Muscle mechanical work requirements during normal walking: the energetic cost of raising the body's center-of-mass is significant

Inverted pendulum models of walking predict that little muscle work is required for the exchange of body potential and kinetic energy in single-limb support. External power during walking (product of the measured ground reaction force and body center-of-mass (COM) velocity) is often analyzed to deduce net work output or mechanical energetic cost by muscles. Based on external power analyses and inverted pendulum theory, it has been suggested that a primary mechanical energetic cost may be associated with the mechanical work required to redirect the COM motion at the step-to-step transition. However, these models do not capture the multi-muscle, multi-segmental properties of walking, co-excitation of muscles to coordinate segmental energetic flow, and simultaneous production of positive and negative muscle work. In this study, a muscle-actuated forward dynamic simulation of walking was used to assess whether: (1). potential and kinetic energy of the body are exchanged with little muscle work; (2). external mechanical power can estimate the mechanical energetic cost for muscles; and (3.) the net work output and the mechanical energetic cost for muscles occurs mostly in double support. We found that the net work output by muscles cannot be estimated from external power and was the highest when the COM moved upward in early single-limb support even though kinetic and potential energy were exchanged, and muscle mechanical (and most likely metabolic) energetic cost is dominated not only by the need to redirect the COM in double support but also by the need to raise the COM in single support.     

Energetics of walking and running: insights from simulated reduced-gravity experiments.

On Earth, a person uses about one-half as much energy to walk a mile as to run a mile. On another planet with lower gravity, would walking still be more economical than running? When people carry weights while they walk or run, energetic cost increases in proportion to the added load. It would seem to follow that if gravity were reduced, energetic cost would decrease in proportion to body weight in both gaits. However, we find that under simulated reduced gravity, the rate of energy consumption decreases in proportion to body weight during running but not during walking. When gravity is reduced by 75%, the rate of energy consumption is reduced by 72% during running but only by 33% during walking. Because reducing gravity decreases the energetic cost much more for running than for walking, walking is not the cheapest way to travel a mile at low levels of gravity. These results suggest that the link between the mechanics of locomotion and energetic cost is fundamentally different for walking and for running.     

Effects of obesity and sex on the energetic cost and preferred speed of walking.

The metabolic energy cost of walking is determined, to a large degree, by body mass, but it is not clear how body composition and mass distribution influence this cost. We tested the hypothesis that walking would be most expensive for obese women compared with obese men and normal-weight women and men. Furthermore, we hypothesized that for all groups, preferred walking speed would correspond to the speed that minimized the gross energy cost per distance. We measured body composition, maximal oxygen consumption, and preferred walking speed of 39 (19 class II obese, 20 normal weight) women and men. We also measured oxygen consumption and carbon dioxide production while the subjects walked on a level treadmill at six speeds (0.50-1.75 m/s). Both obesity and sex affected the net metabolic rate (W/kg) of walking. Net metabolic rates of obese subjects were only approximately 10% greater (per kg) than for normal-weight subjects, and net metabolic rates for women were approximately 10% greater than for men. The increase in net metabolic rate at faster walking speeds was greatest in obese women compared with the other groups. Preferred walking speed was not different across groups (1.42 m/s) and was near the speed that minimized gross energy cost per distance. Surprisingly, mass distribution (thigh mass/body mass) was not related to net metabolic rate, but body composition (% fat) was (r2= 0.43). Detailed biomechanical studies of walking are needed to investigate whether obese individuals adopt novel energy saving mechanisms during walking.     

Minimizing center of mass vertical movement increases metabolic cost in walking.

A human walker vaults up and over each stance limb like an inverted pendulum. This similarity suggests that the vertical motion of a walker's center of mass reduces metabolic cost by providing a mechanism for pendulum-like mechanical energy exchange. Alternatively, some researchers have hypothesized that minimizing vertical movements of the center of mass during walking minimizes the metabolic cost, and this view remains prevalent in clinical gait analysis. We examined the relationship between vertical movement and metabolic cost by having human subjects walk normally and with minimal center of mass vertical movement ("flat-trajectory walking"). In flat-trajectory walking, subjects reduced center of mass vertical displacement by an average of 69% (P = 0.0001) but consumed approximately twice as much metabolic energy over a range of speeds (0.7-1.8 m/s) (P = 0.0001). In flat-trajectory walking, passive pendulum-like mechanical energy exchange provided only a small portion of the energy required to accelerate the center of mass because gravitational potential energy fluctuated minimally. Thus, despite the smaller vertical movements in flat-trajectory walking, the net external mechanical work needed to move the center of mass was similar in both types of walking (P = 0.73). Subjects walked with more flexed stance limbs in flat-trajectory walking (P < 0.001), and the resultant increase in stance limb force generation likely helped cause the doubling in metabolic cost compared with normal walking. Regardless of the cause, these findings clearly demonstrate that human walkers consume substantially more metabolic energy when they minimize vertical motion.     

Modulation of leg muscle function in response to altered demand for body support and forward propulsion during walking

A number of studies have examined the functional roles of individual muscles during normal walking, but few studies have examined which are the primary muscles that respond to changes in external mechanical demand. Here we use a novel combination of experimental perturbations and forward dynamics simulations to determine how muscle mechanical output and contributions to body support and forward propulsion are modulated in response to independent manipulations of body weight and body mass during walking. Experimentally altered weight and/or mass were produced by combinations of added trunk loads and body weight support. Simulations of the same experimental conditions were used to determine muscle contributions to the vertical ground reaction force impulse (body support) and positive horizontal trunk work (forward propulsion). Contributions to the vertical impulse by the soleus, vastii and gluteus maximus increased (decreased) in response to increases (decreases) in body weight; whereas only the soleus increased horizontal work output in response to increased body mass. In addition, soleus had the greatest absolute contribution to both vertical impulse and horizontal trunk work, indicating that it not only provides the largest contribution to both body support and forward propulsion, but the soleus is also the primary mechanism to modulate the mechanical output of the leg in response to increased (decreased) need for body support and forward propulsion. The data also showed that a muscle's contribution to a specific task is likely not independent of its contribution to other tasks (e.g., body support vs. forward propulsion).     

Energy cost and muscular activity required for leg swing during walking.

To investigate the metabolic cost and muscular actions required for the initiation and propagation of leg swing, we applied a novel combination of external forces to subjects walking on a treadmill. We applied a forward pulling force at each foot to assist leg swing, a constant forward pulling force at the waist to provide center of mass propulsion, and a combination of these foot and waist forces to evaluate leg swing. When the metabolic cost and muscle actions were at a minimum, the condition was considered optimal. We reasoned that the difference in energy consumption between the optimal combined waist and foot force trial and the optimal waist force-only trial would reflect the metabolic cost of initiating and propagating leg swing during normal walking. We also reasoned that a lower muscle activity with these assisting forces would indicate which muscles are normally responsible for initiating and propagating leg swing. With a propulsive force at the waist of 10% body weight (BW), the net metabolic cost of walking decreased to 58% of normal walking. With the optimal combination, a propulsive force at the waist of 10% BW plus a pulling force at the feet of 3% BW the net metabolic cost of walking further decreased to 48% of normal walking. With the same combination, the muscle activity of the iliopsoas and rectus femoris muscles during the swing phase was 27 and 60% lower, respectively, but the activity of the medial gastrocnemius and soleus before swing did not change. Thus our data indicate that approximately 10% of the net metabolic cost of walking is required to initiate and propagate leg swing. Additionally, the hip flexor muscles contribute to the initiation and propagation leg swing.     

Metabolic cost of generating muscular force in human walking: insights from load-carrying and speed experiments.

We sought to understand how leg muscle function determines the metabolic cost of walking. We first indirectly assessed the metabolic cost of swinging the legs and then examined the cost of generating muscular force during the stance phase. Four men and four women walked at 0.5, 1.0, 1.5, and 2.0 m/s carrying loads equal to 0, 10, 20, and 30% body mass positioned symmetrically about the waist. The net metabolic rate increased in nearly direct proportion to the external mechanical power during moderate-speed (0.5-1.5 m/s) load carrying, suggesting that the cost of swinging the legs is relatively small. The active muscle volume required to generate force on the ground and the rate of generating this force accounted for >85% of the increase in net metabolic rate across moderate speeds and most loading conditions. Although these factors explained less of the increase in metabolic rate between 1.5 and 2.0 m/s ( approximately 50%), the cost of generating force per unit volume of active muscle [i.e., the cost coefficient (k)] was similar across all conditions [k = 0.11 +/- 0.03 (SD) J/cm3]. These data indicate that, regardless of the work muscles do, the metabolic cost of walking can be largely explained by the cost of generating muscular force during the stance phase.     

Individual limb work does not explain the greater metabolic cost of walking in elderly adults.

Elderly adults consume more metabolic energy during walking than young adults. Our study tested the hypothesis that elderly adults consume more metabolic energy during walking than young adults because they perform more individual limb work on the center of mass. Thus we compared how much individual limb work young and elderly adults performed on the center of mass during walking. We measured metabolic rate and ground reaction force while 10 elderly and 10 young subjects walked at 5 speeds between 0.7 and 1.8 m/s. Compared with young subjects, elderly subjects consumed an average of 20% more metabolic energy (P=0.010), whereas they performed an average of 10% less individual limb work during walking over the range of speeds (P=0.028). During the single-support phase, elderly and young subjects both conserved approximately 80% of the center of mass mechanical energy by inverted pendulum energy exchange and performed a similar amount of individual limb work (P=0.473). However, during double support, elderly subjects performed an average of 17% less individual limb work than young subjects (P=0.007) because their forward speed fluctuated less (P=0.006). We conclude that the greater metabolic cost of walking in elderly adults cannot be explained by a difference in individual limb work. Future studies should examine whether a greater metabolic cost of stabilization, reduced muscle efficiency, greater antagonist cocontraction, and/or a greater cost of generating muscle force cause the elevated metabolic cost of walking in elderly adults.     

Energy cost and muscular activity required for propulsion during walking.

We reasoned that with an optimal aiding horizontal force, the reduction in metabolic rate would reflect the cost of generating propulsive forces during normal walking. Furthermore, the reductions in ankle extensor electromyographic (EMG) activity would indicate the propulsive muscle actions. We applied horizontal forces at the waist, ranging from 15% body weight aiding to 15% body weight impeding, while subjects walked at 1.25 m/s. With an aiding horizontal force of 10% body weight, 1) the net metabolic cost of walking decreased to a minimum of 53% of normal walking, 2) the mean EMG of the medial gastrocnemius (MG) during the propulsive phase decreased to 59% of the normal walking magnitude, and yet 3) the mean EMG of the soleus (Sol) did not decrease significantly. Our data indicate that generating horizontal propulsive forces constitutes nearly half of the metabolic cost of normal walking. Additionally, it appears that the MG plays an important role in forward propulsion, whereas the Sol does not.     

Obesity does not increase external mechanical work per kilogram body mass during walking

Walking is the most common type of physical activity prescribed for the treatment of obesity. The net metabolic rate during level walking (W/kg) is ~10% greater in obese vs. normal weight adults. External mechanical work (W_ext) is one of the primary determinants of the metabolic cost of walking, but the effects of obesity on W_ext have not been clearly established. The purpose of this study was to compare W_ext between obese and normal weight adults across a range of walking speeds. We hypothesized that W_ext (J/step) would be greater in obese adults but W_ext normalized to body mass would be similar in obese and normal weight adults. We collected right leg three-dimensional ground reaction forces (GRF) while twenty adults (10 obese, BMI=35.6 kg/m² and 10 normal weight, BMI=22.1 kg/m²) walked on a level, dual-belt force measuring treadmill at six speeds (0.50–1.75 m/s). We used the individual limb method (ILM) to calculate external work done on the center of mass. Absolute W_ext (J/step) was greater in obese vs. normal weight adults at each walking speed, but relative W_ext (J/step/kg) was similar between the groups. Step frequencies were not different. These results suggest that W_ext is not responsible for the greater metabolic cost of walking (W/kg) in moderately obese adults.     

Effects of aging and arm swing on the metabolic cost of stability in human walking

To gain insight into the mechanical determinants of walking energetics, we investigated the effects of aging and arm swing on the metabolic cost of stabilization. We tested two hypotheses: (1) elderly adults consume more metabolic energy during walking than young adults because they consume more metabolic energy for lateral stabilization, and (2) arm swing reduces the metabolic cost of stabilization during walking in young and elderly adults. To test these hypotheses, we provided external lateral stabilization by applying bilateral forces (10% body weight) to a waist belt via elastic cords while young and elderly subjects walked at 1.3m/s on a motorized treadmill with arm swing and with no arm swing. We found that the external stabilizer reduced the net rate of metabolic energy consumption to a similar extent in elderly and young subjects. This reduction was greater (6-7%) when subjects walked with no arm swing than when they walked normally (3-4%). When young or elderly subjects eliminated arm swing while walking with no external stabilization, net metabolic power increased by 5-6%. We conclude that the greater metabolic cost of walking in elderly adults is not caused by a greater cost of lateral stabilization. Moreover, arm swing reduces the metabolic cost of walking in both young and elderly adults likely by contributing to stability.     

Independent effects of weight and mass on plantar flexor activity during walking: implications for their contributions to body support and forward propulsion.

The ankle plantar flexor muscles, gastrocnemius (Gas) and soleus (Sol), have been shown to play important roles in providing body support and forward propulsion during human walking. However, there has been disagreement about the relative contributions of Gas and Sol to these functional tasks. In this study, using independent manipulations of body weight and body mass, we examined the relative contribution of the individual plantar flexors to support and propulsion. We hypothesized that Gas and Sol contribute to body support, whereas Sol is the primary contributor to forward trunk propulsion. We tested this hypothesis by measuring muscle activity while experimentally manipulating body weight and mass by 1) decreasing body weight using a weight support system, 2) increasing body mass alone using a combination of equal added trunk load and weight support, and 3) increasing trunk loads (increasing body weight and mass). The rationale for this study was that muscles that provide body support would be sensitive to changes in body weight, whereas muscles that provide forward propulsion would be sensitive to changes in body mass. Gas activity increased with added loads and decreased with weight support but showed only a small increase relative to control trials when mass alone was increased. Sol activity showed a similar increase with added loads and with added mass alone and decreased in early stance with weight support. Therefore, we accepted the hypothesis that Sol and Gas contribute to body support, whereas Sol is the primary contributor to forward trunk propulsion.     

Contributions of muscles to mediolateral ground reaction force over a range of walking speeds

Impaired control of mediolateral body motion during walking is an important health concern. Developing treatments to improve mediolateral control is challenging, partly because the mechanisms by which muscles modulate mediolateral ground reaction force (and thereby modulate mediolateral acceleration of the body mass center) during unimpaired walking are poorly understood. To investigate this, we examined mediolateral ground reaction forces in eight unimpaired subjects walking at four speeds and determined the contributions of muscles, gravity, and velocity-related forces to the mediolateral ground reaction force by analyzing muscle-driven simulations of these subjects. During early stance (0-6% gait cycle), peak ground reaction force on the leading foot was directed laterally and increased significantly (p<0.05) with walking speed. During early single support (14-30% gait cycle), peak ground reaction force on the stance foot was directed medially and increased significantly (p<0.01) with speed. Muscles accounted for more than 92% of the mediolateral ground reaction force over all walking speeds, whereas gravity and velocity-related forces made relatively small contributions. Muscles coordinate mediolateral acceleration via an interplay between the medial ground reaction force contributed by the abductors and the lateral ground reaction forces contributed by the knee extensors, plantarflexors, and adductors. Our findings show how muscles that contribute to forward progression and body-weight support also modulate mediolateral acceleration of the body mass center while weight is transferred from one leg to another during double support.     

Men and women adopt similar walking mechanics and muscle activation patterns during load carriage

Although numerous studies have investigated the effects of load carriage on gait mechanics, most have been conducted on active military men. It remains unknown whether men and women adapt differently to carrying load. The purpose of this study was to compare the effects of load carriage on gait mechanics, muscle activation patterns, and metabolic cost between men and women walking at their preferred, unloaded walking speed. We measured whole body motion, ground reaction forces, muscle activity, and metabolic cost from 17 men and 12 women. Subjects completed four walking trials on an instrumented treadmill, each five minutes in duration, while carrying no load or an additional 10%, 20%, or 30% of body weight. Women were shorter (p<0.01), had lower body mass (p=0.01), and had lower fat-free mass (p=0.02) compared to men. No significant differences between men and women were observed for any measured gait parameter or muscle activation pattern. As load increased, so did net metabolic cost, the duration of stance phase, peak stance phase hip, knee, and ankle flexion angles, and all peak joint extension moments. The increase in the peak vertical ground reaction force was less than the carried load (e.g. ground force increased approximately 6% with each 10% increase in load). Integrated muscle activity of the soleus, medial gastrocnemius, lateral hamstrings, vastus medialis, vastus lateralis, and rectus femoris increased with load. We conclude that, despite differences in anthropometry, men and women adopt similar gait adaptations when carrying load, adjusted as a percentage of body weight.     

Metabolic energy and muscular activity required for leg swing in running.

The metabolic cost of leg swing in running is highly controversial. We investigated the cost of initiating and propagating leg swing at a moderate running speed and some of the muscular actions involved. We constructed an external swing assist (ESA) device that applied small anterior pulling forces to each foot during the first part of the swing phase. Subjects ran on a treadmill at 3.0 m/s normally and with ESA forces up to 4% body weight. With the greatest ESA force, net metabolic rate was 20.5% less than during normal running. Thus we infer that the metabolic cost of initiating and propagating leg swing comprises approximately 20% of the net cost of normal running. Even with the greatest ESA, mean electromyograph (mEMG) of the medial gastrocnemius and soleus muscles during later portions of stance phase did not change significantly compared with normal running, indicating that these muscles are not responsible for the initiation of leg swing. However, with ESA, rectus femoris mEMG during the early portions of swing phase was as much as 74% less than during normal running, confirming that it is responsible for the propagation of leg swing.     

Feeding and metabolic compensations in response to different foraging costs

How energetic cost of locomotion affects foraging decisions, and its metabolic consequences are poorly understood. In several groups of animals, including hermit crabs, exploratory walking enhances the efficiency of foraging by increasing the probability of finding more and better food items; however, the net gain of energy will only be enhanced if the costs of walking are lower than the benefits of enhanced food acquisition. In hermit crabs, the cost of walking increases with the mass of the shell type occupied. Thus, we expected that hermit crabs should adjust their foraging strategy to the cost of movement in different shells. We assessed the foraging, the quantity and quality of food intake, and the energetic cost of maintenance of hermit crabs paying different costs of foraging in the wild. The exploratory walking negatively correlated with shell mass, showing that hermit crabs use different foraging strategies in response to the expenditure required to move. Hermit crabs deal with high energetic costs of foraging in heavy shells by reduces their exploratory walking and overall metabolic rate, as a strategy to maximize the net energy intake. This study integrates behavioral and metabolic compensations as a response to foraging at different costs in natural conditions.     

Effects of hip torque during step-to-step transition on center-of-mass dynamics during human walking examined with numerical simulation

Besides the leg force actuator, humans also use a hip torque actuator during the step-to-step transition to redirect the velocity of CoM (Center of Mass). Although the leg force actuator has been widely studied, few researches analyze the hip torque actuator during the step-to-step transition. In this paper, we build a powered walking model which consists of a point mass linked with two compliant legs. Each leg has a spring and a damper in parallel. Two types of active actuators, the force actuator on the leg and the torque actuator at the hip, are added to simulate the leg force and hip torque actuator during the step-to-step transition. The cycle walk is solved by numerical simulations under different hip torque strength, and the energetics and stability are evaluated. The simulation results show that the hip torque actuator can reduce the energy cost and improve the stability of walking. Further analysis shows that the hip torque actuator can reduce mechanical works of both legs with small extra energy cost. To understand the principle of hip torque actuator, the CoM dynamics is analyzed. It is shown that the hip torque actuator is efficient on the redirection of CoM. Thus, it can improve the stability and reduce required forces of both legs, which decreases the energy cost. Our work provides a fundamental understanding of the hip torque during the step-to-step transition, and may help improve the design of bipedal robots and prosthesis.     

Walking in simulated reduced gravity: mechanical energy fluctuations and exchange

Walking humansconserve mechanical and, presumably, metabolic energy with an invertedpendulum-like exchange of gravitational potential energy and horizontalkinetic energy. Walking in simulated reduced gravity involves arelatively high metabolic cost, suggesting that the inverted-pendulummechanism is disrupted because of a mismatch of potential and kineticenergy. We tested this hypothesis by measuring the fluctuations andexchange of mechanical energy of the center of mass at differentcombinations of velocity and simulated reduced gravity. Subjects walkedwith smaller fluctuations in horizontal velocity in lower gravity, suchthat the ratio of horizontal kinetic to gravitational potential energyfluctuations remained constant over a fourfold change in gravity. Theamount of exchange, or percent recovery, at 1.00 m/s was notsignificantly different at 1.00, 0.75, and 0.50 G (average 64.4%),although it decreased to 48% at 0.25 G. As a result, the amount ofwork performed on the center of mass does not explain the relatively high metabolic cost of walking in simulated reduced gravity.

     

Biology of size and gravity]

Gravity is a force that acts on mass. Biological effects of gravity and their magnitude depend on scale of mass and difference in density. One significant contribution of space biology is confirmation of direct action of gravity even at the cellular level. Since cell is the elementary unit of life, existence of primary effects of gravity on cells leads to establish the firm basis of gravitational biology. However, gravity is not limited to produce its biological effects on molecules and their reaction networks that compose living cells. Biological system has hierarchical structure with layers of organism, group, and ecological system, which emerge from the system one layer down. Influence of gravity is higher at larger mass. In addition to this, actions of gravity in each layer are caused by process and mechanism that is subjected and different in each layer of the hierarchy. Because of this feature, summing up gravitational action on cells does not explain gravity for biological system at upper layers. Gravity at ecological system or organismal level can not reduced to cellular mechanism. Size of cells and organisms is one of fundamental characters of them and a determinant in their design of form and function. Size closely relates to other physical quantities, such as mass, volume, and surface area. Gravity produces weight of mass. Organisms are required to equip components to support weight and to resist against force that arise at movement of body or a part of it. Volume and surface area associate with mass and heat transport process at body. Gravity dominates those processes by inducing natural convection around organisms. This review covers various elements and process, with which gravity make influence on living systems, chosen on the basis of biology of size. Cells and biochemical networks are under the control of organism to integrate a consolidated form. How cells adjust metabolic rate to meet to the size of the composed organism, whether is gravity responsible for this feature, are subject we discuss in this article. Three major topics in gravitational and space biology are; how living systems have been adapted to terrestrial gravity and evolved, how living systems respond to exotic gravitational environment, and whether living systems could respond and adapt to microgravity. Biology of size can contribute to find a way to answer these question, and answer why gravity is important in biology, at explaining why gravity has been a dominant factor through the evolutional history on the earth.     

Metabolic turnover rate: a physiological meaning of the metabolic rate per unit body weight.

In analogy to “specific gravity” or “specific heat” the expression “weight specific metabolic rate” (Ultsch, 1973) would be correct if the metabolic rate were directly proportional to body weight. In that case the quotient metabolic rate divided by body weight would be a constant, independent of body weight like density or specific heat are constants. The metabolic rate, however, is not proportional to body weight but to its $\text{3}\text{4}$ power. I have stated that heat flow per unit body weight has no proper physical or physiological meaning (Kleiber, 1970), but since found such a physiological meaning: in work with tracers turnover rates are measured as quotients of transfer rates/pool content. For similometric animals pool contents are proportional to body weight. For such animals therefore the quotient metabolic rate/body weight may have a proper physiological meaning, namely the turnover rate of chemical energy in the animal body.The usefulness of the turnover rate is limited. For the calculation of the energy requirement of horizontal animal locomotion, for example, the calculation from the metabolic rate per animal is preferable to the calculation based on the metabolic rate per unit body weight.