Mammalian muscle model for predicting force and energetics during physiological behaviors

AngoraPy: A Python toolkit for modeling anthropomorphic goal-driven sensorimotor systems

Goal-driven deep learning increasingly supplements classical modeling approaches in computational neuroscience. The strength of deep neural networks as models of the brain lies in their ability to autonomously learn the connectivity required to solve complex and ecologically valid tasks, obviating the need for hand-engineered or hypothesis-driven connectivity patterns. Consequently, goal-driven models can generate hypotheses about the neurocomputations underlying cortical processing that are grounded in macro- and mesoscopic anatomical properties of the network's biological counterpart. Whereas, goal-driven modeling is already becoming prevalent in the neuroscience of perception, its application to the sensorimotor domain is currently hampered by the complexity of the methods required to train models comprising the closed sensation-action loop. This paper describes AngoraPy, a Python library that mitigates this obstacle by providing researchers with the tools necessary to train complex recurrent convolutional neural networks that model the human sensorimotor system. To make the technical details of this toolkit more approachable, an illustrative example that trains a recurrent toy model on in-hand object manipulation accompanies the theoretical remarks. An extensive benchmark on various classical, 3D robotic, and anthropomorphic control tasks demonstrates AngoraPy's general applicability to a wide range of tasks. Together with its ability to adaptively handle custom architectures, the flexibility of this toolkit demonstrates its power for goal-driven sensorimotor modeling.

Muscle redundancy is greatly reduced by the spatiotemporal nature of neuromuscular control

Animals must control numerous muscles to produce forces and movements with their limbs. Current theories of motor optimization and synergistic control are predicated on the assumption that there are multiple highly diverse feasible activations for any motor task ("muscle redundancy"). Here, we demonstrate that the dimensionality of the neuromuscular control problem is greatly reduced when adding the temporal constraints inherent to any sequence of motor commands: the physiological time constants for muscle activation-contraction dynamics. We used a seven-muscle model of a human finger to fully characterize the seven-dimensional polytope of all possible motor commands that can produce fingertip force vector in any direction in 3D, in alignment with the core models of Feasibility Theory. For a given sequence of seven force vectors lasting 300 ms, a novel single-step extended linear program finds the 49-dimensional polytope of all possible motor commands that can produce the sequence of forces. We find that muscle redundancy is severely reduced when the temporal limits on muscle activation-contraction dynamics are added. For example, allowing a generous ± 12% change in muscle activation within 50 ms allows visiting only ∼ 7% of the feasible activation space in the next time step. By considering that every motor command conditions future commands, we find that the motor-control landscape is much more highly structured and spatially constrained than previously recognized. We discuss how this challenges traditional computational and conceptual theories of motor control and neurorehabilitation for which muscle redundancy is a foundational assumption.

Numerical instability of Hill-type muscle models

Hill-type muscle models are highly preferred as phenomenological models for musculoskeletal simulation studies despite their introduction almost a century ago. The use of simple Hill-type models in simulations, instead of more recent cross-bridge models, is well justified since computationally 'light-weight'-although less accurate-Hill-type models have great value for large-scale simulations. However, this article aims to invite discussion on numerical instability issues of Hill-type muscle models in simulation studies, which can lead to computational failures and, therefore, cannot be simply dismissed as an inevitable but acceptable consequence of simplification. We will first revisit the basic premises and assumptions on the force-length and force-velocity relationships that Hill-type models are based upon, and their often overlooked but major theoretical limitations. We will then use several simple conceptual simulation studies to discuss how these numerical instability issues can manifest as practical computational problems. Lastly, we will review how such numerical instability issues are dealt with, mostly in an ad hoc fashion, in two main areas of application: musculoskeletal biomechanics and computer animation.

Muscle active force-length curve explained by an electrophysical model of interfilament spacing

The active isometric force-length relation (FLR) of striated muscle sarcomeres is central to understanding and modeling muscle function. The mechanistic basis of the descending arm of the FLR is well explained by the decreasing thin:thick filament overlap that occurs at long sarcomere lengths. The mechanistic basis of the ascending arm of the FLR (the decrease in force that occurs at short sarcomere lengths), alternatively, has never been well explained. Because muscle is a constant-volume system, interfilament lattice distances must increase as sarcomere length shortens. This increase would decrease thin and thick-filament electrostatic interactions independently of thin:thick filament overlap. To examine this effect, we present here a fundamental, physics-based model of the sarcomere that includes filament molecular properties, calcium binding, sarcomere geometry including both thin:thick filament overlap and interfilament radial distance, and electrostatics. The model gives extremely good fits to existing FLR data from a large number of different muscles across their entire range of measured activity levels, with the optimized parameter values in all cases lying within anatomically and physically reasonable ranges. A local first-order sensitivity analysis (varying individual parameters while holding the values of all others constant) shows that model output is most sensitive to a subset of model parameters, most of which are related to sarcomere geometry, with model output being most sensitive to interfilament radial distance. This conclusion is supported by re-running the fits with only this parameter subset being allowed to vary, which increases fit errors only moderately. These results show that the model well reproduces existing experimental data, and indicate that changes in interfilament spacing play as central a role as changes in filament overlap in determining the FLR, particularly on its ascending arm.

The legacy of A. V. Hill's Nobel Prize winning work on muscle energetics

A. V. Hill was awarded the 1922 Nobel Prize, jointly with Otto Meyerhof, for Physiology or Medicine for his work on energetic aspects of muscle contraction. Hill used his considerable mathematical and experimental skills to investigate the relationships among muscle mechanics, biochemistry and heat production. The main ideas of the work for which the Nobel Prize was awarded were superseded within a decade and the legacy of Hill and Meyerhof's Nobel work was not a set of persistent, influential ideas but rather was a prolonged period of extraordinary activity that advanced the understanding of how muscles work far beyond the concepts that led to the Nobel Prize. Hill pioneered the integration of mathematics into the study of physiology and pharmacology. Particular aspects of Hill's own work that remain in common use in muscle physiology include mathematical descriptions of the relationships between muscle force output and shortening velocity and between force output and calcium concentration and the model of muscle as a contractile element in series with an elastic element. We describe some of the characteristics of Hill's broader scientific activities and then outline how Hill's work on muscle energetics was extended after 1922, as a result of Hill's own work and that of others, to the present day. Abstract figure legend. A. V. Hill's scientific legacy. Vertical from the base. A. V. Hill (pictured) and his colleague Otto Meyerhof shared the 1922 Nobel Prize for Physiology or Medicine. Seven enduring elements of Hill's legacy to muscle physiology are shown. Arrows link concepts and approaches to related disciplines where they have been foundational and highly influential. This article is protected by copyright. All rights reserved.

Control of Mammalian Locomotion by Somatosensory Feedback

When animals walk overground, mechanical stimuli activate various receptors located in muscles, joints, and skin. Afferents from these mechanoreceptors project to neuronal networks controlling locomotion in the spinal cord and brain. The dynamic interactions between the control systems at different levels of the neuraxis ensure that locomotion adjusts to its environment and meets task demands. In this article, we describe and discuss the essential contribution of somatosensory feedback to locomotion. We start with a discussion of how biomechanical properties of the body affect somatosensory feedback. We follow with the different types of mechanoreceptors and somatosensory afferents and their activity during locomotion. We then describe central projections to locomotor networks and the modulation of somatosensory feedback during locomotion and its mechanisms. We then discuss experimental approaches and animal models used to investigate the control of locomotion by somatosensory feedback before providing an overview of the different functional roles of somatosensory feedback for locomotion. Lastly, we briefly describe the role of somatosensory feedback in the recovery of locomotion after neurological injury. We highlight the fact that somatosensory feedback is an essential component of a highly integrated system for locomotor control. © 2021 American Physiological Society. Compr Physiol 11:1-71, 2021.

Costs of position, velocity, and force requirements in optimal control induce triphasic muscle activation during reaching movement

The nervous system activates a pair of agonist and antagonist muscles to determine the muscle activation pattern for a desired movement. Although there is a problem with redundancy, it is solved immediately, and movements are generated with characteristic muscle activation patterns in which antagonistic muscle pairs show alternate bursts with a triphasic shape. To investigate the requirements for deriving this pattern, this study simulated arm movement numerically by adopting a musculoskeletal arm model and an optimal control. The simulation reproduced the triphasic electromyogram (EMG) pattern observed in a reaching movement using a cost function that considered three terms: end-point position, velocity, and force required; the function minimised neural input. The first, second, and third bursts of muscle activity were generated by the cost terms of position, velocity, and force, respectively. Thus, we concluded that the costs of position, velocity, and force requirements in optimal control can induce triphasic EMG patterns. Therefore, we suggest that the nervous system may control the body by using an optimal control mechanism that adopts the costs of position, velocity, and force required; these costs serve to initiate, decelerate, and stabilise movement, respectively.

Force variability is mostly not motor noise: Theoretical implications for motor control

Variability in muscle force is a hallmark of healthy and pathological human behavior. Predominant theories of sensorimotor control assume 'motor noise' leads to force variability and its 'signal dependence' (variability in muscle force whose amplitude increases with intensity of neural drive). Here, we demonstrate that the two proposed mechanisms for motor noise (i.e. the stochastic nature of motor unit discharge and unfused tetanic contraction) cannot account for the majority of force variability nor for its signal dependence. We do so by considering three previously underappreciated but physiologically important features of a population of motor units: 1) fusion of motor unit twitches, 2) coupling among motoneuron discharge rate, cross-bridge dynamics, and muscle mechanics, and 3) a series-elastic element to account for the aponeurosis and tendon. These results argue strongly against the idea that force variability and the resulting kinematic variability are generated primarily by 'motor noise.' Rather, they underscore the importance of variability arising from properties of control strategies embodied through distributed sensorimotor systems. As such, our study provides a critical path toward developing theories and models of sensorimotor control that provide a physiologically valid and clinically useful understanding of healthy and pathologic force variability.

Learning to use Muscles

The human musculoskeletal system is highly complex mechanically. Its neural control must deal successfully with this complexity to perform the diverse, efficient, robust and usually graceful behaviors of which humans are capable. Most of those behaviors might be performed by many different subsets of its myriad possible states, so how does the nervous system decide which subset to use? One solution that has received much attention over the past 50 years would be for the nervous system to be fundamentally limited in the patterns of muscle activation that it can access, a concept known as muscle synergies or movement primitives. Another solution, based on engineering control methodology, is for the nervous system to compute the single optimal pattern of muscle activation for each task according to a cost function. This review points out why neither appears to be the solution used by humans. There is a third solution that is based on trial-and-error learning, recall and interpolation of sensorimotor programs that are good-enough rather than limited or optimal. The solution set acquired by an individual during the protracted development of motor skills starting in infancy forms the basis of motor habits, which are inherently low-dimensional. Such habits give rise to muscle usage patterns that are consistent with synergies but do not reflect fundamental limitations of the nervous system and can be shaped by training or disability. This habit-based strategy provides a robust substrate for the control of new musculoskeletal structures during evolution as well as for efficient learning, athletic training and rehabilitation therapy.

Multiscale Hill-type modeling of the mechanical muscle behavior driven by the neural drive in isometric conditions

In this study, we present a new model describing the mechanical behavior of the skeletal muscle during isometric contraction. This model is based on a former Hill-inspired model detailing the electromechanical behavior of the muscle based on the Huxley formulation. However, in this new multiscale model the muscle is represented at the Motor Unit (MU) scale. The proposed model is driven by a physiological input describing the firing moments of the activated MUs. Definition of both voluntary and evoked MU recruitment schemes are described, enabling the study of both contractions in isometric conditions. During this type of contraction, there is no movement of the joints and the tendon-muscle complex remains at the same length. Moreover, some well-established macroscopic relationships such as force-length or force-velocity properties are considered. A comparison with a twitch model using the same input definition is provided with both recruitment schemes exhibiting limitations of twitch type models. Finally, the proposed model is validated with a comparison between simulated and recorded force profiles following eight electrical stimulations pulses in isometric conditions. The simulated muscle force was generated to mimic the one recorded from the quadriceps of a patient implanted with a functional electrical stimulation neuroprosthesis. This validation demonstrates the ability of the proposed model to reproduce realistically the skeletal muscle contractions and to take into account subject-specific parameters.

Metabolic cost calculations of gait using musculoskeletal energy models, a comparison study

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.

Metabolic Cost of Activation and Mechanical Efficiency of Mouse Soleus Muscle Fiber Bundles During Repetitive Concentric and Eccentric Contractions

Currently available data on the energetics of isolated muscle preparations are based on bouts of less than 10 muscle contractions, whereas metabolic energy consumption is mostly relevant during steady state tasks such as locomotion. In this study we quantified the energetics of small fiber bundles of mouse soleus muscle during prolonged (2 min) series of contractions. Bundles (N = 9) were subjected to sinusoidal length changes, while measuring force and oxygen consumption. Stimulation (five pulses at 100 Hz) occurred either during shortening or during lengthening. Movement frequency (2–3 Hz) and amplitude (0.25–0.50 mm; corresponding to ± 4–8% muscle fiber strain) were close to that reported for mouse soleus muscle during locomotion. The experiments were performed at 32°C. The contributions of cross-bridge cycling and muscle activation to total metabolic energy expenditure were separated using blebbistatin. The mechanical work per contraction cycle decreased sharply during the first 10 cycles, emphasizing the importance of prolonged series of contractions. The mean ± SD fraction of metabolic energy required for activation was 0.37 ± 0.07 and 0.56 ± 0.17 for concentric and eccentric contractions, respectively (both 0.25 mm, 2 Hz). The mechanical efficiency during concentric contractions increased with contraction velocity from 0.12 ± 0.03 (0.25 mm 2 Hz) to 0.15 ± 0.03 (0.25 mm, 3 Hz) and 0.16 ± 0.02 (0.50 mm, 2 Hz) and was -0.22 ± 0.08 during eccentric contractions (0.25 mm, 2 Hz). The percentage of type I fibers correlated positively with mechanical efficiency during concentric contractions, but did not correlate with the fraction of metabolic energy required for activation.

Lack of influence of estrogen on myosin phosphorylation and post-tetanic potentiation in muscles from young adult C57BL mice

Estrogen influences myosin phosphorylation and post-tetanic potentiation in murine fast muscle. We tested the hypothesis that this influence is mediated by estrogen effects on skeletal myosin light chain kinase (skMLCK) activity. To this end, extensor digitorum longus muscles from female wildtype and skMLCK-absent (skMLCK^-/-) mice were grouped as follows: ovariectomized with estrogen (E+), ovariectomized without estrogen (E-), sham surgery, and intact baseline. At 8 weeks of age, the ovariectomized groups were ovariectomized followed by implantation of either a 0.1 mg 17β-estradiol (E+) or placebo pellet (E-). Two weeks later, muscles were isolated and suspended in vitro (25° C) for determination of regulatory light chain phosphorylation and post-tetanic potentiation. Regulatory light chain phosphorylation was not different across conditions within either genotype although wildtype values were significantly greater than skMLCK^-/- values. Consistent with this, the potentiation of concentric twitch force was similar between E+ and E- groups within each genotype but wildtype values were greater than skMLCK^-/- values. However, unaltered estradiol levels following ovariectomy, likely due to previously underappreciated confounds of mouse age, development, and growth during estrogen supplementation, prevented direct testing of the hypothesis. Future studies should note the importance of estrous cycles and continuing physiological developments of young adult mice when working with ovarian hormones.

Proprioceptive Recognition with Artificial Neural Networks Based on Organizations of Spinocerebellar Tract and Cerebellum

Muscle kinematics and kinetics are nonlinearly encoded by proprioceptors, and the changes in muscle length and velocity are integrated into Ia afferent. Besides, proprioceptive signals from multiple muscles are probably mixed in afferent pathways, which all lead to difficulties in proprioceptive recognition for the cerebellum. In this study, the artificial neural networks, whose organizations are biologically based on the spinocerebellar tract and cerebellum, are utilized to decode the proprioceptive signals. Consistent with the controversy of the proprioceptive division in the dorsal spinocerebellar tract, the spinocerebellar tract networks incorporated two distinct inferences, (1) the centralized networks, which mixed Ia, II, and Ib and processed them together; (2) the decentralized networks, which processed Ia, II, and Ib afferents separately. The cerebellar networks were based on the Marr-Albus model to recognize the kinematic states. The networks were trained by a specific movement, and the trained networks were subsequently required to predict kinematic states of six movements. The results demonstrated that the centralized networks, which were more consistent with the physiological findings in recent years, had better recognition accuracy than the decentralized networks, and the networks were still effective even when proprioceptive afferents from multiple muscles were integrated.

Coordination of hamstrings is individual specific and is related to motor performance

The torque-sharing strategies between synergistic muscles may have important functional consequences. This study involved two experiments. The first experiment ( n = 22) aimed 1) to determine the relationship between the distribution of activation and the distribution of torque-generating capacity among the heads of the hamstring, and 2) to describe individual torque-sharing strategies and to determine whether these strategies are similar between legs. The second experiment ( n = 35) aimed to determine whether the distribution of activation between the muscle heads affects endurance performance during a sustained submaximal knee flexion task. Surface electromyography (EMG) was recorded from biceps femoris (BF), semimembranosus (SM), and semitendinosus (ST) during submaximal isometric knee flexions. Torque-generating capacity was estimated by measuring muscle volume, fascicle length, pennation angle, and moment arm. The product of the normalized EMG amplitude and the torque-generating capacity was used as an index of muscle torque. The distributions of muscle activation and of torque-generating capacity were not correlated significantly (all P > 0.18). Thus, there was a torque imbalance between the muscle heads (ST torque > BF and SM torque; P < 0.001), the magnitude of which varied greatly between participants. A significant negative correlation was observed between the imbalance of activation across the hamstring muscles and the time to exhaustion ( P < 0.001); i.e., the larger the imbalance of activation across muscles, the lower the muscle endurance performance. Torque-sharing strategies between the heads of the hamstrings are individual specific and related to muscle endurance performance. Whether these individual strategies play a role in hamstring injury remains to be determined.

NEW & NOTEWORTHY The distribution of activation among the heads of the hamstring is not related to the distribution of torque-generating capacity. The torque-sharing strategies within hamstring muscles vary greatly between individuals but are similar between legs. Hamstring coordination affects endurance performance; i.e., the larger the imbalance of activation across the muscle heads, the lower the muscle endurance.

Epinephrine augments posttetanic potentiation in mouse skeletal muscle with and without myosin phosphorylation

Sympathetic tone may influence force potentiation, that is, the stimulation-induced increase in skeletal muscle mechanical function associated with myosin phosphorylation, although the mechanism for this effect remains unknown. The purpose of this study was to examine the influence of epinephrine on concentric twitch force potentiation of wild-type and skeletal myosin light-chain kinase devoid mouse muscle (skMLCK-/- ). To this end, concentric twitch force was assessed before and after a potentiating stimulus (PS) to determine the peak and the duration of potentiation in the absence (-EPI) and presence (+EPI) of 1 μmol/L epinephrine in both genotypes. Twitch force of wild-type and skMLCK-/- muscles was increased by up to 31 and 35% and 18 and 23% in the -EPI and EPI conditions, respectively (all data n = 8, P < 0.05). In wild-type muscles, the PS increased RLC phosphorylation from 0.14 ± 0.05 (rest) to 0.66 ± 0.08 mol phos mol RLC; by 480 sec RLC phosphorylation had returned to baseline (all data n = 4 each time point, P < 0.05). Neither resting nor peak levels of RLC phosphorylation were altered by +EPI, although the duration of RLC phosphorylation was prolonged. In skMLCK-/- muscles, RLC phosphorylation was not elevated above constituent levels by stimulation in either the -EPI or +EPI condition. Thus, given the similarity in potentiation responses between genotypes our data suggest that the influence of epinephrine on potentiation was independent of skMLCK catalyzed phosphorylation of the RLC, although the clinical significance of this pathway for skeletal muscle function remains to be identified.

Muscle and Limb Mechanics

Understanding of the musculoskeletal system has evolved from the collection of individual phenomena in highly selected experimental preparations under highly controlled and often unphysiological conditions. At the systems level, it is now possible to construct complete and reasonably accurate models of the kinetics and energetics of realistic muscles and to combine them to understand the dynamics of complete musculoskeletal systems performing natural behaviors. At the reductionist level, it is possible to relate most of the individual phenomena to the anatomical structures and biochemical processes that account for them. Two large challenges remain. At a systems level, neuroscience must now account for how the nervous system learns to exploit the many complex features that evolution has incorporated into muscle and limb mechanics. At a reductionist level, medicine must now account for the many forms of pathology and disability that arise from the many diseases and injuries to which this highly evolved system is inevitably prone. © 2017 American Physiological Society. Compr Physiol 7:429-462, 2017.

Modulation of Skeletal Muscle Contraction by Myosin Phosphorylation

The striated muscle sarcomere is a highly organized and complex enzymatic and structural organelle. Evolutionary pressures have played a vital role in determining the structure-function relationship of each protein within the sarcomere. A key part of this multimeric assembly is the light chain-binding domain (LCBD) of the myosin II motor molecule. This elongated "beam" functions as a biological lever, amplifying small interdomain movements within the myosin head into piconewton forces and nanometer displacements against the thin filament during the cross-bridge cycle. The LCBD contains two subunits known as the essential and regulatory myosin light chains (ELC and RLC, respectively). Isoformic differences in these respective species provide molecular diversity and, in addition, sites for phosphorylation of serine residues, a highly conserved feature of striated muscle systems. Work on permeabilized skeletal fibers and thick filament systems shows that the skeletal myosin light chain kinase catalyzed phosphorylation of the RLC alters the "interacting head motif" of myosin motor heads on the thick filament surface, with myriad consequences for muscle biology. At rest, structure-function changes may upregulate actomyosin ATPase activity of phosphorylated cross-bridges. During activation, these same changes may increase the Ca2+ sensitivity of force development to enhance force, work, and power output, outcomes known as "potentiation." Thus, although other mechanisms may contribute, RLC phosphorylation may represent a form of thick filament activation that provides a "molecular memory" of contraction. The clinical significance of these RLC phosphorylation mediated alterations to contractile performance of various striated muscle systems are just beginning to be understood. © 2017 American Physiological Society. Compr Physiol 7:171-212, 2017.

Preliminary investigation of energy comparation between gyroscope, electromyography and VO2 wearable sensors

Building on previous experiments in the domain of energy expenditure estimation using wearable sensors, the measurements of energy ratios of a runner on a treadmill were analyzed to observe any commonalities between an inertia measurement unit and an electromyograph sensor. The subjects were equipped with a VO2 gas measurement device, an Inertial Measurement Unit (IMU) measuring gyroscopic activity and an electromyography (EMG) sensor network whilst running at 5 different speeds on a calibrated treadmill. The observed results established a co-linear relationship with the gyroscope based measurements, EMG based measurements with the VO2 measurements.

Validated Predictions of Metabolic Energy Consumption for Submaximal Effort Movement

Physical performance emerges from complex interactions among many physiological systems that are largely driven by the metabolic energy demanded. Quantifying metabolic demand is an essential step for revealing the many mechanisms of physical performance decrement, but accurate predictive models do not exist. The goal of this study was to investigate if a recently developed model of muscle energetics and force could be extended to reproduce the kinematics, kinetics, and metabolic demand of submaximal effort movement. Upright dynamic knee extension against various levels of ergometer load was simulated. Task energetics were estimated by combining the model of muscle contraction with validated models of lower limb musculotendon paths and segment dynamics. A genetic algorithm was used to compute the muscle excitations that reproduced the movement with the lowest energetic cost, which was determined to be an appropriate criterion for this task. Model predictions of oxygen uptake rate (VO₂) were well within experimental variability for the range over which the model parameters were confidently known. The model's accurate estimates of metabolic demand make it useful for assessing the likelihood and severity of physical performance decrement for a given task as well as investigating underlying physiologic mechanisms.

Muscles consume metabolic energy to generate movement. Performing a movement over a long period of time or at a high intensity strains the respiratory and cardiovascular systems that need to replenish the energy reserves in muscle. Furthermore, consuming and replenishing metabolic energy involves biochemical reactions with byproducts that cause muscle fatigue. These biochemical reactions also produce heat that increases body temperature, potentially causing central fatigue. A model of muscle metabolic demand is therefore necessary for predicting and understanding the interaction of these factors that could limit performance, but currently no model exists for arbitrary physical tasks. In this study, we developed a model of metabolic demand by integrating a recently developed and validated model of muscle energetics into a musculoskeletal model. We showed that model predictions for leg exercise over a wide range of intensities were well within the experimental variability reported in the literature. To our knowledge, the muscle energetics model is the first to make valid predictions of metabolic demand at both the muscle and task level. The model is an important step toward understanding and planning around physical performance decrement, which is particularly useful for rehabilitation, competitive sports, and the military.

Major remaining gaps in models of sensorimotor systems

Experimental descriptions of the anatomy and physiology of individual components of sensorimotor systems have revealed substantial complexity, making it difficult to intuit how complete systems might work. This has led to increasing efforts to develop and employ mathematical models to study the emergent properties of such systems. Conversely, the development of such models tends to reveal shortcomings in the experimental database upon which models must be constructed and validated. In both cases models are most useful when they point up discrepancies between what we think we know and possibilities that we may have overlooked. This overview considers those components of complete sensorimotor systems that currently appear to be potentially important but poorly understood. These are generally omitted completely from modeled systems or buried in implicit assumptions that underlie the design of the model.

ADVANCES REGARDING POWERED PROSTHESIS FOR TRANSTIBIAL AMPUTATION

The necessity for developing advanced prostheses are apparent in light of projections that the forecast for the number of people enduring amputation will double by the year 2050. The transtibial powered prosthesis that enables positive mechanical work about the ankle during the powered plantar flexion aspect of stance phase constitutes a paradigm shift in available transtibial prostheses. The objective of the review is to advocate the state of the art regarding the transtibial powered prosthesis. The historic origins of the prosthesis and motivations for amputation are clarified. The phases of gait and the compensatory mechanisms and asymmetries inherent with passive transtibial prostheses are described. The three general classes of transtibial prosthesis (passive, energy storage and return and powered prostheses) are defined. Subsystems that are integral to the powered prosthesis are explained, such as the series elastic actuator and control architecture. Gait analysis systems and their role for the test and evaluation of energy storage and return and powered prostheses are demonstrated. Future advanced concepts; such as the integration of titin into novel muscle models that account for force enhancement and force depression including their implications for cutting edge bio-inspired actuators are elucidated. The review accounts for the evolution of the prosthetic device with regards to the scope of transtibial amputation and assesses the current state-of-the-art.

Simulation of a computational winding filament model with an exponential spring to represent titin

The goal of developing high fidelity simulation of muscle force is of considerable interest for the biomedical community. Traditionally Hill models have been incorporated. However, feasible scope of the Hill model is inherently limited, especially in light of the growing relevance of muscle history dependence. History dependence is considered to be significant for motor control and stability. Attempts have been made to augment the Hill model to emulate history dependence. The titin winding filament model best elucidates history dependence of muscle force including force enhancement. The recent version of the titin winding filament model accounts for the functionality of titin through a pulley linked with the contractile element and a linear spring to represent the elastic properties of titin. A new and more realistic amendment to the winding filament model is incorporation of an exponential spring to characterize the elastic properties of titin. A sensitivity study as a function of the titin exponential spring constant is presented. Overall the amalgamation of the titin exponential spring to the winding filament model improves the respective force enhancement characteristics with a relatively more optimal exponential spring constant that provides a maximal averaged coefficient of determination.

A highly efficient semiphenomenological model of a half-sarcomere for real-time prediction of mechanical behavior

With existent biomechanical models of skeletal muscle, challenges still exist in implementing real-time predictions for contraction statuses that are particularly significant to biomechanical and biomedical engineering. Because of this difficulty, this paper proposed a decoupled scheme of the links involved in the working process of a sarcomere and established a semiphenomenological model integrating both linear and nonlinear frames of no higher than a second-order system. In order to facilitate engineering application and cybernetics, the proposed model contains a reduced number of parameters and no partial differential equation, making it highly concise and computationally efficient. Through the simulations of various contraction modes, including isometric, isotonic, successive stretch and release, and cyclic contractions, the correctness and efficiency of the model, are validated. Although this study targets half-sarcomeres, the proposed model can be easily extended to describe the larger-scale mechanical behavior of a muscle fiber or a whole muscle.

Effect of vastus lateralis fatigue on load sharing between quadriceps femoris muscles during isometric knee extensions

The present study aimed to investigate the effects of selective fatigue (i.e., one muscle of the quadriceps) on load sharing strategies during submaximal knee extensions. Shear wave elastography was used to measure muscle shear elastic modulus, as this is considered to be an index of individual muscle force. Sixteen participants attended two experimental sessions that each involved six 10-s knee extensions at 20% of maximal voluntary contraction (MVC) followed by a sustained submaximal isometric knee extension at 20% of MVC, until task failure (Tlim). Between the 10-s contractions and Tlim, participants were required to rest (5 min) for the control session or underwent 5 min of electromyostimulation (EMS) on vastus lateralis (EMS session). Compared with the control session, vastus lateralis shear elastic modulus values were significantly lower after EMS considering both the start of Tlim (54.6 ± 11.8 vs. 68.4 ± 19.2 kPa; P = 0.011) and the entire Tlim contraction (59.0 ± 14.0 vs. 74.4 ± 20.3 kPa; P = 0.019). However, no significant differences were observed for the other recorded muscles (vastus medialis and rectus femoris; both P = 1), i.e., different patterns of changes were found between participants. In conclusion, this study demonstrates that prefatiguing a single agonist muscle does not lead to a consistent redistribution of load sharing among the quadriceps muscles between individuals. These results suggest that the central nervous system does not use a common principle among individuals to control load sharing when neuromuscular fatigue occurs.

Efficiency and cross-bridge work output of skeletal muscle is decreased at low levels of activation

The purpose of this study was to determine how the mechanical efficiency of skeletal muscle is affected by level of activation. Experiments were performed in vitro (35 °C) using bundles of fibres from fast-twitch extensor digitorum longus (EDL) and slow-twitch soleus muscles of mice. Measurements were made of the total work and heat produced in response to 10 brief contractions. Mechanical efficiency was the ratio of total work performed to (total heat produced + work performed). Level of activation was varied by altering stimulation frequency between 40 and 160 Hz. Efficiency did not differ significantly between the two muscle types but was significantly lower using 40 Hz stimulation (mean efficiency ± SEM, 0.092 ± 0.012, n = 12, averaged across EDL and soleus) than at any of the other frequencies (160 Hz: 0.147 ± 0.007, n = 12). Measurements of the partitioning of energy output between force-dependent and force-independent components enabled calculation of the amount of Ca(2+) released and number of cross-bridge cycles performed during the contractions. At 40 Hz stimulation frequency, less Ca(2+) was released than at higher frequencies and fewer cross-bridge cycles were performed. Furthermore, less work was performed in each cross-bridge cycle. It is concluded that skeletal muscles are less efficient at low levels of activation than when fully activated and this indicates that level of activation affects not only the number of cycling cross-bridges but also the ability of individual cross-bridges to perform work.

Wrist torque estimation during simultaneous and continuously changing movements: surface vs. untargeted intramuscular EMG

In this paper, the predictive capability of surface and untargeted intramuscular electromyography (EMG) was compared with respect to wrist-joint torque to quantify which type of measurement better represents joint torque during multiple degrees-of-freedom (DoF) movements for possible application in prosthetic control. Ten able-bodied subjects participated in the study. Surface and intramuscular EMG was recorded concurrently from the right forearm. The subjects were instructed to track continuous contraction profiles using single and combined DoF in two trials. The association between torque and EMG was assessed using an artificial neural network. Results showed a significant difference between the two types of EMG (P < 0.007) for all performance metrics: coefficient of determination (R(2)), Pearson correlation coefficient (PCC), and root mean square error (RMSE). The performance of surface EMG (R(2) = 0.93 ± 0.03; PCC = 0.98 ± 0.01; RMSE = 8.7 ± 2.1%) was found to be superior compared with intramuscular EMG (R(2) = 0.80 ± 0.07; PCC = 0.93 ± 0.03; RMSE = 14.5 ± 2.9%). The higher values of PCC compared with R(2) indicate that both methods are able to track the torque profile well but have some trouble (particularly intramuscular EMG) in estimating the exact amplitude. The possible cause for the difference, thus the low performance of intramuscular EMG, may be attributed to the very high selectivity of the recordings used in this study.

Optimal isn't good enough

The notion that biological systems come to embody optimal solutions seems consistent with the competitive drive of evolution. It has been used to interpret many examples of sensorimotor behavior. It is attractive from the viewpoint of control engineers because it solves the redundancy problem by identifying the one optimal motor strategy out of many similarly acceptable possibilities. This perspective examines whether there is sufficient basis to apply the formal engineering tools of optimal control to a reductionist understanding of biological systems. For an experimental biologist, this translates into whether the theory of optimal control generates nontrivial and testable hypotheses that accurately predict novel phenomena, ideally at deeper levels of structure than the observable behavior. The methodology of optimal control is applicable when there is (i) a single, known cost function to be optimized, (ii) an invertible model of the plant, and (iii) simple noise interfering with optimal performance. None of these is likely to be true for biological organisms. Furthermore, their motivation is usually good-enough rather than globally optimal behavior. Even then, the performance of a biological organism is often much farther from optimal than the physical limits of its hardware because the brain is continuously testing the acceptable limits of performance as well as just performing the task. This perspective considers an alternative strategy called "good-enough" control, in which the organism uses trial-and-error learning to acquire a repertoire of sensorimotor behaviors that are known to be useful, but not necessarily optimal. This leads to a diversity of solutions that tends to confer robustness on the individual organism and its evolution. It is also more consistent with the capabilities of higher sensorimotor structures, such as cerebral cortex, which seems to be designed to classify and recall complex sets of information, thereby allowing the organism to learn from experience, rather than to compute new strategies online. Optimal control has been a useful metaphor for understanding some superficial aspects of motor psychophysics. Reductionists who want to understand the underlying neural mechanisms need to move on.

Virtual biomechanics: a new method for online reconstruction of force from EMG recordings

Current methods to reconstruct muscle contributions to joint torque usually combine electromyograms (EMGs) with cadaver-based estimates of biomechanics, but both are imperfect representations of reality. Here, we describe a new method that enables online force reconstruction in which we optimize a "virtual" representation of muscle biomechanics. We first obtain tuning curves for the five major wrist muscles from the mean rectified EMG during the hold phase of an isometric aiming task when a cursor is driven by actual force recordings. We then apply a custom, gradient-descent algorithm to determine the set of "virtual pulling vectors" that best reach the target forces when combined with the observed muscle activity. When these pulling vectors are multiplied by the rectified and low-pass-filtered (1.3 Hz) EMG of the five muscles online, the reconstructed force provides a close spatiotemporal match to the true force exerted at the wrist. In three separate experiments, we demonstrate that the technique works equally well for surface and fine-wire recordings and is sensitive to biomechanical changes elicited by a modification of the forearm posture. In all conditions tested, muscle tuning curves obtained when the task was performed with feedback of reconstructed force were similar to those obtained when the task was performed with real force feedback. This online force reconstruction technique provides new avenues to study the relationship between neural control and limb biomechanics since the "virtual biomechanics" can be systematically altered at will.

Muscle coordination is habitual rather than optimal

When sharing load among multiple muscles, humans appear to select an optimal pattern of activation that minimizes costs such as the effort or variability of movement. How the nervous system achieves this behavior, however, is unknown. Here we show that contrary to predictions from optimal control theory, habitual muscle activation patterns are surprisingly robust to changes in limb biomechanics. We first developed a method to simulate joint forces in real time from electromyographic recordings of the wrist muscles. When the model was altered to simulate the effects of paralyzing a muscle, the subjects simply increased the recruitment of all muscles to accomplish the task, rather than recruiting only the useful muscles. When the model was altered to make the force output of one muscle unusually noisy, the subjects again persisted in recruiting all muscles rather than eliminating the noisy one. Such habitual coordination patterns were also unaffected by real modifications of biomechanics produced by selectively damaging a muscle without affecting sensory feedback. Subjects naturally use different patterns of muscle contraction to produce the same forces in different pronation-supination postures, but when the simulation was based on a posture different from the actual posture, the recruitment patterns tended to agree with the actual rather than the simulated posture. The results appear inconsistent with computation of motor programs by an optimal controller in the brain. Rather, the brain may learn and recall command programs that result in muscle coordination patterns generated by lower sensorimotor circuitry that are functionally "good-enough."