Modeling musculoskeletal kinematic and dynamic redundancy using null space projection

Neuromuscular control: from a biomechanist's perspective

Understanding neural control of movement necessitates a collaborative approach between many disciplines, including biomechanics, neuroscience, and motor control. Biomechanics grounds us to the laws of physics that our musculoskeletal system must obey. Neuroscience reveals the inner workings of our nervous system that functions to control our body. Motor control investigates the coordinated motor behaviours we display when interacting with our environment. The combined efforts across the many disciplines aimed at understanding human movement has resulted in a rich and rapidly growing body of literature overflowing with theories, models, and experimental paradigms. As a result, gathering knowledge and drawing connections between the overlapping but seemingly disparate fields can be an overwhelming endeavour. This review paper evolved as a need for us to learn of the diverse perspectives underlying current understanding of neuromuscular control. The purpose of our review paper is to integrate ideas from biomechanics, neuroscience, and motor control to better understand how we voluntarily control our muscles. As biomechanists, we approach this paper starting from a biomechanical modelling framework. We first define the theoretical solutions (i.e., muscle activity patterns) that an individual could feasibly use to complete a motor task. The theoretical solutions will be compared to experimental findings and reveal that individuals display structured muscle activity patterns that do not span the entire theoretical solution space. Prevalent neuromuscular control theories will be discussed in length, highlighting optimality, probabilistic principles, and neuromechanical constraints, that may guide individuals to families of muscle activity solutions within what is theoretically possible. Our intention is for this paper to serve as a primer for the neuromuscular control scientific community by introducing and integrating many of the ideas common across disciplines today, as well as inspire future work to improve the representation of neural control in biomechanical models.

Predictive simulation of single-leg landing scenarios for ACL injury risk factors evaluation

The Anterior Cruciate Ligament (ACL) rupture is a very common knee injury during sport activities. Landing after jump is one of the most prominent human body movements that can lead to such an injury. The landing-related ACL injury risk factors have been in the spotlight of research interest. Over the years, researchers and clinicians acquire knowledge about human movement during daily-life activities by organizing complex in vivo studies that feature high complexity, costs and technical and most importantly physical challenges. In an attempt to overcome these limitations, this paper introduces a computational modeling and simulation pipeline that aims to predict and identify key parameters of interest that are related to ACL injury during single-leg landings. We examined the following conditions: a) landing height, b) hip internal and external rotation, c) lumbar forward and backward leaning, d) lumbar medial and lateral bending, e) muscle forces permutations and f) effort goal weight. Identified on related research studies, we evaluated the following risk factors: vertical Ground Reaction Force (vGRF), knee joint Anterior force (AF), Medial force (MF), Compressive force (CF), Abduction moment (AbdM), Internal rotation moment (IRM), quadricep and hamstring muscle forces and Quadriceps/Hamstrings force ratio (Q/H force ratio). Our study clearly demonstrated that ACL injury is a rather complicated mechanism with many associated risk factors which are evidently correlated. Nevertheless, the results were mostly in agreement with other research studies regarding the ACL risk factors. The presented pipeline showcased promising potential of predictive simulations to evaluate different aspects of complicated phenomena, such as the ACL injury.

Planning to Minimize the Human Muscular Effort during Forceful Human-Robot Collaboration

This work addresses the problem of planning a robot configuration and grasp to position a shared object during forceful human-robot collaboration, such as a puncturing or a cutting task. Particularly, our goal is to find a robot configuration that positions the jointly manipulated object such that the muscular effort of the human, operating on the same object, is minimized while also ensuring the stability of the interaction for the robot. This raises three challenges. First, we predict the human muscular effort given a human-robot combined kinematic configuration and the interaction forces of a task. To do this, we perform task-space to muscle-space mapping for two different musculoskeletal models of the human arm. Second, we predict the human body kinematic configuration given a robot configuration and the resulting object pose in the workspace. To do this, we assume that the human prefers the body configuration that minimizes the muscular effort. And third, we ensure that, under the forces applied by the human, the robot grasp on the object is stable and the robot joint torques are within limits. Addressing these three challenges, we build a planner that, given a forceful task description, can output the robot grasp on an object and the robot configuration to position the shared object in space. We quantitatively analyze the performance of the planner and the validity of our assumptions. We conduct experiments with human subjects to measure their kinematic configurations, muscular activity, and force output during collaborative puncturing and cutting tasks. The results illustrate the effectiveness of our planner in reducing the human muscular load. For instance, for the puncturing task, our planner is able to reduce muscular load by compared to a user-based selection of object poses.

Using Bayesian inference to estimate plausible muscle forces in musculoskeletal models

Background

Musculoskeletal modeling is currently a preferred method for estimating the muscle forces that underlie observed movements. However, these estimates are sensitive to a variety of assumptions and uncertainties, which creates difficulty when trying to interpret the muscle forces from musculoskeletal simulations. Here, we describe an approach that uses Bayesian inference to identify plausible ranges of muscle forces for a simple motion while representing uncertainty in the measurement of the motion and the objective function used to solve the muscle redundancy problem.

Methods

We generated a reference elbow flexion–extension motion and computed a set of reference forces that would produce the motion while minimizing muscle excitations cubed via OpenSim Moco. We then used a Markov Chain Monte Carlo (MCMC) algorithm to sample from a posterior probability distribution of muscle excitations that would result in the reference elbow motion. We constructed a prior over the excitation parameters which down-weighted regions of the parameter space with greater muscle excitations. We used muscle excitations to find the corresponding kinematics using OpenSim, where the error in position and velocity trajectories (likelihood function) was combined with the sum of the cubed muscle excitations integrated over time (prior function) to compute the posterior probability density.

Results

We evaluated the muscle forces that resulted from the set of excitations that were visited in the MCMC chain (seven parallel chains, 500,000 iterations per chain). The estimated muscle forces compared favorably with the reference forces generated with OpenSim Moco, while the elbow angle and velocity from MCMC matched closely with the reference (average RMSE for elbow angle = 2°; and angular velocity = 32°/s). However, our rank plot analyses and potential scale reduction statistics, which we used to evaluate convergence of the algorithm, indicated that the chains did not fully mix.

Conclusions

While the results from this process are a promising step towards characterizing uncertainty in muscle force estimation, the computational time required to search the solution space with, and the lack of MCMC convergence indicates that further developments in MCMC algorithms are necessary for this process to become feasible for larger-scale models.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12984-022-01008-4.

Understanding redundancy and resilience: Redundancy in life is provided by distributing functions across networks rather than back-up systems: Redundancy in life is provided by distributing functions across networks rather than back-up systems

Understanding how evolution generates and maintains redundancy to cope with damage and loss of function in living systems could inspire applications from new therapies to resilient computer networks.

Muscle forces and the demands of human walking

Reconstructing the locomotor behavior of extinct animals depends on elucidating the principles that link behavior, function, and morphology, which can only be done using extant animals. Within the human lineage, the evolution of bipedalism represents a critical transition, and evaluating fossil hominins depends on understanding the relationship between lower limb forces and skeletal morphology in living humans. As a step toward that goal, here we use a musculoskeletal model to estimate forces in the lower limb muscles of ten individuals during walking. The purpose is to quantify the consistency, timing, and magnitude of these muscle forces during the stance phase of walking. We find that muscles which act to support or propel the body during walking demonstrate the greatest force magnitudes as well as the highest consistency in the shape of force curves among individuals. Muscles that generate moments in the same direction as, or orthogonal to, the ground reaction force show lower forces of greater variability. These data can be used to define the envelope of load cases that need to be examined in order to understand human lower limb skeletal load bearing.

A half marathon shifts the mediolateral force distribution at the tibiofemoral joint

Runners' gait patterns vary during a half marathon and influence the knee joint mechanics. Joint contact force is a better estimate of the net joint loadings than external joint moments and closely correlates to injury risks. This study explored the changes of lower limb joint kinematics, muscle activities, and knee joint loading in runners across the running mileages of a half marathon. Fourteen runners completed a half marathon on an instrumented treadmill where motion capture was conducted every 2 km (from 2 to 20 km). A musculoskeletal model incorporating medial/lateral tibiofemoral compartments was used to process the movement data and report outcome variables at the selected distance checkpoints. Statistics showed no changes in joint angles, muscle co-contraction index, ground reaction force variables, and medial tibiofemoral contact force (p > 0.05). Knee adduction moment at 18 km was significantly lower than those at 2 km (p = 0.002, γ = 0.813) and 6 km (p = 0.001, γ = 0.663). Compared to that at 2 km, lateral tibiofemoral contact force was reduced at 18 km (p = 0.030, Hedges' g = 0.690), 16 km (p < 0.001, Hedges' g = 0.782), 14 km (p = 0.045, Hedges' g = 0.859), and 10 km (p < 0.001, Hedges' g = 0.771) respectively. Mechanical realignment of the lower limb may be the cause of the altered knee loadings and possibly led to reduced running economy in response to a prolonged run. The injury potential of the redistributed tibiofemoral forces warranted further studies.

Sensory modulation of gait characteristics in human locomotion: A neuromusculoskeletal modeling study

The central nervous system of humans and other animals modulates spinal cord activity to achieve several locomotion behaviors. Previous neuromechanical models investigated the modulation of human gait changing selected parameters belonging to CPGs (Central Pattern Generators) feedforward oscillatory structures or to feedback reflex circuits. CPG-based models could replicate slow and fast walking by changing only the oscillation’s properties. On the other hand, reflex-based models could achieve different behaviors through optimizations of large dimensional parameter spaces. However, they could not effectively identify individual key reflex parameters responsible for gait characteristics’ modulation. This study investigates which reflex parameters modulate the gait characteristics through neuromechanical simulations. A recently developed reflex-based model is used to perform optimizations with different target behaviors on speed, step length, and step duration to analyze the correlation between reflex parameters and their influence on these gait characteristics. We identified nine key parameters that may affect the target speed ranging from slow to fast walking (0.48 and 1.71 m/s) as well as a large range of step lengths (0.43 and 0.88 m) and step duration (0.51, 0.98 s). The findings show that specific reflexes during stance significantly affect step length regulation, mainly given by positive force feedback of the ankle plantarflexors’ group. On the other hand, stretch reflexes active during swing of iliopsoas and gluteus maximus regulate all the gait characteristics under analysis. Additionally, the results show that the hamstrings’ group’s stretch reflex during the landing phase is responsible for modulating the step length and step duration. Additional validation studies in simulations demonstrated that the modulation of identified reflexes is sufficient to regulate the investigated gait characteristics. Thus, this study provides an overview of possible reflexes involved in modulating speed, step length, and step duration of human gaits.

This study investigates the possible reflex parameters that the central nervous system could use to modulate human locomotion. Specifically, we target the modulation of three gait characteristics: speed, step length, and step duration. We utilize human locomotion simulations with a previously developed reflex-based model and perform multiple optimizations ranging targeting low to high values of the three gait characteristics investigated. From the data acquired in optimizations, we investigate which reflex parameter correlates most with the gait characteristics changes. We identified nine key reflex parameters affecting gait modulation, performed validation experiments, and verified that the optimization of key reflex parameters alone could generate modulation in the studied locomotion behaviors. Kinematics, ground reaction forces, and muscle activity obtained in simulations show similarities with past experimental studies on gait modulation. Therefore, the identified parameters could potentially be used by the nervous system to regulate locomotion behaviors in a task-dependent manner. Other circuits not modeled in this study could play a crucial role in gait modulation, and further investigations should be done in the co-optimization of feedforward and feedback circuits.

Total Knee Replacement: Subject-Specific Modeling, Finite Element Analysis, and Evaluation of Dynamic Activities

This study presents a semi-automatic framework to create subject-specific total knee replacement finite element models, which can be used to analyze locomotion patterns and evaluate knee dynamics. In recent years, much scientific attention was attracted to pre-clinical optimization of customized total knee replacement operations through computational modeling to minimize post-operational adverse effects. However, the time-consuming and laborious process of developing a subject-specific finite element model poses an obstacle to the latter. One of this work's main goals is to automate the finite element model development process, which speeds up the proposed framework and makes it viable for practical applications. This pipeline's reliability was ratified by developing and validating a subject-specific total knee replacement model based on the 6th SimTK Grand Challenge data set. The model was validated by analyzing contact pressures on the tibial insert in relation to the patient's gait and analysis of tibial contact forces, which were found to be in accordance with the ones provided by the Grand Challenge data set. Subsequently, a sensitivity analysis was carried out to assess the influence of modeling choices on tibial insert's contact pressures and determine possible uncertainties on the models produced by the framework. Parameters, such as the position of ligament origin points, ligament stiffness, reference strain, and implant-bone alignment were used for the sensitivity study. Notably, it was found that changes in the alignment of the femoral component in reference to the knee bones significantly affect the load distribution at the tibiofemoral joint, with an increase of 206.48% to be observed at contact pressures during 5° internal rotation. Overall, the models produced by this pipeline can be further used to optimize and personalize surgery by evaluating the best surgical parameters in a simulated manner before the actual surgery.

Real-Time Musculoskeletal Kinematics and Dynamics Analysis Using Marker- and IMU-Based Solutions in Rehabilitation

This study aims to explore the possibility of estimating a multitude of kinematic and dynamic quantities using subject-specific musculoskeletal models in real-time. The framework was designed to operate with marker-based and inertial measurement units enabling extensions far beyond dedicated motion capture laboratories. We present the technical details for calculating the kinematics, generalized forces, muscle forces, joint reaction loads, and predicting ground reaction wrenches during walking. Emphasis was given to reduce computational latency while maintaining accuracy as compared to the offline counterpart. Notably, we highlight the influence of adequate filtering and differentiation under noisy conditions and its importance for consequent dynamic calculations. Real-time estimates of the joint moments, muscle forces, and reaction loads closely resemble OpenSim's offline analyses. Model-based estimation of ground reaction wrenches demonstrates that even a small error can negatively affect other estimated quantities. An application of the developed system is demonstrated in the context of rehabilitation and gait retraining. We expect that such a system will find numerous applications in laboratory settings and outdoor conditions with the advent of predicting or sensing environment interactions. Therefore, we hope that this open-source framework will be a significant milestone for solving this grand challenge.

Real-Time Prediction of Joint Forces by Motion Capture and Machine Learning

Conventional biomechanical modelling approaches involve the solution of large systems of equations that encode the complex mathematical representation of human motion and skeletal structure. To improve stability and computational speed, being a common bottleneck in current approaches, we apply machine learning to train surrogate models and to predict in near real-time, previously calculated medial and lateral knee contact forces (KCFs) of 54 young and elderly participants during treadmill walking in a speed range of 3 to 7 km/h. Predictions are obtained by fusing optical motion capture and musculoskeletal modeling-derived kinematic and force variables, into regression models using artificial neural networks (ANNs) and support vector regression (SVR). Training schemes included either data from all subjects (LeaveTrialsOut) or only from a portion of them (LeaveSubjectsOut), in combination with inclusion of ground reaction forces (GRFs) in the dataset or not. Results identify ANNs as the best-performing predictor of KCFs, both in terms of Pearson R (0.89-0.98 for LeaveTrialsOut and 0.45-0.85 for LeaveSubjectsOut) and percentage normalized root mean square error (0.67-2.35 for LeaveTrialsOut and 1.6-5.39 for LeaveSubjectsOut). When GRFs were omitted from the dataset, no substantial decrease in prediction power of both models was observed. Our findings showcase the strength of ANNs to predict simultaneously multi-component KCF during walking at different speeds-even in the absence of GRFs-particularly applicable in real-time applications that make use of knee loading conditions to guide and treat patients.

Lower Limb Assistive Device Design Optimization Using Musculoskeletal Modeling: A Review

Many individuals with lower limb amputations or neuromuscular impairments face mobility challenges attributable to suboptimal assistive device design. Forward dynamic modeling and simulation of human walking using conventional biomechanical gait models offer an alternative to intuition-based assistive device design, providing insight into the biomechanics underlying pathological gait. Musculoskeletal models enable better understanding of prosthesis and/or exoskeleton contributions to the human musculoskeletal system, and device and user contributions to both body support and propulsion during gait. This paper reviews current literature that have used forward dynamic simulation of clinical population musculoskeletal models to perform assistive device design optimization using optimal control, optimal tracking, computed muscle control (CMC) and reflex-based control. Musculoskeletal model complexity and assumptions inhibit forward dynamic musculoskeletal modeling in its current state, hindering computational assistive device design optimization. Future recommendations include validating musculoskeletal models and resultant assistive device designs, developing less computationally expensive forward dynamic musculoskeletal modeling methods, and developing more efficient patient-specific musculoskeletal model generation methods to enable personalized assistive device optimization.

On the Relationship Between Muscle Synergies and Redundant Degrees of Freedom in Musculoskeletal Systems

It has been suggested that the human nervous system controls motions in the task (or operational) space. However, little attention has been given to the separation of the control of the task-related and task-irrelevant degrees of freedom. Aim: We investigate how muscle synergies may be used to separately control the task-related and redundant degrees of freedom in a computational model. Approach: We generalize an existing motor control model, and assume that the task and redundant spaces have orthogonal basis vectors. This assumption originates from observations that the human nervous system tightly controls the task-related variables, and leaves the rest uncontrolled. In other words, controlling the variables in one space does not affect the other space; thus, the actuations must be orthogonal in the two spaces. We implemented this assumption in the model by selecting muscle synergies that produce force vectors with orthogonal directions in the task and redundant spaces. Findings: Our experimental results show that the orthogonality assumption performs well in reconstructing the muscle activities from the measured kinematics/dynamics in the task and redundant spaces. Specifically, we found that approximately 70% of the variation in the measured muscle activity can be captured with the orthogonality assumption, while allowing efficient separation of the control in the two spaces. Implications: The developed motor control model is a viable tool in real-time simulations of musculoskeletal systems, as well as model-based control of bio-mechatronic systems, where a computationally efficient representation of the human motion controller is needed.