Sensitivity of a Hill-based muscle model to perturbations in model parameters

Parameter identification and sensitivity analysis of a lower-limb musculoskeletal model

The estimation of joint torque based on wearable sensors is an important content in human-robot interaction research. Despite existing joint torque estimation models providing high accuracy, their application in robotic control is limited due to the number of sensors and real-time output requirements. To address this issue, this paper establishes a knee joint torque estimation model driven by four electromyography (EMG) sensors and proposes a novel method for simplifying musculoskeletal models based on sensitivity analysis. To achieve this, this paper combines multiple advanced Hill-type muscle model components to establish a knee-joint musculoskeletal model that includes four major muscles and employs the genetic algorithm (GA) to identify the model parameters. Then, Sobol's global sensitivity analysis theory is used to analyze the influence of parameter variations on model outputs, and a sensitivity-based model simplification method is proposed. In addition, a lower-limb physical and biological signal collection experiment without ground reaction force is designed for parameter identification and sensitivity analysis. Finally, based on experimental data from several test subjects, the parameters of each individual's musculoskeletal model are identified and evaluated, and the sensitivity index of each parameter is calculated to determine the influence of the number of model parameters on the identification performance. The results indicate that the proposed musculoskeletal model can provide individuals with comparable normalized root mean square error (NRMSE) through parameter identification, and the sensitivity-based model simplification method is effective.

Hindlimb kinematics, kinetics and muscle dynamics during sit-to-stand and sit-to-walk transitions in emus (Dromaius novaehollandiae)

Terrestrial animals not only need to walk and run but also lie prone to rest and then stand up. Sit-to-stand (STS) and sit-to-walk (STW) transitions are vital behaviours little studied in species other than humans so far, but likely impose biomechanical constraints on limb design because they involve near-maximal excursions of limb joints that should require large length changes and force production from muscles. By integrating data from experiments into musculoskeletal simulations, we analysed joint motions, ground reaction forces, and muscle dynamics during STS and STW in a large terrestrial, bipedal and cursorial bird: the emu (Dromaius novaehollandiae; body mass ∼30 kg). Simulation results suggest that in both STS and STW, emus operate near the functional limits (∼50% of shortening/lengthening) of some of their hindlimb muscles, particularly in distal muscles with limited capacity for length change and leverage. Both movements involved high muscle activations (>50%) and force generation of the major joint extensor muscles early in the transition. STW required larger net joint moments and non-sagittal motions than STS, entailing greater demands for muscle capacity. Whilst our study involves multiple assumptions, our findings lay the groundwork for future studies to understand, for example, how tendon contributions may reduce excessive muscle demands, especially in the distal hindlimb. As the first investigation into how an avian species stands up, this study provides a foundational framework for future comparative studies investigating organismal morphofunctional specialisations and evolution, offering potential robotics and animal welfare applications.

Using muscle-tendon load limits to assess unphysiological musculoskeletal model deformation and Hill-type muscle parameter choice

Musculoskeletal simulations are a useful tool for improving our understanding of the human body. However, the physiological validity of predicted kinematics and forces is highly dependent upon the correct calibration of muscle parameters and the structural integrity of a model's internal skeletal structure. In this study, we show how ill-tuned muscle parameters and unphysiological deformations of a model's skeletal structure can be detected by using muscle elements as sensors with which modelling and parameterization inconsistencies can be identified through muscle and tendon strain injury assessment. To illustrate our approach, two modelling issues were recreated. First, a model repositioning simulation using the THUMS AM50 occupant model version 5.03 was performed to show how internal model deformations can occur during a change of model posture. Second, the muscle material parameters of the OpenSim gait2354 model were varied to illustrate how unphysiological muscle forces can arise if material parameters are inadequately calibrated. The simulations were assessed for muscle and tendon strain injuries using previously published injury criteria and a newly developed method to determine tendon strain injury threshold values. Muscle strain injuries in the left and right musculus pronator teres were detected during the model repositioning. This straining was caused by an unphysiologically large gap (12.92 mm) that had formed in the elbow joint. Similarly, muscle and tendon strain injuries were detected in the modified right-hand musculus gastrocnemius medialis of the gait2354 model where an unphysiological reduction of the tendon slack length introduced large pre-strain of the muscle-tendon unit. The results of this work show that the proposed method can quantify the internal distortion behaviour of musculoskeletal human body models and the plausibility of Hill-type muscle parameter choice via strain injury assessment. Furthermore, we highlight possible actions to avoid the presented issues and inconsistencies in literature data concerning the material characteristics of human tendons.

Toward Impedance Control in Human-Machine Interfaces for Upper-Limb Prostheses

OBJECTIVES

Adaptation of upper-limb impeda- nce (stiffness, damping, inertia) is crucial for humans to physically interact with the external environment during grasping and manipulation tasks. Here, we present a novel framework for Adaptive Impedance Control of Upper-limb Prosthesis (AIC-UP) based on surface electromyography (sEMG) signals.

METHODS

AIC-UP uses muscle-tendon models driven by sEMG signals from agonist-antagonist muscle groups to estimate the human motor intent as joint kinematics, stiffness and damping. These estimates are used to implement a variable impedance controller on a simulated robot. Designed for use by amputees, joint torque or stiffness measurements are not used for model calibration. AIC-UP was evaluated with eight able-bodied subjects and a transradial amputee performing target-reaching tasks in simulation through wrist flexion-extension. The control performance was tested in free space and in the presence of unexpected perturbations.

RESULTS

We show that AIC-UP outperformed a neural network that regresses the desired kinematics from sEMG signals, in terms of robustness to muscle coactivations needed to complete the task. These results were in agreement with the qualitative feedback from the participants. Additionally, we observed that AIC-UP enables the user to adapt the stiffness and damping to the tasks at hand.

Digital twin-driven dynamic monitoring system of the upper limb force

Digital twin represents the core technology to realize the dynamic monitoring of complex industrial systems. However, the human body, as the most complex system in the physical world, digital twin is rarely applied in it. In this study, we successfully demonstrated a digital twin in the human biomedical application by proposing a dynamic monitoring system of the upper limb force. In this system, the real upper limb drives the motion of the virtual one in real-time and dynamically updates the force. Meanwhile, the virtual upper limb feeds back the monitoring-results of the force to the controller of the real upper limb via immersive virtual reality interaction. Experimental results of the typical motions of the upper limb revealed that the proposed system functioned interactively in real-time in a non-invasive manner, while ensuring the accurate solving of the muscle force. In conclusion, our digital twin-driven system is of great importance for rehabilitation medicine, biomechanical scientific research and physical training, promoting the application of the digital twin in the human biomedical field.

ArborSim: Articulated, branching, OpenSim routing for constructing models of multi-jointed appendages with complex muscle-tendon architecture

Computational models of musculoskeletal systems are essential tools for understanding how muscles, tendons, bones, and actuation signals generate motion. In particular, the OpenSim family of models has facilitated a wide range of studies on diverse human motions, clinical studies of gait, and even non-human locomotion. However, biological structures with many joints, such as fingers, necks, tails, and spines, have been a longstanding challenge to the OpenSim modeling community, especially because these structures comprise numerous bones and are frequently actuated by extrinsic muscles that span multiple joints-often more than three-and act through a complex network of branching tendons. Existing model building software, typically optimized for limb structures, makes it difficult to build OpenSim models that accurately reflect these intricacies. Here, we introduce ArborSim, customized software that efficiently creates musculoskeletal models of highly jointed structures and can build branched muscle-tendon architectures. We used ArborSim to construct toy models of articulated structures to determine which morphological features make a structure most sensitive to branching. By comparing the joint kinematics of models constructed with branched and parallel muscle-tendon units, we found that among various parameters-the number of tendon branches, the number of joints between branches, and the ratio of muscle fiber length to muscle tendon unit length-the number of tendon branches and the number of joints between branches are most sensitive to branching modeling method. Notably, the differences between these models showed no predictable pattern with increased complexity. As the proportion of muscle increased, the kinematic differences between branched and parallel models units also increased. Our findings suggest that stress and strain interactions between distal tendon branches and proximal tendon and muscle greatly affect the overall kinematics of a musculoskeletal system. By incorporating complex muscle-tendon branching into OpenSim models using ArborSim, we can gain deeper insight into the interactions between the axial and appendicular skeleton, model the evolution and function of diverse animal tails, and understand the mechanics of more complex motions and tasks.

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.

EMG-Constrained and Ultrasound-Informed Muscle-Tendon Parameter Estimation in Post-Stroke Hemiparesis

Secondary morphological and mechanical property changes in the muscle-tendon unit at the ankle joint are often observed in post-stroke individuals. These changes may alter the force generation capacity and affect daily activities such as locomotion. This work aimed to estimate subject-specific muscle-tendon parameters in individuals after stroke by solving the muscle redundancy problem using direct collocation optimal control methods based on experimental electromyography (EMG) signals and measured muscle fiber length. Subject-specific muscle-tendon parameters of the gastrocnemius, soleus, and tibialis anterior were estimated in seven post-stroke individuals and seven healthy controls. We found that the maximum isometric force, tendon stiffness and optimal fiber length in the post-stroke group were considerably lower than in the control group. We also computed the root mean square error between estimated and experimental values of muscle excitation and fiber length. The musculoskeletal model with estimated subject-specific muscle tendon parameters (from the muscle redundancy solver), yielded better muscle excitation and fiber length estimations than did scaled generic parameters. Our findings also showed that the muscle redundancy solver can estimate muscle-tendon parameters that produce force behavior in better accordance with the experimentally-measured value. These muscle-tendon parameters in the post-stroke individuals were physiologically meaningful and may shed light on treatment and/or rehabilitation planning.

The biomechanical influence of transtibial Bone-Anchored limbs during walking

Individuals with unilateral transtibial amputation (TTA) using socket prostheses demonstrate asymmetric joint biomechanics during walking, which increases the risk of secondary comorbidities (e.g., low back pain (LBP), osteoarthritis (OA)). Bone-anchored limbs are an alternative to socket prostheses, yet it remains unknown how they influence multi-joint loading. Our objective was to determine the influence of bone-anchored limb use on multi-joint biomechanics during walking. Motion capture data (kinematics, ground reaction forces) were collected during overground walking from ten participants with unilateral TTA prior to (using socket prostheses) and 12-months after bone-anchored limb implantation. Within this year, each participant completed a rehabilitation protocol that guided progression of loading based on patient pain response and optimized biomechanics. Musculoskeletal models were developed at each testing timepoint (baseline or 12-months after implantation) and used to calculate joint kinematics, internal joint moments, and joint reaction forces (JRFs). Analyses were performed during three stance periods on each limb. The between-limb normalized symmetry index (NSI) was calculated for joint moments and JRF impulses. Discrete (range of motion (ROM), impulse NSI) dependent variables were compared before and after implantation using paired t-tests with Bonferroni-Holm corrections while continuous (ensemble averages of kinematics, moments, JRFs) were compared using statistical parametric mapping (p < 0.05). When using a bone-anchored limb, frontal plane pelvic (residual: pre = 9.6 ± 3.3°, post = 6.3 ± 2.5°, p = 0.004; intact: pre = 10.2 ± 3.9°, post = 7.9 ± 2.6°, p = 0.006) and lumbar (residual: pre = 15.9 ± 7.0°, post = 10.6 ± 2.5°, p = 0.024, intact: pre = 17.1 ± 7.0°, post = 11.4 ± 2.8°, p = 0.014) ROM was reduced compared to socket prosthesis use. The intact limb hip extension moment impulse increased (pre = -11.0 ± 3.6 Nm*s/kg, post = -16.5 ± 4.4 Nm*s/kg, p = 0.005) and sagittal plane hip moment impulse symmetry improved (flexion: pre = 23.1 ± 16.0 %, post = -3.9 ± 19.5 %, p = 0.004, extension: pre = 29.2 ± 20.3 %, post = 8.7 ± 22.9 %, p = 0.049). Residual limb knee extension moment impulse decreased compared to baseline (pre = 15.7 ± 10.8 Nm*s/kg, post = 7.8 ± 3.9 Nm*s/kg, p = 0.030). These results indicate that bone-anchored limb implantation alters multi-joint biomechanics, which may impact LBP or OA risk factors in the TTA population longitudinally.

Muscle Morphology Does Not Solely Determine Knee Flexion Weakness After Anterior Cruciate Ligament Reconstruction with a Semitendinosus Tendon Graft: A Combined Experimental and Computational Modeling Study

The distal semitendinosus tendon is commonly harvested for anterior cruciate ligament reconstruction, inducing substantial morbidity at the knee. The aim of this study was to probe how morphological changes of the semitendinosus muscle after harvest of its distal tendon for anterior cruciate ligament reconstruction affects knee flexion strength and whether the knee flexor synergists can compensate for the knee flexion weakness. Ten participants 8-18 months after anterior cruciate ligament reconstruction with an ipsilateral distal semitendinosus tendon autograft performed isometric knee flexion strength testing (15°, 45°, 60°, and 90°; 0° = knee extension) positioned prone on an isokinetic dynamometer. Morphological parameters extracted from magnetic resonance images were used to inform a musculoskeletal model. Knee flexion moments estimated by the model were then compared with those measured experimentally at each knee angle position. A statistically significant between-leg difference in experimentally-measured maximal isometric strength was found at 60° and 90°, but not 15° or 45°, of knee flexion. The musculoskeletal model matched the between-leg differences observed in experimental knee flexion moments at 15° and 45° but did not well estimate between-leg differences with a more flexed knee, particularly at 90°. Further, the knee flexor synergists could not physiologically compensate for weakness in deep knee flexion. These results suggest additional factors other than knee flexor muscle morphology play a role in knee flexion weakness following anterior cruciate ligament reconstruction with a distal semitendinosus tendon graft and thus more work at neural and microscopic levels is required for informing treatment and rehabilitation in this demographic.

Optimal fibre length and maximum isometric force are the most influential parameters when modelling muscular adaptations to unloading using Hill-type muscle models

Introduction: Spaceflight is associated with severe muscular adaptations with substantial inter-individual variability. A Hill-type muscle model is a common method to replicate muscle physiology in musculoskeletal simulations, but little is known about how the underlying parameters should be adjusted to model adaptations to unloading. The aim of this study was to determine how Hill-type muscle model parameters should be adjusted to model disuse muscular adaptations. Methods: Isokinetic dynamometer data were taken from a bed rest campaign and used to perform tracking simulations at two knee extension angular velocities (30°·s-1 and 180°·s-1). The activation and contraction dynamics were solved using an optimal control approach and direct collocation method. A Monte Carlo sampling technique was used to perturb muscle model parameters within physiological boundaries to create a range of theoretical and feasible parameters to model muscle adaptations. Results: Optimal fibre length could not be shortened by more than 67% and 61% for the knee flexors and non-knee muscles, respectively. Discussion: The Hill-type muscle model successfully replicated muscular adaptations due to unloading, and recreated salient features of muscle behaviour associated with spaceflight, such as altered force-length behaviour. Future researchers should carefully adjust the optimal fibre lengths of their muscle-models when trying to model adaptations to unloading, particularly muscles that primarily operate on the ascending and descending limbs of the force-length relationship.

simMACT, a Software Demonstrator to Improve Maximum Actuation Joint Torques Simulation for Ergonomics Assessment

The maximum actuation joint torques that operators can perform at the workplace are essential parameters for biomechanical risk assessment. However, workstation designers generally only have at their disposal the imprecise and sparse estimates of these quantities provided with digital manikin digital human model (DHM) software. For instance, such tools consider only static postures and ignore important specificities of the human musculoskeletal system such as interjoints couplings. To alleviate the weaknesses of existing approaches implemented in digital human modeling tools relying on torque databases, this paper describes a methodology based on a class of polytopes called zonotopes and musculoskeletal simulation to assess maximum actuation torques. It has two main advantages, the ability to estimate maximum joint torques for any posture and taking into account musculoskeletal specificities unlike existing digital human modeling tools. As a case study, it also compares simulated maximum actuation torques to those recorded during an experiment described in the literature, focusing on an isometric task of the upper limb. This simulation has led to similar or smaller errors than DHM software tools. Hence, this methodology may help in interpreting interjoint couplings, choosing appropriate mathematical models or design experimental protocols. It may also be implemented in DHM software to provide designers with more comprehensive and more reliable data.

Sensitivity Analysis of Upper Limb Musculoskeletal Models During Isometric and Isokinetic Tasks

Sensitivity coefficients are used to understand how errors in subject-specific musculoskeletal model parameters influence model predictions. Previous sensitivity studies in the lower limb calculated sensitivity using perturbations that do not fully represent the diversity of the population. Hence, the present study performs sensitivity analysis in the upper limb using a large synthetic dataset to capture greater physiological diversity. The large dataset (n = 401 synthetic subjects) was created by adjusting maximum isometric force, optimal fiber length, pennation angle, and bone mass to induce atrophy, hypertrophy, osteoporosis, and osteopetrosis in two upper limb musculoskeletal models. Simulations of three isometric and two isokinetic upper limb tasks were performed using each synthetic subject to predict muscle activations. Sensitivity coefficients were calculated using three different methods (two point, linear regression, and sensitivity functions) to understand how changes in Hill-type parameters influenced predicted muscle activations. The sensitivity coefficient methods were then compared by evaluating how well the coefficients accounted for measurement uncertainty. This was done by using the sensitivity coefficients to predict the range of muscle activations given known errors in measuring musculoskeletal parameters from medical imaging. Sensitivity functions were found to best account for measurement uncertainty. Simulated muscle activations were most sensitive to optimal fiber length and maximum isometric force during upper limb tasks. Importantly, the level of sensitivity was muscle and task dependent. These findings provide a foundation for how large synthetic datasets can be applied to capture physiologically diverse populations and understand how model parameters influence predictions.

An investigation of tendon strains in jersey finger injury load cases using a finite element neuromuscular human body model

Introduction: A common hand injury in American football, rugby and basketball is the so-called jersey finger injury (JFI), in which an eccentric overextension of the distal interphalangeal joint leads to an avulsion of the connected musculus flexor digitorum profundus (FDP) tendon. In the field of automotive safety assessment, finite element (FE) neuromuscular human body models (NHBMs) have been validated and are employed to evaluate different injury types related to car crash scenarios. The goal of this study is to show, how such a model can be modified to assess JFIs by adapting the hand of an FE-NHBM for the computational analysis of tendon strains during a generalized JFI load case. Methods: A jersey finger injury criterion (JFIC) covering the injury mechanisms of tendon straining and avulsion was defined based on biomechanical experiments found in the literature. The hand of the Total Human Model for Safety (THUMS) version 3.0 was combined with the musculature of THUMS version 5.03 to create a model with appropriate finger mobility. Muscle routing paths of FDP and musculus flexor digitorum superficialis (FDS) as well as tendon material parameters were optimized using literature data. A simplified JFI load case was simulated as the gripping of a cylindrical rod with finger flexor activation levels between 0% and 100%, which was then retracted with the velocity of a sprinting college football player to forcefully open the closed hand. Results: The optimization of the muscle routing node positions and tendon material parameters yielded good results with minimum normalized mean absolute error values of 0.79% and 7.16% respectively. Tendon avulsion injuries were detected in the middle and little finger for muscle activation levels of 80% and above, while no tendon or muscle strain injuries of any kind occurred. Discussion: The presented work outlines the steps necessary to adapt the hand model of a FE-NHBM for the assessment of JFIs using a newly defined injury criterion called the JFIC. The injury assessment results are in good agreement with documented JFI symptoms. At the same time, the need to rethink commonly asserted paradigms concerning the choice of muscle material parameters is highlighted.

Development and verification of a physiologically motivated internal controller for the open-source extended Hill-type muscle model in LS-DYNA

Nowadays, active human body models are becoming essential tools for the development of integrated occupant safety systems. However, their broad application in industry and research is limited due to the complexity of incorporated muscle controllers, the long simulation runtime, and the non-regular use of physiological motor control approaches. The purpose of this study is to address the challenges in all indicated directions by implementing a muscle controller with several physiologically inspired control strategies into an open-source extended Hill-type muscle model formulated as LS-DYNA user-defined umat41 subroutine written in the Fortran programming language. This results in increased usability, runtime performance and physiological accuracy compared to the standard muscle material existing in LS-DYNA. The proposed controller code is verified with extensive experimental data that include findings for arm muscles, the cervical spine region, and the whole body. Selected verification experiments cover three different muscle activation situations: (1) passive state, (2) open-loop and closed-loop muscle activation, and (3) reflexive behaviour. Two whole body finite element models, the 50th percentile female VIVA OpenHBM and the 50th percentile male THUMS v5, are used for simulations, complemented by the simplified arm model extracted from the 50th percentile male THUMS v3. The obtained results are evaluated additionally with the CORrelation and Analysis methodology and the mean squared error method, showing good to excellent biofidelity and sufficient agreement with the experimental data. It was shown additionally how the integrated controller allows simplified mimicking of the movements for similar musculoskeletal models using the parameters transfer method. Furthermore, the Hill-type muscle model presented in this paper shows better kinematic behaviour even in the passive case compared to the existing one in LS-DYNA due to its improved damping and elastic properties. These findings provide a solid evidence base motivating the application of the enhanced muscle material with the internal controller in future studies with Active Human Body Models under different loading conditions.

American Society of Biomechanics Journal of Biomechanics Award 2022: Computer models do not accurately predict human muscle passive muscle force and fiber length: Evaluating subject-specific modeling impact on musculoskeletal model predictions

Musculoskeletal models are valuable for studying and understanding the human body in a variety of clinical applications that include surgical planning, injury prevention, and prosthetic design. Subject-specific models have proven to be more accurate and useful compared to generic models. Nevertheless, it is important to validate all models when possible. To this end, gracilis muscle-tendon parameters were directly measured intraoperatively and used to test model predictions. The aim of this study was to evaluate the benefits and limitations of systematically incorporating subject-specific variables into muscle models used to predict passive force and fiber length. The results showed that incorporating subject-specific values generally reduced errors, although significant errors still existed. Optimization of the modeling parameter "tendon slack length" was explored in two cases: minimizing fiber length error and minimizing passive force error. The results showed that using all subject-specific values yielded the most favorable outcome in both models and optimization cases. However, the trade-off between fiber length error and passive force error will depend on the specific circumstances and research objectives due to significant individual errors. Notably, individual fiber length and passive force errors were as high as 20% and 37% respectively. Finally, the modeling parameter "tendon slack length" did not correlate with any real-world anatomical length.

A computational musculoskeletal arm model for assessing muscle dysfunction in chronic obstructive pulmonary disease

Computational models have been used extensively to assess diseases and disabilities effects on musculoskeletal system dysfunction. In the current study, we developed a two degree-of-freedom subject-specific second-order task-specific arm model for characterizing upper-extremity function (UEF) to assess muscle dysfunction due to chronic obstructive pulmonary disease (COPD). Older adults (65 years or older) with and without COPD and healthy young control participants (18 to 30 years) were recruited. First, we evaluated the musculoskeletal arm model using electromyography (EMG) data. Second, we compared the computational musculoskeletal arm model parameters along with EMG-based time lag and kinematics parameters (such as elbow angular velocity) between participants. The developed model showed strong cross-correlation with EMG data for biceps (0.905, 0.915) and moderate cross-correlation for triceps (0.717, 0.672) within both fast and normal pace tasks among older adults with COPD. We also showed that parameters obtained from the musculoskeletal model were significantly different between COPD and healthy participants. On average, higher effect sizes were achieved for parameters obtained from the musculoskeletal model, especially for co-contraction measures (effect size = 1.650 ± 0.606, p < 0.001), which was the only parameter that showed significant differences between all pairwise comparisons across the three groups. These findings suggest that studying the muscle performance and co-contraction, may provide better information regarding neuromuscular deficiencies compared to kinematics data. The presented model has potential for assessing functional capacity and studying longitudinal outcomes in COPD.

The force-length relation of the young adult human tibialis anterior

Background

Knowledge of the muscle's lengths at which maximum active isometric force is attained is important for predicting forces during movement. However, there is limited information about the in vivo force-length properties of a human muscle that plays crucial roles during locomotion; the tibialis anterior (TA). We therefore aimed to estimate TA's force-length relation from dorsiflexor torque-angle curves constructed from eight women and eight men.

Methods

Participants performed maximal voluntary fixed-end contractions with their right ankle dorsiflexors from 0° to 30° plantar flexion. Muscle fascicle lengths were estimated from B-mode ultrasound images, and net ankle joint torques were measured using dynamometry. Fascicle forces were estimated by dividing maximal active torques by literature-derived, angle-specific tendon moment arm lengths while assuming a fixed 50% force contribution of TA to the total dorsiflexor force and accounting for fascicle angles.

Results

Maximal active torques were higher at 15° than 20° and 30° plantar flexion (2.4-6.4 Nm, p ≤ 0.012), whereas maximal active TA fascicle forces were higher at 15° than 0°, 20° and 30° plantar flexion (25-61 N, p ≤ 0.042), but not different between 15° and 10° plantar flexion (15 N, p = 0.277). TA fascicle shortening magnitudes during fixed-end contractions were larger at 15° than 30° plantar flexion (3.9 mm, p = 0.012), but less at 15° than 0° plantar flexion (-2.4 mm, p = 0.001), with no significant differences (≤0.7 mm, p = 0.871) between TA's superficial and deep muscle compartments. Series elastic element stiffness was lowest and highest at lengths 5% shorter and 5% longer than optimum fascicle length, respectively (-30 and 15 N/mm, p ≤ 0.003).

Discussion

TA produced its maximum active force at 10-15° plantar flexion, and its normalized force-length relation had ascending and descending limbs that agreed with a simple scaled sarcomere model when active fascicle lengths from within TA's superficial or deep muscle compartment were considered. These findings can be used to inform the properties of the contractile and series elastic elements of Hill-type muscle models.

Unilateral transfemoral osseointegrated prostheses improve joint loading during walking

People with unilateral transfemoral amputation using socket prostheses are at increased risk for developing osteoarthritis in both the residual hip and intact lower-limb joints. Osseointegrated prostheses are a surgical alternative to socket prostheses that directly attach to the residual femur via a bone-anchored implant, however their multi-joint loading effect is largely unknown. Our objective was to establish how osseointegrated prostheses influence joint loading during walking. Motion capture data (kinematics, ground reaction forces) were collected from 12 participants at baseline, with socket prostheses, and 12-months after prosthesis osseointegration during overground walking at self-selected speeds. Subject-specific musculoskeletal models were developed at each timepoint relative to osseointegration. Internal joint moments were calculated using inverse dynamics, muscle and joint reaction forces (JRFs) were estimated with static optimization. Changes in internal joint moments, JRFs, and joint loading-symmetry were compared using statistical parametric mapping (p≤ 0.05) before and after osseointegration. Amputated limb hip flexion moments and anterior JRFs decreased during terminal stance (p = 0.002, <0.001; respectively), while amputated limb hip abduction moments increased during mid-stance (p < 0.001), amputated hip rotation moment changed from internal to external throughout early stance (p < 0.001). Intact limb hip extension and knee flexion moments (p = 0.028, 0.032; respectively), superior and resultant knee JRFs (p = 0.046, 0.049; respectively) decreased during the loading response following prosthesis osseointegration. These results may indicate that the direct loading transmission of these novel prostheses create a more typical mechanical environment in bilateral joints, which is comparable with loading observed in able-bodied individuals and could decrease the risk of development or progression of osteoarthritis.

Linking cortex and contraction-Integrating models along the corticomuscular pathway

Computational models of the neuromusculoskeletal system provide a deterministic approach to investigate input-output relationships in the human motor system. Neuromusculoskeletal models are typically used to estimate muscle activations and forces that are consistent with observed motion under healthy and pathological conditions. However, many movement pathologies originate in the brain, including stroke, cerebral palsy, and Parkinson's disease, while most neuromusculoskeletal models deal exclusively with the peripheral nervous system and do not incorporate models of the motor cortex, cerebellum, or spinal cord. An integrated understanding of motor control is necessary to reveal underlying neural-input and motor-output relationships. To facilitate the development of integrated corticomuscular motor pathway models, we provide an overview of the neuromusculoskeletal modelling landscape with a focus on integrating computational models of the motor cortex, spinal cord circuitry, α-motoneurons  and skeletal muscle in regard to their role in generating voluntary muscle contraction. Further, we highlight the challenges and opportunities associated with an integrated corticomuscular pathway model, such as challenges in defining neuron connectivities, modelling standardisation, and opportunities in applying models to study emergent behaviour. Integrated corticomuscular pathway models have applications in brain-machine-interaction, education, and our understanding of neurological disease.

COVID-19 multiwaves as multiphase percolation: a general N-sigmoidal equation to model the spread

Abstract

The aim of the current study is to investigate the spread of the COVID-19 pandemic as a multiphase percolation process. Mathematical equations have been developed to describe the time dependence of the number of cumulative infected individuals, I t , and the velocity of the pandemic, V p t , as well as to calculate epidemiological characteristics. The study focuses on the use of sigmoidal growth models to investigate multiwave COVID-19. Hill, logistic dose response and sigmoid Boltzmann models fitted successfully a pandemic wave. The sigmoid Boltzmann model and the dose response model were found to be effective in fitting the cumulative number of COVID-19 cases over time 2 waves spread (N = 2). However, for multiwave spread (N > 2), the dose response model was found to be more suitable due to its ability to overcome convergence issues. The spread of N successive waves has also been described as multiphase percolation with a period of pandemic relaxation between two successive waves.

Graphical abstract

Exploring the effects of skeletal architecture and muscle properties on bipedal standing in the common chimpanzee (Pan troglodytes) from the perspective of biomechanics

Introduction: It is well known that the common chimpanzee, as both the closest living relative to humans and a facultative bipedal, has the capability of bipedal standing but cannot do so fully upright. Accordingly, they have been of exceeding significance in elucidating the evolution of human bipedalism. There are many reasons why the common chimpanzee can only stand with its hips-knees bent, such as the distally oriented long ischial tubercle and the almost absent lumbar lordosis. However, it is unknown how the relative positions of their shoulder-hip-knee-ankle joints are coordinated. Similarly, the distribution of the biomechanical characteristics of the lower-limb muscles and the factors that affect the erectness of standing as well as the muscle fatigue of the lower limbs remain a mystery. The answers are bound to light up the evolutional mechanism of hominin bipedality, but these conundrums have not been shed much light upon, because few studies have comprehensively explored the effects of skeletal architecture and muscle properties on bipedal standing in common chimpanzees. Methods: Thus, we first built a musculoskeletal model comprising the head-arms-trunk (HAT), thighs, shanks, and feet segments of the common chimpanzee, and then, the mechanical relationships of the Hill-type muscle-tendon units (MTUs) in bipedal standing were deduced. Thereafter, the equilibrium constraints were established, and a constrained optimization problem was formulated where the optimization objective was defined. Finally, thousands of simulations of bipedal standing experiments were performed to determine the optimal posture and its corresponding MTU parameters including muscle lengths, muscle activation, and muscle forces. Moreover, to quantify the relationship between each pair of the parameters from all the experimental simulation outcomes, the Pearson correlation analysis was employed. Results: Our results demonstrate that in the pursuit of the optimal bipedal standing posture, the common chimpanzee cannot simultaneously achieve maximum erectness and minimum muscle fatigue of the lower limbs. For uni-articular MTUs, the relationship between muscle activation, relative muscle lengths, together with relative muscle forces, and the corresponding joint angle is generally negatively correlated for extensors and positively correlated for flexors. For bi-articular MTUs, the relationship between muscle activation, coupled with relative muscle forces, and the corresponding joint angles does not show the same pattern as in the uni-articular MTUs. Discussion: The results of this study bridge the gap between skeletal architecture, along with muscle properties, and biomechanical performance of the common chimpanzee during bipedal standing, which enhances existing biomechanical theories and advances the comprehension of bipedal evolution in humans.

Numerical instability of Hill-type muscle models

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

Applying a muscle fatigue model when optimizing load-sharing between muscles for short-duration high-intensity exercise: A preliminary study

Introduction: Multiple different mathematical models have been developed to represent muscle force, to represent multiple muscles in the musculoskeletal system, and to represent muscle fatigue. However, incorporating these different models together to describe the behavior of a high-intensity exercise has not been well described. Methods: In this work, we adapted the three-compartment controller (3CCr) muscle fatigue model to be implemented with an inverse-dynamics based optimization algorithm for the muscle recruitment problem for 7 elbow muscles to model a benchmark case: elbow flexion/extension moments. We highlight the difficulties in achieving an accurate subject-specific approach for this multi-level modeling problem, considering different muscular models, compared with experimental measurements. Both an isometric effort and a dynamic bicep curl were considered, where muscle activity and resting periods were simulated to obtain the fatigue behavior. Muscle parameter correction, scaling and calibration are addressed in this study. Moreover, fiber-type recruitment hierarchy in force generation was added to the optimization problem, thus offering an additional novel muscle modeling criterion. Results: It was observed that: i) the results were most accurate for the static case; ii) insufficient torque was predicted by the model at some time points for the dynamic case, which benefitted from a more precise calibration of muscle parameters; iii) modeling the effects of muscular potentiation may be important; and iv) for this multilevel model approach, the 3CCr model had to be modified to avoid reaching situations of unrealistic constant fatigue in high intensity exercise-resting cycles. Discussion: All the methods yield reasonable estimations, but the complexity of obtaining accurate subject-specific human models is highlighted in this study. The proposed novel muscle modeling and force recruitment criterion, which consider the muscular fiber-type distinction, show interesting preliminary results.

On the estimation of hip joint loads through musculoskeletal modeling

Noninvasive estimation of joint loads is still an open challenge in biomechanics. Although musculoskeletal modeling represents a solid resource, multiple improvements are still necessary to obtain accurate predictions of joint loads and to translate such potential into practical utility. The present study, focused on the hip joint, is aimed at reviewing the state-of-the-art literature on the estimation of hip joint reaction forces through musculoskeletal modeling. Our literature inspection, based on well-defined selection criteria, returned seventeen works, which were compared in terms of methods and results. Deviations between predicted and in vivo measured hip joint loads, taken from the OrthoLoad database, were assessed through quantitative deviation indices. Despite the numerous modeling and computational improvements made over the last two decades, predicted hip joint loads still deviate from their experimental counterparts and typically overestimate them. Several critical aspects have emerged that affect muscle force estimation, hence joint loads. Among them, the physical fidelity of the musculoskeletal model, with its parameters and geometry, plays a crucial role. Also, predicted joint loads are markedly affected by the selected muscle recruitment strategy, which reflects the underlying motor control policy. Practical guidelines for researchers interested in noninvasive estimation of hip joint loads are also provided.

Medial gastrocnemius muscle-tendon unit ratios of young females and males

A muscle's contractile element length relative to its muscle-tendon unit (MTU) length is a fundamental design feature affecting MTU function, with high (0.9) or low ratios (0.1) favouring either rapid or economical force production, respectively. Despite the importance for MTU function, little in vivo work has been done to understand contractile element-MTU length ratio variability between individuals and sexes. We therefore compared the medial gastrocnemius (MG) MTU ratios of thirteen females and eighteen males, and explored whether individual ratios could be predicted based on anatomical features. At the presumed tendon slack length ankle joint angle, lengths of MG's MTU, Achilles tendon, muscle belly and its muscle fascicles were measured from B-mode ultrasound images. Contractile element length was represented by the in-series muscle fascicle length (FL) and was calculated by multiplying FL by the cosine of fascicle angle. The mean ± standard deviation in-series FL-MTU length ratio was 0.09 ± 0.02 and ranged from 0.06 to 0.11, whereas the muscle belly length-MTU length ratio was 0.54 ± 0.38 and ranged from 0.47 to 0.60. Neither ratio was significantly different between females and males (p ≥ 0.116). In-series FL was not significantly correlated with MTU length (r = -0.115, p =.538), muscle belly length (r = 0.05, p =.788), or shank length (r = 0.169, p =.364), but MTU length was significantly correlated with muscle belly length (r = 0.641, p <.001), and shank length (r = 0.575, p =.001). A low in-series FL-MTU length ratio suggests that the MG of young, healthy individuals is specialised for energy-efficient stretch-shortening cycles. These findings provide useful inputs for the MTU actuator design of Hill-type models.

Sensitivity analysis guided improvement of an electromyogram-driven lumped parameter musculoskeletal hand model

EMG-driven neuromusculoskeletal models have been used to study many impairments and hold great potential to facilitate human-machine interactions for rehabilitation. A challenge to successful clinical application is the need to optimize the model parameters to produce accurate kinematic predictions. In order to identify the key parameters, we used Monte-Carlo simulations to evaluate the sensitivities of wrist and metacarpophalangeal (MCP) flexion/extension prediction accuracies for an EMG-driven, lumped-parameter musculoskeletal model. Four muscles were modeled with 22 total optimizable parameters. Model predictions from EMG were compared with measured joint angles from 11 able-bodied subjects. While sensitivities varied by muscle, we determined muscle moment arms, maximum isometric force, and tendon slack length were highly influential, while passive stiffness and optimal fiber length were less influential. Removing the two least influential parameters from each muscle reduced the optimization search space from 22 to 14 parameters without significantly impacting prediction correlation (wrist: 0.90 ± 0.05 vs 0.90 ± 0.05, p = 0.96; MCP: 0.74 ± 0.20 vs 0.70 ± 0.23, p = 0.51) and normalized root mean square error (wrist: 0.18 ± 0.03 vs 0.19 ± 0.03, p = 0.16; MCP: 0.18 ± 0.06 vs 0.19 ± 0.06, p = 0.60). Additionally, we showed that wrist kinematic predictions were insensitive to parameters of the modeled MCP muscles. This allowed us to develop a novel optimization strategy that more reliably identified the optimal set of parameters for each subject (27.3 ± 19.5%) compared to the baseline optimization strategy (6.4 ± 8.1%; p = 0.004). This study demonstrated how sensitivity analyses can be used to guide model refinement and inform novel and improved optimization strategies, facilitating implementation of musculoskeletal models for clinical applications.

Lower-limb muscle function in healthy young and older adults across a range of walking speeds

BACKGROUND

Previous studies have compared the functional roles of the individual lower-limb muscles when healthy young and older adults walk at their self-selected speeds. No age-group differences were observed in ankle muscle forces and ankle muscle contributions to support and progression. However, older adults displayed higher gluteus maximus (hip extensor) muscle forces and greater contributions to support during early stance. There are no data that describe the functions of the individual lower-limb muscles in healthy older adults for walking at speeds other than the self-selected speed.

RESEARCH QUESTION

How does walking speed affect the functional roles of the individual lower-limb muscles in healthy older adults?

METHODS

Three-dimensional gait data were recorded for 10 healthy young and 10 healthy older adults walking at slow, normal, and fast speeds (0.7 m/s, 1.4 m/s, and 1.7 m/s, respectively). Both groups walked at the same speed at each condition. The experimental data were combined with a full-body musculoskeletal model to calculate and compare muscle forces and muscle contributions to the vertical, fore-aft, and mediolateral ground reaction forces (support, progression, and balance, respectively) in both groups.

RESULTS

Lower-limb muscle function was similar in young and older adults when both groups walked at the same speed at each condition. The same five muscles - gluteus maximus, gluteus medius, vasti, gastrocnemius, and soleus - contributed most significantly to support, progression, and balance in both groups at all speeds. However, gluteus maximus generated greater support and braking forces during early stance and gastrocnemius contributed less to forward propulsion during late stance at all speeds in the older group.

SIGNIFICANCE

These results provide further insight into the functional roles of the individual lower-limb muscles of older adults during walking and could inform the design of exercise programs aimed at improving support and balance in those at risk of falling.

Clarify Sit-to-Stand Muscle Synergy and Tension Changes in Subacute Stroke Rehabilitation by Musculoskeletal Modeling

Post-stroke patients exhibit distinct muscle activation electromyography (EMG) features in sit-to-stand (STS) due to motor deficiency. Muscle activation amplitude, related to muscle tension and muscle synergy activation levels, is one of the defining EMG features that reflects post-stroke motor functioning and motor impairment. Although some qualitative findings are available, it is not clear if and how muscle activation amplitude-related biomechanical attributes may quantitatively reflect during subacute stroke rehabilitation. To better enable a longitudinal investigation into a patient's muscle activation changes during rehabilitation or an inter-subject comparison, EMG normalization is usually applied. However, current normalization methods using maximum voluntary contraction (MVC) or within-task peak/mean EMG may not be feasible when MVC cannot be obtained from stroke survivors due to motor paralysis and the subject of comparison is EMG amplitude. Here, focusing on the paretic side, we first propose a novel, joint torque-based normalization method that incorporates musculoskeletal modeling, forward dynamics simulation, and mathematical optimization. Next, upon method validation, we apply it to quantify changes in muscle tension and muscle synergy activation levels in STS motor control units for patients in subacute stroke rehabilitation. The novel method was validated against MVC-normalized EMG data from eight healthy participants, and it retained muscle activation amplitude differences for inter- and intra-subject comparisons. The proposed joint torque-based method was also compared with the common static optimization based on squared muscle activation and showed higher simulation accuracy overall. Serial STS measurements were conducted with four post-stroke patients during their subacute rehabilitation stay (137 ± 22 days) in the hospital. Quantitative results of patients suggest that maximum muscle tension and activation level of muscle synergy temporal patterns may reflect the effectiveness of subacute stroke rehabilitation. A quality comparison between muscle synergies computed with the conventional within-task peak/mean EMG normalization and our proposed method showed that the conventional was prone to activation amplitude overestimation and underestimation. The contributed method and findings help recapitulate and understand the post-stroke motor recovery process, which may facilitate developing more effective rehabilitation strategies for future stroke survivors.

Plasticity of the gastrocnemius elastic system in response to decreased work and power demand during growth

Elastic energy storage and release can enhance performance that would otherwise be limited by the force-velocity constraints of muscle. Although functional influence of a biological spring depends on tuning between components of an elastic system (the muscle, spring-driven mass and lever system), we do not know whether elastic systems systematically adapt to functional demand. To test whether altering work and power generation during maturation alters the morphology of an elastic system, we prevented growing guinea fowl (Numida meleagris) from jumping. We compared the jump performance of our treatment group at maturity with that of controls and measured the morphology of the gastrocnemius elastic system. We found that restricted birds jumped with lower jump power and work, yet there were no significant between-group differences in the components of the elastic system. Further, subject-specific models revealed no difference in energy storage capacity between groups, though energy storage was most sensitive to variations in muscle properties (most significantly operating length and least dependent on tendon stiffness). We conclude that the gastrocnemius elastic system in the guinea fowl displays little to no plastic response to decreased demand during growth and hypothesize that neural plasticity may explain performance variation.

Transtibial limb loss does not increase metabolic cost in three-dimensional computer simulations of human walking

Loss of a lower limb below the knee, i.e., transtibial limb loss, and subsequently walking with a prosthesis, is generally thought to increase the metabolic cost of walking vs. able-bodied controls. However, high-functioning individuals with limb loss such as military service members often walk with the same metabolic cost as controls. Here we used a 3-D computer model and optimal control simulation approach to test the hypothesis that transtibial limb loss in and of itself causes an increase in metabolic cost of walking. We first generated N = 36 simulations of walking at 1.45 m/s using a “pre-limb loss” model, with two intact biological legs, that minimized deviations from able-bodied experimental walking mechanics with minimum muscular effort. We then repeated these simulations using a “post-limb loss” model, with the right leg’s ankle muscles and joints replaced with a simple model of a passive transtibial prosthesis. No other changes were made to the post-limb loss model’s remaining muscles or musculoskeletal parameters compared to the pre-limb loss case. Post-limb loss, the gait deviations on average increased by only 0.17 standard deviations from the experimental means, and metabolic cost did not increase (3.58 ± 0.10 J/m/kg pre-limb loss vs. 3.59 ± 0.12 J/m/kg post-limb loss, p = 0.65). The results suggest that transtibial limb loss does not directly lead to an increase in metabolic cost, even when deviations from able-bodied gait mechanics are minimized. High metabolic costs observed in individuals with transtibial limb loss may be due to secondary changes in strength or general fitness after limb loss, modifiable prosthesis issues, or to prioritization of factors that affect locomotor control other than gait deviations and muscular effort.

A fair and EMG-validated comparison of recruitment criteria, musculotendon models and muscle coordination strategies, for the inverse-dynamics based optimization of muscle forces during gait

Experimental studies and EMG collections suggest that a specific strategy of muscle coordination is chosen by the central nervous system to perform a given motor task. A popular mathematical approach for solving the muscle recruitment problem is optimization. Optimization-based methods minimize or maximize some criterion (objective function or cost function) which reflects the mechanism used by the central nervous system to recruit muscles for the movement considered. The proper cost function is not known a priori, so the adequacy of the chosen function must be validated according to the obtained results. In addition of the many criteria proposed, several physiological representations of the musculotendon actuator dynamics (that prescribe constraints for the forces) along with different musculoskeletal models can be found in the literature, which hinders the selection of the best neuromusculotendon model for each application. Seeking to provide a fair base for comparison, this study measures the efficiency and accuracy of: (i) four different criteria within the static optimization approach (where the physiological character of the muscle, which affects the constraints of the forces, is not considered); (ii) three physiological representations of the musculotendon actuator dynamics: activation dynamics with elastic tendon, simplified activation dynamics with rigid tendon and rigid tendon without activation dynamics; (iii) a synergy-based method; all of them within the framework of inverse-dynamics based optimization. Motion/force/EMG gait analyses were performed on ten healthy subjects. A musculoskeletal model of the right leg actuated by 43 Hill-type muscles was scaled to each subject and used to calculate joint moments, musculotendon kinematics and moment arms. Muscle activations were then estimated using the different approaches, and these estimates were compared with EMG measurements. Although no significant differences were obtained with all the methods at statistical level, it must be pointed out that a higher complexity of the method does not guarantee better results, as the best correlations with experimental values were obtained with two simplified approaches: the static optimization and the physiological approach with simplified activation dynamics and rigid tendon, both using the sum of the squares of muscle forces as objective function.

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.

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.

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.

A generic musculoskeletal model of the juvenile lower limb for biomechanical analyses of gait

The aim of this study was to develop a generic musculoskeletal model of a healthy 10-year-old child and examine the effects of geometric scaling on the calculated values of lower-limb muscle forces during gait. Subject-specific musculoskeletal models of five healthy children were developed from in vivo MRI data, and these models were subsequently used to create a generic juvenile (GJ) model. Calculations of lower-limb muscle forces for normal walking obtained from two scaled-generic versions of the juvenile model (SGJ1 and SGJ2) were evaluated against corresponding results derived from an MRI-based model of one subject (SSJ1). The SGJ1 and SGJ2 models were created by scaling the GJ model using gait marker positions and joint centre locations derived from MRI imaging, respectively. Differences in the calculated values of peak isometric muscle forces and muscle moment arms between the scaled-generic models and MRI-based model were relatively small. Peak isometric muscle forces calculated for SGJ1 and SGJ2 were respectively 2.2% and 3.5% lower than those obtained for SSJ1. Model-predicted muscle forces for SGJ2 agreed more closely with calculations obtained from SSJ1 than corresponding results derived from SGJ1. These results suggest that accurate estimates of muscle forces during gait may be obtained by scaling generic juvenile models based on joint centre locations. The generic juvenile model developed in this study may be used as a template for creating subject-specific musculoskeletal models of normally-developing children in studies aimed at describing lower-limb muscle function during gait.

Subject-specific muscle properties from diffusion tensor imaging significantly improve the accuracy of musculoskeletal models

Musculoskeletal modelling is an important platform on which to study the biomechanics of morphological structures in vertebrates and is widely used in clinical, zoological and palaeontological fields. The popularity of this approach stems from the potential to non-invasively quantify biologically important but difficult-to-measure functional parameters. However, while it is known that model predictions are highly sensitive to input values, it is standard practice to build models by combining musculoskeletal data from different sources resulting in 'generic' models for a given species. At present, there are little quantitative data on how merging disparate anatomical data in models impacts the accuracy of these functional predictions. This issue is addressed herein by quantifying the accuracy of both subject-specific human limb models containing individualised muscle force-generating properties and models built using generic properties from both elderly and young individuals, relative to experimental muscle torques obtained from an isokinetic dynamometer. The results show that subject-specific models predict isokinetic muscle torques to a greater degree of accuracy than generic models at the ankle (root-mean-squared error - 7.9% vs. 49.3% in elderly anatomy-based models), knee (13.2% vs. 57.3%) and hip (21.9% vs. 32.8%). These results have important implications for the choice of musculoskeletal properties in future modelling studies, and the relatively high level of accuracy achieved in the subject-specific models suggests that such models can potentially address questions about inter-subject variations of muscle functions. However, despite relatively high levels of overall accuracy, models built using averaged generic muscle architecture data from young, healthy individuals may lack the resolution and accuracy required to study such differences between individuals, at least in certain circumstances. The results do not wholly discourage the continued use of averaged generic data in musculoskeletal modelling studies but do emphasise the need for to maximise the accuracy of input values if studying intra-species form-function relationships in the musculoskeletal system.

Estimating total maximum isometric force output of trunk and hip muscles after spinal cord injury

Functional neuromuscular stimulation (FNS) can be used to restore seated trunk function in individuals paralyzed due to spinal cord injury (SCI). Musculoskeletal models allow for the design and tuning of controllers for use with FNS; however, these models often use aggregated estimates for parameters of the musculotendon elements, the most significant of which is maximum isometric force (MIF). Stimulated MIF for individuals with SCI is typically assumed to be approximately 50% of the values exhibited by able-bodied muscles, which itself varies between studies and individuals. A method for estimating subject-specific MIF during dynamic motions in individuals with SCI produced by electrical stimulation has been developed to test this assumption and obtained more accurate estimates for biomechanical analysis and controller design. A simple on-off controller was applied to individuals with SCI seated in the workspace of a motion capture system to record joint angles of three types of trunk motions: forward flexion, left and right lateral bending followed by returning, un-aided, to upright posture via neural stimulation delivered to activate the muscles of the hips and trunk. System identification was used with a musculoskeletal model to find the optimal MIF values that reproduced the experimentally observed motions. Experiments with five volunteers with SCI indicate that an MIF of the 50% able-bodied values commonly used is significantly lower than the identified estimates in 33 of 44 muscle groups tested. This suggests that the strengths of paralyzed muscles when stimulated with FNS have been underestimated in many situations and their true force outputs may be higher than the values suggested for use in simulation studies with musculoskeletal models. These findings indicate that subject-specific musculoskeletal models can more closely mimic the motions of subjects by using individualized estimates of MIF, which may allow the design and tuning of controllers while reducing the time spent with subjects in the loop.

Short-term Effects of Robot-Resistance Exercises on Muscle Strength and Activations: Types of Muscle Contraction and Speed of Contraction

We developed the isokinetic exercise robot for single joint muscle training. The purpose of this study was to investigate the effects of contraction types (concentric vs. eccentric contractions) and contractile speeds (slow vs. fast contractions) controlled by the developed exercise robot on muscle strength and activations. Ten subjects voluntarily performed the biceps curls exercise by resisting the robot-driven loads. Results indicated that there was no significant change in muscular strength as a result of different type of contraction and contractile velocity. The effect of fatigue, however, might be detected due to decreased maximum moment and increased muscle activities. Further research on the optimal recovery time is needed in order to enhance utilization of exercise robot in fitness areas.

Angle Estimation for Knee Joint Movement Based on PCA-RELM Algorithm

Surface electromyogram (sEMG) signals are easy to record and offer valuable motion information, such as symmetric and periodic motion in human gait. Due to these characteristics, sEMG is widely used in human-computer interaction, clinical diagnosis and rehabilitation medicine, sports medicine and other fields. This paper aims to improve the estimation accuracy and real-time performance, in the case of the knee joint angle in the lower limb, using a sEMG signal, in a proposed estimation algorithm of the continuous motion, based on the principal component analysis (PCA) and the regularized extreme learning machine (RELM). First, the sEMG signals, collected during the lower limb motion, are preprocessed, while feature samples are extracted from the acquired and preconditioned sEMG signals. Next, the feature samples dimensions are reduced by the PCA, as well as the knee joint angle system is measured by the three-dimensional motion capture system, are followed by the normalization of the feature variable value. The normalized sEMG feature is used as the input layer, in the RELM model, while the joint angle is used as the output layer. After training, the RELM model estimates the knee joint angle of the lower limbs, while it uses the root mean square error (RMSE), Pearson correlation coefficient and model training time as key performance indicators (KPIs), to be further discussed. The RELM, the traditional BP neural network and the support vector machine (SVM) estimation results are compared. The conclusions prove that the RELM method, not only has ensured the validity of results, but also has greatly reduced the learning train time. The presented work is a valuable point of reference for further study of the motion estimation in lower limb.

Neuromusculoskeletal Modeling-Based Prostheses for Recovery After Spinal Cord Injury

Concurrent stimulation and reinforcement of motor and sensory pathways has been proposed as an effective approach to restoring function after developmental or acquired neurotrauma. This can be achieved by applying multimodal rehabilitation regimens, such as thought-controlled exoskeletons or epidural electrical stimulation to recover motor pattern generation in individuals with spinal cord injury (SCI). However, the human neuromusculoskeletal (NMS) system has often been oversimplified in designing rehabilitative and assistive devices. As a result, the neuromechanics of the muscles is seldom considered when modeling the relationship between electrical stimulation, mechanical assistance from exoskeletons, and final joint movement. A powerful way to enhance current neurorehabilitation is to develop the next generation prostheses incorporating personalized NMS models of patients. This strategy will enable an individual voluntary interfacing with multiple electromechanical rehabilitation devices targeting key afferent and efferent systems for functional improvement. This narrative review discusses how real-time NMS models can be integrated with finite element (FE) of musculoskeletal tissues and interface multiple assistive and robotic devices with individuals with SCI to promote neural restoration. In particular, the utility of NMS models for optimizing muscle stimulation patterns, tracking functional improvement, monitoring safety, and providing augmented feedback during exercise-based rehabilitation are discussed.

In vivo human lower limb muscle architecture dataset obtained using diffusion tensor imaging

'Gold standard' reference sets of human muscle architecture are based on elderly cadaveric specimens, which are unlikely to be representative of a large proportion of the human population. This is important for musculoskeletal modeling, where the muscle force-generating properties of generic models are defined by these data but may not be valid when applied to models of young, healthy individuals. Obtaining individualized muscle architecture data in vivo is difficult, however diffusion tensor magnetic resonance imaging (DTI) has recently emerged as a valid method of achieving this. DTI was used here to provide an architecture data set of 20 lower limb muscles from 10 healthy adults, including muscle fiber lengths, which are important inputs for Hill-type muscle models commonly used in musculoskeletal modeling. Maximum isometric force and muscle fiber lengths were found not to scale with subject anthropometry, suggesting that these factors may be difficult to predict using scaling or optimization algorithms. These data also highlight the high level of anatomical variation that exists between individuals in terms of lower limb muscle architecture, which supports the need of incorporating subject-specific force-generating properties into musculoskeletal models to optimize their accuracy for clinical evaluation.

Kinematics and muscle forces in women with patellofemoral pain during the propulsion phase of the single leg triple hop test

BACKGROUND

Approximately 25% of orthopedic knee conditions are related to patellofemoral pain (PFP), with young women being the most affected. It is thought that this condition is associated with modifications in the kinematics and muscle control patterns of the lower limb during weight-bearing support activities, which increases femur movement under the patella.

OBJECTIVES

To compare kinematics and muscle induced acceleration patterns between PFP subjects and healthy controls during the preparation phase of the single leg triple hop test.

STUDY DESIGN

Biomechanical analysis was performed using OpenSim. Ten physically active women (23.2 ± 4 years, 59.3 ± 5.8 kg, and 1.63 ± 0.06 m) with no history of lower limb injury (CG) and 11 volunteers (23.5 ± 2 years, 55.4 ± 4.9 kg, and 1.66 ± 0.04 m) with PFP (PFPG) were recruited. The participants performed a series of single leg triple hop tests while the ground reaction forces and kinematic data were recorded.

RESULTS

Vector field statistical analysis indicated increased lumbar extension, anterior pelvic tilt, contralateral pelvic drop, and lower induced accelerations from the core and hip muscles in PFPG.

CONCLUSION

PFP volunteers presented with alterations in lumbar muscle control associated with a possible compensatory pelvic strategy to minimize knee extensor moment.

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.

The influence of model parameters on model validation

The study examined the sensitivity of two musculoskeletal models to the parameters describing each model. Two different models were examined: a phenomenological model of human jumping with parameters based on live subject data, and the second a model of the First Dorsal Interosseous with parameters based on cadaveric measurements. Both models were sensitive to the model parameters, with the use of mean group data not producing model outputs reflective of either the performance of any group member or the mean group performance. These results highlight the value of subject specific model parameters, and the problems associated with model validation.