The energetic cost of walking: a comparison of predictive methods

From cockroaches to tanks: The same power-mass-speed relation describes both biological and artificial ground-mobile systems

This paper explores whether artificial ground-mobile systems exhibit a consistent regularity of relation among mass, power, and speed, similar to that which exists for biological organisms. To this end, we investigate an empirical allometric formula proposed in the 1980s for estimating the mechanical power expended by an organism of a given mass to move at a given speed, applicable over several orders of magnitude of mass, for a broad range of species, to determine if a comparable regularity applies to a range of vehicles. We show empirically that not only does a similar regularity apply to a wide variety of mobile systems; moreover, the formula is essentially the same, describing organisms and systems ranging from a roach (1 g) to a battle tank (35,000 kg). We also show that for very heavy vehicles (35,000–100,000,000 kg), the formula takes a qualitatively different form. These findings point to a fundamental similarity between biological and artificial locomotion that transcends great differences in morphology, mechanisms, materials, and behaviors. To illustrate the utility of this allometric relation, we investigate the significant extent to which ground robotic systems exhibit a higher cost of transport than either organisms or conventional vehicles, and discuss ways to overcome inefficiencies.

Energetic cost of walking in fossil hominins

OBJECTIVE

Many biomechanical studies consistently show that a broader pelvis increases the reaction forces and bending moments across the femoral shaft, increasing the energetic costs of unloaded locomotion. However, a biomechanical model does not provide the real amount of metabolic energy expended in walking. The aim of this study is to test the influence of pelvis breadth on locomotion cost and to evaluate the locomotion efficiency of extinct Pleistocene hominins.

MATERIAL AND METHODS

The current study measures in vivo the influence of pelvis width on the caloric cost of locomotion, integrating anthropometry, body composition and indirect calorimetry protocols in a sample of 46 subjects of both sexes.

RESULTS

We show that a broader false pelvis is substantially more efficient for locomotion than a narrower one and that the influence of false pelvis width on the energetic cost is similar to the influence of leg length. Two models integrating body mass, femur length and bi-iliac breadth are used to estimate the net and gross energetic costs of locomotion in a number of extinct hominins. The results presented here show that the locomotion of Homo was not energetically more efficient than that of Australopithecus and that the locomotion of extinct Homo species was not less efficient than that of modern Homo sapiens.

DISCUSSION

The changes in the anatomy of the pelvis and lower limb observed with the appearance of Homo ergaster probably did not fully offset the increased expenditure resulting from a larger body mass. Moreover, the narrow pelvis in modern humans does not contribute to greater efficiency of locomotion.

Effect of Nonspecific Chronic Low Back Pain on Walking Economy: An Observational Study

The authors investigated the effects of chronic low back pain (LBP) and walking speed (WS) on metabolic power and cost of transport (CT). Subjects with chronic nonspecific LBP (LBP group [LG]; n = 9) and healthy (control group [CG]; n = 9) were included. The test battery was divided into 3 blocks according to WS as follows: preferred self-selected speed (PS), and lower and higher than the PS. In each block, the volunteers walked 5 min, during which oxygen consumption was measured. Although without differences between groups, the LG had CT lower in slower speeds than in faster speeds. Walking speed affected CT only in the LG, which the group had the greatest walking economy at slower speeds.

Prediction equations of energy expenditure in Chinese youth based on step frequency during walking and running

PURPOSE

This study set out to examine the relationship between step frequency and velocity to develop a step frequency-based equation to predict Chinese youth's energy expenditure (EE) during walking and running.

METHOD

A total of 173 boys and girls aged 11 to 18 years old participated in this study. The participants walked and ran on a treadmill at speeds of 3 km/hr, 4 km/hr, 5 km/hr, 6 km/hr, 7 km/hr, and 8 km/hr. EE was measured using indirect calorimetry of open circuit spirometry (Cosmed K4b2 metabolic analyzer). Using multiple regression analysis, the relationship between step frequency and velocity was first examined, and the prediction equation of EE based on step frequency, age, and gender was derived.

RESULTS

The hypothesized relationship between step frequency and velocity was confirmed and an accurate (R2 = .78) EE prediction equation was derived: NetEE = - 13.7744 + 1.8004 (step frequency) - 5.5715 (age) - 11.5244 (gender).

CONCLUSION

A step frequency-, age-, and gender-based equation was derived to predict the EE of youth during walking and running. The equation can be used to develop a simple device to estimate EE during walking and running in this population.

Validation of physical activity monitors in individuals with diabetes: energy expenditure estimation by the multisensor SenseWear Armband Pro3 and the step counter Omron HJ-720 against indirect calorimetry during walking

BACKGROUND

The purpose of this study is to test the agreement between energy expenditure estimate of the SenseWear(®) Armband Pro3 (SWA) (BodyMedia, Pittsburgh, PA) and the Omron HJ-720 (Omron Healthcare, Kyoto, Japan) step counter with indirect calorimetry (IC) as a gold standard in older individuals with type 1 and type 2 diabetes mellitus while walking on a treadmill.

SUBJECTS AND METHODS

In total, six men (60.3±3.1 years old) and 13 women (51.1±11.0 years old) with type 1 or type 2 diabetes mellitus were included in the study. Each subject performed three 15-min walking sessions with different combinations of speed and incline (3 km/h, 0%; 4 km/h, 0%; 5 km/h, 5%) on a treadmill. Energy expenditure (EE) was simultaneously measured by the SWA, Omron, and IC. Mean over-/underestimation and Pearson's correlation coefficients were used for statistical evaluation of the agreement between tested methods and IC.

RESULTS

At the speed of 3 km/h with 0% incline, mean overestimation of +81.19±23.81% was found for SWA (r=0.79, P<0.001) and +70.51±20.91% for Omron (r=0.77, P<0.001). At the speed of 4 km/h and 0% incline, mean overestimation found for SWA was +78.18±33.96% (r=0.63, P<0.01) and +75.77±33.36% for Omron (r=0.52, P<0.05). At the level of high-intensity exercise at the speed of 5 km/h and 5% incline, mean underestimation was -7.88±16.86% for SWA (r=0.74, P<0.001) and -7.37±16.07% for Omron (r=0.75, P<0.001).

CONCLUSIONS

Both methods led to considerable overestimation of calculated EE in level walking and a relatively minor underestimation during fast uphill walking.

Humans, geometric similarity and the Froude number: is ''reasonably close'' really close enough?

Understanding locomotor energetics is imperative, because energy expended during locomotion, a requisite feature of primate subsistence, is lost to reproduction. Although metabolic energy expenditure can only be measured in extant species, using the equations of motion to calculate mechanical energy expenditure offers unlimited opportunities to explore energy expenditure, particularly in extinct species on which empirical experimentation is impossible. Variability, either within or between groups, can manifest as changes in size and/or shape. Isometric scaling (or geometric similarity) requires that all dimensions change equally among all individuals, a condition that will not be met in naturally developing populations. The Froude number (Fr), with lower limb (or hindlimb) length as the characteristic length, has been used to compensate for differences in size, but does not account for differences in shape.To determine whether or not shape matters at the intraspecific level, we used a mechanical model that had properties that mimic human variation in shape. We varied crural index and limb segment circumferences (and consequently, mass and inertial parameters) among nine populations that included 19 individuals that were of different size. Our goal in the current work is to understand whether shape variation changes mechanical energy sufficiently enough to make shape a critical factor in mechanical and metabolic energy assessments.Our results reaffirm that size does not affect mass-specific mechanical cost of transport (Alexander and Jayes, 1983) among geometrically similar individuals walking at equal Fr. The known shape differences among modern humans, however, produce sufficiently large differences in internal and external work to account for much of the observed variation in metabolic energy expenditure, if mechanical energy is correlated with metabolic energy. Any species or other group that exhibits shape differences should be affected similarly to that which we establish for humans. Unfortunately, we currently do not have a simple method to control or adjust for size-shape differences in individuals that are not geometrically similar, although musculoskeletal modeling is a viable, and promising, alternative. In mouse-to-elephant comparisons, size differences could represent the largest source of morphological variation, and isometric scaling factors such as Fr can compensate for much of the variability. Within species, however, shape differences may dominate morphological variation and Fr is not designed to compensate for shape differences. In other words, those shape differences that are "reasonably close" at the mouse-to-elephant level may become grossly different for within-species energetic comparisons.