Prediction of ground reaction forces during gait based on kinematics and a neural network model

Kinetic information during human gait can be estimated with inverse dynamics, which is based on anthropometric, kinematic, and ground reaction data. While collecting ground reaction data with a force plate is useful, it is costly and requires regulated space. The goal of this study was to propose a new, accurate methodology for predicting ground reaction forces (GRFs) during level walking without the help of a force plate. To predict GRFs without a force plate, the traditional method of Newtonian mechanics was used for the single support phase. In addition, an artificial neural network (ANN) model was applied for the double support phase to solve statically indeterminate structure problems. The input variables of the ANN model, which were selected to have both dependency and independency, were limited to the trajectory, velocity, and acceleration of the whole segment's mass centre to minimise errors. The predicted GRFs were validated with actual GRFs through a ten-fold cross-validation method, and the correlation coefficients (R) for the ground forces were 0.918 in the medial–lateral axis, 0.985 in the anterior–posterior axis, and 0.991 in the vertical axis during gait. The ground moments were 0.987 in the sagittal plane, 0.841 in the frontal plane, and 0.868 in the transverse plane during gait. The high correlation coefficients(R) are due to the improvement of the prediction rate in the double support phase. This study also proved the possibility of calculating joint forces and moments based on the GRFs predicted with the proposed new hybrid method. Data generated with the proposed method may thus be used instead of raw GRF data in gait analysis and in calculating joint dynamic data using inverse dynamics.     

A comparison of static and dynamic optimization muscle force predictions during wheelchair propulsion

The primary purpose of this study was to compare static and dynamic optimization muscle force and work predictions during the push phase of wheelchair propulsion. A secondary purpose was to compare the differences in predicted shoulder and elbow kinetics and kinematics and handrim forces. The forward dynamics simulation minimized differences between simulated and experimental data (obtained from 10 manual wheelchair users) and muscle co-contraction. For direct comparison between models, the shoulder and elbow muscle moment arms and net joint moments from the dynamic optimization were used as inputs into the static optimization routine. RMS errors between model predictions were calculated to quantify model agreement. There was a wide range of individual muscle force agreement that spanned from poor (26.4% F_max error in the middle deltoid) to good (6.4% F_max error in the anterior deltoid) in the prime movers of the shoulder. The predicted muscle forces from the static optimization were sufficient to create the appropriate motion and joint moments at the shoulder for the push phase of wheelchair propulsion, but showed deviations in the elbow moment, pronation–supination motion and hand rim forces. These results suggest the static approach does not produce results similar enough to be a replacement for forward dynamics simulations, and care should be taken in choosing the appropriate method for a specific task and set of constraints. Dynamic optimization modeling approaches may be required for motions that are greatly influenced by muscle activation dynamics or that require significant co-contraction.     

An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo

This paper examined if an electromyography (EMG) driven musculoskeletal model of the human knee could be used to predict knee moments, calculated using inverse dynamics, across a varied range of dynamic contractile conditions. Muscle-tendon lengths and moment arms of 13 muscles crossing the knee joint were determined from joint kinematics using a three-dimensional anatomical model of the lower limb. Muscle activation was determined using a second-order discrete non-linear model using rectified and low-pass filtered EMG as input. A modified Hill-type muscle model was used to calculate individual muscle forces using activation and muscle tendon lengths as inputs. The model was calibrated to six individuals by altering a set of physiologically based parameters using mathematical optimisation to match the net flexion/extension (FE) muscle moment with those measured by inverse dynamics. The model was calibrated for each subject using 5 different tasks, including passive and active FE in an isokinetic dynamometer, running, and cutting manoeuvres recorded using three-dimensional motion analysis. Once calibrated, the model was used to predict the FE moments, estimated via inverse dynamics, from over 200 isokinetic dynamometer, running and sidestepping tasks. The inverse dynamics joint moments were predicted with an average R(2) of 0.91 and mean residual error of approximately 12 Nm. A re-calibration of only the EMG-to-activation parameters revealed FE moments prediction across weeks of similar accuracy. Changing the muscle model to one that is more physiologically correct produced better predictions. The modelling method presented represents a good way to estimate in vivo muscle forces during movement tasks.     

In vivo tests of an improved method for functional location of the subtalar joint axis

The subtalar joint is important in frontal plane movement and posture of the hindfoot. Abnormal subtalar joint moments caused by muscle forces and the ground reaction force acting on the foot are thought to play a role in various foot deformities. Calculating joint moments typically requires knowledge of the location of the joint axis; however, location of the subtalar axis from measured movement is difficult because the talus cannot be tracked using skin-mounted markers. The accuracy of a novel technique for locating the subtalar axis was assessed in vivo using magnetic resonance imaging. The method was also tested with skin-mounted markers and video motion analysis. The technique involves applying forces to the foot that cause pure subtalar joint motion (with negligible talocrural joint motion), and then using helical axis decomposition of the resulting tibiocalcaneal motion. The resulting subtalar axis estimates differed by 6° on average from the true best-fit subtalar axes in the MRI tests. Motion was found to have been applied primarily about the subtalar joint with an average of only 3° of talocrural joint motion. The proposed method provides a potential means for obtaining subject-specific subtalar axis estimates which can then be used in inverse dynamic analyses and subject-specific musculoskeletal models.     

Higher medially-directed joint reaction forces are a characteristic of dysplastic hips: A comparative study using subject-specific musculoskeletal models

Acetabular dysplasia is a known cause of hip osteoarthritis. In addition to abnormal anatomy, changes in kinematics, joint reaction forces (JRFs), and muscle forces could cause tissue damage to the cartilage and labrum, and may contribute to pain and fatigue. The objective of this study was to compare lower extremity joint angles, moments, hip JRFs and muscle forces during gait between patients with symptomatic acetabular dysplasia and healthy controls. Marker trajectories and ground reaction forces were measured in 10 dysplasia patients and 10 typically developing control subjects. A musculoskeletal model was scaled in OpenSim to each subject and subject-specific hip joint centers were determined using reconstructions from CT images. Joint kinematics and moments were calculated using inverse kinematics and inverse dynamics, respectively. Muscle forces and hip JRFs were estimated with static optimization. Inter-group differences were tested for statistical significance (p ≤ 0.05) and large effect sizes (d ≥ 0.8). Results demonstrated that dysplasia patients had higher medially directed JRFs. Joint angles and moments were mostly similar between the groups, but large inter-group effect sizes suggested some restriction in range of motion by patients at the hip and ankle. Higher medially-directed JRFs and inter-group differences in hip muscle forces likely stem from lateralization of the hip joint center in dysplastic patients. Joint force differences, combined with reductions in range of motion at the hip and ankle may also indicate compensatory strategies by patients with dysplasia to maintain joint stability.     

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.     

Modeling and inverse simulation of somersaults on the trampoline

This paper describes a biomechanical model for numerical simulation of front and back somersaults, without twist, performed on the trampoline. The developed mathematical formulation is used to solve an inverse dynamics problem, in which the moments of muscle forces at the joints that result in a given (measured) motion are determined. The nature of the stunts and the way the human body is maneuvered and controlled can be studied. The calculated torques can then be used as control signals for a dynamic simulation. This provides a way to check the inverse dynamics procedures, and influence of typical control errors on somersault performance can be studied. To achieve these goals, the nonlinear dynamical model of the trampolinist and the interacting trampoline bed has been identified, and a methodology for recording the actual somersault performances was proposed. Some results of numerical simulations are reported.     

Static and dynamic optimization solutions for gait are practically equivalent

The proposition that dynamic optimization provides better estimates of muscle forces during gait than static optimization is examined by comparing a dynamic solution with two static solutions. A 23-degree-of-freedom musculoskeletal model actuated by 54 Hill-type musculotendon units was used to simulate one cycle of normal gait. The dynamic problem was to find the muscle excitations which minimized metabolic energy per unit distance traveled, and which produced a repeatable gait cycle. In the dynamic problem, activation dynamics was described by a first-order differential equation. The joint moments predicted by the dynamic solution were used as input to the static problems. In each static problem, the problem was to find the muscle activations which minimized the sum of muscle activations squared, and which generated the joint moments input from the dynamic solution. In the first static problem, muscles were treated as ideal force generators; in the second, they were constrained by their force-length-velocity properties; and in both, activation dynamics was neglected. In terms of predicted muscle forces and joint contact forces, the dynamic and static solutions were remarkably similar. Also, activation dynamics and the force-length-velocity properties of muscle had little influence on the static solutions. Thus, for normal gait, if one can accurately solve the inverse dynamics problem and if one seeks only to estimate muscle forces, the use of dynamic optimization rather than static optimization is currently not justified. Scenarios in which the use of dynamic optimization is justified are suggested.     

Validation of the Delft Shoulder and Elbow Model using in-vivo glenohumeral joint contact forces

The Delft Shoulder and Elbow Model (DSEM), a large-scale musculoskeletal model, is used for the estimation of muscle and joint reaction forces in the shoulder and elbow complex. Although the model has been qualitatively verified using EMG-signals, quantitative validation has until recently not been feasible. The development of an instrumented shoulder endoprosthesis has now made this possible. To this end, motion data, EMG-signals, external forces, and in-vivo glenohumeral joint reaction forces (GH-JRF) were recorded for two patients with an instrumented shoulder hemi-arthroplasty, during dynamic tasks (including abduction and anteflexion) and force tasks with the arm held in a static position. Motions and external forces served as the model inputs to estimate the GH-JRF. In the modeling process, the effect of two different (stress and energy) optimization cost functions and uniform size and mass scaling were evaluated. The model-estimated GH-JRF followed the in-vivo measured force for dynamic tasks up to about 90° arm elevations, but generally underestimates the peak forces up to 31%; whereas a different behavior (ascending measured but descending estimated force) was found for angles above 90°. For the force tasks the model generally overestimated the peak GH-JRF for most directions (on average up to 34%). Applying the energy cost function improved model predictions for the dynamic anteflexion task (up to 9%) and for the force task (on average up to 23%). Scaling also led to improvement of the model predictions during the dynamic tasks (up to 26%), but had a negligible effect (<2%) on the force task results. Although results indicated a reasonable compatibility between model and measured data, adjustments will be necessary to individualize the generic model with the patient-specific characteristics.     

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.     

Neuromusculoskeletal modeling: estimation of muscle forces and joint moments and movements from measurements of neural command

This paper provides an overview of forward dynamic neuromusculoskeletal modeling. The aim of such models is to estimate or predict muscle forces, joint moments, and/or joint kinematics from neural signals. This is a four-step process. In the first step, muscle activation dynamics govern the transformation from the neural signal to a measure of muscle activation-a time varying parameter between 0 and 1. In the second step, muscle contraction dynamics characterize how muscle activations are transformed into muscle forces. The third step requires a model of the musculoskeletal geometry to transform muscle forces to joint moments. Finally, the equations of motion allow joint moments to be transformed into joint movements. Each step involves complex nonlinear relationships. The focus of this paper is on the details involved in the first two steps, since these are the most challenging to the biomechanician. The global process is then explained through applications to the study of predicting isometric elbow moments and dynamic knee kinetics.     

A well-posed, embedded constraint representation of joint moments from kinesiological measurements

Joint moment estimation using the traditional inverse dynamics analysis presents two challenging problems, which limit its reliability. First, the quality of the computed moments depends directly on unreliable estimates of the segment accelerations obtained numerically by differentiating noisy marker measurements. Second, the representation of joint moments from combined video and force plate measurements belongs to a class of ill-posed problems, which does not possess a unique solution. This paper presents a well-posed representation derived from an embedded constraint equation. The proposed method, referred to as the embedded constraint representation (ECR), provides unique moment estimates, which satisfy all measurement constraints and boundary conditions and require fewer acceleration components than the traditional inverse dynamics method. Specifically, for an n-segment open chain planar system, the ECR requires n-3 acceleration components as compared to 3(n-1) components required by the traditional (from ground up) inverse dynamics analysis. Based on a simulated experiment using a simple three-segment model, the precision of the ECR is evaluated at different noise levels and compared to the traditional inverse dynamics technique. At the lowest noise levels, the inverse dynamics method is up to 50 percent more accurate while at the highest noise levels the ECR method is up to 100 percent more accurate. The ECR results over the entire range of noise levels reveals an average improvement on the order 20 percent in estimating the moments distal to the force plate and no significant improvement in estimating moments proximal to the force plate. The new method is particularly advantageous in a combined video, force plate, and accelerometery sensing strategy.     

A procedure to estimate normal and friction contact parameters in the stance phase of the human gait

A new approach to estimate normal and tangential contact parameters in the foot-ground contact during human gait was proposed. A correct estimation of the contact parameters would be very important in the resolution of predictive forward dynamic problems. The normal contact forces have been well estimated in the literature. But accurate estimation of tangential forces has not been reached yet. This work proposed a new procedure to accurately estimate friction forces. The approach has been based on the consideration of the modulus of the tangential force instead of its components. This modulus was introduced together with the modulus of the normal contact force and its two associated moments in an optimization algorithm to fit the contact forces provided by the model to the experimental data obtained with a force plate. An inverse dynamics problem was solved as a step previous to the optimization algorithm. The results showed that both the normal and tangential forces and the moments in the horizontal plane were in agreement with the experimental measurements. This work also analyzed the influence on the results of the friction law. The results obtained with the general friction law, which considered dry (static and dynamic) and viscous friction, were compared with results provided by simpler laws. The analysis of the components of the friction forces pointed out the importance of the Stribeck component in the resultant force instead of the viscous friction which played a minimal role. But for modelling the stick-slip transition, the implementation of a general friction law is necessary.     

Effect of low pass filtering on joint moments from inverse dynamics: implications for injury prevention

Analyses of joint moments are important in the study of human motion, and are crucial for our understanding of e.g. how and why ACL injuries occur. Such analyses may be affected by artifacts due to inconsistencies in the equations of motion when force and movement data are filtered with different cut-off frequencies. The purpose of this study was to quantify the effect of these artifacts, and compare joint moments calculated with the same or different cut-off frequency for the filtering of force and movement data. 123 elite handball players performed sidestep cutting while the movement was recorded by eight 240 Hz cameras and the ground reaction forces were recorded by a 960 Hz force plate. Knee and hip joint moments were calculated through inverse dynamics, with four different combinations of cut-off frequencies for signal filtering: movement 10 Hz, force 10 Hz, (10-10); movement 15 Hz, force 15 Hz; movement 10 Hz, force 50 Hz (10-50); movement 15 Hz, force 50 Hz. The results revealed significant differences, especially between conditions with different filtering of force and movement. Mean (SD) peak knee abduction moment for the 10-10 and 10-50 condition were 1.27 (0.53) and 1.64 (0.68) Nm/kg, respectively. Ranking of players based on knee abduction moments were affected by filtering condition. Out of 20 players with peak knee abduction moment higher than mean+1S D with the 10-50 condition, only 11 were still above mean+1 SD when the 10-10 condition was applied. Hip moments were very sensitive to filtering cut-off. Mean (SD) peak hip flexion moment was 3.64 (0.75) and 5.92 (1.80) under the 10-10 and 10-50 conditions, respectively. Based on these findings, force and movement data should be processed with the same filter. Conclusions from previous inverse dynamics studies, where this was not the case, should be treated with caution.     

Estimation of muscle forces in gait using a simulation of the electromyographic activity and numerical optimization

Clinical gait analysis provides great contributions to the understanding of gait patterns. However, a complete distribution of muscle forces throughout the gait cycle is a current challenge for many researchers. Two techniques are often used to estimate muscle forces: inverse dynamics with static optimization and computer muscle control that uses forward dynamics to minimize tracking. The first method often involves limitations due to changing muscle dynamics and possible signal artefacts that depend on day-to-day variation in the position of electromyographic (EMG) electrodes. Nevertheless, in clinical gait analysis, the method of inverse dynamics is a fundamental and commonly used computational procedure to calculate the force and torque reactions at various body joints. Our aim was to develop a generic musculoskeletal model that could be able to be applied in the clinical setting. The musculoskeletal model of the lower limb presents a simulation for the EMG data to address the common limitations of these techniques. This model presents a new point of view from the inverse dynamics used on clinical gait analysis, including the EMG information, and shows a similar performance to another model available in the OpenSim software. The main problem of these methods to achieve a correct muscle coordination is the lack of complete EMG data for all muscles modelled. We present a technique that simulates the EMG activity and presents a good correlation with the muscle forces throughout the gait cycle. Also, this method showed great similarities whit the real EMG data recorded from the subjects doing the same movement.     

A Lagrange-based generalised formulation for the equations of motion of simple walking models

Simple 2D models of walking often approximate the human body to multi-link dynamic systems, where body segments are represented by rigid links connected by frictionless hinge joints. Performing forward dynamics on the equations of motion (EOM) of these systems can be used to simulate their movement. However, deriving these equations can be time consuming. Using Lagrangian mechanics, a generalised formulation for the EOM of n-link open-loop chains is derived. This can be used for single support walking models. This has an advantage over Newton–Euler mechanics in that it is independent of coordinate system and prior knowledge of the ground reaction force (GRF) is not required. Alternative strategies, such as optimisation algorithms, can be used to estimate joint activation and simulate motion. The application of Lagrange multipliers, to enforce motion constraints, is used to adapt this general formulation for application to closed-loop chains. This can be used for double support walking models. Finally, inverse dynamics are used to calculate the GRF for these general n-link chains. The necessary constraint forces to maintain a closed-loop chain, calculated from the Lagrange multipliers, are one solution to the indeterminate problem of GRF distribution in double support models. An example of this method’s application is given, whereby an optimiser estimates the joint moments by tracking kinematic data.     

Simultaneous prediction of muscle and contact forces in the knee during gait

Musculoskeletal models are currently the primary means for estimating in vivo muscle and contact forces in the knee during gait. These models typically couple a dynamic skeletal model with individual muscle models but rarely include articular contact models due to their high computational cost. This study evaluates a novel method for predicting muscle and contact forces simultaneously in the knee during gait. The method utilizes a 12 degree-of-freedom knee model (femur, tibia, and patella) combining muscle, articular contact, and dynamic skeletal models. Eight static optimization problems were formulated using two cost functions (one based on muscle activations and one based on contact forces) and four constraints sets (each composed of different combinations of inverse dynamic loads). The estimated muscle and contact forces were evaluated using in vivo tibial contact force data collected from a patient with a force-measuring knee implant. When the eight optimization problems were solved with added constraints to match the in vivo contact force measurements, root-mean-square errors in predicted contact forces were less than 10 N. Furthermore, muscle and patellar contact forces predicted by the two cost functions became more similar as more inverse dynamic loads were used as constraints. When the contact force constraints were removed, estimated medial contact forces were similar and lateral contact forces lower in magnitude compared to measured contact forces, with estimated muscle forces being sensitive and estimated patellar contact forces relatively insensitive to the choice of cost function and constraint set. These results suggest that optimization problem formulation coupled with knee model complexity can significantly affect predicted muscle and contact forces in the knee during gait. Further research using a complete lower limb model is needed to assess the importance of this finding to the muscle and contact force estimation process.     

Subject-specific hip geometry and hip joint centre location affects calculated contact forces at the hip during gait

Hip loading affects the development of hip osteoarthritis, bone remodelling and osseointegration of implants. In this study, we analyzed the effect of subject-specific modelling of hip geometry and hip joint centre (HJC) location on the quantification of hip joint moments, muscle moments and hip contact forces during gait, using musculoskeletal modelling, inverse dynamic analysis and static optimization. For 10 subjects, hip joint moments, muscle moments and hip loading in terms of magnitude and orientation were quantified using three different model types, each including a different amount of subject-specific detail: (1) a generic scaled musculoskeletal model, (2) a generic scaled musculoskeletal model with subject-specific hip geometry (femoral anteversion, neck-length and neck-shaft angle) and (3) a generic scaled musculoskeletal model with subject-specific hip geometry including HJC location. Subject-specific geometry and HJC location were derived from CT. Significant differences were found between the three model types in HJC location, hip flexion–extension moment and inclination angle of the total contact force in the frontal plane. No model agreement was found between the three model types for the calculation of contact forces in terms of magnitude and orientations, and muscle moments. Therefore, we suggest that personalized models with individualized hip joint geometry and HJC location should be used for the quantification of hip loading. For biomechanical analyses aiming to understand modified hip joint loading, and planning hip surgery in patients with osteoarthritis, the amount of subject-specific detail, related to bone geometry and joint centre location in the musculoskeletal models used, needs to be considered.     

Development and validation of a multi-body model of the canine stifle joint

Multi-body musculoskeletal models that can be used concurrently to predict joint contact pressures and muscle forces would be extremely valuable in studying the mechanics of joint injury. The purpose of this study was to develop an anatomically correct canine stifle joint model and validate it against experimental data. A cadaver pelvic limb from one adult dog was used in this study. The femoral head was subjected to axial motion in a mechanical tester. Kinematic and force data were used to validate the computational model. The maximum RMS error between the predicted and measured kinematics during the complete testing cycle was 11.9 mm translational motion between the tibia and the femur and 4.3° rotation between patella and femur. This model is the first step in the development of a musculoskeletal model of the hind limb with anatomically correct joints to study cartilage loading under dynamic conditions.