weight supported against gravity.

“Per our minimum mechanics hypothesis, we were able to predict walking economy accurately across a broad range of conditions from only three mechanical variables: speed, grade, and the total weight supported against gravity.”

The empirically derived decline coefficient of 0.73 is consistent with the metabolic reductions suggested by the slope of the force-velocity curve for eccentric muscular contractions in vivo.

“The empirically derived decline coefficient of 0.73 (Table 4) is consistent with the metabolic reductions suggested by the slope of the forcevelocity curve for eccentric muscular contractions in vivo (60).”

• cites [60] sourceNot checked — no full text of the source

A small portion of the fivefold range in walking economy values observed across grade at each protocol speed tested here can be attributed to within-fiber rates of ATP utilization being greater during concentric uphill vs. eccentric downhill contractions.

“A small portion of the fivefold range in walking economy values observed across grade at each protocol speed tested here (Fig. 2B) can be attributed to within-fiber rates of ATP utilization being greater during concentric uphill vs. eccentric downhill contractions (34,35,39,70).”

• cites [34] sourceNot checked — no full text of the source
• cites [35] Hill AV, 1950, Sci ProgNot matched

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

• cites [39] sourceNot checked — no full text of the source
• cites [70] Taylor CR, 1994, Adv Vet Sci Comp MedNot checked yet

Our earlier efforts employing body size stratification and stride frequency variation as experimental tools support the possibility that the Wb/tc approach may provide a general mechanistic explanation for human walking economy across speed that we report for the different grades investigated here.

“Our earlier efforts employing body size stratification and stride frequency variation as experimental tools (74) support the possibility that the W b /t c approach may provide a general mechanistic explanation for human walking economy across speed that we report for the different grades investigated here.”

• cites [74] sourceNot checked — no full text of the source

The error potentially introduced by an oversubtraction of 1.4 ml O2·kg−1·min−1 is substantial because the metabolic rates measured under typical walking conditions are quite small.

“The error potentially introduced by an oversubtraction of 1.4 ml O 2•kg Ϫ1 •min Ϫ1 is substantial because the metabolic rates measured under typical walking conditions are quite small (Fig. 7).”

Sitting metabolism may be able to serve as a reasonable supine resting rate surrogate.

“Second, our measurements suggest that sitting metabolism may be able to serve as a reasonable supine resting rate surrogate.”

Assuming the limb's leverage is not altered by balanced loading, the volume of limb extensor muscle activated, and therefore the rate at which chemical energy is used, to provide the requisite support forces should be a direct function of the total body-plus-load mass supported.

“Assuming the limb's leverage is not altered by balanced loading, the volume of limb extensor muscle activated, and, therefore, the rate at which chemical energy is used, to provide the requisite support forces should be a direct function of the total body-plus-load mass supported.”

• AssumptionThe authors state this as an assumption: The limb's leverage is not altered by balanced loading.

Margaria recognized that the rate at which metabolic energy was expended to support and displace the body on steep positive and steep negative grades matched the metabolic cost of generating force during concentric and eccentric muscular contractions in isolated skeletal muscle.

“This pioneering investigator recognized that the rate at which metabolic energy was expended to support and displace the body on steep positive and steep negative grades matched the metabolic cost of generating force during concentric and eccentric muscular contractions in isolated skeletal muscle.”

• cites Margaria [49] Margaria R, 1938, Atti Accad Naz LinceiNot checked yet

Abe et al. reported that the speed identified as most economical differed over a 20% range depending upon the baseline quantity subtracted from their gross metabolic rates.

“These authors reported that the speed identified as most economical differed over a 20% range, depending upon the baseline quantity subtracted from their gross metabolic rates.”

• cites [1] sourceNot checked yet

  Checked before — its earlier verdict is held back until a new check runs.

If limb repositioning accounted for an appreciable portion of the total walking metabolic rate at any given speed and grade, then load-induced increases in economy should have been substantially less than the 1:1 relationship that consistently resulted across different speeds and grades.

“Thus, if limb repositioning accounted for an appreciable portion of the total walking metabolic rate at any given speed and grade, then load-induced increases in economy should have been substantially less than the 1:1 relationship that consistently resulted across different speeds and grades (Figs.2B and 3).”

The ACSM model equation overpredicts walking metabolic rates on all nonzero grades.

“However, the more significant limitation of the ACSM model equation is the overprediction of walking metabolic rates on all nonzero grades.”

Relatively greater volumes of muscle must be activated during the relatively low-force concentric contractions that simultaneously support and elevate the body's weight on positive grades.

“Relatively greater volumes of muscle must be activated during the relatively low-force concentric contractions that simultaneously support and elevate the body's weight on positive grades.”

Our load results are consistent with the manner in which our model incorporates the mechanical consequences of added mass, with each kilogram of body or load mass supported requiring the application of the same ground support force (= 1.0 kg × gravitational acceleration) over the course of each stride.

“Mechanistically, our load results are consistent with the manner in which our model incorporates the mechanical consequences of added mass, with each kilogram of body or load mass supported requiring the application of the same ground support force ( ϭ 1.0 kg ϫ gravitational acceleration) over the course of each stride.”

Removing a quantity larger than the actual contributions of resting to the gross metabolic rates measured disproportionately deflates the metabolic requirements of walking in the unloaded condition.

“Removing a quantity larger than the actual contributions of resting to the gross metabolic rates measured disproportionately deflates the metabolic requirements of walking in the unloaded condition.”

The quantitative agreement between tissue and whole body levels allowed Margaria to deduce that essentially all of the metabolic energy being expended to walk on steep gradients was attributable to supporting and displacing the body's mass either positively via concentric contractions on steep inclines or negatively via eccentric contractions on steep declines.

“The quantitative agreement between tissue and whole body levels allowed Margaria (49) to deduce that essentially all of the metabolic energy being expended to walk on steep gradients was attributable to supporting and displacing the body's mass either positively via concentric contractions on steep inclines or negatively via eccentric contractions on steep declines.”

• cites Margaria [49] Margaria R, 1938, Atti Accad Naz LinceiNot checked yet

Resting supine metabolic rates are a sound standard for quantifying exercise metabolic rates more broadly.

“More generally, these results identify resting supine metabolic rates as a sound standard for quantifying exercise metabolic rates more broadly.”

• AssumptionRests on an assumption: Gravitational support is the primary determinant of walking metabolism.

Our results, the foundational context provided by Margaria and colleagues, and the muscle activation and length-change data now available from the tissue level all support the same mechanistic explanation for differences in walking economy across grade.

“Our results, the foundational context provided by Margaria and colleagues (49,50), and the muscle activation and lengthchange data now available from the tissue level (24,61) all support the same mechanistic explanation for differences in walking economy across grade.”

• cites [49] Margaria R, 1938, Atti Accad Naz LinceiNot checked yet
• cites [50] sourceNot checked — no full text of the source
• cites [24] sourceNot checked yet

  Checked before — its earlier verdict is held back until a new check runs.

• cites [61] sourceNot checked — no full text of the source

Both the ACSM and Pandolf et al. model equations are amalgams of a series of smaller studies and data sets.

“In contrast, both the ACSM (3); and Pandolf et al. (56) model equations are amalgams of a series of smaller studies and data sets (for ACSM, see Refs 17 and 55; for Pandolf et al, see Refs. 25”

• cites [3] American College of Sports Medicine, 2013Not checked yet
• cites [56] Pandolf KB, 1977, J Appl Physiol Respir Environ Exerc Physiol sourceNot checked — no full text of the source
• cites 17 and 55Not matched

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