A neuromusculoskeletal tracking method for estimating individual muscle forces in human movement

A neuromusculoskeletal tracking (NMT) method was developed to estimate muscle forces from observed motion data. The NMT method combines skeletal motion tracking and optimal neuromuscular tracking to produce forward simulations of human movement quickly and accurately. The skeletal motion tracker calculates the joint torques needed to actuate a skeletal model and track observed segment angles and ground forces in a forward simulation of the motor task. The optimal neuromuscular tracker resolves the muscle redundancy problem dynamically and finds the muscle excitations (and muscle forces) needed to produce the joint torques calculated by the skeletal motion tracker. To evaluate the accuracy of the NMT method, kinematics and ground forces obtained from an optimal control (parameter optimization) solution for maximum-height jumping were contaminated with both random and systematic noise. These data served as input observations to the NMT method as well as an inverse dynamics analysis. The NMT solution was compared to the input observations, the original optimal solution, and a simulation driven by the inverse dynamics torques. The results show that, in contrast to inverse dynamics, the NMT method is able to produce an accurate forward simulation consistent with the optimal control solution. The NMT method also requires 3 orders-of-magnitude less CPU time than parameter optimization. The speed and accuracy of the NMT method make it a promising new tool for estimating muscle forces using experimentally obtained kinematics and ground force data.     

A sensitivity analysis method for the body segment inertial parameters based on ground reaction and joint moment regressor matrices

This paper presents a method allowing a simple and efficient sensitivity analysis of dynamics parameters of complex whole-body human model. The proposed method is based on the ground reaction and joint moment regressor matrices, developed initially in robotics system identification theory, and involved in the equations of motion of the human body. The regressor matrices are linear relatively to the segment inertial parameters allowing us to use simple sensitivity analysis methods. The sensitivity analysis method was applied over gait dynamics and kinematics data of nine subjects and with a 15 segments 3D model of the locomotor apparatus. According to the proposed sensitivity indices, 76 segments inertial parameters out the 150 of the mechanical model were considered as not influent for gait. The main findings were that the segment masses were influent and that, at the exception of the trunk, moment of inertia were not influent for the computation of the ground reaction forces and moments and the joint moments. The same method also shows numerically that at least 90% of the lower-limb joint moments during the stance phase can be estimated only from a force-plate and kinematics data without knowing any of the segment inertial parameters.     

Kinematics of lower limbs during walking are emulated by springy walking model with a compliantly connected,off-centered curvy foot

The dynamics of the center of mass (CoM) during walking and running at various gait conditions are well described by the mechanics of a simple passive spring loaded inverted pendulum (SLIP). Due to its simplicity, however, the current form of the SLIP model is limited at providing any further information about multi-segmental lower limbs that generate oscillatory CoM behaviors and their corresponding ground reaction forces. Considering that the dynamics of the CoM are simply achieved by mass-spring mechanics, we wondered whether any of the multi-joint motions could be demonstrated by simple mechanics. In this study, we expand a SLIP model of human locomotion with an off-centered curvy foot connected to the leg by a springy segment that emulates the asymmetric kinematics and kinetics of the ankle joint. The passive dynamics of the proposed expansion of the SLIP model demonstrated the empirical data of ground reaction forces, center of mass trajectories, ankle joint kinematics and corresponding ankle joint torque at various gait speeds. From the mechanically simulated trajectories of the ankle joint and CoM, the motion of lower-limb segments, such as thigh and shank angles, could be estimated from inverse kinematics. The estimation of lower limb kinematics showed a qualitative match with empirical data of walking at various speeds. The representability of passive compliant mechanics for the kinetics of the CoM and ankle joint and lower limb joint kinematics implies that the coordination of multi-joint lower limbs during gait can be understood with a mechanical framework.     

Determining residual reduction algorithm kinematic tracking weights for a sidestep cut via numerical optimization

Musculoskeletal modeling allows for the determination of various parameters during dynamic maneuvers by using in vivo kinematic and ground reaction force (GRF) data as inputs. Differences between experimental and model marker data and inconsistencies in the GRFs applied to these musculoskeletal models may not produce accurate simulations. Therefore, residual forces and moments are applied to these models in order to reduce these differences. Numerical optimization techniques can be used to determine optimal tracking weights of each degree of freedom of a musculoskeletal model in order to reduce differences between the experimental and model marker data as well as residual forces and moments. In this study, the particle swarm optimization (PSO) and simplex simulated annealing (SIMPSA) algorithms were used to determine optimal tracking weights for the simulation of a sidestep cut. The PSO and SIMPSA algorithms were able to produce model kinematics that were within 1.4° of experimental kinematics with residual forces and moments of less than 10 N and 18 Nm, respectively. The PSO algorithm was able to replicate the experimental kinematic data more closely and produce more dynamically consistent kinematic data for a sidestep cut compared to the SIMPSA algorithm. Future studies should use external optimization routines to determine dynamically consistent kinematic data and report the differences between experimental and model data for these musculoskeletal simulations.     

Using computed muscle control to generate forward dynamic simulations of human walking from experimental data

The objective of this study was to develop an efficient methodology for generating muscle-actuated simulations of human walking that closely reproduce experimental measures of kinematics and ground reaction forces. We first introduce a residual elimination algorithm (REA) to compute pelvis and low back kinematic trajectories that ensure consistency between whole-body dynamics and measured ground reactions. We then use a computed muscle control (CMC) algorithm to vary muscle excitations to track experimental joint kinematics within a forward dynamic simulation. CMC explicitly accounts for delays in muscle force production resulting from activation and contraction dynamics while using a general static optimization framework to resolve muscle redundancy. CMC was used to compute muscle excitation patterns that drove a 21-degrees-of-freedom, 92 muscle model to track experimental gait data of 10 healthy young adults. Simulated joint kinematics closely tracked experimental quantities (mean root-mean-squared errors generally less than 1 degrees), and the time histories of muscle activations were similar to electromyographic recordings. A simulation of a half-cycle of gait could be generated using approximately 30 min of computer processing time. The speed and accuracy of REA and CMC make it practical to generate subject-specific simulations of gait.     

A constrained extended Kalman filter for the optimal estimate of kinematics and kinetics of a sagittal symmetric exercise

This paper presents a method for real-time estimation of the kinematics and kinetics of a human body performing a sagittal symmetric motor task, which would minimize the impact of the stereophotogrammetric soft tissue artefacts (STA). The method is based on a bi-dimensional mechanical model of the locomotor apparatus the state variables of which (joint angles, velocities and accelerations, and the segments lengths and inertial parameters) are estimated by a constrained extended Kalman filter (CEKF) that fuses input information made of both stereophotogrammetric and dynamometric measurement data. Filter gains are made to saturate in order to obtain plausible state variables and the measurement covariance matrix of the filter accounts for the expected STA maximal amplitudes. We hypothesised that the ensemble of constraints and input redundant information would allow the method to attenuate the STA propagation to the end results. The method was evaluated in ten human subjects performing a squat exercise. The CEKF estimated and measured skin marker trajectories exhibited a RMS difference lower than 4 mm, thus in the range of STAs. The RMS differences between the measured ground reaction force and moment and those estimated using the proposed method (9 N and 10 N m) were much lower than obtained using a classical inverse dynamics approach (22 N and 30 N m). From the latter results it may be inferred that the presented method allows for a significant improvement of the accuracy with which kinematic variables and relevant time derivatives, model parameters and, therefore, intersegmental moments are estimated.     

Optimization of muscle activity for task-level goals predicts complex changes in limb forces across biomechanical contexts

Optimality principles have been proposed as a general framework for understanding motor control in animals and humans largely based on their ability to predict general features movement in idealized motor tasks. However, generalizing these concepts past proof-of-principle to understand the neuromechanical transformation from task-level control to detailed execution-level muscle activity and forces during behaviorally-relevant motor tasks has proved difficult. In an unrestrained balance task in cats, we demonstrate that achieving task-level constraints center of mass forces and moments while minimizing control effort predicts detailed patterns of muscle activity and ground reaction forces in an anatomically-realistic musculoskeletal model. Whereas optimization is typically used to resolve redundancy at a single level of the motor hierarchy, we simultaneously resolved redundancy across both muscles and limbs and directly compared predictions to experimental measures across multiple perturbation directions that elicit different intra- and interlimb coordination patterns. Further, although some candidate task-level variables and cost functions generated indistinguishable predictions in a single biomechanical context, we identified a common optimization framework that could predict up to 48 experimental conditions per animal (n = 3) across both perturbation directions and different biomechanical contexts created by altering animals' postural configuration. Predictions were further improved by imposing experimentally-derived muscle synergy constraints, suggesting additional task variables or costs that may be relevant to the neural control of balance. These results suggested that reduced-dimension neural control mechanisms such as muscle synergies can achieve similar kinetics to the optimal solution, but with increased control effort (≈2×) compared to individual muscle control. Our results are consistent with the idea that hierarchical, task-level neural control mechanisms previously associated with voluntary tasks may also be used in automatic brainstem-mediated pathways for balance.     

Influence of body segment parameter estimation on calculated ground reaction forces in highly dynamic movements

The effect of body segment parameter estimation (BSP) on the inverse dynamics modelling results has not yet been demonstrated in specific groups during athletic movements with high segment accelerations. Therefore, the purpose of this study was to analyse this effect in ski-jumpers as representatives of a specific group (i.e. low body mass index) by comparing calculated and measured ground reaction forces during ski-jumping imitation jumps. Full body kinematics and vertical ground reaction forces were recorded of 9 ski-jumpers performing three imitation jumps each. BSP were estimated using three previously published, one individually optimized and one ski-jumper group specific model. Vertical ground reaction forces were calculated using the vertical acceleration of the segments as well as the BSP of the single models in a top-down approach. Statistical analysis revealed a main model effect concerning the root mean square error between the calculated and the measured ground reaction force with deviations between the models of 53%. Individual optimization and the application of the ski-jumper group specific model increased the accuracy of the calculated ground reaction forces by 11 and 7%, respectively, compared to the best performing published model. The results of inverse dynamics modelling are very sensitive to the BSP estimation for specific groups like ski-jumpers during movements incorporating high segment accelerations. This emphasizes the importance of selecting adequate BSP estimation models or methods when analysing specific groups in highly dynamic movements in order to increase the accuracy of the inverse dynamics analyses results.     

Sensitivity of the tibio-femoral response to finite element modeling parameters

A generic finite element (FE) model of the lower limb was used to study the knee response in-vivo during a one-legged hop. The approach uses an explicit FE code and a combination of estimated muscle forces and measured three-dimensional tibio-femoral kinematics and ground reaction force as input to the FE model. The sensitivity of the simulated tibio-femoral response to variations of key geometric and material parameters was investigated by performing a total of 38 different simulations. The amplitudes of both kinematic and kinetic responses were affected by the change of these parameters. For the current approach, the results suggest that while cartilage mechanical and geometric properties are very important for the estimation of tibio-femoral cartilage pressure, they have limited effects on the overall kinematic response. The study may help to better define the relative importance of modeling parameters for the development of subject-specific models.     

Ground reaction force estimation using an insole-type pressure mat and joint kinematics during walking

Kinetic analysis of walking requires joint kinematics and ground reaction force (GRF) measurement, which are typically obtained from a force plate. GRF is difficult to measure in certain cases such as slope walking, stair climbing, and track running. Nevertheless, estimating GRF continues to be of great interest for simulating human walking. The purpose of the study was to develop reaction force models placed on the sole of the foot to estimate full GRF when only joint kinematics are provided (Type-I), and to estimate ground contact shear forces when both joint kinematics and foot pressure are provided (Type-II and Type-II-val). The GRF estimation models were attached to a commercial full body skeletal model using the AnyBody Modeling System, which has an inverse dynamics-based optimization solver. The anterior–posterior shear force and medial–lateral shear force could be estimated with approximate accuracies of 6% BW and 2% BW in all three methods, respectively. Vertical force could be estimated in the Type-I model with an accuracy of 13.75% BW. The accuracy of the force estimation was the highest during the mid-single-stance period with an average RMS for errors of 3.10% BW, 1.48% BW, and 7.48% BW for anterior–posterior force, medial–lateral force, and vertical force, respectively. The proposed GRF estimation models could predict full and partial GRF with high accuracy. The design of the contact elements of the proposed model should make it applicable to various activities where installation of a force measurement system is difficult, including track running and treadmill walking.     

An optimisation-based model for full-body upright reaching movements

An optimal simulation 3D model for full-body upright reaching movements was developed using graphic-based modelling tools (SimMechanics) to generate an inverse dynamics model of the skeleton and using parameterisation methods for a sensory motor controller. The adaptive weight coefficient of the cost function based on the final motor task error (i.e. distance between end-effector and target at the end of movement) was used to correct motor task error and physiological measurements (e.g. joint power, centre of mass displacement, etc.). The output of the simulation models using various cost functions were compared to experimental data from 15 healthy participants performing full-body upright reaching movements. The proposed method can reasonably predict full-body voluntary movements in terms of final posture, joint power, and movement of the centre of mass (COM) using simple algebraic calculations of inverse dynamics and forward kinematics instead of the complicated integrals of the forward dynamics. We found that the combination of several control strategies, i.e. minimising end-effector error, total joint power and body COM produced the best fit of the full-body reaching task.     

A validated three-dimensional computational model of a human knee joint

This paper presents a three-dimensional finite element tibio-femoral joint model of a human knee that was validated using experimental data. The geometry of the joint model was obtained from magnetic resonance (MR) images of a cadaveric knee specimen. The same specimen was biomechanically tested using a robotic/universal force-moment sensor (UFS) system and knee kinematic data under anterior-posterior tibial loads (up to 100 N) were obtained. In the finite element model (FEM), cartilage was modeled as an elastic material, ligaments were represented as nonlinear elastic springs, and menisci were simulated by equivalent-resistance springs. Reference lengths (zero-load lengths) of the ligaments and stiffness of the meniscus springs were estimated using an optimization procedure that involved the minimization of the differences between the kinematics predicted by the model and those obtained experimentally. The joint kinematics and in-situ forces in the ligaments in response to axial tibial moments of up to 10 Nm were calculated using the model and were compared with published experimental data on knee specimens. It was also demonstrated that the equivalent-resistance springs representing the menisci are important for accurate calculation of knee kinematics. Thus, the methodology developed in this study can be a valuable tool for further analysis of knee joint function and could serve as a step toward the development of more advanced computational knee models.     

Optimization-based prediction of asymmetric human gait

An optimization-based formulation and solution method are presented to predict asymmetric human gait for a large-scale skeletal model. Predictive dynamics approach is used in which both the joint angles and joint torques are treated as unknowns in the equations of motion. For the optimization formulation, the joint angle profiles are treated as the primary unknowns, and velocities and accelerations are calculated using them. In numerical implementation, the joint angle profiles are discretized using the B-spline interpolation. An algorithm is presented to inversely calculate the joint torques and the ground reaction forces. The sum of the joint-torques squared, called the dynamic effort, is minimized as the human performance measure. Constraints are imposed on the joint strengths (torques) and joint ranges of motion along with other physical constraints. The formulation is validated by simulating a symmetric gait and comparing the results with the experimental data. Then asymmetric gait motion is simulated, where the left and right step lengths are different. The kinematics and kinetics results from the simulation are presented and discussed. Predicted ground reaction forces are explained by using the inverted pendulum model. Predicted kinematics and kinetics have trends that are similar to those reported in the literature. Potential practical applications of the formulation and the solution approach are discussed.     

On the estimate of the two dominant axes of the knee using an instrumented spatial linkage

This article presents the validation of a technique to assess the appropriateness of a 2 degree-of-freedom model for the human knee, and, in which case, the dominant axes of flexion/extension and internal/external longitudinal rotation are estimated. The technique relies on the use of an instrumented spatial linkage for the accurate detection of passive knee kinematics, and it is based on the assumption that points on the longitudinal rotation axis describe nearly circular and planar trajectories, whereas the flexion/extension axis is perpendicular to those trajectories through their centers of rotation. By manually enforcing a tibia rotation while bending the knee in flexion, a standard optimization algorithm is used to estimate the approximate axis of longitudinal rotation, and the axis of flexion is estimated consequently. The proposed technique is validated through simulated data and experimentally applied on a 2 degree-of-freedom mechanical joint. A procedure is proposed to verify the fixed axes assumption for the knee model. The suggested methodology could be possibly valuable in understanding knee kinematics, and in particular for the design and implant of customized hinged external fixators, which have shown to be effective in knee dislocation treatment and rehabilitation.     

Motor control of voluntary arm movements

The motor control of pointing and reaching-to-grasp movements was investigated using two different approaches (kinematic and modelling) in order to establish whether the type of control varies according to modifications of arm kinematics. Kinematic analysis of arm movements was performed on subjects' hand trajectories directed to large and small stimuli located at two different distances. The subjects were required either to grasp and to point to each stimulus. The kinematics of the subsequent movement, during which subject's hand came back to the starting position, were also studied. For both movements, kinematic analysis was performed on hand linear trajectories as well as on joint angular trajectories of shoulder and elbow. The second approach consisted in the parametric identification of the black box (ARMAX) model of the controller driving the arm movement. Such controller is hypothesized to work for the correct execution of the motor act. The order of the controller ARMAX model was analyzed with respect to the different experimental conditions (distal task, stimulus size and distance). Results from kinematic analysis showed that target distance and size influenced kinematic parameters both of angular and linear displacements. Nevertheless, the structure of the motor program was found to remain constant with distane and distal task, while it varied with precision requirements due to stimulus size. The estimated model order of the controller confirmed the invariance of the control law with regard to movement amplitude, whereas it was sensitive to target size.     

Estimating the muscle forces generated in the human lower extremity when walking: a physiological solution

A model capable of estimating individual muscle activity during human lower extremity activity has been developed. This model was implemented and applied to normal gait. Both 3D cinematography and force platform records were collected to define the kinematics of the lower limb segments and the ground reaction forces. From these data the lengths, velocities, and moment arms of the muscles and the net muscle moments were calculated. These data were then used to estimate the output from a set of pattern generators which specified the neural input to and hence the force generated in each muscle. Results were obtained which demonstrate that it is feasible to construct a hierarchical physiological model which will estimate individual muscle forces. This statement must be tempered somewhat in that better anatomical and neurophysiological data must be made available and that this model, and all others attempting to estimate individual muscle forces, must be rigorously tested before being applied in a research, sports, or clinical setting.     

Shoulder model validation and joint contact forces during wheelchair activities

Chronic shoulder impingement is a common problem for manual wheelchair users. The loading associated with performing manual wheelchair activities of daily living is substantial and often at a high frequency. Musculoskeletal modeling and optimization techniques can be used to estimate the joint contact forces occurring at the shoulder to assess the soft tissue loading during an activity and to possibly identify activities and strategies that place manual wheelchair users at risk for shoulder injuries. The purpose of this study was to validate an upper extremity musculoskeletal model and apply the model to wheelchair activities for analysis of the estimated joint contact forces. Upper extremity kinematics and handrim wheelchair kinetics were measured over three conditions: level propulsion, ramp propulsion, and a weight relief lift. The experimental data were used as input to a subject-specific musculoskeletal model utilizing optimization to predict joint contact forces of the shoulder during all conditions. The model was validated using a mean absolute error calculation. Model results confirmed that ramp propulsion and weight relief lifts place the shoulder under significantly higher joint contact loading than level propulsion. In addition, they exhibit large superior contact forces that could contribute to impingement. This study highlights the potential impingement risk associated with both the ramp and weight relief lift activities. Level propulsion was shown to have a low relative risk of causing injury, but with consideration of the frequency with which propulsion is performed, this observation is not conclusive.     

A control theoretic model of the forearm

In this paper, a control theoretic model of the forearm is developed and analyzed, and a computational method for predicting muscle activations necessary to generate specified motions is described. A detailed geometric model of the forearm kinematics, including the carrying angle and models of how the biceps and the supinator tendons wrap around the bones, is used. Also, including a dynamics model, the final model is a system of differential equations where the muscle activations play the role of control signals. Due to the large number of muscles, the problem of finding muscle activations is redundant, and this problem is solved by an optimization procedure. The computed muscle activations for ballistic movements clearly recaptures the triphasic ABC (Activation-Braking-Clamping) pattern. It is also transparent, from the muscle activation patterns, how the muscles cooperate and counteract in order to accomplish desired motions. A comparison with previously reported experimental data is included and the model predictions can be seen to be partially in agreement with the experimental data.     

Quantification of the segmental kinematics of spontaneous infant movements

This article introduces a method to capture the movements of the upper and the lower limb of infants using an electromagnetic tracking system and to reliably calculate the segmental kinematics. Analysis of the spontaneous movements of infants is important e.g. in the context of the "General Movement Analysis", which aims at the early diagnosis of motor dysfunctions. Due to special constraints regarding infant anatomy, previous approaches based on optical tracking could only gather position data of the infant' segments, whereas with this method in addition relative segment angles can be calculated. The spontaneous movements of the infant and simple calibration movements of the hand and the foot are used to calculate the joint centers and the joint axes of a multi-segmental chain model. The quality of the calibration movements is assessed at calibration time by calculating the root mean square deviation from the total least squares regression plane. The general accuracy of the recording is evaluated by the difference between recorded and estimated sensor positions and the difference between recorded and estimated sensor orientations. Movements of 20 infants between term and 3 months post term age were recorded and processed. A first application illustrates how abnormal movement patterns are manifested in the segmental kinematics. The results show that the presented method is a practicable and reliable way to record spontaneous infant movements and to calculate the segmental kinematics.