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.     

Kinetic chain of overarm throwing in terms of joint rotations revealed by induced acceleration analysis

This study investigated how baseball players generate large angular velocity at each joint by coordinating the joint torque and velocity-dependent torque during overarm throwing. Using a four-segment model (i.e., trunk, upper arm, forearm, and hand) that has 13 degrees of freedom, we conducted the induced acceleration analysis to determine the accelerations induced by these torques by multiplying the inverse of the system inertia matrix to the torque vectors. We found that the proximal joint motions (i.e., trunk forward motion, trunk leftward rotation, and shoulder internal rotation) were mainly accelerated by the joint torques at their own joints, whereas the distal joint motions (i.e., elbow extension and wrist flexion) were mainly accelerated by the velocity-dependent torques. We further examined which segment motion is the source of the velocity-dependent torque acting on the elbow and wrist accelerations. The results showed that the angular velocities of the trunk and upper arm produced the velocity-dependent torque for initial elbow extension acceleration. As a result, the elbow joint angular velocity increased, and concurrently, the forearm angular velocity relative to the ground also increased. The forearm angular velocity subsequently accelerated the elbow extension and wrist flexion. It also accelerated the shoulder internal rotation during the short period around the ball-release time. These results indicate that baseball players accelerate the distal elbow and wrist joint rotations by utilizing the velocity-dependent torque that is originally produced by the proximal trunk and shoulder joint torques in the early phase.     

Lower extremity joint torque predicted by using artificial neural network during vertical jump

The purpose of this study was to develop an artificial neural network (ANN) for predicting lower extremity joint torques using the ground reaction force (GRF) and related parameters derived by the GRF during counter-movement jump (CMJ) and squat jump (SJ). Ten student athletes performed CMJ and SJ. Force plate and kinematic data were recorded. Joint torques were calculated using inverse dynamics and ANN. We used a fully connected, feed-forward network. The network comprised of one input layer, one hidden layer and one output layer. It was trained by error back-propagation algorithm using Steepest Descent Method. Input parameters of the ANN were GRF measurements and related parameters. Output parameters were three lower extremity joint torques. ANN model fitted well with the results of the inverse dynamics output. Our observations indicate that the model developed in this study can be used to estimate three lower extremity joint torques for CMJ and SJ based on ground reaction force data and related parameters.     

Validity of the top-down approach of inverse dynamics analysis in fast and large rotational trunk movements

This study investigated the validity of the top-down approach of inverse dynamics analysis in fast and large rotational movements of the trunk about three orthogonal axes of the pelvis for nine male collegiate students. The maximum angles of the upper trunk relative to the pelvis were approximately 47°, 49°, 32°, and 55° for lateral bending, flexion, extension, and axial rotation, respectively, with maximum angular velocities of 209°/s, 201°/s, 145°/s, and 288°/s, respectively. The pelvic moments about the axes during the movements were determined using the top-down and bottom-up approaches of inverse dynamics and compared between the two approaches. Three body segment inertial parameter sets were estimated using anthropometric data sets (Ae et al., Biomechanism 11, 1992; De Leva, J Biomech, 1996; Dumas et al., J Biomech, 2007). The root-mean-square errors of the moments and the absolute errors of the peaks of the moments were generally smaller than 10 N·m. The results suggest that the pelvic moment in motions involving fast and large trunk movements can be determined with a certain level of validity using the top-down approach in which the trunk is modeled as two or three rigid-link segments.     

Dynamic optimization: inverse analysis for the Yurchenko layout vault in women's artistic gymnastics

The use of dynamic optimization to compute the trajectory of joint torques is not popular due to the large amount of computation required, the choice of initial "guesstimates" of torque values and the mathematical sophistication required to understand the technique. Modern optimal control algorithms circumvent most of these objections to the method. It is our aim to demonstrate that the dynamic optimization technique is feasible for complex movements, using the Yurchenko layout vault as an example. A dynamic optimization method to compute joint torques so that the histories of the angular orientations of the model segments closely approximate the corresponding observed angular coordinate histories is demonstrated with the Yurchenko layout vault using an optimal control package. The objective function used is a measure of distance of fitted segment angles to the data, plus the distance of the fitted whole body centre of mass (CM), from the whole body CM computed from the data. Including the CM into the objective function, facilitates the optimization process so as to obtain a set of torques which reproduced the data. The paper shows that the approach works well for the task examined, that is, where the dynamics of the system change during a movement (impact to postflight).     

Inverse and forward dynamics: models of multi-body systems

Connected multi-body systems exhibit notoriously complex behaviour when driven by external and internal forces and torques. The problem of reconstructing the internal forces and/or torques from the movements and known external forces is called the 'inverse dynamics problem', whereas calculating motion from known internal forces and/or torques and resulting reaction forces is called the 'forward dynamics problem'. When stepping forward to cross the street, people use muscle forces that generate angular accelerations of their body segments and, by virtue of reaction forces from the street, a forward acceleration of the centre of mass of their body. Inverse dynamics calculations applied to a set of motion data from such an event can teach us how temporal patterns of joint torques were responsible for the observed motion. In forward dynamics calculations we may attempt to create motion from such temporal patterns, which is extremely difficult, because of the complex mechanical linkage along the chains forming the multi-body system. To understand, predict and sometimes control multi-body systems, we may want to have mathematical expressions for them. The Newton-Euler, Lagrangian and Featherstone approaches have their advantages and disadvantages. The simulation of collisions and the inclusion of muscle forces or other internal forces are discussed. Also, the possibility to perform a mixed inverse and forward dynamics calculation are dealt with. The use and limitations of these approaches form the conclusion.     

A three-dimensional whole-body model to predict human walking on level ground

Predictive simulation of human walking has great potential in clinical motion analysis and rehabilitation engineering assessment, but large computational cost and reliance on measurement data to provide initial guess have limited its wide use. We developed a computationally efficient model combining optimization and inverse dynamics to predict three-dimensional whole-body motions and forces during human walking without relying on measurement data. Using the model, we explored two different optimization objectives, mechanical energy expenditure and the time integral of normalized joint torque. Of the two criteria, the sum of the time integrals of the normalized joint torques produced a more realistic walking gait. The reason for this difference is that most of the mechanical energy expenditure is in the sagittal plane (based on measurement data) and this leads to difficulty in prediction in the other two planes. We conclude that mechanical energy may only account for part of the complex performance criteria driving human walking in three dimensions.

     

A Novel Approach for Dynamic Testing of Total Hip Dislocation under Physiological Conditions

Constant high rates of dislocation-related complications of total hip replacements (THRs) show that contributing factors like implant position and design, soft tissue condition and dynamics of physiological motions have not yet been fully understood. As in vivo measurements of excessive motions are not possible due to ethical objections, a comprehensive approach is proposed which is capable of testing THR stability under dynamic, reproducible and physiological conditions. The approach is based on a hardware-in-the-loop (HiL) simulation where a robotic physical setup interacts with a computational musculoskeletal model based on inverse dynamics. A major objective of this work was the validation of the HiL test system against in vivo data derived from patients with instrumented THRs. Moreover, the impact of certain test conditions, such as joint lubrication, implant position, load level in terms of body mass and removal of muscle structures, was evaluated within several HiL simulations. The outcomes for a normal sitting down and standing up maneuver revealed good agreement in trend and magnitude compared with in vivo measured hip joint forces. For a deep maneuver with femoral adduction, lubrication was shown to cause less friction torques than under dry conditions. Similarly, it could be demonstrated that less cup anteversion and inclination lead to earlier impingement in flexion motion including pelvic tilt for selected combinations of cup and stem positions. Reducing body mass did not influence impingement-free range of motion and dislocation behavior; however, higher resisting torques were observed under higher loads. Muscle removal emulating a posterior surgical approach indicated alterations in THR loading and the instability process in contrast to a reference case with intact musculature. Based on the presented data, it can be concluded that the HiL test system is able to reproduce comparable joint dynamics as present in THR patients.     

In vitro assessment of a motion-based optimization method for locating the talocrural and subtalar joint axes

The locations of the joint axes of the ankle complex vary considerably between subjects, yet no noninvasive method with demonstrated accuracy exists for locating these axes. The moments of muscle and ground reaction forces about the joint axes are dependent on axis locations, making knowledge of these locations critical to accurate musculoskeletal modeling of the foot and ankle. The accuracy of a computational optimization method that fits a two-revolute model to measured motion was assessed using computer-generated data, a two-revolute mechanical linkage, and three lower-leg cadaver specimens. Motions were applied to cadaver specimens under axial load while bone-mounted markers attached to the tibia, talus, and calcaneus were tracked using a video-based motion analysis system. Estimates of the talocrural and subtalar axis locations were computed from motions of the calcaneus relative to the tibia using the optimization method. These axes were compared to mean helical axes computed directly from tibia, talus, and calcaneus motions. The optimization method performed well when the motions were computer-generated or measured in the mechanical linkage, with angular differences between optimization and mean helical axes ranging from 1 deg to 5 deg. In the cadaver specimens, however, these differences exceeded 20 deg. Optimization methods that locate the anatomical joint axes of the ankle complex by fitting two revolute joints to measured tibia-calcaneus motions may be limited because of problems arising from non-revolute behavior.     

Use of dual Euler angles to quantify the three-dimensional joint motion and its application to the ankle joint complex

This paper presents a modified Euler angles method, dual Euler angles approach, to describe general spatial human joint motions. In dual Euler angles approach, the three-dimensional joint motion is considered as three successive screw motions with respect to the axes of the moving segment coordinate system; accordingly, the screw motion displacements are represented by dual Euler angles. The algorithm for calculating dual Euler angles from coordinates of markers on the moving segment is also provided in this study. As an example, the proposed method is applied to describe motions of ankle joint complex during dorsiflexion–plantarflexion. A Flock of Birds electromagnetic tracking device (FOB) was used to measure joint motion in vivo. Preliminary accuracy tests on a gimbal structure demonstrate that the mean errors of dual Euler angles evaluated by using source data from FOB are less than 1° for rotations and 1 mm for translations, respectively. Based on the pilot study, FOB is feasible for quantifying human joint motions using dual Euler angles approach.     

Getting in shape: Reconstructing three-dimensional long-track speed skating kinematics by comparing several body pose reconstruction techniques

In gait studies body pose reconstruction (BPR) techniques have been widely explored, but no previous protocols have been developed for speed skating, while the peculiarities of the skating posture and technique do not automatically allow for the transfer of the results of those explorations to kinematic skating data. The aim of this paper is to determine the best procedure for body pose reconstruction and inverse dynamics of speed skating, and to what extend this choice influences the estimation of joint power. The results show that an eight body segment model together with a global optimization method with revolute joint in the knee and in the lumbosacral joint, while keeping the other joints spherical, would be the most realistic model to use for the inverse kinematics in speed skating. To determine joint power, this method should be combined with a least-square error method for the inverse dynamics. Reporting on the BPR technique and the inverse dynamic method is crucial to enable comparison between studies. Our data showed an underestimation of up to 74% in mean joint power when no optimization procedure was applied for BPR and an underestimation of up to 31% in mean joint power when a bottom-up inverse dynamics method was chosen instead of a least square error approach. Although these results are aimed at speed skating, reporting on the BPR procedure and the inverse dynamics method, together with setting a golden standard should be common practice in all human movement research to allow comparison between studies.     

A dynamic optimization technique for predicting muscle forces in the swing phase of gait

The muscle force sharing problem was solved for the swing phase of gait using a dynamic optimization algorithm. For comparison purposes the problem was also solved using a typical static optimization algorithm. The objective function for the dynamic optimization algorithm was a combination of the tracking error and the metabolic energy consumption. The latter quantity was taken to be the sum of the total work done by the muscles and the enthalpy change during the contraction. The objective function for the static optimization problem was the sum of the cubes of the muscle stresses. To solve the problem using the static approach, the inverse dynamics problem was first solved in order to determine the resultant joint torques required to generate the given hip, knee and ankle trajectories. To this effect the angular velocities and accelerations were obtained by numerical differentiation using a low-pass digital filter. The dynamic optimization problem was solved using the Fletcher-Reeves conjugate gradient algorithm, and the static optimization problem was solved using the Gradient-restoration algorithm. The results show influence of internal muscle dynamics on muscle control histories vis a vis muscle forces. They also illustrate the strong sensitivity of the results to the differentiation procedure used in the static optimization approach.     

Maximum voluntary joint torque as a function of joint angle and angular velocity: model development and application to the lower limb

Measurements of human strength can be important during analyses of physical activities. Such measurements have often taken the form of the maximum voluntary torque at a single joint angle and angular velocity. However, the available strength varies substantially with joint position and velocity. When examining dynamic activities, strength measurements should account for these variations. A model is presented of maximum voluntary joint torque as a function of joint angle and angular velocity. The model is based on well-known physiological relationships between muscle force and length and between muscle force and velocity and was tested by fitting it to maximum voluntary joint torque data from six different exertions in the lower limb. Isometric, concentric and eccentric maximum voluntary contractions were collected during hip extension, hip flexion, knee extension, knee flexion, ankle plantar flexion and dorsiflexion. Model parameters are reported for each of these exertion directions by gender and age group. This model provides an efficient method by which strength variations with joint angle and angular velocity may be incorporated into comparisons between joint torques calculated by inverse dynamics and the maximum available joint torques.     

Biomechanics of reactions to impending falls

Responses of 11 young adult males, initially standing, to support surface forward accelerations of 0.18 g were investigated. In response to the impending falls this stimulus initiated, body segment motions and myoelectric activities in six muscles were measured. These measurements were then input to 9 or 12 segment whole body biomechanical models and the reaction joint torques needed to produce the motions were calculated. Mean relative joint rotations were as large as 92.8 degrees and calculated relative joint angular accelerations as large as 29.7 rad s-2. Mean myoelectric signal latencies in the six muscles monitored ranged from 135 ms at the ankles to 176 ms at the shoulders with intermediate values at intermediate joints. Mean values of calculated maximum joint torques ranged to 70 Nm at the ankles, 82 Nm at the knees, 73 Nm at the hips, and 19 Nm at the shoulders.     

A musculoskeletal foot model for clinical gait analysis

Several full body musculoskeletal models have been developed for research applications and these models may potentially be developed into useful clinical tools to assess gait pathologies. Existing full-body musculoskeletal models treat the foot as a single segment and ignore the motions of the intrinsic joints of the foot. This assumption limits the use of such models in clinical cases with significant foot deformities. Therefore, a three-segment musculoskeletal model of the foot was developed to match the segmentation of a recently developed multi-segment kinematic foot model. All the muscles and ligaments of the foot spanning the modeled joints were included. Muscle pathways were adjusted with an optimization routine to minimize the difference between the muscle flexion–extension moment arms from the model and moment arms reported in literature. The model was driven by walking data from five normal pediatric subjects (aged 10.6±1.57 years) and muscle forces and activation levels required to produce joint motions were calculated using an inverse dynamic analysis approach. Due to the close proximity of markers on the foot, small marker placement error during motion data collection may lead to significant differences in musculoskeletal model outcomes. Therefore, an optimization routine was developed to enforce joint constraints, optimally scale each segment length and adjust marker positions. To evaluate the model outcomes, the muscle activation patterns during walking were compared with electromyography (EMG) activation patterns reported in the literature. Model-generated muscle activation patterns were observed to be similar to the EMG activation patterns.     

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.     

Bottom-up estimation of joint moments during manual lifting using orientation sensors instead of position sensors

L5/S1, hip and knee moments during manual lifting tasks are, in a laboratory environment, frequently established by bottom-up inverse dynamics, using force plates to measure ground reaction forces (GRFs) and an optoelectronic system to measure segment positions and orientations. For field measurements, alternative measurement systems are being developed. One alternative is the use of small body-mounted inertial/magnetic sensors (IMSs) and instrumented force shoes to measure segment orientation and GRFs, respectively. However, because IMSs measure segment orientations only, the positions of segments relative to each other and relative to the GRFs have to be determined by linking them, assuming fixed segment lengths and zero joint translation. This will affect the estimated joint positions and joint moments. This study investigated the effect of using segment orientations only (orientation-based method) instead of using orientations and positions (reference method) on three-dimensional joint moments. To compare analysis methods (and not measurement methods), GRFs were measured with a force plate and segment positions and/or orientations were measured using optoelectronic marker clusters for both analysis methods. Eleven male subjects lifted a box from floor level using three lifting techniques: a stoop, a semi-squat and a squat technique. The difference between the two analysis methods remained small for the knee moments: <4%. For the hip and L5/S1 moments, the differences were more substantial: up to 8% for the stoop and semi-squat techniques and up to 14% for the squat technique. In conclusion, joint moments during lifting can be estimated with good accuracy at the knee joint and with reasonable accuracy at the hip and L5/S1 joints using segment orientation and GRF data only.     

Joint forces and torques when walking in shallow water

This study reports for the first time an estimation of the internal net joint forces and torques on adults' lower limbs and pelvis when walking in shallow water, taking into account the drag forces generated by the movement of their bodies in the water and the equivalent data when they walk on land. A force plate and a video camera were used to perform a two-dimensional gait analysis at the sagittal plane of 10 healthy young adults walking at comfortable speeds on land and in water at a chest-high level. We estimated the drag force on each body segment and the joint forces and torques at the ankle, knee, and hip of the right side of their bodies using inverse dynamics. The observed subjects' apparent weight in water was about 35% of their weight on land and they were about 2.7 times slower when walking in water. When the subjects walked in water compared with walking on land, there were no differences in the angular displacements but there was a significant reduction in the joint torques which was related to the water's depth. The greatest reduction was observed for the ankle and then the knee and no reduction was observed for the hip. All joint powers were significantly reduced in water. The compressive and shear joint forces were on average about three times lower during walking in water than on land. These quantitative results substantiate the use of water as a safe environment for practicing low-impact exercises, particularly walking.     

Modeling of control and learning in a stepping motion

In a previous study (Beuter et al. 1986) the authors modeled a stepping motion using a three-body linkage with four degrees of freedom. Stepping was simulated by using three task parameters (i.e., step height, length, and duration) and sinusoidal joint angular velocity profiles. The results supported the concept of a hierarchical control structure with open-loop control during normal operation. In this study we refine the dynamic model and improve the simulation technique by incorporating the dynamics of the leg after landing, adding a foot segment to the model, and preprogramming the complete step motion using cycloids. The equations of the forces and torques developed on the ground by the foot during the landing phase are derived using the Lagrangian method. Simulation results are compared to experimental data collected on a subject stepping four times over an obstacle using a Selspot motion analysis system. A hierarchical control model that incorporates a learning process is proposed. The model allows an efficient combination of open and closed loop control strategies and involves hardwired movement segments. We also test the hypothesis of cycloidal velocity profiles in the joint programs against experimental data using a novel curve-fitting procedure based on analytical rather than numerical differentiation. The results suggest multiob-jective optimization of the joint's motion. The control and learning model proposed here will help the understanding of the mechanisms responsible for assembling selected movement segments into goaldirected movement sequences in humans.