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A biologically-inspired actuation system, including muscles, spinal reflexes, and vestibular feedback, may be capable of achieving more natural gait mechanics in powered prostheses or exoskeletons. In this study, we developed a Virtual Muscle Reflex (VMR) system to control ankle torque and tuned it using data from human responses to anteroposterior mechanical perturbations at three walking speeds. The system consists of three Hill-Type muscles, simulated in real time, and uses feedback from ground reaction force and from stretch sensors on the virtual muscle fibers. Controller gains, muscle properties, and reflex/vestibular time delays were optimized using Covariance Matrix Adaptation (CMA) to minimize the difference between the VMR torque output and the torque measured from the experiment. We repeated the procedure using a conventional finite-state impedance controller. For both controllers, the coefficient of determination (R2) and root-mean-square error (RMSE) was calculated as a function of time within the gait cycle. The VMR had lower RMSE than the impedance controller in 70%, and in 60% of the trials, the R2 of the VMR controller was higher than for the impedance controller. We concluded that the VMR system can better reproduce the human responses to perturbations than the impedance controller.
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Background: Humans have a remarkable capability to maintain balance while walking. There is, however, a lack of publicly available research data on reactive responses to destabilizing perturbations during gait. Methods: Here, we share a comprehensive dataset collected from 10 participants who experienced random perturbations while walking on an instrumented treadmill. Each participant performed six 5-min walking trials at a rate of 1.2 m/s, during which rapid belt speed perturbations could occur during the participant's stance phase. Each gait cycle had a 17% probability of being perturbed. The perturbations consisted of an increase of belt speed by 0.75 m/s, delivered with equal probability at 10%, 20%, 30%, 40%, 50%, 60%, 70%, or 80% of the stance phase. Data were recorded using motion capture with 25 markers, eight inertial measurement units (IMUs), and electromyography (EMG) from the tibialis anterior (TA), soleus (SOL), lateral gastrocnemius (LG), rectus femoris (RF), vastus lateralis (VL), vastus medialis (VM), biceps femoris (BF), and gluteus maximus (GM). The full protocol is described in detail. Results: We provide marker trajectories, force plate data, EMG data, and belt speed information for all trials and participants. IMU data is provided for most participants. This data can be useful for identifying neural feedback control in human gait, biologically inspired control systems for robots, and the development of clinical applications.
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Eletromiografia , Marcha , Caminhada , Humanos , Fenômenos Biomecânicos/fisiologia , Caminhada/fisiologia , Masculino , Adulto , Feminino , Marcha/fisiologia , Equilíbrio Postural/fisiologia , Músculo Esquelético/fisiologia , Adulto Jovem , Teste de Esforço/métodosRESUMO
In alpine skiing, estimation of the muscle forces and joint loads such as the forces in the ACL of the knee are essential to quantify the loading pattern of the skier during turning maneuvers. Since direct measurement of these forces is generally not feasible, non-invasive methods based on musculoskeletal modeling should be considered. In alpine skiing, however, muscle forces and ACL forces have not been analyzed during turning maneuvers due to the lack of three dimensional musculoskeletal models. In the present study, a three dimensional musculoskeletal skier model was successfully applied to track experimental data of a professional skier. During the turning maneuver, the primary activated muscles groups of the outside leg, bearing the highest loads, were the gluteus maximus, vastus lateralis as well as the medial and lateral hamstrings. The main function of these muscles was to generate the required hip extension and knee extension moments. The gluteus maximus was also the main contributor to the hip abduction moment when the hip was highly flexed. Furthermore, the lateral hamstrings and gluteus maximus contributed to the hip external rotation moment in addition to the quadratus femoris. Peak ACL forces reached 211 N on the outside leg with the main contribution in the frontal plane due to an external knee abduction moment. Sagittal plane contributions were low due to consistently high knee flexion (> 60[Formula: see text]), substantial co-activation of the hamstrings and the ground reaction force pushing the anteriorly inclined tibia backwards with respect to the femur. In conclusion, the present musculoskeletal simulation model provides a detailed insight into the loading of a skier during turning maneuvers that might be used to analyze appropriate training loads or injury risk factors such as the speed or turn radius of the skier, changes of the equipment or neuromuscular control parameters.
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Lesões do Ligamento Cruzado Anterior , Esqui , Humanos , Esqui/fisiologia , Articulação do Joelho/fisiologia , Músculo Esquelético/fisiologia , Joelho , Nádegas , Fenômenos BiomecânicosRESUMO
Functional electrical stimulation (FES) is a promising technology for restoring reaching motions to individuals with upper-limb paralysis caused by a spinal cord injury (SCI). However, the limited muscle capabilities of an individual with SCI have made achieving FES-driven reaching difficult. We developed a novel trajectory optimization method that used experimentally measured muscle capability data to find feasible reaching trajectories. In a simulation based on a real-life individual with SCI, we compared our method to attempting to follow naive direct-to-target paths. We tested our trajectory planner with three control structures that are commonly used in applied FES: feedback, feedforward-feedback, and model predictive control. Overall, trajectory optimization improved the ability to reach targets and improved the accuracy for the feedforward-feedback and model predictive controllers ( ). The trajectory optimization method should be practically implemented to improve the FES-driven reaching performance.
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Terapia por Estimulação Elétrica , Traumatismos da Medula Espinal , Humanos , Músculo Esquelético/fisiologia , Terapia por Estimulação Elétrica/métodos , Hemiplegia , Estimulação Elétrica/métodosRESUMO
Competitive skiers encounter a high risk of sustaining an ACL injury during jump-landing in downhill ski racing. Facing an injury-prone landing manoeuvre, there is a lack of knowledge regarding optimum control strategies. So, the purpose of the present study was to investigate possible neuromuscular control patterns to avoid injury during injury-prone jump-landing manoeuvres. A computational approach was used to generate a series of 190 injury-prone jump-landing manoeuvres based on a 25-degree-of-freedom sagittal plane musculoskeletal skier model. Using a dynamic optimization framework, each injury-prone landing manoeuvre was resolved to identify muscle activation patterns of the lower limbs and corresponding kinematic changes that reduce peak ACL force. In the 190 injury-prone jump-landing simulations, ACL forces peaked during the first 50â ms after ground contact. Optimized muscle activation patterns, that reduced peak ACL forces, showed increased activation of the monoarticular hip flexors, ankle dorsi- and plantar flexors as well as hamstrings prior to or during the early impact phase (<50â ms). The corresponding kinematic changes were characterized by increased hip and knee flexion and less backward lean of the skier at initial ground contact and the following impact phase. Injury prevention strategies should focus on increased activation of the monoarticular hip flexors, ankle plantar flexors and rapid and increased activation of the hamstrings in combination with a flexed landing position and decreased backward lean to reduce ACL injury risk during the early impact phase (<50â ms) of jump landing.HighlightsFirst study investigating advantageous control strategies during injury-prone jump-landing manoeuvres in downhill skiing using a musculoskeletal simulation model and dynamic optimization framework.The simulation results predicted high injury risk during the first 50â ms after initial ground contact.Optimized neuromuscular control patterns showed adapted activation patterns (timing and amplitude) of muscles crossing the knee as well as the hip and ankle joints prior to and after initial ground contact, respectively.An optimized control strategy during an injury-prone landing manoeuvre was characterized kinematically by increasing hip and knee flexion and less backward lean of the skier at initial ground contact and the following impact phase.
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Lesões do Ligamento Cruzado Anterior , Esqui , Humanos , Lesões do Ligamento Cruzado Anterior/prevenção & controle , Esqui/fisiologia , Articulação do Joelho/fisiologia , Extremidade Inferior , Fenômenos BiomecânicosRESUMO
In alpine skiing, estimation of the joint moments acting onto the skier is essential to quantify the loading of the skier during turning maneuvers. In the present study, a novel forward dynamics optimization framework is presented to estimate the joint moments acting onto the skier incorporating a three dimensional musculoskeletal model (53 kinematic degrees of freedom, 94 muscles). Kinematic data of a professional skier performing a turning maneuver were captured and used as input data to the optimization framework. In the optimization framework, the musculoskeletal model of the skier was applied to track the experimental data of a skier and to estimate the underlying joint moments of the skier at the hip, knee and ankle joints of the outside and inside leg as well as the lumbar joint. During the turning maneuver the speed of the skier was about 14 m/s with a minimum turn radius of about 16 m. The highest joint moments were observed at the lumbar joint with a maximum of 1.88 Nm/kg for lumbar extension. At the outside leg, the highest joint moments corresponded to the hip extension moment with 1.27 Nm/kg, the knee extension moment with 1.02 Nm/kg and the ankle plantarflexion moment with 0.85 Nm/kg. Compared to the classical inverse dynamics analysis, the present framework has four major advantages. First, using a forward dynamic optimization framework the underlying kinematics of the skier as well as the corresponding ground reaction forces are dynamically consistent. Second, the present framework can cope with incomplete data (i.e., without ground reaction force data). Third, the computation of the joint moments is less sensitive to errors in the measurement data. Fourth, the computed joint moments are constrained to stay within the physiological limits defined by the musculoskeletal model.
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Muscular co-contraction of antagonistic muscle pairs is often observed in human movement, but it is considered inefficient and it can currently not be predicted in simulations where muscular effort or metabolic energy are minimized. Here, we investigated the relationship between minimizing effort and muscular co-contraction in systems with random uncertainty to see if muscular co-contraction can minimize effort in such system. We also investigated the effect of time delay in the muscle, by varying the time delay in the neural control as well as the activation time constant. We solved optimal control problems for a one-degree-of-freedom pendulum actuated by two identical antagonistic muscles, using forward shooting, to find controller parameters that minimized muscular effort while the pendulum remained upright in the presence of noise added to the moment at the base of the pendulum. We compared a controller with and without feedforward control. Task precision was defined by bounding the root mean square deviation from the upright position, while different perturbation levels defined task difficulty. We found that effort was minimized when the feedforward control was nonzero, even when feedforward control was not necessary to perform the task, which indicates that co-contraction can minimize effort in systems with uncertainty. We also found that the optimal level of co-contraction increased with time delay, both when the activation time constant was increased and when neural time delay was added. Furthermore, we found that for controllers with a neural time delay, a different trajectory was optimal for a controller with feedforward control than for one without, which indicates that simulation trajectories are dependent on the controller architecture. Future movement predictions should therefore account for uncertainty in dynamics and control, and carefully choose the controller architecture. The ability of models to predict co-contraction from effort or energy minimization has important clinical and sports applications. If co-contraction is undesirable, one should aim to remove the cause of co-contraction rather than the co-contraction itself.
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Movimento , Músculo Esquelético , Humanos , Músculo Esquelético/fisiologia , Incerteza , Movimento/fisiologia , Contração Muscular/fisiologia , Posição OrtostáticaRESUMO
Individuals with an above-knee (AK) amputation typically use passive prostheses, whether reactive (microprocessor) or purely mechanical. Though sufficient for walking, these solutions lack the positive power generation observed in able-bodied individuals. Active (powered) prostheses can provide positive power but suffer complex control and limited energy storage capacities. These shortcomings motivate the development of an active prosthesis implementing a novel impedance controller design with energy regeneration. The controller requires only five tuning parameters that are intuitive to adjust in contrast to the current standard-finite state machine impedance scheduling of up to 45 gains. This simplification is uniquely achieved by modulating knee joint impedance by axial shank force. Furthermore, the proposed control approach introduces analytical guidance for impedance tuning to purposely integrate energy regeneration; specifically, a precise amount of negative damping is injected into the joint. A pilot study conducted with a volunteer with an AK amputation walking at three distinct speeds and at continually self-selected varying speeds demonstrated the adaptability of the controller to changes in speed. Self-powered operation was attained for all trials despite low mechanical component efficiencies. These early results suggest the efficacy of simplifying impedance control tuning and fusing control and energy regeneration in transfemoral prostheses.
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Amputados , Membros Artificiais , Prótese do Joelho , Fenômenos Biomecânicos , Impedância Elétrica , Marcha , Humanos , Projetos Piloto , Desenho de Prótese , CaminhadaRESUMO
This paper presents an innovative design methodology for development of lower limb exoskeletons with the fabrication and experimental evaluation of prototype hardware. The proposed design approach is specifically conceived to be suitable for the pediatric population and uses additive manufacturing and a model parameterized in terms of subject anthropometrics to give a person-specific custom fit. The methodology is applied to create computer-aided design models using average anthropometrics of children 6-11 years old and using anthropometrics of an individual measured by the researchers. This demonstrates that the approach can scale to subject weight and height. A prototype exoskeleton is fabricated, which can actuate the hip and knee joints without restricting hip abduction-adduction motion. In order to test usability of the device and evaluate walking assistance, user effort is quantified in an assisted condition where the subject walks on a level treadmill with the exoskeleton powered. This is compared to an unassisted condition with the exoskeleton unpowered and a baseline condition with the subject not wearing the exoskeleton. Comparing assisted to baseline conditions, torque magnitudes increased at the hip and knee, mechanical energy generated increased at the hip but decreased at the knee, and muscle activations increased in the Vastus Lateralis but decreased in the Biceps Femoris. While the preliminary evidence for walking assistance is not entirely convincing for the tested conditions, the presented design methodology itself is promising as it has been successfully validated through the creation of computer-aided design models for children and fabrication of a serviceable exoskeleton prototype.
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Exoesqueleto EnergizadoRESUMO
Restoration of balance control is a primary focus of rehabilitation after a stroke. The study developed a gait perturbation, treadmill-based, balance assessment protocol and demonstrated that it can be used to quantify improvements in reactive balance responses among individuals post-stroke. The protocol consists of a sequence of fifteen 90-second treadmill walking trials, with a single perturbation applied during the middle third of each trial. Gait was perturbed by rapid acceleration-deceleration of the treadmill belt at mid-stance of the unaffected leg during a randomly selected gait cycle. The initial perturbation magnitude was based on the participant's maximum walking speed and increased or decreased in each trial, based on success or failure of recovery, as determined from an instrumented harness. The protocol was used before and after a 10-week period of therapy in twenty-four stroke survivors. Outcomes included maximum recoverable perturbation (MRP), self-selected gait speed, levels progressed through the algorithm, and falls versus recoveries.Participants were able to take recovery steps in response to the perturbation. Twelve participants completed the full assessment protocol before and after the therapeutic intervention. After the intervention, they had fewer falls and more recoveries (p < 0.001), progressed through more algorithm levels (p = 0.043), had a higher MRP (p = 0.005), and had higher gait speeds. The protocol was found to be feasible in stroke survivors with moderate gait deficits. The data supports the conclusion that this protocol can be used in clinical research to quantify improvements in balance during walking.
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Reabilitação do Acidente Vascular Cerebral , Acidente Vascular Cerebral , Acidentes por Quedas , Marcha , Humanos , Equilíbrio Postural , Sobreviventes , CaminhadaRESUMO
BACKGROUND: Musculoskeletal modelling is a common means by which to non-invasively analyse movement. Such models have largely been used to observe function in both healthy and patient populations. However, utility in a clinical environment is largely unknown. The aim of this review was to explore existing uses of musculoskeletal models as a clinical intervention, or decision-making, tool. METHODS: A literature search was performed using PubMed and Scopus to find articles published since 2010 and relating to musculoskeletal modelling and joint and muscle forces. FINDINGS: 4662 abstracts were found, of which 39 relevant articles were reviewed. Journal articles were categorised into 5 distinct groups: non-surgical treatment, orthoses assessment, surgical decision making, surgical intervention assessment and rehabilitation regime assessment. All reviewed articles were authored by collaborations between clinicians and engineers/modellers. Current uses included insight into the development of osteoarthritis, identifying candidates for hamstring lengthening surgery, and the assessment of exercise programmes to reduce joint damage. INTERPRETATION: There is little evidence showing the use of musculoskeletal modelling as a tool for patient care, despite the ability to assess long-term joint loading and muscle overuse during functional activities, as well as clinical decision making to avoid unfavourable treatment outcomes. Continued collaboration between model developers should aim to create clinically-friendly models which can be used with minimal input and experience by healthcare professionals to determine surgical necessity and suitability for rehabilitation regimes, and in the assessment of orthotic devices.
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Atenção à Saúde , Aparelhos Ortopédicos , Tomada de Decisões , HumanosRESUMO
Jump landing is a common situation leading to knee injuries involving the anterior cruciate ligament (ACL) in sports. Although neuromuscular control is considered as a key injury risk factor, there is a lack of knowledge regarding optimum control strategies that reduce ACL forces during jump landing. In the present study, a musculoskeletal model-based computational approach is presented that allows identifying neuromuscular control patterns that minimize ACL forces during jump landing. The approach is demonstrated for a jump landing maneuver in downhill skiing, which is one out of three main injury mechanisms in competitive skiing.
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Ligamento Cruzado Anterior/fisiologia , Locomoção/fisiologia , Modelos Biológicos , Junção Neuromuscular/fisiologia , Articulação do Tornozelo/fisiologia , Fenômenos Biomecânicos , Simulação por Computador , Articulação do Quadril/fisiologia , Humanos , Articulação do Joelho/fisiologiaRESUMO
Standing balance is a simple motion task for healthy humans but the actions of the central nervous system (CNS) have not been described by generalized and sufficiently sophisticated control laws. While system identification approaches have been used to extracted models of the CNS, they either focus on short balance motions, leading to task-specific control laws, or assume that the standing balance system is linear. To obtain comprehensive control laws for human standing balance, complex balance motions, long duration tests, and nonlinear controller models are all needed. In this paper, we demonstrate that trajectory optimization with the direct collocation method can achieve these goals to identify complex CNS models for the human standing balance task. We first examined this identification method using synthetic motion data and showed that correct control parameters can be extracted. Then, six types of controllers, from simple linear to complex nonlinear, were identified from 100 s of motion data from randomly perturbed standing. Results showed that multiple time-delay paths and nonlinear properties are both needed in order to fully explain human feedback control of standing balance.
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Equilíbrio Postural , HumanosRESUMO
Trajectory optimization with musculoskeletal models can be used to reconstruct measured movements and to predict changes in movements in response to environmental changes. It enables an exhaustive analysis of joint angles, joint moments, ground reaction forces, and muscle forces, among others. However, its application is still limited to simplified problems in two dimensional space or straight motions. The simulation of movements with directional changes, e.g. curved running, requires detailed three dimensional models which lead to a high-dimensional solution space. We extended a full-body three dimensional musculoskeletal model to be specialized for running with directional changes. Model dynamics were implemented implicitly and trajectory optimization problems were solved with direct collocation to enable efficient computation. Standing, straight running, and curved running were simulated starting from a random initial guess to confirm the capabilities of our model and approach: efficacy, tracking and predictive power. Altogether the simulations required 1 h 17 min and corresponded well to the reference data. The prediction of curved running using straight running as tracking data revealed the necessity of avoiding interpenetration of body segments. In summary, the proposed formulation is able to efficiently predict a new motion task while preserving dynamic consistency. Hence, labor-intensive and thus costly experimental studies could be replaced by simulations for movement analysis and virtual product design.
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Corrida/fisiologia , Humanos , Imageamento Tridimensional , Modelos Biológicos , Movimento/fisiologia , Fenômenos Fisiológicos Musculoesqueléticos , Sistema Musculoesquelético/anatomia & histologiaRESUMO
Machine learning is a promising approach to evaluate human movement based on wearable sensor data. A representative dataset for training data-driven models is crucial to ensure that the model generalizes well to unseen data. However, the acquisition of sufficient data is time-consuming and often infeasible. We present a method to create realistic inertial sensor data with corresponding biomechanical variables by 2D walking and running simulations. We augmented a measured inertial sensor dataset with simulated data for the training of convolutional neural networks to estimate sagittal plane joint angles, joint moments, and ground reaction forces (GRFs) of walking and running. When adding simulated data, the root mean square error (RMSE) of the test set of hip, knee, and ankle joint angles decreased up to 17%, 27% and 23%, the RMSE of knee and ankle joint moments up to 6% and the RMSE of anterior-posterior and vertical GRF up to 2 and 6%. Simulation-aided estimation of joint moments and GRFs was limited by inaccuracies of the biomechanical model. Improving the physics-based model and domain adaptation learning may further increase the benefit of simulated data. Future work can exploit biomechanical simulations to connect different data sources in order to create representative datasets of human movement. In conclusion, machine learning can benefit from available domain knowledge on biomechanical simulations to supplement cumbersome data collections.
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Predictive gait simulations currently do not account for environmental or internal noise. We describe a method to solve predictive simulations of human movements in a stochastic environment using a collocation method. The optimization is performed over multiple noisy episodes of the trajectory, instead of a single episode in a deterministic environment. Each episode used the same control parameters. The method was verified on a torque-driven pendulum swing-up problem. A different optimal trajectory was found in a stochastic environment than in the deterministic environment. Next, it was applied to gait to show its application in predictive simulation of human movement. We show that, unlike in a deterministic model, a nonzero minimum foot clearance during swing is predicted by a minimum-effort criterion in a stochastic environment. The predicted amount of foot clearance increased with the noise amplitude.
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Pé , Marcha , Simulação por Computador , Humanos , Cinética , Movimento , TorqueRESUMO
BACKGROUND: System identification can be used to obtain a model of the human postural control system from experimental data in which subjects are mechanically perturbed while standing. However, unstable controllers were sometimes found, which obviously do not explain human balance and cannot be applied in control of humanoid robots. Eigenvalue constraints can be used to avoid unstable controllers. However, this method is hard to apply to highly nonlinear systems and large identification datasets. NEW METHOD: To address these issues, we perform the system identification with a stochastic system model where process noise is modeled. The parameter identification is performed by simultaneous trajectory optimizations on multiple episodes that have different instances of the process noise. RESULTS: The stochastic and deterministic identification methods were tested on three types of controllers, including both linear and nonlinear controller architectures. Stochastic identification tracked the experimental data nearly as well as the deterministic identification, while avoiding the unstable controllers that were found with a deterministic system model. COMPARISON WITH EXISTING METHOD: Comparing to eigenvalue constraints, stochastic identification has wider application potentials. Since linearization is not needed in the stochastic identification, it is applicable to highly nonlinear systems, and it can be applied on large data-sets. CONCLUSIONS: Stochastic identification can be used to avoid unstable controllers in human postural control identification.
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Prosthetic devices for hand difference have advanced considerably in recent years, to the point where the mechanical dexterity of a state-of-the-art prosthetic hand approaches that of the natural hand. Control options for users, however, have not kept pace, meaning that the new devices are not used to their full potential. Promising developments in control technology reported in the literature have met with limited commercial and clinical success. We have previously described a biomechanical model of the hand that could be used for prosthesis control. The goal of this study was to evaluate the feasibility of this approach in terms of kinematic fidelity of model-predicted finger movement and the computational performance of the model. We show the performance of the model in replicating recorded hand and finger kinematics and find average correlations of 0.89 between modelled and recorded motions; we show that the computational performance of the simulations is fast enough to achieve real-time control with a robotic hand in the loop; and we describe the use of the model for controlling object gripping. Despite some limitations in accessing sufficient driving signals, the model performance shows promise as a controller for prosthetic hands when driven with recorded EMG signals. User-in-the-loop testing with amputees is necessary in future work to evaluate the suitability of available driving signals, and to examine translation of offline results to online performance.
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Membros Artificiais , Mãos , Eletromiografia , Dedos , Humanos , Movimento , Desenho de PróteseRESUMO
The International Society of Biomechanics (ISB) has charged this committee with development of a standard similar in scope to the kinematic standard proposed in Wu et al. (2002) and Wu et al. (2005). Given the variety of purposes for which intersegmental forces and moments are used in biomechanical research, it is not possible to recommend a particular set of analysis standards that will be acceptable in all applications. Instead, it is the purpose of this paper to recommend a set of reporting standards that will result in an understanding of the differences between investigations and the ability to reproduce the research. The end products of this standard are (1) a critical checklist that can be used during submission of manuscripts and abstracts to insure adequate description of methods, and (2) a web based visualization tool that can be used to alter the coordinate system, normalization technique and internal/external perspective of intersegmental forces and moments during walking and running so that the shape and magnitude of the curves can be compared to one's own data.
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Fenômenos Mecânicos , Movimento , Fenômenos Biomecânicos , Humanos , Corrida , CaminhadaRESUMO
This paper compares predictions of metabolic energy expenditure in gait using seven metabolic energy expenditure models to assess their correlation with experimental data. Ground reaction forces, marker data, and pulmonary gas exchange data were recorded for six walking trials at combinations of two speeds, 0.8 m/s and 1.3 m/s, and three inclines, -8% (downhill), level, and 8% (uphill). The metabolic cost, calculated with the metabolic energy models was compared to the metabolic cost from the pulmonary gas exchange rates. A repeated measures correlation showed that all models correlated well with experimental data, with correlations of at least 0.9. The model by Bhargava et al. (J Biomech, 2004: 81-88) and the model by Lichtwark and Wilson (J Exp Biol, 2005: 2831-3843) had the highest correlation, 0.95. The model by Margaria (Int Z Angew Physiol Einschl Arbeitsphysiol, 1968: 339-351) predicted the increase in metabolic cost following a change in dynamics best in absolute terms.