Metabolic Cost Of Transport Research Articles

Gait changes in a line of mice artificially selected for longer limbs.

In legged terrestrial locomotion, the duration of stance phase, i.e., when limbs are in contact with the substrate, is positively correlated with limb length, and negatively correlated with the metabolic cost of transport. These relationships are well documented at the interspecific level, across a broad range of body sizes and travel speeds. However, such relationships are harder to evaluate within species (i.e., where natural selection operates), largely for practical reasons, including low population variance in limb length, and the presence of confounding factors such as body mass, or training. Here, we compared spatiotemporal kinematics of gait in Longshanks, a long-legged mouse line created through artificial selection, and in random-bred, mass-matched Control mice raised under identical conditions. We used a gait treadmill to test the hypothesis that Longshanks have longer stance phases and stride lengths, and decreased stride frequencies in both fore- and hind limbs, compared with Controls. Our results indicate that gait differs significantly between the two groups. Specifically, and as hypothesized, stance duration and stride length are 8–10% greater in Longshanks, while stride frequency is 8% lower than in Controls. However, there was no difference in the touch-down timing and sequence of the paws between the two lines. Taken together, these data suggest that, for a given speed, Longshanks mice take significantly fewer, longer steps to cover the same distance or running time compared to Controls, with important implications for other measures of variation among individuals in whole-organism performance, such as the metabolic cost of transport.

Overground vs. treadmill walking on biomechanical energy harvesting: An energetics and EMG study

A biomechanical energy harvester is a wearable device that generates electricity from human motion. Walking on a treadmill has been used almost exclusively by researchers for studying the energetic effects of biomechanical energy harvesters and wearable robotics. A treadmill provides the advantage of having long duration trials within a stationary motion capture volume. However, no consensus exists on whether the results from treadmill walking accurately represent overground walking. We aim to investigate how a biomechanical energy harvester performs overground compared to on a treadmill by measuring energy expenditure and muscle activity. Participants (n=15) walked both overground and on a treadmill with and without a lower limb-driven biomechanical energy harvester. Energy expenditure was measured using indirect calorimetry and muscle activity was collected with surface electromyograms on seven superficial lower limb muscles. We observed a similar increase in metabolic cost of transport (Δoverground: 0.28±0.24J/kgm, Δtreadmill: 0.30±0.24J/kgm) from normal walking (overground: 2.56±0.33J/kgm, treadmill: 3.39±0.31J/kgm) to harvester walking (overground: 2.83±0.35J/kgm, treadmill: 3.69±0.32J/kgm) in both walking modes (p>0.05). This was accompanied a significant increase in muscle activity of select muscle groups (p<0.05). There was also a significant increase observed during walking on a treadmill compared to overground walking (p<0.05). In conclusion, our results suggest that although the metabolic cost of transport and muscle activation for treadmill walking is higher than that of overground, when studying the effects of a biomechanical energy harvester, treadmill will give similar net increases when compared to a controlled walking condition, such as normal walking, on the same walking surface.

Human Leg Model Predicts Muscle Forces, States, and Energetics during Walking.

Humans employ a high degree of redundancy in joint actuation, with different combinations of muscle and tendon action providing the same net joint torque. Both the resolution of these redundancies and the energetics of such systems depend on the dynamic properties of muscles and tendons, particularly their force-length relations. Current walking models that use stock parameters when simulating muscle-tendon dynamics tend to significantly overestimate metabolic consumption, perhaps because they do not adequately consider the role of elasticity. As an alternative, we posit that the muscle-tendon morphology of the human leg has evolved to maximize the metabolic efficiency of walking at self-selected speed. We use a data-driven approach to evaluate this hypothesis, utilizing kinematic, kinetic, electromyographic (EMG), and metabolic data taken from five participants walking at self-selected speed. The kinematic and kinetic data are used to estimate muscle-tendon lengths, muscle moment arms, and joint moments while the EMG data are used to estimate muscle activations. For each subject we perform an optimization using prescribed skeletal kinematics, varying the parameters that govern the force-length curve of each tendon as well as the strength and optimal fiber length of each muscle while seeking to simultaneously minimize metabolic cost and maximize agreement with the estimated joint moments. We find that the metabolic cost of transport (MCOT) values of our participants may be correctly matched (on average 0.36±0.02 predicted, 0.35±0.02 measured) with acceptable joint torque fidelity through application of a single constraint to the muscle metabolic budget. The associated optimal muscle-tendon parameter sets allow us to estimate the forces and states of individual muscles, resolving redundancies in joint actuation and lending insight into the potential roles and control objectives of the muscles of the leg throughout the gait cycle.

Joint contact forces when minimizing the external knee adduction moment by gait modification: A computer simulation study

Background and purposeGait modification is often used to reduce the external knee adduction moment (KAM) in human walking, but the relationship between KAM reduction and changes in medial knee joint contact force (JCF) is not well established. Our purpose was to examine the limiting case of KAM-based gait modification: reducing the KAM as much as possible, and the resulting effects on JCF. MethodsWe used musculoskeletal modeling to perform three optimal control simulations: normal walking, a modified gait that reduced the KAM as much as theoretically possible (Min(KAM) simulation), and a second modified gait that minimized the KAM plus the metabolic cost of transport (Min(KAM+CoT) simulation). ResultsThe two modified gaits both reduced the peak KAM from normal walking (−82% for Min(KAM) simulation, −74% for Min(KAM+CoT) simulation) by increasing trunk lean, toe-out, and step width, and reducing knee flexion. Even though the Min(KAM+CoT) simulation had the larger KAM, it had a greater reduction in peak medial JCF (−27%) than the Min(KAM) simulation (−15%) because it reduced the KAM using less knee muscle activity. These results were qualitatively robust to a sensitivity analysis of the knee joint model, but the magnitude of changes varied by an order of magnitude. ConclusionsThe results suggest that (i) gait modification can benefit from considering whole-body motion rather than single adjustments, (ii) accurate interpretation of KAM effects on medial JCF requires consideration of muscle forces, and (iii) subject-specific knee models are needed to accurately determine the magnitude of KAM reduction effects on JCF.

Metabolic cost of lateral stabilization during walking in people with incomplete spinal cord injury

People with incomplete spinal cord injury (iSCI) expend considerable energy to walk, which can lead to rapid fatigue and limit community ambulation. Selecting locomotor patterns that enhance lateral stability may contribute to this population's elevated cost of transport. The goal of the current study was to quantify the metabolic energy demands of maintaining lateral stability during gait in people with iSCI. To quantify this metabolic cost, we observed ten individuals with iSCI walking with and without external lateral stabilization. We hypothesized that with external lateral stabilization, people with iSCI would adapt their gait by decreasing step width, which would correspond with a substantial decrease in cost of transport. Our findings support this hypothesis. Subjects significantly (p<0.05) decreased step width by 22%, step width variability by 18%, and minimum lateral margin of stability by 25% when they walked with external lateral stabilization compared to unassisted walking. Metabolic cost of transport also decreased significantly (p<0.05) by 10% with external lateral stabilization. These findings suggest that this population is capable of adapting their gait to meet changing demands placed on balance. The percent reduction in cost of transport when walking with external lateral stabilization was strongly correlated with functional impairment level as assessed by subjects’ scores on the Berg Balance Scale (r=0.778) and lower extremity motor score (r=0.728). These relationships suggest that as functional balance and strength decrease, the amount of metabolic energy used to maintain lateral stability during gait will increase.

A Critical Characteristic in the Transverse Galloping Pattern.

Transverse gallop is a common gait used by a large number of quadrupeds. This paper employs the simplified dimensionless quadrupedal model to discuss the underlying mechanism of the transverse galloping pattern. The model is studied at different running speeds and different values of leg stiffness, respectively. If the horizontal running speed reaches up to a critical value at a fixed leg stiffness, or if the leg stiffness reaches up to a critical value at a fixed horizontal speed, a key property would emerge which greatly reduces the overall mechanical forces of the dynamic system in a proper range of initial pitch angular velocities. Besides, for each horizontal speed, there is an optimal stiffness of legs that can reduce both the mechanical loads and the metabolic cost of transport. Furthermore, different body proportions and landing distance lags of a pair of legs are studied in the transverse gallop. We find that quadrupeds with longer length of legs compared with the length of the body are more suitable to employ the transverse galloping pattern, and the landing distance lag of a pair of legs could reduce the cost of transport and the locomotion frequency.

Prophylactic Ankle Taping

Prophylactic ankle taping (PAT) is commonly used in sport. Prophylactic ankle taping may restrict ankle motion, which would affect the kinetic chain and alter gait. The purpose of this study was to examine the effects of PAT on lower extremity (LE) kinematics and running economy during treadmill running. Twelve recreational runners (9 women, 3 men; M ± SD age = 31.33 ± 8.04 years, height = 1.67 ± 0.81 m, mass = 61.84 ± 9.38 kg) completed two 20-minute running sessions (PAT and no tape: control [CON]) at a self-selected pace. Before each run, reflective markers were placed along the right side of the body. Sagittal plane kinematic data (60 Hz) were captured 4 times, and expired gases were measured for 2-minute after each video capture during both trials. Stride frequency, stride length, LE kinematic variables at initial contact and end contact (EC) were calculated. Cardiorespiratory variables and heart rate were also measured. Running economy was normalized to oxygen uptake per unit body mass per kilometer (milliliter per kilogram per kilometer) as running speeds varied. At EC, the PAT hip angle significantly decreased (p = 0.01) by 3.82°, whereas CON decreased by 0.85°. The range of motion tended to decrease over the 20-minute run (p = 0.08). Heart rate significantly increased over time (6.7%) but was not different between conditions. Prophylactic ankle taping did not significantly affect the physiological measures associated with the metabolic cost of treadmill running or the other kinematic variables. These findings suggest that the hip angle continued to decrease during the PAT condition at push-off in recreational runners without impacting the metabolic cost of transport.

Physiological vagility and its relationship to dispersal and neutral genetic heterogeneity in vertebrates

Vagility is the inherent power of movement by individuals. Vagility and the available duration of movement determine the dispersal distance individuals can move to interbreed, which affects the fine-scale genetic structure of vertebrate populations. Vagility and variation in population genetic structure are normally explained by geographic variation and not by the inherent power of movement by individuals. We present a new, quantitative definition for physiological vagility that incorporates aerobic capacity, body size, body temperature and the metabolic cost of transport, variables that are independent of the physical environment. Physiological vagility is the speed at which an animal can move sustainably based on these parameters. This meta-analysis tests whether this definition of physiological vagility correlates with empirical data for maximal dispersal distances and measured microsatellite genetic differentiation with distance {[F(ST)/[1-F(ST))]/ln distance} for amphibians, reptiles, birds and mammals utilizing three locomotor modes (running, flying, swimming). Maximal dispersal distance and physiological vagility increased with body mass for amphibians, reptiles and mammals utilizing terrestrial movement. The relative slopes of these relationships indicate that larger individuals require longer movement durations to achieve maximal dispersal distances. Both physiological vagility and maximal dispersal distance were independent of body mass for flying vertebrates. Genetic differentiation with distance was greatest for terrestrial locomotion, with amphibians showing the greatest mean and variance in differentiation. Flying birds, flying mammals and swimming marine mammals showed the least differentiation. Mean physiological vagility of different groups (class and locomotor mode) accounted for 98% of the mean variation in genetic differentiation with distance in each group. Genetic differentiation with distance was not related to body mass. The physiological capacity for movement (physiological vagility) quantitatively predicts genetic isolation by distance in the vertebrates examined.

The mechanical cost of transport of fast running animals

Regarding running animals, algebraic expressions for the horizontal (ωx) and vertical (ωy) components of the mechanical cost of transport are deduced for a ground force pattern based on the Spring–mass model. Defining μ˜ as the maximum ground forces ratio μ˜=max(Fx)/max(Fy), the analysis shows that the mechanical cost of transport ωx+ωy for fast running animals is approximately proportional to μ˜, and to the relative contact length, and positively correlated to the limb take-off angle and the collision angle. The vertical cost ωy is shown to approximate to zero for fast running animals. Sustained top running speeds are predicted to require the largest possible values of μ˜ and therefore relatively large horizontal propulsive forces, as well as a minimum possible ground contact time. The equations also show that animals running relatively slow would tend to prefer certain interval of values for parameter μ˜, which would minimize both their mechanical cost of transport and their metabolic cost of transport. Very large animals are suspected to be less capable of developing large values of μ˜, which possibly renders them incapable of developing great speeds.

Changes in Metabolic Cost of Transport Following Locomotor Training Poststroke

Background: The energy cost of transport is higher for persons with stroke compared with neurologically intact subjects, and this has a negative impact on ambulatory activity and function. Whether the high energy cost of walking after stroke is influenced by gait training interventions is generally not considered. Objective: To examine changes in the energy cost of transport with a gait training intervention after stroke and to identify whether energy cost changes independent of changes in walking speed. Methods: Persons with chronic (>6 months) stroke participated in an intervention combining fast walking and functional electrical stimulation of the ankle dorsi-and plantarflexor muscles. Oxygen consumption, walking speed, and endurance were measured pre and post training. Energy and caloric cost of transport were calculated at self-selected and absolute speeds at each time point. Results: Eleven subjects (age 61.8 ± 8 years) participated. Self-selected and fastest walking speed and 6-minute walk test distance improved after the intervention (F = 67.5, P < .001; F = 40.9, P < .001; F = 20.2, P = .001, respectively). Energy and caloric cost of transport at self-selected speed improved (F = 8.63, P = .015, and F = 7.87, P = .019, respectively) but did not change at an absolute speed pre-to postintervention. Conclusions: Energy and caloric cost of transport at self-selected walking speeds improved pre to post training but were unaffected at an absolute walking speed, suggesting that the improved energy cost of transport was through improvements in the subject’s self-selected walking speed. These results illustrate that improvements in walking speed following an intervention are an important mechanism by which the energy cost of transport can be reduced post stroke.

Factors affecting energy cost of running during an ultra-endurance race

The aim of this study was to investigate: (1) the role of , the fraction of (F) and the metabolic cost of transport (CoT) in determining performance during an ultra-endurance competition and (2) the effects of the race on several biomechanical and morphological parameters of the lower limbs that are likely to affect CoT. Eleven runners (aged 29-54 years) participated in an ultra-endurance competition consisting of three running stages of 25, 55 and 13 km on three consecutive days. Anthropometric characteristics, body composition, morphological properties of the gastrocnemius medialis, maximal explosive power of the lower limb and were determined before the competition. In addition, biomechanics of running and CoT were determined, before and immediately after each running stage. Performance was directly proportional to (r=0.77) and F (r=0.36), and inversely proportional to CoT (r=-0.30). Low CoT values were significantly related to high maximal power of the lower limbs (r=-0.74) and vertical stiffness (r=-0.65) and low footprint index (FPI, r=0.70), step frequency (r=0.62) and external work (r=0.60). About 50% of the increase in CoT during the stages of the competition was accounted for by changes in FPI, which represents a global evaluation of medio-lateral displacement of the foot during the whole stance phase, which in turn is associated with the myotendinous characteristics of the lower limb. Thus, lower CoT values were related to greater muscular power and lower FPI, suggesting that a better ankle stability is likely to achieve better performance in an ultra-endurance running competition.

The cost of transport of human running is not affected, as in walking, by wide acceleration/deceleration cycles

Although most of the literature on locomotion energetics and biomechanics is about constant-speed experiments, humans and animals tend to move at variable speeds in their daily life. This study addresses the following questions: 1) how much extra metabolic energy is associated with traveling a unit distance by adopting acceleration/deceleration cycles in walking and running, with respect to constant speed, and 2) how can biomechanics explain those metabolic findings. Ten males and ten females walked and ran at fluctuating speeds (5 ± 0, ± 1, ± 1.5, ± 2, ± 2.5 km/h for treadmill walking, 11 ± 0, ± 1, ± 2, ± 3, ± 4 km/h for treadmill and field running) in cycles lasting 6 s. Field experiments, consisting of subjects following a laser spot projected from a computer-controlled astronomic telescope, were necessary to check the noninertial bias of the oscillating-speed treadmill. Metabolic cost of transport was found to be almost constant at all speed oscillations for running and up to ±2 km/h for walking, with no remarkable differences between laboratory and field results. The substantial constancy of the metabolic cost is not explained by the predicted cost of pure acceleration/deceleration. As for walking, results from speed-oscillation running suggest that the inherent within-stride, elastic energy-free accelerations/decelerations when moving at constant speed work as a mechanical buffer for among-stride speed fluctuations, with no extra metabolic cost. Also, a recent theory about the analogy between sprint (level) running and constant-speed running on gradients, together with the mechanical determinants of gradient locomotion, helps to interpret the present findings.

The rising cost of warming waters: effects of temperature on the cost of swimming in fishes.

Understanding the effects of water temperature on the swimming performance of fishes is central in understanding how fish species will respond to global climate change. Metabolic cost of transport (COT)-a measure of the energy required to swim a given distance-is a key performance parameter linked to many aspects of fish life history. We develop a quantitative model to predict the effect of water temperature on COT. The model facilitates comparisons among species that differ in body size by incorporating the body mass-dependence of COT. Data from 22 fish species support the temperature and mass dependencies of COT predicted by our model, and demonstrate that modest differences in water temperature can result in substantial differences in the energetic cost of swimming.

The mechanics and energetics of human walking and running: a joint level perspective

Humans walk and run at a range of speeds. While steady locomotion at a given speed requires no net mechanical work, moving faster does demand both more positive and negative mechanical work per stride. Is this increased demand met by increasing power output at all lower limb joints or just some of them? Does running rely on different joints for power output than walking? How does this contribute to the metabolic cost of locomotion? This study examined the effects of walking and running speed on lower limb joint mechanics and metabolic cost of transport in humans. Kinematic and kinetic data for 10 participants were collected for a range of walking (0.75, 1.25, 1.75, 2.0 m s(-1)) and running (2.0, 2.25, 2.75, 3.25 m s(-1)) speeds. Net metabolic power was measured by indirect calorimetry. Within each gait, there was no difference in the proportion of power contributed by each joint (hip, knee, ankle) to total power across speeds. Changing from walking to running resulted in a significant (p = 0.02) shift in power production from the hip to the ankle which may explain the higher efficiency of running at speeds above 2.0 m s(-1) and shed light on a potential mechanism behind the walk-run transition.

Powered Ankle--Foot Prosthesis Improves Walking Metabolic Economy

At moderate to fast walking speeds, the human ankle provides net positive work at high-mechanical-power output to propel the body upward and forward during the stance period. On the contrary, conventional ankle-foot prostheses exhibit a passive-elastic response during stance, and consequently, cannot provide net work. Clinical studies indicate that transtibial amputees using conventional prostheses have higher gait metabolic rates than normal. Researchers believe that the main cause for these higher rates is due to the inability of conventional prostheses to provide sufficient positive power at terminal stance in the trailing leg to limit heel strike losses of the adjacent leading leg. In this investigation, we evaluate the hypothesis that a powered ankle-foot prosthesis, capable of providing human-like ankle work and power during stance, can decrease the metabolic cost of transport (COT) compared to a conventional passive-elastic prosthesis. To test the hypothesis, a powered prosthesis is built that comprises a unidirectional spring, configured in parallel with a force-controllable actuator with series elasticity. The prosthesis is shown to deliver the high mechanical power and net positive work observed in normal human walking. The rate of oxygen consumption and carbon dioxide production is measured as a determinant of metabolic rate on three unilateral transtibial amputees walking at self-selected speeds. We find that the powered prosthesis decreases the amputee's metabolic COT on average by 14% compared to the conventional passive-elastic prostheses evaluated (Flex-Foot Ceterusreg and Freedom Innovations Sierra), even though the powered system is over twofold heavier than the conventional devices. These results highlight the clinical importance of prosthetic interventions that closely mimic the mass distribution, kinetics, and kinematics of the missing limb.

Effect of augmented plantarflexion power on preferred walking speed and economy in young and older adults

With age, loss of skeletal muscle mass (sarcopenia) results in decreased muscle strength and power. Decreased strength and power, in turn, are closely linked with declines in physical function. Preferred walking speed, a marker of physical function, is slower in older adults compared to young adults. Research suggests that older adults may walk slower as a consequence of decreased plantarflexor power at push-off. In this study, we hypothesized that providing additional plantarflexion (PF) power during push-off would (1) increase preferred walking speed, and (2) reduce metabolic cost of transport (MCOT), in young and older adults. PF power was augmented using powered ankle-foot orthoses (PAFOs). The PAFOs, which use pneumatic actuators to provide an additional PF moment, were based on a design by Ferris et al. [Ferris DP, Czerniecki JM, Hannaford B. An ankle-foot orthosis powered by artificial pneumatic muscles. J Appl Biomech 2005;21:189–97.]. Nine young (23.3 ± 1.6 years) and seven older (74.6 ± 6.6 years) adults participated. For the young adults, eight out of nine increased their preferred walking speed when push-off power was augmented (1.18 ± 0.16 to 1.25 ± 0.16 m/s, p = 0.03). A similar, but non-significant, trend in preferred walking speed was observed for the older adults. With augmented push-off power, MCOT for young adults decreased from 0.395 ± 0.057 to 0.343 ± 0.047 ( p = 0.008); indicating that the neuromuscular system was able to adapt to use external energy to reduce metabolic cost. Only three older adults were tested but MCOT values showed a similar trend. Augmenting PF power increases gait speed and reduces MCOT in young adults. Older adults may need a longer period to take advantage of additional push-off power.

Models and the scaling of energy costs for locomotion

To achieve the required generality, models designed to predict scaling relationships for diverse groups of animals generally need to be simple. An argument based on considerations of dynamic similarity predicts correctly that the mechanical cost of transport for running [power/(body mass x speed)] will be independent of body mass; but measurements of oxygen consumption for running birds and mammals show that the metabolic cost of transport is proportional to (body mass)-0.32. Thus the leg muscles seem to work more efficiently in larger animals. A model that treats birds as fixed wing aircraft predicts that the mechanical power required for flight at the maximum range speed will be proportional to (body mass)1.02, but the metabolic power is found to be proportional to (body mass)0.83; again, larger animals seem to have more efficient muscles. A model that treats hovering hummingbirds and insects as helicopters predicts mechanical power to be approximately proportional to body mass, but measurements of oxygen consumption once again show efficiency increasing with body mass. A model of swimming fish as rigid submarines predicts power to be proportional to (body mass)0.5 x (speed)2.5 or to (body mass)0.6 x (speed)2.8, depending on whether flow in the boundary layer is laminar or turbulent. Unfortunately, this prediction cannot easily be compared with available compilations of metabolic data. The finding that efficiency seems to increase with body mass, at least in running and flight, is discussed in relation to the metabolic energy costs of muscular work and force.

A model of scale effects in mammalian quadrupedal running.

Although the effects of body size on mammalian locomotion are well documented, the underlying mechanisms are not fully understood. Here, we present a computational model of the mechanics, control and energetics that unifies some well-known scale effects in running quadrupeds. The model consists of dynamic, physics-based simulations of six running mammals ranging in size from a chipmunk to a horse (0.115-676 kg). The 'virtual animals' are made up of rigid segments (head, trunk and four legs) linked by joints and are similar in morphology to particular species. In the model, each stance limb acts as a spring operating within a narrow range of stiffness, forward motion is powered and controlled by active hip and shoulder torques, and metabolic cost is predicted from the time course of supporting body weight. Model parameters that are important for stability (joint stiffnesses, limb-retraction times and target positions and velocities of the limbs) are selected such that (i) running kinematics (aerial height, forward speed and body pitch) is smooth and periodic and (ii) overall leg stiffness is in agreement with published data. Both trotting and galloping gaits are modeled, and comparisons across size are made at speeds that are physiologically similar among species. Model predictions are in agreement with data on vertical stiffness, limb angles, metabolic cost of transport, stride frequency, peak force and duty factor. This work supports the idea that a single, integrative model can predict important features of running across size by employing simple strategies to control overall leg stiffness. More broadly, the model provides a quantitative framework for testing hypotheses that relate limb control, stability and metabolic cost.

Multiple Walking Speed–frequency Relations are Predicted by Constrained Optimization

A person constrained to walk at a given speed v on a treadmill, chooses a particular step frequency f and step length d=v/f. Testing over a range of speeds generates a speed–frequency (v–f) relationship. This relationship is commonly posited as a basic feature of human gait. It is often further posited that this curve follows from minimum energy cost strategy. We observed that individuals walking under different constraint circumstances—walking to a range of fixed metronome frequencies (fixed f) or over a range of spaced markers (fixed d)—produce speed–frequency relations distinct from the constrained v relation. We show here that three distinct speed–frequency curves, similar to those observed, are predicted by the assumption that a walking person optimizes an underlying objective function F (v, f) that has a minimum at the preferred gait. Further, the metabolic cost of transport is a reasonable approximate candidate for the function F.

Legged insects select the optimal locomotor pattern based on the energetic cost.

The gait transition in legged animals has attracted many researchers, and its relation to metabolic cost and mechanical work has been discussed in recent decades. We assumed that the energetic cost during locomotion is given by the sum of positive mechanical work and the heat energy loss that is proportional to the square of joint torque and examined the optimal locomotor pattern based on the energetic cost in a simple dynamical model of a hexapod by computer simulations. The obtained results well agree with characteristics in the locomotor patterns in legged animals; for example, the leg protraction time, step length, and the metabolic cost of transport are almost constant for many velocities, the leg cycling period decreases with velocity, and the energetic cost of locomotion induced by carrying loads linearly increases with mass loaded. This correspondence of the results of calculation to experimental results suggest that the heat energy loss for torque generation is proportional to the square of the torque during locomotion, and that the locomotor pattern in legged animals is highly optimized based on the energetic cost.