Experiment-guided tuning of muscle-tendon parameters to estimate muscle fiber lengths and passive forces.

The workflow to simulate motion with recorded data usually starts with selecting a generic musculoskeletal model and scaling it to represent subject-specific characteristics. Simulating muscle dynamics with muscle-tendon parameters computed from existing scaling methods in literature, however, yields some inconsistencies compared to measurable outcomes. For instance, simulating fiber lengths and muscle excitations during walking with linearly scaled parameters does not resemble established patterns in the literature. This study presents a tool that leverages reported in vivo experimental observations to tune muscle-tendon parameters and evaluates their influence in estimating muscle excitations and metabolic costs during walking. From a scaled generic musculoskeletal model, we tuned optimal fiber length, tendon slack length, and tendon stiffness to match reported fiber lengths from ultrasound imaging and muscle passive force-length relationships to match reported in vivo joint moment-angle relationships. With tuned parameters, muscle contracted more isometrically, and soleus's operating range was better estimated than with linearly scaled parameters. Also, with tuned parameters, on/off timing of nearly all muscles' excitations in the model agreed with reported electromyographic signals, and metabolic rate trajectories varied significantly throughout the gait cycle compared to linearly scaled parameters. Our tool, freely available online, can customize muscle-tendon parameters easily and be adapted to incorporate more experimental data.

A dynamic foot model for predictive simulations of human gait reveals causal relations between foot structure and whole-body mechanics.

The unique structure of the human foot is seen as a crucial adaptation for bipedalism. The foot's arched shape enables stiffening the foot to withstand high loads when pushing off, without compromising foot flexibility. Experimental studies demonstrated that manipulating foot stiffness has considerable effects on gait. In clinical practice, altered foot structure is associated with pathological gait. Yet, experimentally manipulating individual foot properties (e.g. arch height or tendon and ligament stiffness) is hard and therefore our understanding of how foot structure influences gait mechanics is still limited. Predictive simulations are a powerful tool to explore causal relationships between musculoskeletal properties and whole-body gait. However, musculoskeletal models used in three-dimensional predictive simulations assume a rigid foot arch, limiting their use for studying how foot structure influences three-dimensional gait mechanics. Here, we developed a four-segment foot model with a longitudinal arch for use in predictive simulations. We identified three properties of the ankle-foot complex that are important to capture ankle and knee kinematics, soleus activation, and ankle power of healthy adults: (1) compliant Achilles tendon, (2) stiff heel pad, (3) the ability to stiffen the foot. The latter requires sufficient arch height and contributions of plantar fascia, and intrinsic and extrinsic foot muscles. A reduced ability to stiffen the foot results in walking patterns with reduced push-off power. Simulations based on our model also captured the effects of walking with anaesthetised intrinsic foot muscles or an insole limiting arch compression. The ability to reproduce these different experiments indicates that our foot model captures the main mechanical properties of the foot. The presented four-segment foot model is a potentially powerful tool to study the relationship between foot properties and gait mechanics and energetics in health and disease.

Assessment of stabilizing feedback control of walking: A tutorial.

Walking without falling requires stabilization of the trajectory of the body center of mass relative to the base of support. Model studies suggest that this requires active, feedback control, i.e., the nervous system must process sensory information on the state of the body to generate descending motor commands to the muscles to stabilize walking, especially in the mediolateral direction. Stabilization of bipedal gait is challenging and can be impaired in older and diseased individuals. In this tutorial, we illustrate how gait analysis can be used to assess the stabilizing feedback control of gait. We present methods ranging from those that require limited input data (e.g. position data of markers placed on the feet and pelvis only) to those that require full-body kinematics and electromyography. Analyses range from simple kinematics analyses to inverse dynamics. These methods assess stabilizing feedback control of human walking at three levels: 1) the level of center of mass movement and horizontal ground reaction forces, 2) the level of center of mass movement and foot placement and 3) the level of center of mass movement and the joint moments or muscle activity. We show how these can be calculated and provide a GitHub repository (https://github.com/VU-HMS/Tutorial-stabilizing-walking) which contains open access Matlab and Python code to calculate these. Finally, we discuss what information on feedback control can be learned from each of these.

Accuracy-speed-stability trade-offs in a targeted stepping task are similar in young and older adults.

Introduction: Stepping accuracy, speed, and stability are lower in older compared to young adults. Lower stepping performance in older adults may be due to larger accuracy-speed-stability trade-offs because of reduced ability to simultaneously fulfill these task-level goals. Our goal was to evaluate whether trade-offs are larger in older compared to young adults in a targeted stepping task. Since sensorimotor function declines with age, our secondary goal was to evaluate whether poorer sensorimotor function was associated with larger trade-offs. Methods: Twenty-five young (median 22 years old) and 25 older (median 70 years old) adults stepped into projected targets in conditions with various levels of accuracy, speed, and stability requirements. We determined trade-offs as the change in performance, i.e., foot placement error, step duration, and mediolateral center of pressure path length, between each of these conditions and a control condition. To assess age-related differences in the magnitude of trade-offs, we compared the change in performance between age groups. Associations between trade-offs and measures of sensorimotor function were tested using correlations. Results: We found an accuracy-speed and an accuracy-stability trade-off in both young and older adults, but trade-offs were not different between young and older adults. Inter-subject differences in sensorimotor function could not explain inter-subject differences in trade-offs. Conclusion: Age-related differences in the ability to combine task-level goals do not explain why older adults stepped less accurate and less stable than young adults. However, lower stability combined with an age-independent accuracy-stability trade-off could explain lower accuracy in older adults.

Evaluation of musculoskeletal models, scaling methods, and performance criteria for estimating muscle excitations and fiber lengths across walking speeds.

Muscle-driven simulations have been widely adopted to study muscle-tendon behavior; several generic musculoskeletal models have been developed, and their biofidelity improved based on available experimental data and computational feasibility. It is, however, not clear which, if any, of these models accurately estimate muscle-tendon dynamics over a range of walking speeds. In addition, the interaction between model selection, performance criteria to solve muscle redundancy, and approaches for scaling muscle-tendon properties remain unclear. This study aims to compare estimated muscle excitations and muscle fiber lengths, qualitatively and quantitatively, from several model combinations to experimental observations. We tested three generic models proposed by Hamner et al., Rajagopal et al., and Lai-Arnold et al. in combination with performance criteria based on minimization of muscle effort to the power of 2, 3, 5, and 10, and four approaches to scale the muscle-tendon unit properties of maximum isometric force, optimal fiber length, and tendon slack length. We collected motion analysis and electromyography data in eight able-bodied subjects walking at seven speeds and compared agreement between estimated/modelled muscle excitations and observed muscle excitations from electromyography and computed normalized fiber lengths to values reported in the literature. We found that best agreement in on/off timing in vastus lateralis, vastus medialis, tibialis anterior, gastrocnemius lateralis, gastrocnemius medialis, and soleus was estimated with minimum squared muscle effort than to higher exponents, regardless of model and scaling approach. Also, minimum squared or cubed muscle effort with only a subset of muscle-tendon unit scaling approaches produced the best time-series agreement and best estimates of the increment of muscle excitation magnitude across walking speeds. There were discrepancies in estimated fiber lengths and muscle excitations among the models, with the largest discrepancy in the Hamner et al. model. The model proposed by Lai-Arnold et al. best estimated muscle excitation estimates overall, but failed to estimate realistic muscle fiber lengths, which were better estimated with the model proposed by Rajagopal et al. No single model combination estimated the most accurate muscle excitations for all muscles; commonly observed disagreements include onset delay, underestimated co-activation, and failure to estimate muscle excitation increments across walking speeds.

Modeling toes contributes to realistic stance knee mechanics in three-dimensional predictive simulations of walking.

Physics-based predictive simulations have been shown to capture many salient features of human walking. Yet they often fail to produce realistic stance knee and ankle mechanics. While the influence of the performance criterion on the predicted walking pattern has been previously studied, the influence of musculoskeletal mechanics has been less explored. Here, we investigated the influence of two mechanical assumptions on the predicted walking pattern: the complexity of the foot model and the stiffness of the Achilles tendon. We found, through three-dimensional muscle-driven predictive simulations of walking, that modeling the toes, and thus using two-segment instead of single-segment foot models, contributed to robustly eliciting physiological stance knee flexion angles, knee extension torques, and knee extensor activity. Modeling toes also slightly decreased the first vertical ground reaction force peak, increasing its agreement with experimental data, and improved stance ankle kinetics. It nevertheless slightly worsened predictions of ankle kinematics. Decreasing Achilles tendon stiffness improved the realism of ankle kinematics, but there remain large discrepancies with experimental data. Overall, this simulation study shows that not only the performance criterion but also mechanical assumptions affect predictive simulations of walking. Improving the realism of predictive simulations is required for their application in clinical contexts. Here, we suggest that using more complex foot models might contribute to such realism.

Adaptations in Reactive Balance Strategies in Healthy Older Adults After a 3-Week Perturbation Training Program and After a 12-Week Resistance Training Program.

Both resistance training (RT) and perturbation-based training (PBT) have been proposed and applied as interventions to improve reactive balance performance in older adults. PBT is a promising approach but the adaptations in underlying balance-correcting mechanisms through which PBT improves reactive balance performance are not well-understood. Besides it is unclear whether PBT induces adaptations that generalize to movement tasks that were not part of the training and whether those potential improvements would be larger than improvements induced by RT. We performed two training interventions with two groups of healthy older adults: a traditional 12-week RT program and a 3-week PBT program consisting of support-surface perturbations of standing balance. Reactive balance performance during standing and walking as well as a set of neuro-muscular properties to quantify muscle strength, sensory and motor acuity, were assessed pre- and post-intervention. We found that both PBT and RT induced training specific improvements, i.e., standing PBT improved reactive balance during perturbed standing and RT increased strength, but neither intervention affected reactive balance performance during perturbed treadmill walking. Analysis of the reliance on different balance-correcting strategies indicated that specific improvements in the PBT group during reactive standing balance were due to adaptations in the stepping threshold. Our findings indicate that the strong specificity of PBT can present a challenge to transfer improvements to fall prevention and should be considered in the design of an intervention. Next, we found that lack of improvement in muscle strength did not limit improving reactive balance in healthy older adults. For improving our understanding of generalizability of specific PBT in future research, we suggest performing an analysis of the reliance on the different balance-correcting strategies during both the training and assessment tasks.

Similar sensorimotor transformations control balance during standing and walking.

Standing and walking balance control in humans relies on the transformation of sensory information to motor commands that drive muscles. Here, we evaluated whether sensorimotor transformations underlying walking balance control can be described by task-level center of mass kinematics feedback similar to standing balance control. We found that delayed linear feedback of center of mass position and velocity, but not delayed linear feedback from ankle angles and angular velocities, can explain reactive ankle muscle activity and joint moments in response to perturbations of walking across protocols (discrete and continuous platform translations and discrete pelvis pushes). Feedback gains were modulated during the gait cycle and decreased with walking speed. Our results thus suggest that similar task-level variables, i.e. center of mass position and velocity, are controlled across standing and walking but that feedback gains are modulated during gait to accommodate changes in body configuration during the gait cycle and in stability with walking speed. These findings have important implications for modelling the neuromechanics of human balance control and for biomimetic control of wearable robotic devices. The feedback mechanisms we identified can be used to extend the current neuromechanical models that lack balance control mechanisms for the ankle joint. When using these models in the control of wearable robotic devices, we believe that this will facilitate shared control of balance between the user and the robotic device.

A probabilistic method to estimate gait kinetics in the absence of ground reaction force measurements.

Human joint torques during gait are usually computed using inverse dynamics. This method requires a skeletal model, kinematics and measured ground reaction forces and moments (GRFM). Measuring GRFM is however only possible in a controlled environment. This paper introduces a probabilistic method based on probabilistic principal component analysis to estimate the joint torques for healthy gait without measured GRFM. A gait dataset of 23 subjects was obtained containing kinematics, measured GRFM and joint torques from inverse dynamics in order to obtain a probabilistic model. This model was then used to estimate the joint torques of other subjects without measured GRFM. Only kinematics, a skeletal model and timing of gait events are needed. Estimation only takes 0.28 ms per time instant. Using cross-validation, the resulting root mean square estimation errors for the lower-limb joint torques are found to be approximately 0.1 Nm/kg, which is 6-18% of the range of the ground truth joint torques. Estimated joint torque and GRFM errors are up to two times smaller than model-based state-of-the-art methods. Model-free artificial neural networks can achieve lower errors than our method, but are less repeatable, do not contain uncertainty information on the estimates and are difficult to use in situations which are not in the learning set. In contrast, our method performs well in a new situation where the walking speed is higher than in the learning dataset. The method can for example be used to estimate the kinetics during overground walking without force plates, during treadmill walking without (separate) force plates and during ambulatory measurements.

Inverse dynamic estimates of muscle recruitment and joint contact forces are more realistic when minimizing muscle activity rather than metabolic energy or contact forces.

BACKGROUND: Assessment of contact forces is essential for a better understanding of mechanical factors affecting progression of osteoarthritis. Since contact forces cannot be measured non-invasively, computer simulations are often used to assess joint loading. Contact forces are to a large extent determined by muscle forces. These muscle forces are computed using optimization techniques that solve the muscle redundancy problem by assuming that muscles are coordinated in a way that optimizes performance (e.g., minimizes muscle activity or metabolic energy). However, it is unclear which of the many proposed performance criteria best describes muscle coordination. RESEARCH QUESTION: Which performance criterion best describes muscle recruitment patterns and knee contact forces recorded using electromyography (EMG) and load cell instrumented prostheses?. METHODS: We solved the muscle redundancy problem based on six different groups of performance criteria: muscle activations, volume-scaled activations, forces, stresses, metabolic energy, and joint contact forces. Computed muscle excitations and knee contact forces during over-ground walking were validated against recorded EMG signals and measured contact forces for four subjects with instrumented knee prostheses in the "Grand Challenge Competition to Predict in Vivo Knee Loads" dataset. RESULTS: Performance criteria based on either stress or muscle activation (either unscaled or scaled by muscle volume), both to a power of 3 or 4, resulted in the best agreement between measured and simulated values. These performance criteria outperformed all other criteria in terms of agreement between simulated muscle excitations and EMG, whereas good agreement between measured and predicted contact forces was also observed for minimization of contact forces and metabolic energy. SIGNIFICANCE: Given the large differences in accuracy obtained with different performance criteria (e.g., root mean square errors of contact forces differed up to 0.45 body weight), the results of our study are important to improve the validity of in silico assessment of joint loading.

Model-based control for exoskeletons with series elastic actuators evaluated on sit-to-stand movements.

BACKGROUND: Currently, control of exoskeletons in rehabilitation focuses on imposing desired trajectories to promote relearning of motions. Furthermore, assistance is often provided by imposing these desired trajectories using impedance controllers. However, lower-limb exoskeletons are also a promising solution for mobility problems of individuals in daily life. To develop an assistive exoskeleton which allows the user to be autonomous, i.e. in control of his motions, remains a challenge. This paper presents a model-based control method to tackle this challenge. METHODS: The model-based control method utilizes a dynamic model of the exoskeleton to compensate for its own dynamics. After this compensation of the exoskeleton dynamics, the exoskeleton can provide a desired assistance to the user. While dynamic models of exoskeletons used in the literature focus on gravity compensation only, the need for modelling and monitoring of the ground contact impedes their widespread use. The control strategy proposed here relies on modelling of the full exoskeleton dynamics and of the contacts with the environment. A modelling strategy and general control scheme are introduced. RESULTS: Validation of the control method on 15 non-disabled adults performing sit-to-stand motions shows that muscle effort and joint torques are similar in the conditions with dynamically compensated exoskeleton and without exoskeleton. The condition with exoskeleton in which the compensating controller was not active showed a significant increase in human joint torques and muscle effort at the knee and hip. Motor saturation occurred during the assisted condition, which limited the assistance the exoskeleton could deliver. CONCLUSIONS: This work presents the modelling steps and controller design to compensate the exoskeleton dynamics. The validation seems to indicate that the presented model-based controller is able to compensate the exoskeleton.

Increased use of stepping strategy in response to medio-lateral perturbations in the elderly relates to altered reactive tibialis anterior activity.

BACKGROUND: The influence of aging on reactive control of balance during walking has been mainly investigated in the sagittal plane, whereas balance control in response to frontal plane perturbations is largely unexplored in the elderly. This is remarkable, given that walking mainly requires active control in the frontal plane. An extensive gait perturbation protocol was used to test whether reactive control of walking balance changes with aging and whether these changes are more pronounced in the frontal than in the sagittal plane. RESEARCH QUESTION: Do alterations in reactive muscle activity cause an age-related shift in stepping strategy in response to perturbations in the frontal and sagittal planes during walking? METHOD: A treadmill-based perturbation protocol imposed frontal and sagittal plane perturbations of different magnitudes during different phases of the gait cycle. Motion capture and electromyography measured the response to the different perturbations in a group of eighteen young and ten older adults. RESULTS: Only for a small subset of the perturbations, reactive muscle activity and kinematic strategies differed between young and older subjects. When perturbation magnitude increased, the older adults relied more on a stepping strategy for inward directed frontal plane perturbations and for sagittal plane perturbation just before heelstrike. Tibialis anterior activity increased less in the older compared to the young subjects. Using simulations, we related tibialis anterior activity to backward and outward movement of the center of pressure in the stance foot and confirmed its contribution to the ankle strategy. We concluded that deficient tibialis anterior activity predisposes elderly to use stepping rather than lateral ankle strategies to control balance. SIGNIFICANCE: Rehabilitation targets for fall prevention in elderly need to also focus on ankle muscle reactivity.

Modulation of gluteus medius activity reflects the potential of the muscle to meet the mechanical demands during perturbed walking.

Mediolateral stability during walking can be controlled by adjustment of foot placement. Reactive activity of gluteus medius (GM) is modulated during the gait cycle. However, the mechanisms behind the modulation are yet unclear. We measured reactive GM activity and kinematics in response to a mediolateral platform translation during different phases of the gait cycle. Forward simulations of perturbed walking were used to evaluate the isolated effect of the perturbation and the GM response on gait stability. We showed that the potential of GM to adjust lateral foot placement and prevent collisions during swing varies during the gait cycle and explains the observed modulation. The observed increase in stance, swing or combined GM activity causes an outward foot placement and therefore compensates for the loss of stability caused by a perturbation early in the gait cycle. GM activity of the swing leg in response to a platform translation late in the gait cycle counteracts foot placement, but prevents collision of the swing foot with the stance leg. This study provides insights in the neuromechanics of reactive control of gait stability and proposes a novel method to distinguish between the effect of perturbation force and reactive muscle activity on gait stability.

Increased sensory noise and not muscle weakness explains changes in non-stepping postural responses following stance perturbations in healthy elderly.

The response to stance perturbations changes with age. The shift from an ankle to a hip strategy with increasing perturbation magnitude occurs at lower accelerations in older than in young adults. This strategy shift has been related to age-related changes in muscle and sensory function. However, the effect of isolated changes in muscle or sensory function on the responses following stance perturbations cannot be determined experimentally since changes in muscle and sensory function occur simultaneously. Therefore, we used predictive simulations to estimate the effect of isolated changes in (rates of change in) maximal joint torques, functional base of support, and sensory noise on the response to backward platform translations. To evaluate whether these modeled changes in muscle and sensory function could explain the observed changes in strategy; simulated postural responses with a torque-driven double inverted pendulum model controlled using optimal state feedback were compared to measured postural responses in ten healthy young and ten healthy older adults. The experimentally observed peak hip angle during the response was significantly larger (5°) and the functional base of support was smaller (0.04m) in the older than in the young adults but peak joint torques and rates of joint torque were similar during the recovery. The addition of noise to the sensed states in the predictive simulations could explain the observed increase in peak hip angle in the elderly, whereas changes in muscle function could not. Hence, our results suggest that strength training alone might be insufficient to improve postural control in elderly.

Real-Time Gait Event Detection Based on Kinematic Data Coupled to a Biomechanical Model.

Real-time detection of multiple stance events, more specifically initial contact (IC), foot flat (FF), heel off (HO), and toe off (TO), could greatly benefit neurorobotic (NR) and neuroprosthetic (NP) control. Three real-time threshold-based algorithms have been developed, detecting the aforementioned events based on kinematic data in combination with a biomechanical model. Data from seven subjects walking at three speeds on an instrumented treadmill were used to validate the presented algorithms, accumulating to a total of 558 steps. The reference for the gait events was obtained using marker and force plate data. All algorithms had excellent precision and no false positives were observed. Timing delays of the presented algorithms were similar to current state-of-the-art algorithms for the detection of IC and TO, whereas smaller delays were achieved for the detection of FF. Our results indicate that, based on their high precision and low delays, these algorithms can be used for the control of an NR/NP, with the exception of the HO event. Kinematic data is used in most NR/NP control schemes and is thus available at no additional cost, resulting in a minimal computational burden. The presented methods can also be applied for screening pathological gait or gait analysis in general in/outside of the laboratory.

Mechanical effort predicts the selection of ankle over hip strategies in nonstepping postural responses.

Experimental studies have shown that a continuum of ankle and hip strategies is used to restore posture following an external perturbation. Postural responses can be modeled by feedback control with feedback gains that optimize a specific objective. On the one hand, feedback gains that minimize effort have been used to predict muscle activity during perturbed standing. On the other hand, hip and ankle strategies have been predicted by minimizing postural instability and deviation from upright posture. It remains unclear, however, whether and how effort minimization influences the selection of a specific postural response. We hypothesize that the relative importance of minimizing mechanical work vs. postural instability influences the strategy used to restore upright posture. This hypothesis was investigated based on experiments and predictive simulations of the postural response following a backward support surface translation. Peak hip flexion angle was significantly correlated with three experimentally determined measures of effort, i.e., mechanical work, mean muscle activity and metabolic energy. Furthermore, a continuum of ankle and hip strategies was predicted in simulation when changing the relative importance of minimizing mechanical work and postural instability, with increased weighting of mechanical work resulting in an ankle strategy. In conclusion, the combination of experimental measurements and predictive simulations of the postural response to a backward support surface translation showed that the trade-off between effort and postural instability minimization can explain the selection of a specific postural response in the continuum of potential ankle and hip strategies.

The effect of muscle weakness on the capability gap during gross motor function: a simulation study supporting design criteria for exoskeletons of the lower limb.

BACKGROUND: Enabling persons with functional weaknesses to perform activities of daily living (ADL) is one of the main challenges for the aging society. Powered orthoses, or exoskeletons, have the potential to support ADL while promoting active participation of the user. For this purpose, assistive devices should be designed and controlled to deliver assistance as needed (AAN). This means that the level of assistance should bridge the capability gap, i.e. the gap between the capabilities of the subjects and the task requirements. However, currently the actuators of exoskeletons are mainly designed using inverse dynamics (ID) based calculations of joint moments. The goal of the present study is to calculate the capability gap for the lower limb during ADL when muscle weakness is present, which is needed for appropriate selection of actuators to be integrated in exoskeletons. METHODS: A musculoskeletal model (MM) is used to calculate the joint kinematics, joint kinetics and muscle forces of eight healthy subjects during ADL (gait, sit-to-stand, stand-to-sit, stair ascent, stair descent). Muscle weakness was imposed to the MM by a stepwise decrease in maximal isometric force imposed to all muscles. Muscle forces were calculated using static optimization. In order to compensate for muscle weakness, ideal moment actuators that represent the motors of an exoskeleton in the simulation were added to deliver AAN required to perform the task. RESULTS: The ID approach overestimates the required assistance since it relies solely on the demands of the task, whereas the AAN approach incorporates the capabilities of the subject. Furthermore, the ID approach delivers continuous support whereas the AAN approach targets the period where a capability gap occurs. The level of muscle weakness for which the external demands imposed by ADL can no longer be met by active muscle force production, is respectively 40%, 70%, 80% and 30%. CONCLUSIONS: The present workflow allows estimating the AAN during ADL for different levels of muscle weakness, which can be used in the mechatronic design and control of powered exoskeletons. The AAN approach is a more physiological approach than the ID approach, since the MM accounts for the subject-specific capabilities of the user.