Determination of Feasible Muscle Forces in Human Walking Using Static Optimization and Hill's Muscle Dynamics Constraints (original) (raw)
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Muscle forces and the demands of human walking
Biology Open, 2021
Reconstructing the locomotor behavior of extinct animals depends on elucidating the principles that link behavior, function, and morphology, which can only be done using extant animals. Within the human lineage, the evolution of bipedalism represents a critical transition, and evaluating fossil hominins depends on understanding the relationship between lower limb forces and skeletal morphology in living humans. As a step toward that goal, here we use a musculoskeletal model to estimate forces in the lower limb muscles of ten individuals during walking. The purpose is to quantify the consistency, timing, and magnitude of these muscle forces during the stance phase of walking. We find that muscles which act to support or propel the body during walking demonstrate the greatest force magnitudes as well as the highest consistency in the shape of force curves among individuals. Muscles that generate moments in the same direction as, or orthogonal to, the ground reaction force show lower forces of greater variability. These data can be used to define the envelope of load cases that need to be examined in order to understand human lower limb skeletal load bearing.
A dynamic optimization technique for predicting muscle forces in the swing phase of gait
Journal of Biomechanics, 1987
The muscle force sharing problem was solved for the swing phase of gait using a dynamic optimization algorithm. For comparison purposes the problem was also solved using a typical static optimization algorithm. The objective function for the dynamic optimization algorithm was a combination of the tracking error and the metabolic energy consumption. The latter quantity was taken to be the sum of the total work done by the muscles and the enthalpy change during the contraction. The objective function for the static optimization problem was the sum of the cubes of the muscle stresses. To solve the problem using the static approach, the inverse dynamics problem was first solved in order to determine the resultant joint torques required to generate the given hip, knee and ankle trajectories. To this effect the angular velocities and accelerations were obtained by numerical differentiation using a low-pass digital filter. The dynamic optimization problem was solved using the Fletcher-Reeves conjugate gradient algorithm, and the static optimization problem was solved using the Gradient-restoration algorithm. The results show influence of internal muscle dynamics on muscle control histories visa vis muscle forces. They also illustrate the strong sensitivity of the results to the differentiation procedure used in the static optimization approach.
Journal of Biomechanics, 2001
There are different opinions in the literature on whether the cost functions: the sum of muscle stresses squared and the sum of muscle stresses cubed, can reasonably predict muscle forces in humans. One potential reason for the discrepancy in the results could be that different authors use different sets of model parameters which could substantially affect forces predicted by optimizationbased models. In this study, the sensitivity of the optimal solution obtained by minimizing the above cost functions for a planar three degrees-of-freedom (DOF) model of the leg with nine muscles was investigated analytically for the quadratic function and numerically for the cubic function. Analytical results revealed that, generally, the non-zero optimal force of each muscle depends in a very complex non-linear way on moments at all three joints and moment arms and physiological cross-sectional areas (PCSAs) of all muscles. Deviations of the model parameters (moment arms and PCSAs) from their nominal values within a physiologically feasible range affected not only the magnitude of the forces predicted by both criteria, but also the number of non-zero forces in the optimal solution and the combination of muscles with non-zero predicted forces. Muscle force magnitudes calculated by both criteria were similar. They could change several times as model parameters changed, whereas patterns of muscle forces were typically not as sensitive. It is concluded that different opinions in the literature about the behavior of optimization-based models can be potentially explained by differences in employed model parameters. r : S 0 0 2 1 -9 2 9 0 ( 0 1 ) 0 0 0 9 7 -5
Current understanding of how muscles coordinate walking in humans is derived from analyses of body motion, ground reaction force and EMG measurements. This is Part I of a two-part review that emphasizes how muscle-driven dynamics-based simulations assist in the understanding of individual muscle function in walking, especially the causal relationships between muscle force generation and walking kinematics and kinetics. Part I reviews the strengths and limitations of Newton Á/Euler inverse dynamics and dynamical simulations, including the ability of each to find the contributions of individual muscles to the acceleration/deceleration of the body segments. We caution against using the concept of biarticular muscles transferring power from one joint to another to infer muscle coordination principles because energy flow among segments, even the adjacent segments associated with the joints, cannot be inferred from computation of joint powers and segmental angular velocities alone. Rather, we encourage the use of dynamical simulations to perform muscle-induced segmental acceleration and power analyses. Such analyses have shown that the exchange of segmental energy caused by the forces or accelerations induced by a muscle can be fundamentally invariant to whether the muscle is shortening, lengthening, or neither. How simulation analyses lead to understanding the coordination of seated pedaling, rather than walking, is discussed in this first part because the dynamics of pedaling are much simpler, allowing important concepts to be revealed. We elucidate how energy produced by muscles is delivered to the crank through the synergistic action of other non-energy producing muscles; specifically, that a major function performed by a muscle arises from the instantaneous segmental accelerations and redistribution of segmental energy throughout the body caused by its force generation. Part II reviews how dynamical simulations provide insight into muscle coordination of walking. Published by Elsevier Science B.V.
Walking dynamics from mechanism models to parameter optimization
2011
The paper deals with the historical development of human body dynamics, and it presents results received for simple models by parameter optimization. The scientific research on human walking dynamics started already in the 19 th century and was later promoted by the physicist and physiologist Otto Fischer who published in 1906 his fundamental book. Fischer used the mechanism theory for modeling and analysis of human walking. His research was based on the barycenters of the corresponding reduced mechanisms. By the end of the 20 th century computational multibody dynamics provided more complex models which were applied to human body dynamics, too. More recently parameter optimization has been used to deal with the overactuation of biomechanical systems still a very active research topic in biomechanics. As an example a gait disorder simulation is presented showing that even today mechanism models, muscle group selection, inverse dynamics approaches and parameter optimization techniques using energy and aesthetics criteria are essential tools.
Biomechanics and muscle coordination of human walking
Gait & Posture, 2003
Current understanding of how muscles coordinate walking in humans is derived from analyses of body motion, ground reaction force and EMG measurements. This is Part I of a two-part review that emphasizes how muscle-driven dynamics-based simulations assist in the understanding of individual muscle function in walking, especially the causal relationships between muscle force generation and walking kinematics and kinetics. Part I reviews the strengths and limitations of Newton Á/Euler inverse dynamics and dynamical simulations, including the ability of each to find the contributions of individual muscles to the acceleration/deceleration of the body segments. We caution against using the concept of biarticular muscles transferring power from one joint to another to infer muscle coordination principles because energy flow among segments, even the adjacent segments associated with the joints, cannot be inferred from computation of joint powers and segmental angular velocities alone. Rather, we encourage the use of dynamical simulations to perform muscle-induced segmental acceleration and power analyses. Such analyses have shown that the exchange of segmental energy caused by the forces or accelerations induced by a muscle can be fundamentally invariant to whether the muscle is shortening, lengthening, or neither. How simulation analyses lead to understanding the coordination of seated pedaling, rather than walking, is discussed in this first part because the dynamics of pedaling are much simpler, allowing important concepts to be revealed. We elucidate how energy produced by muscles is delivered to the crank through the synergistic action of other non-energy producing muscles; specifically, that a major function performed by a muscle arises from the instantaneous segmental accelerations and redistribution of segmental energy throughout the body caused by its force generation. Part II reviews how dynamical simulations provide insight into muscle coordination of walking. Published by Elsevier Science B.V.
Analysis of muscle forces during downhill walking
The aim of this study was to analyse gait parameters and to quantify lower extremity muscles forces in downhill walking at different inclinations. Ten healthy male subjects walked at self-paced and at constant pre-set speed of 4 km/h on a ramp at different inclinations of -18°, -12°, -6° and 0°. Muscle forces were analysed by a musculoskeletal model (AnyBody) and were divided in four groups: quadriceps, hamstrings, calf muscles and shin muscles. Results showed significant increases in quadriceps and decreases in calf muscle forces with increasing inclination. Furthermore, quadriceps muscle forces were affected by walking speed. Hamstrings, quadriceps and calf muscle forces can be correlated with hip, knee and ankle joint moments, respectively. Therefore, it can be concluded that forces of major muscle groups can explain the joint extension moments.
Energy expenditure during human gait. II - Role of muscle groups
Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference, 2010
A phenomenological model of muscle energy expenditure developed in part I of the paper, is utilized as a physiological cost function to estimate the muscle forces during normal locomotion. The model takes into account muscular behaviors typically observed during human gait, such as submaximal activation, variable muscular contraction conditions and muscular fiber type. The solution of the indeterminate biomechanical problem is obtained by integrating multibody dynamics and the global static optimization technique that considers the whole motion. The results for an application case indicate the important role of muscle groups in coordinating multijoint motion with the objective of minimizing metabolic costs of transport during locomotion.
Journal of Biomechanics, 2013
Comparing the available electromyography (EMG) and the related uncertainties with the space of muscle forces potentially driving the same motion can provide insights into understanding human motion in healthy and pathological neuromotor conditions. However, it is not clear how effective the available computational tools are in completely sample the possible muscle forces. In this study, we compared the effectiveness of METABOLICA and the Null-Space algorithm at generating a comprehensive spectrum of possible muscle forces for a representative motion frame. The hip force peak during a selected walking trial was identified using a lower-limb musculoskeletal model. The joint moments, the muscle lever arms, and the muscle force constraints extracted from the model constituted the indeterminate equilibrium equation at the joints. Two spectra, each containing 200,000 muscle force samples, were calculated using METABOLICA and the Null-Space algorithm. The full hip force range was calculated using optimization and compared with the hip force ranges derived from the METABOLICA and the Null-Space spectra. The METABOLICA spectrum spanned a much larger force range than the NS spectrum, reaching 811 N difference for the gluteus maximus intermediate bundle. The METABOLICA hip force range exhibited a 0.3-0.4 BW error on the upper and lower boundaries of the full hip force range (3.4-11.3 BW), whereas the full range was imposed in the NS spectrum. The results suggest that METABOLICA is well suited for exhaustively sample the spectrum of possible muscle recruitment strategy. Future studies will investigate the muscle force range in healthy and pathological neuromotor conditions.