Biomechanical modeling for the estimation of muscle forces: toward a common language in biomechanics, medical engineering, and neurosciences.

Different research fields, such as biomechanics, medical engineering or neurosciences take part in the development of biomechanical models allowing for the estimation of individual muscle forces involved in motor action. The heterogeneity of the terminology used to describe these models according to the research field is a source of confusion and can hamper collaboration between the different fields. This paper proposes a common language based on lexical disambiguation and a synthesis of the terms used in the literature in order to facilitate the understanding of the different elements of biomechanical modeling for force estimation, without questioning the relevance of the terms used in each field or the different model components or their interest. We suggest that the description should start with an indication of whether the muscle force estimation problem is solved following the physiological movement control (from the nervous drive to the muscle force production) or in the opposite direction. Next, the suitability of the model for force production estimation at a given time or for monitoring over time should be specified. Authors should pay particular attention to the method description used to find solutions, specifying whether this is done during or after data collection, with possible method adaptations during processing. Finally, the presence of additional data must be specified by indicating whether they are used to drive, assist, or calibrate the model. Describing and classifying models in this way will facilitate the use and application in all fields where the estimation of muscle forces is of real, direct, and concrete interest.

Predictions of Anterior Cruciate Ligament Dynamics From Subject-Specific Musculoskeletal Models and Dynamic Biplane Radiography.

In vivo knee ligament forces are important to consider for informing rehabilitation or clinical interventions. However, they are difficult to directly measure during functional activities. Musculoskeletal models and simulations have become the primary methods by which to estimate in vivo ligament loading. Previous estimates of anterior cruciate ligament (ACL) forces range widely, suggesting that individualized anatomy may have an impact on these predictions. Using ten subject-specific (SS) lower limb musculoskeletal models, which include individualized musculoskeletal geometry, muscle architecture, and six degree-of-freedom knee joint kinematics from dynamic biplane radiography (DBR), this study provides SS estimates of ACL force (anteromedial-aACL; and posterolateral-pACL bundles) during the full gait cycle of treadmill walking. These forces are compared to estimates from scaled-generic (SG) musculoskeletal models to assess the effect of musculoskeletal knee joint anatomy on predicted forces and the benefit of SS modeling in this context. On average, the SS models demonstrated a double force peak during stance (0.39-0.43 xBW per bundle), while only a single force peak during stance was observed in the SG aACL. No significant differences were observed between continuous SG and SS ACL forces; however, root mean-squared differences between SS and SG predictions ranged from 0.08 xBW to 0.27 xBW, suggesting SG models do not reliably reflect forces predicted by SS models. Force predictions were also found to be highly sensitive to ligament resting length, with ±10% variations resulting in force differences of up to 84%. Overall, this study demonstrates the sensitivity of ACL force predictions to SS anatomy, specifically musculoskeletal joint geometry and ligament resting lengths, as well as the feasibility for generating SS musculoskeletal models for a group of subjects to predict in vivo tissue loading during functional activities.

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.

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

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

Muscle Synergies Modify Optimization Estimates of Joint Stiffness During Walking.

Because of its simplicity, static optimization (SO) is frequently used to resolve the muscle redundancy problem (i.e., more muscles than degrees-of-freedom (DOF) in the human musculoskeletal system). However, SO minimizes antagonistic co-activation and likely joint stiffness as well, which may not be physiologically realistic since the body modulates joint stiffness during movements such as walking. Knowledge of joint stiffness is limited due to the difficulty of measuring it experimentally, leading researchers to estimate it using computational models. This study explores how imposing a synergy structure on the muscle activations estimated by optimization (termed "synergy optimization," or SynO) affects calculated lower body joint stiffnesses during walking. By limiting the achievable muscle activations and coupling all time frames together, a synergy structure provides a potential mechanism for reducing indeterminacy and improving physiological co-activation but at the cost of a larger optimization problem. To compare joint stiffnesses produced by SynO (2-6 synergies) and SO, we used both approaches to estimate lower body muscle activations and forces for sample experimental overground walking data obtained from the first knee grand challenge competition. Both optimizations used a custom Hill-type muscle model that permitted analytic calculation of individual muscle contributions to the stiffness of spanned joints. Both approaches reproduced inverse dynamic joint moments well over the entire gait cycle, though SynO with only two synergies exhibited the largest errors. Maximum and mean joint stiffnesses for hip and knee flexion in particular decreased as the number of synergies increased from 2 to 6, with SO producing the lowest joint stiffness values. Our results suggest that SynO increases joint stiffness by increasing muscle co-activation, and furthermore, that walking with a reduced number of synergies may result in increased joint stiffness and perhaps stability.

A Procedure to Define Customized Musculoskeletal Models for the Analysis of the Crutch-Orthosis-Assisted Gait of Spinal Cord Injured Subjects.

Subjects suffering from spinal cord injury with lower extremity impairment generally use a wheelchair to move. However, some of them are capable of walking with the help of orthoses and crutches. Standing up and walking regularly have huge benefits for the general health state of these subjects, since it reduces the negative consequences of sedentarism. Therefore, achieving adherence to assisted gait is important, but there is a risk of abandoning due to several issues such as pain, fatigue, or very low speed, which can make the subject return to solely use the wheelchair. Musculoskeletal models can provide estimations of muscular forces and activations, which in turn enable to calculate magnitudes such as joint reactions, energetic cost, and bone stress and strain. These magnitudes can serve to evaluate the impact of assisted gait in the subject's health and to assess the likelihood of adherence. Moreover, they can be used as indicators to compare different assistive devices for a particular subject. As every spinal cord-injured (SCI) subject represents a different case, a procedure to define customized musculoskeletal models for the crutch-orthosis-assisted gait of SCI subjects is proposed in this paper. Issues such as selection of muscles and integration of models of trunk, upper and lower extremities, and assistive devices (crutches and orthoses) are addressed. An inverse-dynamics-based physiological static optimization method that takes into account muscle dynamics at low computational cost is applied to obtain estimates of muscle forces and joint reactions. The method is experimentally validated by electromyography in a case study.

Effects of Optimization Technique on Simulated Muscle Activations and Forces.

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

OpenSim Versus Human Body Model: A Comparison Study for the Lower Limbs During Gait.

Musculoskeletal modeling and simulations have become popular tools for analyzing human movements. However, end users are often not aware of underlying modeling and computational assumptions. This study investigates how these assumptions affect biomechanical gait analysis outcomes performed with Human Body Model and the OpenSim gait2392 model. The authors compared joint kinematics, kinetics, and muscle forces resulting from processing data from 7 healthy adults with both models. Although outcome variables had similar patterns, there were statistically significant differences in joint kinematics (maximal difference: 9.8° [1.5°] in sagittal plane hip rotation), kinetics (maximal difference: 0.36 [0.10] N·m/kg in sagittal plane hip moment), and muscle forces (maximal difference: 8.51 [1.80] N/kg for psoas). These differences might be explained by differences in hip and knee joint center locations up to 2.4 (0.5) and 1.9 (0.2) cm in the posteroanterior and inferosuperior directions, respectively, and by the offset in pelvic reference frames of about 10° around the mediolateral axis. The choice of model may not influence the conclusions in clinical settings, where the focus is on interpreting deviations from the reference data, but it will affect the conclusions of mechanical analyses in which the goal is to obtain accurate estimates of kinematics and loading.

Predicted vs. measured paraspinal muscle activity in adolescent idiopathic scoliosis patients: EMG validation of optimization-based musculoskeletal simulations.

Musculoskeletal (MSK) models offer great potential for predicting the muscle forces required to inform more detailed simulations of vertebral endplate loading in adolescent idiopathic scoliosis (AIS). In this work, simulations based on static optimization were compared with in vivo measurements in two AIS patients to determine whether computational approaches alone are sufficient for accurate prediction of paraspinal muscle activity during functional activities. We used biplanar radiographs and marker-based motion capture, ground reaction force, and electromyography (EMG) data from two patients with mild and moderate thoracolumbar AIS (Cobb angles: 21° and 45°, respectively) during standing while holding two weights in front (reference position), walking, running, and object lifting. Using a fully automated approach, 3D spinal shape was extracted from the radiographs. Geometrically personalized OpenSim-based MSK models were created by deforming the spine of pre-scaled full-body models of children/adolescents. Simulations were performed using an experimentally controlled backward approach. Differences between model predictions and EMG measurements of paraspinal muscle activity (both expressed as a percentage of the reference position values) at three different locations around the scoliotic main curve were quantified by root mean square error (RMSE) and cross-correlation (XCorr). Predicted and measured muscle activity correlated best for mild AIS during object lifting (XCorr's ≥ 0.97), with relatively low RMSE values. For moderate AIS as well as the walking and running activities, agreement was lower, with XCorr reaching values of 0.51 and comparably high RMSE values. This study demonstrates that static optimization alone seems not appropriate for predicting muscle activity in AIS patients, particularly in those with more than mild deformations as well as when performing upright activities such as walking and running.

Use of computational modeling to examine fingertip force production in children with hemiplegic cerebral palsy.

Most children with hemiplegic cerebral palsy (HCP), one of the most prevalent subtypes of cerebral palsy, struggle with grasping and manipulating objects. This impairment may arise from a diminished capacity to properly direct forces created with the finger pad due to aberrant force application. Children with HCP were asked to create maximal force with the index finger pad in the palmar (normal) direction with both the paretic and non-paretic hands. The resulting forces and finger postures were then applied to a computational musculoskeletal model of the hand to estimate the corresponding muscle activation patterns. Subjects tended to create greater shear force relative to normal force with the paretic hand (p < 0.05). The resultant force was directed 33.6°±10.8° away from the instructed palmar direction in the paretic hand, but only 8.0°±7.3° in the non-paretic hand. Additionally, participants created greater palmar force with the non-paretic hand than with the paretic hand (p < 0.05). These differences in force production are likely due to differences in muscle activation pattern, as our computational models showed differences in which muscles are active and their relative activations when recreating the measured force vectors for the two hands (p < 0.01). The models predicted reduced activation in the extrinsic and greater reductions in activation in the intrinsic finger muscles, potentially due to reduced voluntary activation or muscle atrophy. As the large shear forces could lead to objects slipping from grasp, muscle activation patterns may provide an important target for therapeutic treatment in children with HCP.

Comparison of Synergy Extrapolation and Static Optimization for Estimating Multiple Unmeasured Muscle Activations during Walking.

Background: Calibrated electromyography (EMG)-driven musculoskeletal models can provide great insight into internal quantities (e.g., muscle forces) that are difficult or impossible to measure experimentally. However, the need for EMG data from all involved muscles presents a significant barrier to the widespread application of EMG-driven modeling methods. Synergy extrapolation (SynX) is a computational method that can estimate a single missing EMG signal with reasonable accuracy during the EMG-driven model calibration process, yet its performance in estimating a larger number of missing EMG signals remains unclear. Methods: This study assessed the accuracy with which SynX can use eight measured EMG signals to estimate muscle activations and forces associated with eight missing EMG signals in the same leg during walking while simultaneously performing EMG-driven model calibration. Experimental gait data collected from two individuals post-stroke, including 16 channels of EMG data per leg, were used to calibrate an EMG-driven musculoskeletal model, providing "gold standard" muscle activations and forces for evaluation purposes. SynX was then used to predict the muscle activations and forces associated with the eight missing EMG signals while simultaneously calibrating EMG-driven model parameter values. Due to its widespread use, static optimization (SO) was also utilized to estimate the same muscle activations and forces. Estimation accuracy for SynX and SO was evaluated using root mean square errors (RMSE) to quantify amplitude errors and correlation coefficient r values to quantify shape similarity, each calculated with respect to "gold standard" muscle activations and forces. Results: On average, SynX produced significantly more accurate amplitude and shape estimates for unmeasured muscle activations (RMSE 0.08 vs. 0.15,r value 0.55 vs. 0.12) and forces (RMSE 101.3 N vs. 174.4 N,r value 0.53 vs. 0.07) compared to SO. SynX yielded calibrated Hill-type muscle-tendon model parameter values for all muscles and activation dynamics model parameter values for measured muscles that were similar to "gold standard" calibrated model parameter values. Conclusions: These findings suggest that SynX could make it possible to calibrate EMG-driven musculoskeletal models for all important lower-extremity muscles with as few as eight carefully chosen EMG signals and eventually contribute to the design of personalized rehabilitation and surgical interventions for mobility impairments.

Head supported mass, moment of inertia, neck loads and stability: A simulation study.

Occupations or activities where donning head-supported mass (HSM) is commonplace put operators at an elevated risk of chronic neck pain. Yet, there is no consensus about what features of HSM influence the relative contributions to neck loads. Therefore, we tested four hypotheses that could increase neck loads: (i) HSM increases gravitational moments; (ii) more muscle activation is required to stabilize the head with HSM; (iii) the position of the HSM centre of mass (COM) induces gravitational moments; and (iv) the added moment of inertia (MOI) from HSM increases neck loads during head repositioning tasks. We performed a sensitivity analysis on the C5-C6 compression evaluated from a 24-degree freedom cervical spine model in OpenSim for static and dynamic movement trials. For static trials, we varied the magnitude of HSM, the position of its COM, and developed a novel stability constraint for static optimization. In dynamic trials, we varied HSM and the three principle MOIs. HSM magnitude and compression were linearly related to one another for both static and dynamic trials, with amplification factors varying between 1.9 and 3.9. Similar relationships were found for the COM position, although the relationship between C5-C6 peak compression and MOI in dynamic trials was generally nonlinear. This sensitivity analysis uncovered evidence in favour of hypotheses (i), (ii) and (iii). However, the model's prediction of C5-C6 compression was not overly sensitive to the magnitude of MOI. Therefore, the HSM mass properties may be more influential on neck compression than MOI properties, even during dynamic tasks.

Can static optimization detect changes in peak medial knee contact forces induced by gait modifications?

Medial knee contact force (MCF) is related to the pathomechanics of medial knee osteoarthritis. However, MCF cannot be directly measured in the native knee, making it difficult for therapeutic gait modifications to target this metric. Static optimization, a musculoskeletal simulation technique, can estimate MCF, but there has been little work validating its ability to detect changes in MCF induced by gait modifications. In this study, we quantified the error in MCF estimates from static optimization compared to measurements from instrumented knee replacements during normal walking and seven different gait modifications. We then identified minimum magnitudes of simulated MCF changes for which static optimization correctly identified the direction of change (i.e., whether MCF increased or decreased) at least 70% of the time. A full-body musculoskeletal model with a multi-compartment knee and static optimization was used to estimate MCF. Simulations were evaluated using experimental data from three subjects with instrumented knee replacements who walked with various gait modifications for a total of 115 steps. Static optimization underpredicted the first peak (mean absolute error = 0.16 bodyweights) and overpredicted the second peak (mean absolute error = 0.31 bodyweights) of MCF. Average root mean square error in MCF over stance phase was 0.32 bodyweights. Static optimization detected the direction of change with at least 70% accuracy for early-stance reductions, late-stance reductions, and early-stance increases in peak MCF of at least 0.10 bodyweights. These results suggest that a static optimization approach accurately detects the direction of change in early-stance medial knee loading, potentially making it a valuable tool for evaluating the biomechanical efficacy of gait modifications for knee osteoarthritis.

Limiting the Use of Electromyography and Ground Reaction Force Data Changes the Magnitude and Ranking of Modelled Anterior Cruciate Ligament Forces.

Neuromusculoskeletal models often require three-dimensional (3D) body motions, ground reaction forces (GRF), and electromyography (EMG) as input data. Acquiring these data in real-world settings is challenging, with barriers such as the cost of instruments, setup time, and operator skills to correctly acquire and interpret data. This study investigated the consequences of limiting EMG and GRF data on modelled anterior cruciate ligament (ACL) forces during a drop-land-jump task in late-/post-pubertal females. We compared ACL forces generated by a reference model (i.e., EMG-informed neural mode combined with 3D GRF) to those generated by an EMG-informed with only vertical GRF, static optimisation with 3D GRF, and static optimisation with only vertical GRF. Results indicated ACL force magnitude during landing (when ACL injury typically occurs) was significantly overestimated if only vertical GRF were used for either EMG-informed or static optimisation neural modes. If 3D GRF were used in combination with static optimisation, ACL force was marginally overestimated compared to the reference model. None of the alternative models maintained rank order of ACL loading magnitudes generated by the reference model. Finally, we observed substantial variability across the study sample in response to limiting EMG and GRF data, indicating need for methods incorporating subject-specific measures of muscle activation patterns and external loading when modelling ACL loading during dynamic motor tasks.

EMG optimization in OpenSim: A model for estimating lower back kinetics in gait.

Participant-specific musculoskeletal models are needed to accurately estimate lower back internal kinetic demands and injury risk. In this study we developed the framework for incorporating an electromyography optimization (EMGopt) approach within OpenSim (https://simtk.org/projects/emg_opt_tool) and evaluated lower back demands estimated from the model during gait. Kinematic, external kinetic, and EMG data were recorded from six participants as they performed walking and carrying tasks on a treadmill. For evaluation, predicted lumbar vertebral joint forces were compared to those from a generic static optimization approach (SOpt) and to previous studies. Further, model-estimated muscle activations were compared to recorded EMG, and model sensitivity to day-to-day EMG variability was evaluated. Results showed the vertebral joint forces from the model were qualitatively similar in pattern and magnitude to literature reports. Compared to SOpt, the EMGopt approach predicted larger joint loads (p<.01) with muscle activations better matching individual participant EMG patterns. L5/S1 vertebral joint forces from EMGopt were sensitive to the expected variability of recorded EMG, but the magnitude of these differences (±4%) did not impact between-task comparisons. Despite limitations inherent to such models, the proposed musculoskeletal model and EMGopt approach appears well-suited for evaluating internal lower back demands during gait tasks.

Smoothness preserving layout for dynamic labels by hybrid optimization.

Stable label movement and smooth label trajectory are critical for effective information understanding. Sudden label changes cannot be avoided by whatever forced directed methods due to the unreliability of resultant force or global optimization methods due to the complex trade-off on the different aspects. To solve this problem, we proposed a hybrid optimization method by taking advantages of the merits of both approaches. We first detect the spatial-temporal intersection regions from whole trajectories of the features, and initialize the layout by optimization in decreasing order by the number of the involved features. The label movements between the spatial-temporal intersection regions are determined by force directed methods. To cope with some features with high speed relative to neighbors, we introduced a force from future, called temporal force, so that the labels of related features can elude ahead of time and retain smooth movements. We also proposed a strategy by optimizing the label layout to predict the trajectories of features so that such global optimization method can be applied to streaming data. ELECTRONIC SUPPLEMENTARY MATERIAL: Supplementary material is available in the online version of this article at 10.1007/s41095-021-0231-y.

The effectiveness of EMG-driven neuromusculoskeletal model calibration is task dependent.

Calibration of neuromusculoskeletal models using functional tasks is performed to calculate subject-specific musculotendon parameters, as well as coefficients describing the shape of muscle excitation and activation functions. The objective of the present study was to employ a neuromusculoskeletal model of the shoulder driven entirely from muscle electromyography (EMG) to quantify the influence of different model calibration strategies on muscle and joint force predictions. Three healthy adults performed dynamic shoulder abduction and flexion, followed by calibration tasks that included reaching, head touching as well as active and passive abduction, flexion and axial rotation, and submaximal isometric abduction, flexion and axial rotation contractions. EMG data were simultaneously measured from 16 shoulder muscles using surface and intramuscular electrodes, and joint motion evaluated using video motion analysis. Muscle and joint forces were calculated using subject-specific EMG-driven neuromusculoskeletal models that were uncalibrated and calibrated using (i) all calibration tasks (ii) sagittal plane calibration tasks, and (iii) scapular plane calibration tasks. Joint forces were compared to published instrumented implant data. Calibrating models across all tasks resulted in glenohumeral joint force magnitudes that were more similar to instrumented implant data than those derived from any other model calibration strategy. Muscles that generated greater torque were more sensitive to calibration than those that contributed less. This study demonstrates that extensive model calibration over a broad range of contrasting tasks produces the most accurate and physiologically relevant musculotendon and EMG-to-activation parameters. This study will assist in development and deployment of subject-specific neuromusculoskeletal models.

InverseMuscleNET: Alternative Machine Learning Solution to Static Optimization and Inverse Muscle Modeling.

InverseMuscleNET, a machine learning model, is proposed as an alternative to static optimization for resolving the redundancy issue in inverse muscle models. A recurrent neural network (RNN) was optimally configured, trained, and tested to estimate the pattern of muscle activation signals. Five biomechanical variables (joint angle, joint velocity, joint acceleration, joint torque, and activation torque) were used as inputs to the RNN. A set of surface electromyography (EMG) signals, experimentally measured around the shoulder joint for flexion/extension, were used to train and validate the RNN model. The obtained machine learning model yields a normalized regression in the range of 88-91% between experimental data and estimated muscle activation. A sequential backward selection algorithm was used as a sensitivity analysis to discover the less dominant inputs. The order of most essential signals to least dominant ones was as follows: joint angle, activation torque, joint torque, joint velocity, and joint acceleration. The RNN model required 0.06 s of the previous biomechanical input signals and 0.01 s of the predicted feedback EMG signals, demonstrating the dynamic temporal relationships of the muscle activation profiles. The proposed approach permits a fast and direct estimation ability instead of iterative solutions for the inverse muscle model. It raises the possibility of integrating such a model in a real-time device for functional rehabilitation and sports evaluation devices with real-time estimation and tracking. This method provides clinicians with a means of estimating EMG activity without an invasive electrode setup.

Two efficient static optimization algorithms that account for muscle-tendon equilibrium: approaching the constraint Jacobian via a constant or a cubic spline function.

Despite recent advances in algorithms for estimating muscle activities, static optimization remains the most used. Static optimization estimates muscle activations required to obtain a particular set of estimated kinematics. Although fast, static optimization may require considerable time for long trials. Improvements have been proposed in the past, but the current implementations are either accurate and slow (such as the most traditional implementation) or fast but less accurate (such as the linearized at maximal activations method used by OpenSim). Two innovative algorithms are proposed to improve both optimization time and accuracy of the static optimization. The first, designed to be fast, linearizes the constraint-i.e., constructing a constant constraint Jacobian-at the activations of the previous frame. The second, designed to be as accurate as possible, approaches the constraint Jacobian by cubic splines. Their performance and accuracy are compared to the traditional and OpenSim implementations. The linearized method performed as fast as the OpenSim implementation and was more accurate (0.3% of RMSE versus 5.9%). The spline method had excellent accuracy (0.1% of RMSE), but was 2X slower than the linearized approaches. Nevertheless, it was 100X faster than the traditional implementation. Our linearized method is therefore recommended when fast computation is needed, such as real-time applications, while the spline method is recommended otherwise.

Musculoskeletal full-body models including a detailed thoracolumbar spine for children and adolescents aged 6-18 years.

Currently available musculoskeletal inverse-dynamics thoracolumbar spine models are entirely based on data from adults and might therefore not be applicable for simulations in children and adolescents. In addition, these models lack lower extremities, which are required for comprehensive evaluations of functional activities or therapeutic exercises. We therefore created OpenSim-based musculoskeletal full-body models including a detailed thoracolumbar spine for children and adolescents aged 6-18 years and validated by comparing model predictions to in vivo data. After combining our recently developed adult thoracolumbar spine model with a lower extremity model, children and adolescent models were created for each year of age by adjusting segmental length and mass distribution, center of mass positions and moments of inertia of the major body segments as well as sagittal pelvis and spine alignment based on literature data. Similarly, muscle strength properties were adjusted based on CT-derived cross-sectional area measurements. Simulations were conducted from in vivo studies reported in the literature involving children and adolescents evaluating maximum trunk muscle strength (MTMS), lumbar disc compressibility (LDC), intradiscal pressure (IDP) and trunk muscle activity (MA). Model predictions correlated highly with in vivo data (MTMS: r ≥ 0.82, p ≤ 0.03; LDC: r = 0.77, p < 0.001; IDP: r ≥ 0.78, p < 0.001; MA: r ≥ 0.90, p < 0.001), indicating suitability for the reasonably accurate prediction of maximal trunk muscle strength, segmental loading and trunk muscle activity in children and adolescents. When aiming at investigating children or adolescents with pathologies such as idiopathic scoliosis, our models can serve as a basis for the creation of deformed spine models and for comparative purposes.