Adjustment of muscle mechanics model parameters to simulate dynamic contractions in older adults

MRI-based anatomical characterisation of lower-limb muscles in older women

The ability of muscles to produce force depends, among others, on their anatomical features and it is altered by ageing-associated weakening. However, a clear characterisation of these features, highly relevant for older individuals, is still lacking. This study hence aimed at characterising muscle volume, length, and physiological cross-sectional area (PCSA) and their variability, between body sides and between individuals, in a group of post-menopausal women. Lower-limb magnetic resonance images were acquired from eleven participants (69 (7) y. o., 66.9 (7.7) kg, 159 (3) cm). Twenty-three muscles were manually segmented from the images and muscle volume, length and PCSA were calculated from this dataset. Personalised maximal isometric force was then calculated using the latter information. The percentage difference between the muscles of the two lower limbs was up to 89% and 22% for volume and length, respectively, and up to 84% for PCSA, with no recognisable pattern associated with limb dominance. Between-subject coefficients of variation reached 36% and 13% for muscle volume and length, respectively. Generally, muscle parameters were similar to previous literature, but volumes were smaller than those from in-vivo young adults and slightly higher than ex-vivo ones. Maximal isometric force was found to be on average smaller than those obtained from estimates based on linear scaling of ex-vivo-based literature values. In conclusion, this study quantified for the first time anatomical asymmetry of lower-limb muscles in older women, suggesting that symmetry should not be assumed in this population. Furthermore, we showed that a scaling approach, widely used in musculoskeletal modelling, leads to an overestimation of the maximal isometric force for most muscles. This heavily questions the validity of this approach for older populations. As a solution, the unique dataset of muscle segmentation made available with this paper could support the development of alternative population-based scaling approaches, together with that of automatic tools for muscle segmentation.

An EMG-Driven Musculoskeletal Model for Estimating Continuous Wrist Motion

EMG-based continuous wrist joint motion estimation has been identified as a promising technique with huge potential in assistive robots. Conventional data-driven model-free methods tend to establish the relationship between the EMG signal and wrist motion using machine learning or deep learning techniques, but cannot interpret the functional relationship between neuro-commands and relevant joint motion. In this paper, an EMG-driven musculoskeletal model is proposed to estimate continuous wrist joint motion. This model interprets the muscle activation levels from EMG signals. A muscle-tendon model is developed to compute the muscle force during the voluntary flexion/extension movement, and a joint kinematic model is established to estimate the continuous wrist motion. To optimize the subject-specific physiological parameters, a genetic algorithm is designed to minimize the differences of joint motion prediction from the musculoskeletal model and joint motion measurement using motion data during training. Results show that mean root-mean-square-errors are 10.08°, 10.33°, 13.22° and 17.59° for single flexion/extension, continuous cycle and random motion trials, respectively. The mean coefficient of determination is over 0.9 for all the motion trials. The proposed EMG-driven model provides an accurate tracking performance based on user's intention.

Muscle contributions to maximal single-leg forward braking and backward acceleration in elite athletes

Abrupt deceleration is a common practice in several sports, where sudden changes of direction are needed to reach the highest performance level. When inappropriately performed, these actions can impose excessive mechanical loads at the lower limb joints, specifically at the knee and ankle joints, usually associated with increased risk of injury. This work aims to estimate muscle forces and muscle contributions to the acceleration of the center of mass during a rapid maximal single-leg forward braking and backward acceleration task. Fourteen elite male injury-free indoor-sports athletes participated in this work. Scaled generic musculoskeletal models, consisting of 12 segments, 23 degrees of freedom, and 92 muscle-tendon actuators were used in OpenSim software. Due to the nature of the musculoskeletal system, all muscles are considered when joint and segment positions, velocities, and accelerations are calculated, resulting in muscles acting to accelerate joints it does not span. The knowledge of muscle interaction during this multijoint task is important and was achieved through an induced acceleration analysis. The vasti (-9.18 ± 2.09 and -7.63 ± 1.33 N/Kg) were the main contributors to the centre of mass deceleration profile along the anterior/posterior direction, aided by the soleus muscle (9.72 ± 2.35 and 9.62 ± 2.07 N/Kg), which counteracted most of the effects applied by gravity along the vertical direction, during both phases. This study provides a computational approach to quantify the dynamical interactions between muscles and joints during an abrupt anterior/posterior deceleration task, thus giving robust and insightful indicators that can be implemented in injury prevention protocols.

Differences between joint-space and musculoskeletal estimations of metabolic rate time profiles

Motion capture laboratories can measure multiple variables at high frame rates, but we can only measure the average metabolic rate of a stride using respiratory measurements. Biomechanical simulations with equations for calculating metabolic rate can estimate the time profile of metabolic rate within the stride cycle. A variety of methods and metabolic equations have been proposed, including metabolic time profile estimations based on joint parameters. It is unclear whether differences in estimations are due to differences in experimental data or due to methodological differences. This study aimed to compare two methods for estimating the time profile of metabolic rate, within a single dataset. Knowledge about the consistency of different methods could be useful for applications such as detecting which part of the gait cycle causes increased metabolic cost in patients. Here we compare estimations of metabolic rate time profiles using a musculoskeletal and a joint-space method. The musculoskeletal method was driven by kinematics and electromyography data and used muscle metabolic rate equations, whereas the joint-space method used metabolic rate equations based on joint parameters. Both estimations of changes in stride average metabolic rate correlated significantly with large changes in indirect calorimetry from walking on different grades showing that both methods accurately track changes. However, estimations of changes in stride average metabolic rate did not correlate significantly with more subtle changes in indirect calorimetry due to walking with different shoe inclinations, and both the musculoskeletal and joint-space time profile estimations did not correlate significantly with each other except in the most downward shoe inclination. Estimations of the relative cost of stance and swing matched well with previous simulations with similar methods and estimations from experimental perturbations. Rich experimental datasets could further advance time profile estimations. This knowledge could be useful to develop therapies and assistive devices that target the least metabolically economic part of the gait cycle.

Efficient Actor-Critic Reinforcement Learning With Embodiment of Muscle Tone for Posture Stabilization of the Human Arm

This letter proposes a new idea to improve learning efficiency in reinforcement learning (RL) with the actor-critic method used as a muscle controller for posture stabilization of the human arm. Actor-critic RL (ACRL) is used for simulations to realize posture controls in humans or robots using muscle tension control. However, it requires very high computational costs to acquire a better muscle control policy for desirable postures. For efficient ACRL, we focused on embodiment that is supposed to potentially achieve efficient controls in research fields of artificial intelligence or robotics. According to the neurophysiology of motion control obtained from experimental studies using animals or humans, the pedunculopontine tegmental nucleus (PPTn) induces muscle tone suppression, and the midbrain locomotor region (MLR) induces muscle tone promotion. PPTn and MLR modulate the activation levels of mutually antagonizing muscles such as flexors and extensors in a process through which control signals are translated from the substantia nigra reticulata to the brain stem. Therefore, we hypothesized that the PPTn and MLR could control muscle tone, that is, the maximum values of activation levels of mutually antagonizing muscles using different sigmoidal functions for each muscle; then we introduced antagonism function models (AFMs) of PPTn and MLR for individual muscles, incorporating the hypothesis into the process to determine the activation level of each muscle based on the output of the actor in ACRL. ACRL with AFMs representing the embodiment of muscle tone successfully achieved posture stabilization in five joint motions of the right arm of a human adult male under gravity in predetermined target angles at an earlier period of learning than the learning methods without AFMs. The results obtained from this study suggest that the introduction of embodiment of muscle tone can enhance learning efficiency in posture stabilization disorders of humans or humanoid robots.

Development of a multiscale model of the human lumbar spine for investigation of tissue loads in people with and without a transtibial amputation during sit-to-stand

Quantification of lumbar spine load transfer is important for understanding low back pain, especially among persons with a lower limb amputation. Computational modeling provides a helpful solution for obtaining estimates of in vivo loads. A multiscale model was constructed by combining musculoskeletal and finite element (FE) models of the lumbar spine to determine tissue loading during daily activities. Three-dimensional kinematic and ground reaction force data were collected from participants with ([Formula: see text]) and without ([Formula: see text]) a unilateral transtibial amputation (TTA) during 5 sit-to-stand trials. We estimated tissue-level load transfer from the multiscale model by controlling the FE model with intervertebral kinematics and muscle forces predicted by the musculoskeletal model. Annulus fibrosis stress, intradiscal pressure (IDP), and facet contact forces were calculated using the FE model. Differences in whole-body kinematics, muscle forces, and tissue-level loads were found between participant groups. Notably, participants with TTA had greater axial rotation toward their intact limb ([Formula: see text]), greater abdominal muscle activity ([Formula: see text]), and greater overall tissue loading throughout sit-to-stand ([Formula: see text]) compared to able-bodied participants. Both normalized (to upright standing) and absolute estimates of L4-L5 IDP were close to in vivo values reported in the literature. The multiscale model can be used to estimate the distribution of loads within different lumbar spine tissue structures and can be adapted for use with different activities, populations, and spinal geometries.

Effect of Varying Soft Actuator Band Positions of a Wearable Assist Device on Gait Simulation of Lower Limb Muscle Force

The purpose of this study is to investigate the effect of changing the application points and directions of the soft actuator band of a wearable hip assist device on muscle force and joint kinematics during gait. Healthy adult participants walked under four conditions with varying band positions of a soft wearable hip assist device. The three-dimensional coordinates of markers and ground reaction force data were measured during gait. Lower limb muscle forces and joint angles were calculated using a musculoskeletal model. Our results showed that the position and running direction of the soft actuator band decreased the forces of the iliopsoas and hamstring muscles.

Added mass in rat plantaris muscle causes a reduction in mechanical work

Most of what we know about whole muscle behaviour comes from experiments on single fibres or small muscles that are scaled up in size without considering the effects of the additional muscle mass. Previous modelling studies have shown that tissue inertia acts to slow the rate of force development and maximum velocity of muscle during shortening contractions and decreases the work and power per cycle during cyclic contractions; however, these results have not yet been confirmed by experiments on living tissue. Therefore, in this study we conducted in situ work-loop experiments on rat plantaris muscle to determine the effects of increasing the mass of muscle on mechanical work during cyclic contractions. We additionally simulated these experimental contractions using a mass-enhanced Hill-type model to validate our previous modelling work. We found that greater added mass resulted in lower mechanical work per cycle relative to the unloaded trials in which no mass was added to the muscle (P=0.041 for both 85 and 123% increases in muscle mass). We additionally found that greater strain resulted in lower work per cycle relative to unloaded trials at the same strain to control for length change and velocity effects on the work output, possibly due to greater accelerations of the muscle mass at higher strains. These results confirm that tissue mass reduces muscle mechanical work at larger muscle sizes, and that this effect is likely amplified for lower activations.

A novel ex vivo protocol to mimic human walking gait: implications for Duchenne muscular dystrophy

We developed a novel ex vivo mouse protocol to mimic in vivo human soleus muscle function predicted by musculoskeletal simulations to better understand eccentric contractions during gait and ultimately to better understand their effects in Duchenne muscular dystrophy (DMD) muscles. DMD muscles are susceptible to eccentric injury because the protein dystrophin is absent. The mdx mouse, a DMD model that also lacks dystrophin, is often subjected to ex vivo acute but nonphysiological eccentric injury protocols. It is possible these acute protocols either over- or underestimate eccentric stresses and strains compared with those from humans during gait. To explore this possibility, healthy human soleus excitation, force, and length change profiles during a single walking stride (gait cycle) were simulated using OpenSim and then scaled to an ex vivo mouse soleus preparation based on muscle architectural measurements. Aurora Scientific, Inc., software and a 701C electrical stimulator were modified to discretely modulate muscle stimulation voltage at constant frequency and finely control muscle length changes to produce a force pattern that correctly mimicked the gait cycle from simulations. In a proof-of-principle study, wild-type and mdx mice soleus muscles were subjected to 25 gait cycles. Modest fatigue was evident in the muscles at the 25th versus first gait cycle for both genotypes, but both rapidly recovered isometric force within 1 min of the last cycle. These data indicate that the ex vivo gait protocol was well tolerated. More important, this protocol provides a novel assessment tool to determine the effects of physiological eccentric contractions on dystrophic muscle.NEW & NOTEWORTHY A novel ex vivo mouse soleus protocol that mimics scaled length change and excitation profiles predicted by a mathematical model of human soleus during gait is presented. A custom stimulator was developed that enabled an innovative muscle stimulation technique to modulate voltage to closely match the excitation pattern of human soleus during gait. This ex vivo protocol provides assessment of simulated human movement in mouse muscle, including components of eccentric contractions.

Optimal time-varying postural control in a single-link neuromechanical model with feedback latencies

Maintaining balance during quiet standing is a challenging task for the neural control mechanisms due to the inherent instabilities involved in the task. The feedback latencies and the lowpass characteristics of skeletal muscle add to the difficulty of regulating postural dynamics in real-time. Inverted-pendulum (IP) type robotic models have served as a popular paradigm to investigate control of postural balance. In this study, an in-depth neuromechanical postural control model is developed from physiological principles. The model comprises a single-segment IP robotic model, Hill-type muscle model, and proprioceptive feedback from the muscle spindle (MS) and golgi tendon organ (GTO). An optimal proportional-integral-derivative (PID) controller is proposed to realize effective postural control amid latencies in sensory feedback. The neural commands for postural stabilization are generated by a time-varying PID controller, tuned using linear quadratic regulator (LQR) principles. Computer simulations are used to assess the efficacy of the tuned PID-LQR controller. Sensitivity analysis of the controlled system shows a delay tolerance of 300ms. Preliminary empirical data in support of the mathematical model were obtained from perturbation experiments. The model response to perturbation torque, measured in terms of the center of mass (COM) excursion in the anterior-posterior (AP) direction, displays a high degree of correlation with the empirical data ([Formula: see text]).

Ergonomics assessment of passive upper-limb exoskeletons in an automotive assembly plant

Over the years, the industry's interest in using external support devices, such as exoskeletons, is increasing. They are introduced as a new technique for improving the conditions of workers and for reducing the risk of musculoskeletal injuries. An investigation of muscle activity, Jonsson's (Jonsson, 1982) ergonomic acceptance ranges, and shoulder range of motion was conducted with a sample of 12 workers using an upper extremity exoskeleton in an automotive assembly line. The operators performed continuous cycles of dynamic overhead work consisting of the assembly of the car body at the underside of the car making use of pneumatic screwdrivers. The EMGs (anterior part of deltoid, trapezius, latissimus dorsi and erector spinae) were measured for the muscle activity analysis on the one hand, and for the ergonomics study on the other hand. The latter consisted of an approach based on Jonsson's work, that establishes acceptance thresholds of cumulative percentage of maximum voluntary contraction of muscle activity (%MVC) in a work cycle. The joint angles motion capture was carried out by measuring the angles of the neck, back, and arms joints. All measurements were performed during experimental sessions with and without an exoskeleton. The key findings show reductions of 34% and 18% of the deltoid and the trapezius muscular activities, respectively, which in turn could lead to a reduction of discomfort and fatigue. The erector spinae and latissimus dorsi muscles were not significantly affected by exoskeleton. The values of muscular activity were also represented over Jonsson's acceptance areas. Referring to the posture, some differences were found in the range of movement of back, neck, and arms owing to the use of the exoskeleton; however, the differences were smaller than 5% in all cases.

Effects of Varying Plantarflexion Stiffness of Ankle-Foot Orthosis on Achilles Tendon and Propulsion Force During Gait

An ankle-foot orthosis (AFO) with a plantarflexion resistance function, improves post-stroke gait. An AFO with a plantarflexion resistance function not only affects the first rocker function and the weight acceptance but also the late stance phase. Achilles tendon extension is important for ankle joint function and for forward propulsion during the late stance phase; however, the effect of an AFO with a plantarflexion resistance function on the Achilles tendon is unclear. The purpose of this study was to investigate the effect of plantarflexion resistance on the extension of the Achilles tendon and the forward-propulsive force. Herein, 10 healthy adult males participated who walked under three different conditions: a no-AFO condition and two AFO conditions that had different levels of plantarflexion resistance (P1 and P2). The stiffness value of the P1 and P2 conditions was 0.56 and 1.47 Nm/°, respectively. A three-dimensional (3D) motion analysis system and a musculoskeletal model were used to assess the tendon-length change, the ground reaction force, kinematics, and kinetics data. The change in Achilles tendon length was significantly lower in the P1 and P2 conditions than the no-AFO condition. Furthermore, changes in the length of the Achilles tendon significantly decreased in the P2 condition when compared with that in the P1 condition. The peak anterior ground reaction force was significantly lower in the P2 condition than the no-AFO condition. These results suggest that excessive assist provided by an AFO prevents efficient gait by decreasing both the forward-propulsive force and tendon function.

Effects of Optimization Technique on Simulated Muscle Activations and Forces

Two optimization techniques, static optimization (SO) and computed muscle control (CMC), are often used in OpenSim to estimate the muscle activations and forces responsible for movement. Although differences between SO and CMC muscle function have been reported, the accuracy of each technique and the combined effect of optimization and model choice on simulated muscle function is unclear. The purpose of this study was to quantitatively compare the SO and CMC estimates of muscle activations and forces during gait with the experimental data in the Gait2392 and Full Body Running models. In OpenSim (version 3.1), muscle function during gait was estimated using SO and CMC in 6 subjects in each model and validated against experimental muscle activations and joint torques. Experimental and simulated activation agreement was sensitive to optimization technique for the soleus and tibialis anterior. Knee extension torque error was greater with CMC than SO. Muscle forces, activations, and co-contraction indices tended to be higher with CMC and more sensitive to model choice. CMC's inclusion of passive muscle forces, muscle activation-contraction dynamics, and a proportional-derivative controller to track kinematics contributes to these differences. Model and optimization technique choices should be validated using experimental activations collected simultaneously with the data used to generate the simulation.

Muscle Synergy Control During Hand Reach Task on Varying Shoulder Configuration

Control of human arm in reaching task is a result of complex neural interaction involving central nervous and musculoskeletal system, where, group of muscle activation are planned through synergistic and coordinated recruitment, often to reach an optimal strategy. Aim of this paper is to explore muscle synergy distribution on several reaching task of similar elbow trajectory but changing shoulder configuration. A musculoskeletal model of human arm comprising shoulder, elbow and wrist joint have been designed and is used to calculate muscle activation required to perform three specific reaching tasks. Muscle synergy have been computed on the simulated activation to find a relation between synergy and energy requirement with the change of rotation and elevation of shoulder and its effect on the motion path of the elbow joint. These findings may help to define optimal joint configuration for a planned range of motion during rehabilitation exercises and also in developing neural prosthesis and myoelectric interfaces for efficient arm motion control.

Shear Wave Tensiometry Reveals an Age-Related Deficit in Triceps Surae Work at Slow and Fast Walking Speeds

Prior studies have observed an age-related decline in net ankle power and work at faster walking speeds. However, the underlying changes in muscle-tendon behavior are not well-understood, and are challenging to infer from joint level analyses. This study used shear wave tensiometry to investigate the modulation of force and work done by the triceps surae across walking speeds. Fourteen healthy young (7F/7M, 26 ± 5 years) and older (7F/7M, 67 ± 5 years) adults were tested. Subjects walked on an instrumented treadmill at four walking speeds (0.75, 1.00, 1.25, and 1.50 m/s) while lower extremity kinematics and Achilles tendon shear wave speeds were collected. Subject-specific calibrations were used to compute Achilles tendon force from wave speed. Excursions of the soleus and gastrocnemius muscle-tendon units were computed from the kinematic data and subject-specific measures of the Achilles tendon moment arm. Work loop plots were then used to assess effective muscle-tendon stiffness during lengthening, and positive, negative, and net work production during stance. Two-way mixed ANOVAs were used to evaluate the effects of age group and walking speed on each outcome measure. Tendon loading during muscle-tendon lengthening (effective stiffness) did not differ between age groups, but did vary with speed. The soleus became effectively stiffer with increasing speed while the gastrocnemius became effectively more compliant. There was a marked age-related deficit in net soleus (−66% on average) and gastrocnemius (−36%) work across all walking speeds. We did not observe an age-speed interaction effect on net work production. These results suggest the age-related deficit in triceps surae output in walking is pervasive across speed, and hence seemingly not linked to absolute mechanical demands of the task.

Just Don’t Fall: An AI Agent’s Learning Journey Towards Posture Stabilisation

Learning to maintain postural balance while standing requires a significant, fine coordination effort between the neuromuscular system and the sensory system. It is one of the key contributing factors towards fall prevention, especially in the older population. Using artificial intelligence (AI), we can similarly teach an agent to maintain a standing posture, and thus teach the agent not to fall. In this paper, we investigate the learning progress of an AI agent and how it maintains a stable standing posture through reinforcement learning. We used the Deep Deterministic Policy Gradient method (DDPG) and the OpenSim musculoskeletal simulation environment based on OpenAI Gym. During training, the AI agent learnt three policies. First, it learnt to maintain the Centre-of-Gravity and Zero-Moment-Point in front of the body. Then, it learnt to shift the load of the entire body on one leg while using the other leg for fine tuning the balancing action. Finally, it started to learn the coordination between the two pre-trained policies. This study shows the potentials of using deep reinforcement learning in human movement studies. The learnt AI behaviour also exhibited attempts to achieve an unplanned goal because it correlated with the set goal (e.g., walking in order to prevent falling). The failed attempts to maintain a standing posture is an interesting by-product which can enrich the fall detection and prevention research efforts.

Limited fascicle shortening and fascicle rotation may be associated with impaired voluntary force-generating capacity in pennate muscles of chronic stroke survivors

BACKGROUND

Muscle weakness is one of the most common motor impairments after stroke. A variety of progressive muscular changes are reported in chronic stroke survivors, and it is now feasible to consider these changes as an added source of weakness. However, the net contributions of such muscular changes towards muscle weakness have not been fully quantified.

METHODS

Accordingly, this study aims: (1) to compare muscle architecture of the human medial gastrocnemius between paretic and non-paretic sides in seven chronic hemispheric stroke survivors under passive conditions; (2) to characterize fascicle behavior (i.e., fascicle shortening and fascicle rotation) of the muscle during voluntary isometric contractions; and (3) to assess potential associations between muscle architectural parameters and muscle weakness. Muscle architecture of the medial gastrocnemius (including fascicle length, fascicle pennation angle, and muscle thickness) was characterized using B-mode ultrasonography, and fascicle behavior was then quantified as a function of isometric plantarflexion torque normalized to body mass.

FINDINGS

Our experimental results showed that under passive conditions, there was a significant difference in fascicle length and muscle thickness between paretic and non-paretic muscles, but no difference in resting fascicle pennation angle. However, during isometric contraction, both fascicle shortening and fascicle rotation on the paretic side were significantly decreased, compared to the non-paretic side. Moreover, the relative (i.e., paretic/non-paretic) fascicle rotation-shortening ratio (i.e., fascicle rotation per fascicle shortening) was strongly correlated with the relative maximum voluntary isometric plantarflexion torque.

INTERPRETATION

This association implies that such fascicle changes could impair the force-generating capacity of the muscle in chronic stroke survivors.

Direct Validation of Model-Predicted Muscle Forces in the Cat Hindlimb During Locomotion

Various methods are available for simulating the movement patterns of musculoskeletal systems and determining individual muscle forces, but the results obtained from these methods have not been rigorously validated against experiment. The aim of this study was to compare model predictions of muscle force derived for a cat hindlimb during locomotion against direct measurements of muscle force obtained in vivo. The cat hindlimb was represented as a 5-segment, 13-degrees-of-freedom (DOF), articulated linkage actuated by 25 Hill-type muscle-tendon units (MTUs). Individual muscle forces were determined by combining gait data with two widely used computational methods-static optimization and computed muscle control (CMC)-available in opensim, an open-source musculoskeletal modeling and simulation environment. The forces developed by the soleus, medial gastrocnemius (MG), and tibialis anterior muscles during free locomotion were measured using buckle transducers attached to the tendons. Muscle electromyographic activity and MTU length changes were also measured and compared against the corresponding data predicted by the model. Model-predicted muscle forces, activation levels, and MTU length changes were consistent with the corresponding quantities obtained from experiment. The calculated values of muscle force obtained from static optimization agreed more closely with experiment than those derived from CMC.

Inclusion of actuator dynamics in simulations of assisted human movement

Simulation of musculoskeletal systems using dynamic optimization is a powerful approach for studying the biomechanics of human movements and can be applied to human-robot interactions. The simulation results of human movements augmented by robotic devices may be used to evaluate and optimize the device design and controller. However, simulations are limited by the accuracy of the models which are usually simplified for computation efficiency. Typically, the powered robotic devices are often modeled as massless, ideal torque actuators that is without mass and internal dynamics, which may have significant impacts on the simulation results. This article investigates the effects of including the mass and internal dynamics of the device in simulations of assisted human movement. The device actuator was modeled in various ways with different detail levels. Dynamic optimization was used to find the muscle activations and actuator commands in motion tracking and predictive simulations. The results showed that while the effects of device mass and inertia can be small, the electrical dynamics of the motor can significantly impact the results. This outcome suggests the importance of using an accurate actuator model in simulations of human movement augmented by assistive devices. NOVELTY: Demonstrating the effects of including mass and internal dynamics of the actuator in simulations of assisted human movement A new OpenSim electric motor actuator class to capture the electromechanical dynamics for use in simulation of human movement assisted by powered robotic devices.

Lower-limb joint reaction forces and moments during modified cycling in healthy controls and individuals with knee osteoarthritis

BACKGROUND

Osteoarthritis (OA) is a clinical problem affecting an estimated 27 million adults in the United States, with the only clear treatment options being pain management. Cycling is an integral component of exercise for individuals with knee osteoarthritis, while the joint reaction forces during cycling remain unknown.

METHODS

Thirteen subjects with medial compartment knee osteoarthritis and eleven healthy subjects performed a cycling protocol with a neutral pedal and four pedal modifications. Six hundred muscle-actuated inverse-dynamic simulations (24 subjects, 5 trials in each of 5 conditions) were performed to estimate joint reaction force differences between conditions.

FINDINGS

Subjects with knee osteoarthritis had many significant changes among them was a reduction in knee adduction-abduction moment by 45% (5° lateral wedge), 77% (10° lateral wedge), 54% (5° toe-in) and 58% (10° toe-in). Conversely the healthy subjects had no significant changes in the knee adduction-abduction moment for the lateral wedge conditions and the 5° toe-in but did decrease by 18% for the 10° toe-in condition. When comparing the cohorts across the different pedal conditions, the data showed many significant differences among the groups.

INTERPRETATION

This study showed that while cycling in different pedal modifications, the knee osteoarthritis subjects had more beneficial changes in their knee adduction-abduction moment compared to the healthy subjects with the lateral-wedge modification resulting in the greatest impact on the subjects with knee osteoarthritis. Both groups had greater contact forces at the hip and ankle across pedal modifications compared to neutral. For the knee, subjects with osteoarthritis mostly decreased their knee contact forces but the healthy subjects mostly increased these forces with all pedal modifications.

Biomechanical musculoskeletal models of the cervical spine: A systematic literature review

BACKGROUND

As the work load has been shifting from heavy manufacturing to office work, neck disorders are increasing. However, most of the current cervical spine biomechanical models were created to simulate crash situations. Therefore, the biomechanics of cervical spine during daily living and occupational activities remain unknown. In this effort, cervical spine biomechanical models were systematically reviewed based upon different features including approach, biomechanical properties, and validation methods.

METHODS

The objective of this review was to systematically categorize cervical spine models and compare the underlying logic in order to identify voids in the literature.

FINDINGS

Twenty-two models met our selection criteria and revealed several trends: 1) The multi-body dynamics modeling approach, equipped for simulating impact situations were the most common technique; 2) Straight muscle lines of action, inverse dynamic/optimization muscle force calculation, Hill-type muscle model with only active component were typically used in the majority of neck models; and 3) Several models have attempted to validate their results by comparing their approach with previous studies, but mostly were unable to provide task-specific validation.

INTERPRETATION

EMG-driven dynamic model for simulating occupational activities, with accurate muscle geometry and force representation, and person- or task-specific validation of the model would be necessary to improve model fidelity.

Linking Joint Impairment and Gait Biomechanics in Patients with Juvenile Idiopathic Arthritis

Juvenile Idiopathic Arthritis (JIA) is a paediatric musculoskeletal disease of unknown aetiology, leading to walking alterations when the lower-limb joints are involved. Diagnosis of JIA is mostly clinical. Imaging can quantify impairments associated to inflammation and joint damage. However, treatment planning could be better supported using dynamic information, such as joint contact forces (JCFs). To this purpose, we used a musculoskeletal model to predict JCFs and investigate how JCFs varied as a result of joint impairment in eighteen children with JIA. Gait analysis data and magnetic resonance images (MRI) were used to develop patient-specific lower-limb musculoskeletal models, which were evaluated for operator-dependent variability (< 3.6°, 0.05 N kg-1 and 0.5 BW for joint angles, moments, and JCFs, respectively). Gait alterations and JCF patterns showed high between-subjects variability reflecting the pathology heterogeneity in the cohort. Higher joint impairment, assessed with MRI-based evaluation, was weakly associated to overall joint overloading. A stronger correlation was observed between impairment of one limb and overload of the contralateral limb, suggesting risky compensatory strategies being adopted, especially at the knee level. This suggests that knee overloading during gait might be a good predictor of disease progression and gait biomechanics should be used to inform treatment planning.

Integrative Biomimetics of Autonomous Hexapedal Locomotion

Despite substantial advances in many different fields of neurorobotics in general, and biomimetic robots in particular, a key challenge is the integration of concepts: to collate and combine research on disparate and conceptually disjunct research areas in the neurosciences and engineering sciences. We claim that the development of suitable robotic integration platforms is of particular relevance to make such integration of concepts work in practice. Here, we provide an example for a hexapod robotic integration platform for autonomous locomotion. In a sequence of six focus sections dealing with aspects of intelligent, embodied motor control in insects and multipedal robots-ranging from compliant actuation, distributed proprioception and control of multiple legs, the formation of internal representations to the use of an internal body model-we introduce the walking robot HECTOR as a research platform for integrative biomimetics of hexapedal locomotion. Owing to its 18 highly sensorized, compliant actuators, light-weight exoskeleton, distributed and expandable hardware architecture, and an appropriate dynamic simulation framework, HECTOR offers many opportunities to integrate research effort across biomimetics research on actuation, sensory-motor feedback, inter-leg coordination, and cognitive abilities such as motion planning and learning of its own body size.

Force perceptual bias caused by muscle activity in unimanual steering

This study sought to investigate whether force perceptual bias was affected by differences in posture while steering an automobile using a psychophysical experiment to examine the relationship with muscle activity. The human perceptual characteristics of weight and force are known to be nonlinear, and a perceptual bias can occur, that is, bias that causes a perception of something that is larger or smaller than the actual scale. This is considered to be caused by physical and/or psychological conditions. Sense of effort is believed to be one influential factor. It is known to correlate with muscle activity intensity, and bias may be caused by muscle activity changes. In the current study, we hypothesized that force perceptual bias would depend on posture due to the intensity of muscle activity changes caused by changing postures during steering operation. By investigating this hypothesis, we can clarify the relationship between sense of effort and muscle activity. To investigate this issue, we conducted a psychophysical experiment to confirm postural dependence, and estimated muscle activity using a three-dimensional musculoskeletal model simulation with postural and arm force data during the experiment. In addition, prediction of bias was conducted based on a simulation in the psychophysical experiment using these data. The results revealed that bias existed, as measured by differences in postures. Additionally, a significant moderate correlation was found between the predicted bias and the actual bias, indicating the existence of a relationship between muscle activity and bias.

Predicting gait adaptations due to ankle plantarflexor muscle weakness and contracture using physics-based musculoskeletal simulations

Deficits in the ankle plantarflexor muscles, such as weakness and contracture, occur commonly in conditions such as cerebral palsy, stroke, muscular dystrophy, Charcot-Marie-Tooth disease, and sarcopenia. While these deficits likely contribute to observed gait pathologies, determining cause-effect relationships is difficult due to the often co-occurring biomechanical and neural deficits. To elucidate the effects of weakness and contracture, we systematically introduced isolated deficits into a musculoskeletal model and generated simulations of walking to predict gait adaptations due to these deficits. We trained a planar model containing 9 degrees of freedom and 18 musculotendon actuators to walk using a custom optimization framework through which we imposed simple objectives, such as minimizing cost of transport while avoiding falling and injury, and maintaining head stability. We first generated gaits at prescribed speeds between 0.50 m/s and 2.00 m/s that reproduced experimentally observed kinematic, kinetic, and metabolic trends for walking. We then generated a gait at self-selected walking speed; quantitative comparisons between our simulation and experimental data for joint angles, joint moments, and ground reaction forces showed root-mean-squared errors of less than 1.6 standard deviations and normalized cross-correlations above 0.8 except for knee joint moment trajectories. Finally, we applied mild, moderate, and severe levels of muscle weakness or contracture to either the soleus (SOL) or gastrocnemius (GAS) or both of these major plantarflexors (PF) and retrained the model to walk at a self-selected speed. The model was robust to all deficits, finding a stable gait in all cases. Severe PF weakness caused the model to adopt a slower, "heel-walking" gait. Severe contracture of only SOL or both PF yielded similar results: the model adopted a "toe-walking" gait with excessive hip and knee flexion during stance. These results highlight how plantarflexor weakness and contracture may contribute to observed gait patterns.

Number of Segments Within Musculoskeletal Foot Models Influences Ankle Kinematics and Strains of Ligaments and Muscles

Multi-segment foot models (MFMs) are becoming a common tool in musculoskeletal research on the ankle-foot complex. The purpose of this study was to compare ankle joint kinematics as well as ligament and muscle strains that result from MFM with a different number of segments during vertical hopping. Ten participants were recruited and performed double-limb vertical hops. Marker positions and ground reaction forces were collected. Two-segment (2MFM), three-segment (3MFM), and five-segment MFM (5MFM) were used to calculate ankle kinematics and the strains of the anterior talofibular and calcaneofibular ligaments and of the soleus and gastrocnemius muscles. Ranges of motion and peak strains were analyzed with Kruskal-Wallis and post hoc tests, whereas the time-series of the ankle kinematics and ligament and muscle strains were analyzed with statistical parametric mapping. There were significant main effects for MFM in the talocrural joint range of motion and peak strains of ligaments and muscles. In addition, there were significant main effects for MFM in time-series data of the talocrural joint angle as well as for ligament and muscle strains. In all cases, the post hoc analyses showed that the 2MFM consistently overestimated the range of motion and tissue strains compared to the 3MFM and 5MFM, while 3MFM and 5MFM did not differ from each other in the most variables. This study showed that the number of segments in MFM significantly affects the biomechanical estimates of joint kinematics and tissue strains during hopping. Clinical significance: MFM that combine all foot structures beyond the talus into one segment likely overestimate ankle joint biomechanics. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 37:2231-2240, 2019.

A Quick Turn of Foot: Rigid Foot-Ground Contact Models for Human Motion Prediction

Computer simulation can be used to predict human walking motions as a tool of basic science, device design, and for surgical planning. One the challenges of predicting human walking is accurately synthesizing both the movements and ground forces of the stance foot. Though the foot is commonly modeled as a viscoelastic element, rigid foot-ground contact models offer some advantages: fitting is reduced to a geometric problem, and the numerical stiffness of the equations of motion is similar in both swing and stance. In this work, we evaluate two rigid-foot ground contact models: the ellipse-foot (a single-segment foot), and the double-circle foot (a two-segment foot). To evaluate the foot models we use three different comparisons to experimental data: first we compare how accurately the kinematics of the ankle frame fit those of the model when it is forced to track the measured center-of-pressure (CoP) kinematics; second, we compare how each foot affects how accuracy of a sagittal plane gait model that tracks a subjects walking motion; and third, we assess how each model affects a walking motion prediction. For the prediction problem we consider a unique cost function that includes terms related to both muscular effort and foot-ground impacts. Although the ellipse-foot is superior to the double-circle foot in terms of fit and the accuracy of the tracking OCP solution, the predictive simulation reveals that the ellipse-foot is capable of producing large force transients due to its geometry: when the ankle quickly traverses its u-shaped trajectory, the body is accelerated the body upwards, and large ground forces result. In contrast, the two-segment double-circle foot produces ground forces that are of a similar magnitude to the experimental subject because the additional forefoot segment plastically contacts the ground, arresting its motion, similar to a human foot.

Large data and Bayesian modeling-aging curves of NBA players

Researchers interested in changes that occur as people age are faced with a number of methodological problems, starting with the immense time scale they are trying to capture, which renders laboratory experiments useless and longitudinal studies rather rare. Fortunately, some people take part in particular activities and pastimes throughout their lives, and often these activities are systematically recorded. In this study, we use the wealth of data collected by the National Basketball Association to describe the aging curves of elite basketball players. We have developed a new approach rooted in the Bayesian tradition in order to understand the factors behind the development and deterioration of a complex motor skill. The new model uses Bayesian structural modeling to extract two latent factors, those of development and aging. The interaction of these factors provides insight into the rates of development and deterioration of skill over the course of a player's life. We show, for example, that elite athletes have different levels of decline in the later stages of their career, which is dependent on their skill acquisition phase. The model goes beyond description of the aging function, in that it can accommodate the aging curves of subgroups (e.g., different positions played in the game), as well as other relevant factors (e.g., the number of minutes on court per game) that might play a role in skill changes. The flexibility and general nature of the new model make it a perfect candidate for use across different domains in lifespan psychology.

From Rough to Precise: Human-Inspired Phased Target Learning Framework for Redundant Musculoskeletal Systems

Redundant muscles in human-like musculoskeletal robots provide additional dimensions to the solution space. Consequently, the computation of muscle excitations remains an open question. Conventional methods like dynamic optimization and reinforcement learning usually have high computational costs or unstable learning processes when applied to a complex musculoskeletal system. Inspired by human learning, we propose a phased target learning framework that provides different targets to learners at varying levels, to guide their training process and to avoid local optima. By introducing an extra layer of neurons reflecting a preference, we improve the Q-network method to generate continuous excitations. In addition, based on information transmission in the human nervous system, two kinds of biological noise sources are introduced into our framework to enhance exploration over the solution space. Tracking experiments based on a simplified musculoskeletal arm model indicate that under guidance of phased targets, the proposed framework prevents divergence of excitations, thus stabilizing training. Moreover, the enhanced exploration of solutions results in smaller motion errors. The phased target learning framework can be expanded for general-purpose reinforcement learning, and it provides a preliminary interpretation for modeling the mechanisms of human motion learning.

Effects of kinematic complexity and number of muscles on musculoskeletal model robustness to muscle dysfunction

The robustness of motor outputs to muscle dysfunction has been investigated using musculoskeletal modeling, but with conflicting results owing to differences in model complexity and motor tasks. Our objective was to systematically study how the number of kinematic degrees of freedom, and the number of independent muscle actuators alter the robustness of motor output to muscle dysfunction. We took a detailed musculoskeletal model of the human leg and systematically varied the model complexity to create six models with either 3 or 7 kinematic degrees of freedom and either 14, 26, or 43 muscle actuators. We tested the redundancy of each model by quantifying the reduction in sagittal plane feasible force set area when a single muscle was removed. The robustness of feasible force set area to the loss of any single muscle, i.e. general single muscle loss increased with the number of independent muscles and decreased with the number of kinematic degrees of freedom, with the robust area varying from 1% and 52% of the intact feasible force set area. The maximum sensitivity of the feasible force set to the loss of any single muscle varied from 75% to 26% of the intact feasible force set area as the number of muscles increased. Additionally, the ranges of feasible muscle activation for maximum force production were largely unconstrained in many cases, indicating ample musculoskeletal redundancy even for maximal forces. We propose that ratio of muscles to kinematic degrees of freedom can be used as a rule of thumb for estimating musculoskeletal redundancy in both simulated and real biomechanical systems.

Musculoskeletal modeling to predict and reduce Antetrior Cruciate Ligament injury during single leg drop jump activity: Synergistic muscle co-activation approach

This paper presents a `drop jump' modeling to study the effect of synergistic muscle activation on controlling Anterior Cruciate Ligament (ACL) injury. ACL injuries are mostly caused during high impact loading. A full body musculoskeletal model with knee ligaments have been developed in `OpenSim platform' to simulate ACL injury during drop jump activity. The model is used to quantify the effect of change in muscle activation on different kinetic and kinematic parameters, which are associated with ACL injury. A neuromusculoskeletal controller have been designed which selects optimal muscle activation of Quadriceps, Hamstrings, Gastrocnemius and Tibilias anterior muscle group so as to reduce the chance of ACL injury and ankle inversion risk while jumping from elevated platforms. The OpenSim model along with the neuro-muscular controller forms an injury `predict-adapt' system, which can be useful in designing specific training sessions for athletics or for planning personalized rehabilitation therapy.

Long-term muscle changes after hamstring lengthening in children with bilateral cerebral palsy

AIM

To evaluate short-term (1y postoperatively; E1) and long-term (at least 4y postoperatively; E2) changes in hamstring muscle-tendon length (MTL) and lengthening velocity after hamstring lengthening in children with bilateral cerebral palsy (CP).

METHOD

Three-dimensional gait analysis was performed in 19 children (16 males, 3 females; 36 limbs; mean age at surgery 9y [SD 3y]; range 6-10y) with flexed knee gait, preoperative ankle dorsiflexion lower than 20 degrees, and CP before bilateral hamstring lengthening (E0), at E1 and E2. Hamstring MTL (normalized by leg length) and velocity were assessed via OpenSim software.

RESULTS

MTL increased from E0 to E1 (p=0.004) and decreased from E1 to E2 (p<0.020). Hamstring lengthening velocity did not change. In the subgroup with short, not slow hamstrings, the increase in MTL was maintained at E2.

INTERPRETATION

Hamstring lengthening is an efficient procedure to lengthen short and/or slow hamstrings short-term. The desired outcome with maintenance of the postoperative changes in hamstring MTL is only achieved for preoperatively short, not slow hamstrings.

WHAT THIS PAPER ADDS

Surgical hamstring lengthening can be confirmed via musculoskeletal modelling in OpenSim software. Surgical hamstring lengthening in cerebral palsy does not change hamstring lengthening velocity. Short, not slow hamstrings present a long-lasting muscle-tendon length (MTL) increase after hamstring lengthening. Changes in MTL after hamstring lengthening cannot be maintained for slow hamstrings. MTL does not change after hamstring lengthening for neither short nor slow hamstrings.

Modeling of Motorized Orthosis Control

Orthotic devices are defined as externally applied devices that are used to modify the structural and functional characteristics of the neuro-muscular and skeletal systems. The aim of the current study is to improve the control and movement of a robotic arm orthosis by means of an intelligent optimization system. Firstly, the control problem settlement is defined with the muscle, brain, and arm model. Subsequently, the optimization control, which based on a differential evolution algorithm, is developed to calculate the optimum gain values. Additionally, a cost function is defined in order to control and minimize the effort that is made by the subject and to assure that the algorithm follows as close as possible the defined setpoint value. The results show that, with the optimization algorithm, the necessary development force of the muscles is close to zero and the neural excitation level of biceps and triceps signal values are getting lower with a gain increase. Furthermore, the necessary development force of the biceps muscle to overcome a load added to the orthosis control system is practically the half of the one that is necessary without the optimization algorithm.

Assessment of the energy-related cost function over a range of walking speeds

Cost funtions are needed for calculation of muscle forces in musculoskeletal models. The behavior of the energy-related cost function, proposed by Praagman et al. (J Biomech 39(4):758-765, 2006. https://doi.org/10.1016/j.jbiomech.2004.11.034 ) (CFP), can be used as an optimization criteria in musculoskeletal models for studying gait. In particular, in this work, its performance is compared against two empirical phenomenological models at different walking speed conditions. Also, the sensitivity of the CFP function to model parameters, such as muscle mass, maximal isometric muscle force, optimal muscle fiber length and maximum muscle velocity of the contractile element, was analyzed. The obtained results showed that CFP presents different behavior (in terms of the normalized root-mean-squared deviation (NRMSD) and the coefficient of multiple correlation (CMC)) for different muscles. Also, it provided estimates with median of NRMSD between 0.176 and 0.299 and median of CMC between 0.703 and 0.865 both metrics for slow, free and fast walking speed, which could be considered as acceptable results. Furthermore, the results indicated that CFP is insensitive to changes in muscle mass and relatively sensitive to maximal isometric muscle force. However, CFP presented a noisy behavior on estimations of muscle energy rate for some muscle as compared to phenomenological models. Finally, estimations by CFP during gait are within the values obtained by the empirical phenomenological models.

The effects of electromyography-assisted modelling in estimating musculotendon forces during gait in children with cerebral palsy

Neuro-musculoskeletal modelling can provide insight into the aberrant muscle function during walking in those suffering cerebral palsy (CP). However, such modelling employs optimization to estimate muscle activation that may not account for disturbed motor control and muscle weakness in CP. This study evaluated different forms of neuro-musculoskeletal model personalization and optimization to estimate musculotendon forces during gait of nine children with CP (GMFCS I-II) and nine typically developing (TD) children. Data collection included 3D-kinematics, ground reaction forces, and electromyography (EMG) of eight lower limb muscles. Four different optimization methods estimated muscle activation and musculotendon forces of a scaled-generic musculoskeletal model for each child walking, i.e. (i) static optimization that minimized summed-excitation squared; (ii) static optimization with maximum isometric muscle forces scaled to body mass; (iii) an EMG-assisted approach using optimization to minimize summed-excitation squared while reducing tracking errors of experimental EMG-linear envelopes and joint moments; and (iv) EMG-assisted with musculotendon model parameters first personalized by calibration. Both static optimization approaches showed a relatively low model performance compared to EMG envelopes. EMG-assisted approaches performed much better, especially in CP, with only a minor mismatch in joint moments. Calibration did not affect model performance significantly, however it did affect musculotendon forces, especially in CP. A model more consistent with experimental measures is more likely to yield more physiologically representative results. Therefore, this study highlights the importance of calibrated EMG-assisted modelling when estimating musculotendon forces in TD children and even more so in children with CP.

Muscle Function from Organisms to Molecules

Gaps in our understanding of muscle contraction at the molecular level limit the ability to predict in vivo muscle forces in humans and animals during natural movements. Because muscles function as motors, springs, brakes, or struts, it is not surprising that uncertainties remain as to how sarcomeres produce these different behaviors. Current theories fail to explain why a single extra stimulus, added shortly after the onset of a train of stimuli, doubles the rate of force development. When stretch and doublet stimulation are combined in a work loop, muscle force doubles and work increases by 50% per cycle, yet no theory explains why this occurs. Current theories also fail to predict persistent increases in force after stretch and decreases in force after shortening. Early studies suggested that all of the instantaneous elasticity of muscle resides in the cross-bridges. Subsequent cross-bridge models explained the increase in force during active stretch, but required ad hoc assumptions that are now thought to be unreasonable. Recent estimates suggest that cross-bridges account for only ∼12% of the energy stored by muscles during active stretch. The inability of cross-bridges to account for the increase in force that persists after active stretching led to development of the sarcomere inhomogeneity theory. Nearly all predictions of this theory fail, yet the theory persists. In stretch-shortening cycles, muscles with similar activation and contractile properties function as motors or brakes. A change in the phase of activation relative to the phase of length changes can convert a muscle from a motor into a spring or brake. Based on these considerations, it is apparent that the current paradigm of muscle mechanics is incomplete. Recent advances in our understanding of giant muscle proteins, including twitchin and titin, allow us to expand our vision beyond cross-bridges to understand how muscles contribute to the biomechanics and control of movement.

A Synergy-Based Motor Control Framework for the Fast Feedback Control of Musculoskeletal Systems

This paper presents a computational framework for the fast feedback control of musculoskeletal systems using muscle synergies. The proposed motor control framework has a hierarchical structure. A feedback controller at the higher level of hierarchy handles the trajectory planning and error compensation in the task space. This high-level task space controller only deals with the task-related kinematic variables, and thus is computationally efficient. The output of the task space controller is a force vector in the task space, which is fed to the low-level controller to be translated into muscle activity commands. Muscle synergies are employed to make this force-to-activation (F2A) mapping computationally efficient. The explicit relationship between the muscle synergies and task space forces allows for the fast estimation of muscle activations that result in the reference force. The synergy-enabled F2A mapping replaces a computationally heavy nonlinear optimization process by a vector decomposition problem that is solvable in real time. The estimation performance of the F2A mapping is evaluated by comparing the F2A-estimated muscle activities against the measured electromyography (EMG) data. The results show that the F2A algorithm can estimate the muscle activations using only the task-related kinematics/dynamics information with ∼70% accuracy. An example predictive simulation is also presented, and the results show that this feedback motor control framework can control arbitrary movements of a three-dimensional (3D) musculoskeletal arm model quickly and near optimally. It is two orders-of-magnitude faster than the optimal controller, with only 12% increase in muscle activities compared to the optimal. The developed motor control model can be used for real-time near-optimal predictive control of musculoskeletal system dynamics.

A Novel Optimization Framework to Improve the Computational Cost of Muscle Activation Prediction for a Neuromusculoskeletal System

The high computational cost (CC) of neuromusculoskeletal modeling is usually considered a serious barrier in clinical applications. Different approaches have been developed to lessen CC and amplify the accuracy of muscle activation prediction based on forward and inverse analyses by applying different optimization algorithms. This study is aimed at proposing two novel approaches, inverse muscular dynamics with inequality constraints (IMDIC) and inverse-forward muscular dynamics with inequality constraints (IFMDIC), not only to reduce CC but also to amend the computational errors compared to the well-known approach of extended inverse dynamics (EID). To do that, the equality constraints of optimization problem, which are computationally tough to satisfy, are replaced by inequality constraints, which are easier to satisfy. To verify the practical application of the proposed approaches, the muscle activations of the lower limbs during the half of a gait cycle are quantified. The simulation results of the optimal muscle activations are then compared to the experimental ones. The results reveal that IMDIC requires less CC (87.5%) compared to EID. In addition, CC of IMDIC was about 33.3% improved by the application of IFMDIC. The findings of this study suggest that although the novel approach of IFMDIC decreases CC compared to IMDIC, the convergence of its results is very sensitive to the primary guess of the optimization variables.

Effect of Low-Frequency Vibration on Muscle Response under Different Neurointact Conditions

Stretch reflex is an important factor that influences the biomechanical response of the human body under whole-body vibration. However, there is a lack of quantitative evaluation at lower frequencies. Thus, the aim of this study was to investigate the effects of vibration on the stretch reflex and, in particular, to explore the quantitative relationship between dynamic muscle responses and low-frequency vibrations. The gastrocnemius muscle of 45 Sprague-Dawley rats was dissected. Sinusoidal vibrations of five discrete frequencies (2~16 Hz) with peak-to-peak amplitudes of 1 mm were applied to the gastrocnemius muscles with 2 mm or 3 mm prelengthening. Variables including dynamic muscle force, vibration acceleration, and displacement were recorded in two conditions, with and without the stretch reflex. Results showed that the dynamic muscle forces decreased by 20% on average for the 2 mm prelengthening group after the stretch reflex was blocked and by 24% for the 3 mm prelengthening group. Statistical analysis indicated that the amplitude of dynamic muscle force in the "with stretch reflex" condition was significantly larger than that in the "without stretch reflex" condition (p < 0.001). The tension-length curve was found to be a nonlinear hysteresis loop that changed with frequency. The phase difference between the dynamic muscle force and the length change was affected significantly by vibration frequency (p < 0.01), and the minimum frequency was 4-8 Hz. Experimental results of this study could benefit musculoskeletal model by providing a theoretical support to build a stretch reflex model for low-frequency vibration.

Modeling musculoskeletal kinematic and dynamic redundancy using null space projection

The coordination of the human musculoskeletal system is deeply influenced by its redundant structure, in both kinematic and dynamic terms. Noticing a lack of a relevant, thorough treatment in the literature, we formally address the issue in order to understand and quantify factors affecting the motor coordination. We employed well-established techniques from linear algebra and projection operators to extend the underlying kinematic and dynamic relations by modeling the redundancy effects in null space. We distinguish three types of operational spaces, namely task, joint and muscle space, which are directly associated with the physiological factors of the system. A method for consistently quantifying the redundancy on multiple levels in the entire space of feasible solutions is also presented. We evaluate the proposed muscle space projection on segmental level reflexes and the computation of the feasible muscle forces for arbitrary movements. The former proves to be a convenient representation for interfacing with segmental level models or implementing controllers for tendon driven robots, while the latter enables the identification of force variability and correlations between muscle groups, attributed to the system’s redundancy. Furthermore, the usefulness of the proposed framework is demonstrated in the context of estimating the bounds of the joint reaction loads, where we show that misinterpretation of the results is possible if the null space forces are ignored. This work presents a theoretical analysis of the redundancy problem, facilitating application in a broad range of fields related to motor coordination, as it provides the groundwork for null space characterization. The proposed framework rigorously accounts for the effects of kinematic and dynamic redundancy, incorporating it directly into the underlying equations using the notion of null space projection, leading to a complete description of the system.