An energy 'sources' and 'fractions' approach to the mechanical energy expenditure problem--V. The mechanical energy expenditure reduction during motion of the multi-link system

Mechanical energy economy during motion of the multi-link system is analyzed on the basis of the theory developed in the previous publications (parts I-IV of this series, J. Biomechanics 19, 287-309). The compensation coefficients for the F- and M-sources and also the absolute compensation coefficient reflecting the mechanical energy economy due to four possible resources are introduced. These resources are the antiphase fluctuations of (I) each link's total energy fractions involving energy transformations between (1) rotational and translational fractions by F-sources, (2) kinetic and potential fractions by mg-source; (II) the links' total energies involving energy transfers between (3) links by F-sources, (4) links by M-sources. The conditions of mechanical energy economy, particularly due to M-sources, are analyzed.     

An energy 'sources' and 'fractions' approach to the mechanical energy expenditure problem--IV. Criticism of the concept of 'energy transfers within and between links'

The methods of evaluation of mechanical energy economy during human movement based on the calculation of three different values of work (Wwb, Ww, Wn), corresponding to three hypothetical types of energy exchange, are subject to criticism. Only the value of work, Wwb, calculated under the assumption of energy transfers between links and energy transformations within links, can be useful as the lowest limit of mechanical energy expenditure (MEE) for the control (for the cases when the powers of the external sources are equal to zero). In the particular case when all of the joint powers Mi,i+1 (phi i+1 -phi i) have the same signs and all sources of external energy are absent, Wwb equals the MEE for the control.     

An energy 'sources' and 'fractions' approach to the mechanical energy expenditure problem--II. Movement of the multi-link chain model

Movement of a multi-link chain model is treated using the 'sources' and 'fractions' concept introduced earlier (part I of this series, J. Biomechanics 19, 287-293). 'The energy balance equations', i.e. the relations between the powers of the sources and the time rate of change of the total energy of the links are obtained. It is shown that the action of joint forces can promote energy transfers between links and energy transformations of the energy fractions of the links but it cannot change the total energy of the system. A formula for the mechanical energy expenditure for the control moments is deduced. 'External' and 'internal' energy balance equations are derived. 'External' energy is the energy of the general center of mass, 'internal' energy is the energy of the links in their motion relative to the general center of mass. It is shown that 'external' and 'internal' work depend on each other and their sum is not equal to the mechanical energy expenditure which occurs during movement of the body. This is because of the possibility of some source powers to change the external and internal energy of the system simultaneously out of phase with each other.     

Mechanical energy analysis identifies compensatory strategies in disabled elders' gait

Current concepts in disablement emphasize the importance of identifying mobility impairments in aging humans to enable timely intervention and, ultimately, prevent disability. Because mobility impairments are likely to result in compensatory movement strategies, recognizing and understanding those strategies may be critical in designing effective interventions for preventing disability. We sought to determine if mechanical energy methods are useful for identifying and understanding lower extremity compensatory movement strategies due to disabilities. Aleshinski's method was used to compute mechanical energy expenditure (MEE) and mechanical energy compensation (MEC) for the sagittal plane stance leg and low-back joints of healthy elders (HE) and disabled elders (DE) during preferred speed and paced (120 steps min(-1)) gait. DE subjects expended less ankle energy in late-stance and more low-back energy in mid-stance than did the HE subjects. When controlling for walking speed, the difference in ankle MEE disappeared, but mid-stance hip MEE was significantly higher for the DE subjects. Despite increased hip and low-back MEE, the DE subjects compensated hip and low-back muscles greater then HE subjects by increasing energy transferred into the pelvis, particularly when walking faster than their self-selected speed. Increased energy transfers into the pelvis during mid-stance may be a strategy used to assist in advancing and controlling the contralateral limb's swing phase. Increased trunk energy, however, may compromise dynamic stability and increase the risk of falling. We conclude that mechanical energy methods are useful for identifying and understanding compensatory movement strategies in elders with disabilities.     

Determination of equivalent amounts of kinetic energy, work, and heat energy in the human body

The goal of this study is determine the mechanical equivalent of heat and the functional capacity of metabolism of walking at a slow pace (velocity = 4022m/hour, length of a step=75cm, energy utilization of a 70 kg person is 200kcal/hour). 50 healthy physicians were chosen randomly, and up and down motion of the body were determined as 6cm while stepping. Based on these, the heat equivalent is 37.5kcal/hour for horizontal motion and 52.7kcal/hour for 6cm up-and-down bobbing motions of body, and the functional capacity of metabolism is at least 45% ([37.5+52.7]/200=45%) for slow walking state, that this capacity is twofold more than earlier information. Muscle converts kinetic energy (work) to heat via friction, and heat sources of the body, and the concepts of thermogenesis and the functional capacity of metabolism should be revised.     

Mechanical energy expenditure on human movement and the anthropomorphic mechanism]

Mechanical energy expenditures of the man and anthropomorphic locomotion machine during movement are compared theoretically. Sources of the mechanical energy affecting movement of human's lower extremity are modelled by 8 muscles, 3 of which are the two-joint muscles. The model of the lower extremity of anthropomorphic locomotion machine is moved by joint moments. It was shown that in the same movement the model of the human lower extremity can spend less mechanical energy than that of the model of the anthropomorphic locomotion machine. It is caused by the presence of two-joint muscles in the first model. Such an economy of mechanical energy expenditures realized by the two-joint muscle is possible at simultaneous execution of three conditions: 1) signs of the muscle powers, which are produced by that muscle at both joints, are opposite; 2) moments produced by that muscle at each of both joints have the same direction with the joint moments at these joints; 3) one-joint antagonistic muscles are not active. An expression which makes it possible to estimate the mechanical energy savings by the two-joint muscles during humans' movement was developed.     

Mechanical energy states during running

Changes in total mechanical work and its partitioning into different energy states (kinetic, potential and rotational) during a step cycle of running were investigated on six well trained athletes who ran at the test speeds of 40, 60, 80, and 100% (9.3 +/- 0.3 m/s) of maximum. Cinematographic techniques were utilized to calculate the mechanical energy states as described by Norman et al. (1976), using a 13 segment mechanical model of a runner as the basis for the computations. The data showed that both the kinetic and rotational energy increased parabolically but the potential energy decreased linearly with increases in running velocity. The calculated power of the positive work phase increased quadratically with running speed. During the phase when the runner was in contact with the ground, the applied calculations gave similar increases for the positive and negative works, and the power ratio (Wneg/Wpos) stayed the same at all measured speeds. Therefore, it is likely that the method used to calculate the various mechanical energy states did not reflect accurately enough the physiological energy costs at higher running speeds. It may, however, be quite acceptable for estimating the mechanical energy states during walking and slow running, in which case the role of negative work is less and consequently the storage and utilization of elastic energy is small.     

Accelerometry predicts daily energy expenditure in a bird with high activity levels

Animal ecology is shaped by energy costs, yet it is difficult to measure fine-scale energy expenditure in the wild. Because metabolism is often closely correlated with mechanical work, accelerometers have the potential to provide detailed information on energy expenditure of wild animals over fine temporal scales. Nonetheless, accelerometry needs to be validated on wild animals, especially across different locomotory modes. We merged data collected on 20 thick-billed murres (Uria lomvia) from miniature accelerometers with measurements of daily energy expenditure over 24 h using doubly labelled water. Across three different locomotory modes (swimming, flying and movement on land), dynamic body acceleration was a good predictor of daily energy expenditure as measured independently by doubly labelled water (R² = 0.73). The most parsimonious model suggested that different equations were needed to predict energy expenditure from accelerometry for flying than for surface swimming or activity on land (R² = 0.81). Our results demonstrate that accelerometers can provide an accurate integrated measure of energy expenditure in wild animals using many different locomotory modes.     

Microalgal hydrogen production: prospects of an essential technology for a clean and sustainable energy economy

Modern energy production is required to undergo a dramatic transformation. It will have to replace fossil fuel use by a sustainable and clean energy economy while meeting the growing world energy needs. This review analyzes the current energy sector, available energy sources, and energy conversion technologies. Solar energy is the only energy source with the potential to fully replace fossil fuels, and hydrogen is a crucial energy carrier for ensuring energy availability across the globe. The importance of photosynthetic hydrogen production for a solar-powered hydrogen economy is highlighted and the development and potential of this technology are discussed. Much successful research for improved photosynthetic hydrogen production under laboratory conditions has been reported, and attempts are underway to develop upscale systems. We suggest that a process of integrating these achievements into one system to strive for efficient sustainable energy conversion is already justified. Pursuing this goal may lead to a mature technology for industrial deployment.     

A comparison of muscular mechanical energy expenditure and internal work in cycling

The hypothesis that the sum of the absolute changes in mechanical energy (internal work) is correlated with the muscular mechanical energy expenditure (MMEE) was tested using two elliptical chainrings, one that reduced and one that increased the internal work (compared to circular). Upper and lower bounds were put on the extra MMEE (work done by net joint torques in excess of the external work) with respect to the effect of intercompensation between joint torques due to biarticular muscles. This was done by having two measures of MMEE, one that allowed no intercompensation and one that allowed complete intercompensation between joints spanned by biarticular muscles. Energy analysis showed no correlation between internal work and the two measures of MMEE. When compared to circular, the chainring that reduced internal work increased MMEE, and phases of increased crank velocity associated with the elliptical shape resulted in increased power absorbed by the upstroke leg as it was accelerated against gravity. The resulting negative work necessitated additional positive work. Thus, the hypothesis that the internal work is correlated with MMEE was found to be invalid, and the total mechanical work done cannot be estimated by summing the internal and external work. Changes in the dynamics of cycling caused by a non-circular chainring may affect performance and must be considered during the non-circular chainring design process.     

Patterns of mechanical energy change in tetrapod gait: pendula, springs and work

Kinematic and center of mass (CoM) mechanical variables used to define terrestrial gaits are compared for various tetrapod species. Kinematic variables (limb phase, duty factor) provide important timing information regarding the neural control and limb coordination of various gaits. Whereas, mechanical variables (potential and kinetic energy relative phase, %Recovery, %Congruity) provide insight into the underlying mechanisms that minimize muscle work and the metabolic cost of locomotion, and also influence neural control strategies. Two basic mechanisms identified by Cavagna et al. (1977. Am J Physiol 233:R243-R261) are used broadly by various bipedal and quadrupedal species. During walking, animals exchange CoM potential energy (PE) with kinetic energy (KE) via an inverted pendulum mechanism to reduce muscle work. During the stance period of running (including trotting, hopping and galloping) gaits, animals convert PE and KE into elastic strain energy in spring elements of the limbs and trunk and regain this energy later during limb support. The bouncing motion of the body on the support limb(s) is well represented by a simple mass-spring system. Limb spring compliance allows the storage and return of elastic energy to reduce muscle work. These two distinct patterns of CoM mechanical energy exchange are fairly well correlated with kinematic distinctions of limb movement patterns associated with gait change. However, in some cases such correlations can be misleading. When running (or trotting) at low speeds many animals lack an aerial period and have limb duty factors that exceed 0.5. Rather than interpreting this as a change of gait, the underlying mechanics of the body's CoM motion indicate no fundamental change in limb movement pattern or CoM dynamics has occurred. Nevertheless, the idealized, distinctive patterns of CoM energy fluctuation predicted by an inverted pendulum for walking and a bouncing mass spring for running are often not clear cut, especially for less cursorial species. When the kinematic and mechanical patterns of a broader diversity of quadrupeds and bipeds are compared, more complex patterns emerge, indicating that some animals may combine walking and running mechanics at intermediate speeds or at very large size. These models also ignore energy costs that are likely associated with the opposing action of limbs that have overlapping support times during walking. A recent model of terrestrial gait (Ruina et al., 2005. J Theor Biol, in press) that treats limb contact with the ground in terms of collisional energy loss indicates that considerable CoM energy can be conserved simply by matching the path of CoM motion perpendicular to limb ground force. This model, coupled with the earlier ones of pendular exchange during walking and mass-spring elastic energy savings during running, provides compelling argument for the view that the legged locomotion of quadrupeds and other terrestrial animals has generally evolved to minimize muscle work during steady level movement.     

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.     

An energy 'sources' and 'fractions' approach to the mechanical energy expenditure problem--I. Basic concepts, description of the model, analysis of a one-link system movement

Different methods of determining mechanical energy expenditure for human movement are used in scientific research. However, the validity of some of these methods is open to question. The concept of 'sources' and 'fractions' of mechanical energy is introduced in this paper. Power phenomena in moving a one-link system are analyzed through the use of 'energy balance equations'. They represent the interrelationships between the powers of the 'sources' and the time rate of change the mechanical energy 'fractions'. Two ways of minimizing mechanical energy expenditure are discussed. They correspond to 'whip-type' and 'pendulum-type' motion.     

An artificial neural network model of energy expenditure using nonintegrated acceleration signals.

Accelerometers are a promising tool for characterizing physical activity patterns in free living. The major limitation in their widespread use to date has been a lack of precision in estimating energy expenditure (EE), which may be attributed to the oversimplified time-integrated acceleration signals and subsequent use of linear regression models for EE estimation. In this study, we collected biaxial raw (32 Hz) acceleration signals at the hip to develop a relationship between acceleration and minute-to-minute EE in 102 healthy adults using EE data collected for nearly 24 h in a room calorimeter as the reference standard. From each 1 min of acceleration data, we extracted 10 signal characteristics (features) that we felt had the potential to characterize EE intensity. Using these data, we developed a feed-forward/back-propagation artificial neural network (ANN) model with one hidden layer (12 x 20 x 1 nodes). Results of the ANN were compared with estimations using the ActiGraph monitor, a uniaxial accelerometer, and the IDEEA monitor, an array of five accelerometers. After training and validation (leave-one-subject out) were completed, the ANN showed significantly reduced mean absolute errors (0.29 +/- 0.10 kcal/min), mean squared errors (0.23 +/- 0.14 kcal(2)/min(2)), and difference in total EE (21 +/- 115 kcal/day), compared with both the IDEEA (P < 0.01) and a regression model for the ActiGraph accelerometer (P < 0.001). Thus ANN combined with raw acceleration signals is a promising approach to link body accelerations to EE. Further validation is needed to understand the performance of the model for different physical activity types under free-living conditions.     

Unstable electron pairing and the energy loan model of enzyme catalysis

A theory of enzyme catalysis is described which utilizes a thermodynamically consistent construction of a free energy diagram with different pathways for complex formation and decomposition. The switch to the decomposition pathway occurs when downward uncertainty and thermal fluctuations make possible a short-lived potential energy dominance in which parallel spin electrons are paired and thus free to drop below the energy floor normally maintained by the Pauli exclusion principle. Such pairing is possible if van der Waal's and other weak interactions holding the complex together impose confinement constraints on parallel spin electrons, thereby both increasing uncertainty fluctuations in their kinetic energy and weakly favoring a phase correlation in their motion (which can be interpreted in terms of an exchange of virtual particles). The paired configuration is highly unstable and thus energy released by pair falling is either immediately recaptured to re-establish a normal orbital structure or, if the pair persists long enough to produce a nuclear motion, recaptured at the end of this motion. In the latter case the release of energy can be thought of as an energy loan which finances the switch to the lower activation energy pathway without compromising an energy-balanced regeneration of the enzyme. The advantage is that the complex (because of its instability) has a real free energy which is lower than the free energy which would be assigned to it on the basis of its equilibrium concentration. This increases the specificity and speed of complex formation without decreasing the speed of decomposition. The theory predicts that the magnetic moment which marks the pair should accompany the nuclear (e.g. allosteric) motion and that the pair formation stage of the enzymatic process should have an anomalous temperature dependence. Variations of the model may be constructed to deal with a number of processes involving macromolecular motions, including sequential processes in catalysis, allosteric control, persistent molecular motions, self-assembly, energy transfer, channeled transport, and protection against inhibitors.     

Evaluation of the kinetic energy of the torso by magneto-inertial measurement unit during the sit-to-stand movement

Sit-to-stand tests are used in geriatrics as a qualitative issue in order to evaluate motor control and stability. In terms of measured indicators, it is traditionally the duration of the task that is reported, however it appears that the use of the kinetic energy as a new quantitative criterion allows getting a better understanding of musculoskeletal deficits of elderly subjects. The aim of this study was to determine the feasibility to obtain the measure of kinetic energy using magneto-inertial measurement units (MIMU) during sit-to-stand movements at various paces. 26 healthy subjects contributed to this investigation. Measured results were compared to a marker-based motion capture using the correlation coefficient and the normalized root mean square error (nRMSE). nRMSE were below 10% and correlation coefficients were over 0.97. In addition, errors on the mean kinetic energy were also investigated using Bland-Altman 95% limits of agreement (0.63 J–0.77 J), RMSE (0.29 J–0.38 J) and correlation coefficient (0.96–0.98). The results obtained highlighted that the method based on MIMU data could be an alternative to optoelectronic data acquisition to assess the kinetic energy of the torso during the sit-to-stand test, suggesting this method as being a promising alternative to determine kinetic energy during the sit-to-stand movement.     

A note on energy expenditure in walking on level ground and uphill

In walking, energy is wasted in the process of up-and-down movement of the center of gravity of the body during each step, as well as in the kinetic energy involved in the swinging forward of each extrèmity. In this paper the frictional loss in muscles is not considered. It is shown that for a prescribed available amount of metabolic power expenditure there exists an optimal size of the step and an optimal (maximal) speed of walking for the size of the step. Calculated values are of the correct order of magnitude. In walking uphill there exists a type of step for which there is no “lost” up-and-down motion of the center of gravity of the body. This step is optimal for walking up a hill of a given incline.     

A model of human muscle energy expenditure

A model of muscle energy expenditure was developed for predicting thermal, as well as mechanical energy liberation during simulated muscle contractions. The model was designed to yield energy (heat and work) rate predictions appropriate for human skeletal muscle contracting at normal body temperature. The basic form of the present model is similar to many previous models of muscle energy expenditure, but parameter values were based almost entirely on mammalian muscle data, with preference given to human data where possible. Nonlinear phenomena associated with submaximal activation were also incorporated. The muscle energy model was evaluated at varying levels of complexity, ranging from simulated contractions of isolated muscle, to simulations of whole body locomotion. In all cases, acceptable agreement was found between simulated and experimental energy liberation. The present model should be useful in future studies of the energetics of human movement using forward dynamic computer simulation.