Predicting sagittal plane biomechanics that minimize the axial knee joint contact force during walking

Patterns of asymmetry and energy cost generated from predictive simulations of hemiparetic gait

Hemiparesis, defined as unilateral muscle weakness, often occurs in people post-stroke or people with cerebral palsy, however it is difficult to understand how this hemiparesis affects movement patterns as it often presents alongside a variety of other neuromuscular impairments. Predictive musculoskeletal modeling presents an opportunity to investigate how impairments affect gait performance assuming a particular cost function. Here, we use predictive simulation to quantify the spatiotemporal asymmetries and changes to metabolic cost that emerge when muscle strength is unilaterally reduced and how reducing spatiotemporal symmetry affects metabolic cost. We modified a 2-D musculoskeletal model by uniformly reducing the peak isometric muscle force unilaterally. We then solved optimal control simulations of walking across a range of speeds by minimizing the sum of the cubed muscle excitations. Lastly, we ran additional optimizations to test if reducing spatiotemporal asymmetry would result in an increase in metabolic cost. Our results showed that the magnitude and direction of effort-optimal spatiotemporal asymmetries depends on both the gait speed and level of weakness. Also, the optimal speed was 1.25 m/s for the symmetrical and 20% weakness models but slower (1.00 m/s) for the 40% and 60% weakness models, suggesting that hemiparesis can account for a portion of the slower gait speed seen in people with hemiparesis. Modifying the cost function to minimize spatiotemporal asymmetry resulted in small increases (~4%) in metabolic cost. Overall, our results indicate that spatiotemporal asymmetry may be optimal for people with hemiparesis. Additionally, the effect of speed and the level of weakness on spatiotemporal asymmetry may help explain the well-known heterogenous distribution of spatiotemporal asymmetries observed in the clinic. Future work could extend our results by testing the effects of other neuromuscular impairments on optimal gait strategies, and therefore build a more comprehensive understanding of the gait patterns observed in clinical populations.

Predictive Simulations to Replicate Human Gait Adaptations and Energetics With Exoskeletons

Robotic exoskeletons have the potential to restore and enhance human mobility. However, optimally controlling these devices, to work in concert with human users, is challenging. Accurate model simulations of the interaction between exoskeletons and users may expedite the design process and improve control. Here, as a proof of principle, we tested if we could use predictive simulations to replicate human gait adaptations and changes in energy expenditure from an experiment where participants walked with exoskeletons. We recreated a past experimental paradigm, where robotic exoskeletons were used to shift people's energetically optimal step frequency to frequencies higher and lower than normally preferred. To match the experimental controller, we modelled knee-worn exoskeletons that applied resistive torques, either proportional or inversely proportional to step frequency-decreasing or increasing the energy optimal step frequency, respectively. We were able to replicate the experiment, finding higher and lower optimal step frequencies than in natural walking under each respective condition. Our simulated resistive torques and objective landscapes resembled the measured experimental resistive torque and energy landscapes. Individual muscle energetics revealed distinct coordination strategies consistent with each exoskeleton controller condition. Increasing the accuracy of step frequency and energetic predictions was best achieved by increasing the number of virtual participants (varying whole-body anthropometrics), rather than the number of muscle parameter sets (varying muscle anthropometrics). In future, our approach can be used to design controllers in advance of human testing, to help identify reasonable solution spaces or tailor design to individual users.

Muscle coordination retraining inspired by musculoskeletal simulations reduces knee contact force

Humans typically coordinate their muscles to meet movement objectives like minimizing energy expenditure. In the presence of pathology, new objectives gain importance, like reducing loading in an osteoarthritic joint, but people often do not change their muscle coordination patterns to meet these new objectives. Here we use musculoskeletal simulations to identify simple changes in coordination that can be taught using electromyographic biofeedback, achieving the therapeutic goal of reducing joint loading. Our simulations predicted that changing the relative activation of two redundant ankle plantarflexor muscles—the gastrocnemius and soleus—could reduce knee contact force during walking, but it was unclear whether humans could re-coordinate redundant muscles during a complex task like walking. Our experiments showed that after a single session of walking with biofeedback of summary measures of plantarflexor muscle activation, healthy individuals reduced the ratio of gastrocnemius-to-soleus muscle activation by 25 ± 15% (p = 0.004, paired t test, n = 10). Participants who walked with this “gastrocnemius avoidance” gait pattern reduced late-stance knee contact force by 12 ± 12% (p = 0.029, paired t test, n = 8). Simulation-informed coordination retraining could be a promising treatment for knee osteoarthritis and a powerful tool for optimizing coordination for a variety of rehabilitation and performance applications.

Predicting neuromuscular control patterns that minimize ACL forces during injury prone jump landing maneuvers in downhill skiing using a musculoskeletal simulation model

Competitive skiers encounter a high risk of sustaining an ACL injury during jump-landing in downhill ski racing. Facing an injury-prone landing manoeuvre, there is a lack of knowledge regarding optimum control strategies. So, the purpose of the present study was to investigate possible neuromuscular control patterns to avoid injury during injury-prone jump-landing manoeuvres. A computational approach was used to generate a series of 190 injury-prone jump-landing manoeuvres based on a 25-degree-of-freedom sagittal plane musculoskeletal skier model. Using a dynamic optimization framework, each injury-prone landing manoeuvre was resolved to identify muscle activation patterns of the lower limbs and corresponding kinematic changes that reduce peak ACL force. In the 190 injury-prone jump-landing simulations, ACL forces peaked during the first 50 ms after ground contact. Optimized muscle activation patterns, that reduced peak ACL forces, showed increased activation of the monoarticular hip flexors, ankle dorsi- and plantar flexors as well as hamstrings prior to or during the early impact phase (<50 ms). The corresponding kinematic changes were characterized by increased hip and knee flexion and less backward lean of the skier at initial ground contact and the following impact phase. Injury prevention strategies should focus on increased activation of the monoarticular hip flexors, ankle plantar flexors and rapid and increased activation of the hamstrings in combination with a flexed landing position and decreased backward lean to reduce ACL injury risk during the early impact phase (<50 ms) of jump landing.HighlightsFirst study investigating advantageous control strategies during injury-prone jump-landing manoeuvres in downhill skiing using a musculoskeletal simulation model and dynamic optimization framework.The simulation results predicted high injury risk during the first 50 ms after initial ground contact.Optimized neuromuscular control patterns showed adapted activation patterns (timing and amplitude) of muscles crossing the knee as well as the hip and ankle joints prior to and after initial ground contact, respectively.An optimized control strategy during an injury-prone landing manoeuvre was characterized kinematically by increasing hip and knee flexion and less backward lean of the skier at initial ground contact and the following impact phase.

Antagonistic co-contraction can minimize muscular effort in systems with uncertainty

Muscular co-contraction of antagonistic muscle pairs is often observed in human movement, but it is considered inefficient and it can currently not be predicted in simulations where muscular effort or metabolic energy are minimized. Here, we investigated the relationship between minimizing effort and muscular co-contraction in systems with random uncertainty to see if muscular co-contraction can minimize effort in such system. We also investigated the effect of time delay in the muscle, by varying the time delay in the neural control as well as the activation time constant. We solved optimal control problems for a one-degree-of-freedom pendulum actuated by two identical antagonistic muscles, using forward shooting, to find controller parameters that minimized muscular effort while the pendulum remained upright in the presence of noise added to the moment at the base of the pendulum. We compared a controller with and without feedforward control. Task precision was defined by bounding the root mean square deviation from the upright position, while different perturbation levels defined task difficulty. We found that effort was minimized when the feedforward control was nonzero, even when feedforward control was not necessary to perform the task, which indicates that co-contraction can minimize effort in systems with uncertainty. We also found that the optimal level of co-contraction increased with time delay, both when the activation time constant was increased and when neural time delay was added. Furthermore, we found that for controllers with a neural time delay, a different trajectory was optimal for a controller with feedforward control than for one without, which indicates that simulation trajectories are dependent on the controller architecture. Future movement predictions should therefore account for uncertainty in dynamics and control, and carefully choose the controller architecture. The ability of models to predict co-contraction from effort or energy minimization has important clinical and sports applications. If co-contraction is undesirable, one should aim to remove the cause of co-contraction rather than the co-contraction itself.

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

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

Perspective on musculoskeletal modelling and predictive simulations of human movement to assess the neuromechanics of gait

Locomotion results from complex interactions between the central nervous system and the musculoskeletal system with its many degrees of freedom and muscles. Gaining insight into how the properties of each subsystem shape human gait is challenging as experimental methods to manipulate and assess isolated subsystems are limited. Simulations that predict movement patterns based on a mathematical model of the neuro-musculoskeletal system without relying on experimental data can reveal principles of locomotion by elucidating cause-effect relationships. New computational approaches have enabled the use of such predictive simulations with complex neuro-musculoskeletal models. Here, we review recent advances in predictive simulations of human movement and how those simulations have been used to deepen our knowledge about the neuromechanics of gait. In addition, we give a perspective on challenges towards using predictive simulations to gain new fundamental insight into motor control of gait, and to help design personalized treatments in patients with neurological disorders and assistive devices that improve gait performance. Such applications will require more detailed neuro-musculoskeletal models and simulation approaches that take uncertainty into account, tools to efficiently personalize those models, and validation studies to demonstrate the ability of simulations to predict gait in novel circumstances.

Musculoskeletal Model Personalization Affects Metabolic Cost Estimates for Walking

Assessment of metabolic cost as a metric for human performance has expanded across various fields within the scientific, clinical, and engineering communities. As an alternative to measuring metabolic cost experimentally, musculoskeletal models incorporating metabolic cost models have been developed. However, to utilize these models for practical applications, the accuracy of their metabolic cost predictions requires improvement. Previous studies have reported the benefits of using personalized musculoskeletal models for various applications, yet no study has evaluated how model personalization affects metabolic cost estimation. This study investigated the effect of musculoskeletal model personalization on estimates of metabolic cost of transport (CoT) during post-stroke walking using three commonly used metabolic cost models. We analyzed walking data previously collected from two male stroke survivors with right-sided hemiparesis. The three metabolic cost models were implemented within three musculoskeletal modeling approaches involving different levels of personalization. The first approach used a scaled generic OpenSim model and found muscle activations via static optimization (SOGen). The second approach used a personalized electromyographic (EMG)-driven musculoskeletal model with personalized functional axes but found muscle activations via static optimization (SOCal). The third approach used the same personalized EMG-driven model but calculated muscle activations directly from EMG data (EMGCal). For each approach, the muscle activation estimates were used to calculate each subject's CoT at different gait speeds using three metabolic cost models (Umberger et al., 2003; Bhargava et al., 2004; Umberger, 2010). The calculated CoT values were compared with published CoT data as a function of walking speed, step length asymmetry, stance time asymmetry, double support time asymmetry, and severity of motor impairment (i.e., Fugl-Meyer score). Overall, only SOCal and EMGCal with the Bhargava metabolic cost model were able to reproduce accurately published experimental trends between CoT and various clinical measures of walking asymmetry post-stroke. Tuning of the parameters in the different metabolic cost models could potentially resolve the observed CoT magnitude differences between model predictions and experimental measurements. Realistic CoT predictions may allow researchers to predict human performance, surgical outcomes, and rehabilitation outcomes reliably using computational simulations.

A model-based approach to predict neuromuscular control patterns that minimize ACL forces during jump landing

Jump landing is a common situation leading to knee injuries involving the anterior cruciate ligament (ACL) in sports. Although neuromuscular control is considered as a key injury risk factor, there is a lack of knowledge regarding optimum control strategies that reduce ACL forces during jump landing. In the present study, a musculoskeletal model-based computational approach is presented that allows identifying neuromuscular control patterns that minimize ACL forces during jump landing. The approach is demonstrated for a jump landing maneuver in downhill skiing, which is one out of three main injury mechanisms in competitive skiing.

A solution method for predictive simulations in a stochastic environment

Predictive gait simulations currently do not account for environmental or internal noise. We describe a method to solve predictive simulations of human movements in a stochastic environment using a collocation method. The optimization is performed over multiple noisy episodes of the trajectory, instead of a single episode in a deterministic environment. Each episode used the same control parameters. The method was verified on a torque-driven pendulum swing-up problem. A different optimal trajectory was found in a stochastic environment than in the deterministic environment. Next, it was applied to gait to show its application in predictive simulation of human movement. We show that, unlike in a deterministic model, a nonzero minimum foot clearance during swing is predicted by a minimum-effort criterion in a stochastic environment. The predicted amount of foot clearance increased with the noise amplitude.

Effects of Load Carriage and Step Length Manipulation on Achilles Tendon and Knee Loads

INTRODUCTION

Longer steps with load carriage is common in shorter Soldiers when matching pace with taller Soldiers whereas shorter steps are hypothesized to reduce risk of injury with load carriage. The effects of load carriage with and without step length manipulation on loading patterns of three commonly injured structures were determined: Achilles tendon, patellofemoral joint (PFJ) and medial tibiofemoral joint (mTFJ).

MATERIALS AND METHODS

ROTC Cadets (n = 16; 20.1 years ± 2.5) walked with and without load carriage (20-kg). Cadets then altered preferred step lengths ±7.5% with load carriage. Achilles tendon, PFJ and mTFJ loads were estimated via musculoskeletal modeling.

RESULTS

Large increases in peak Achilles tendon load (p < 0.001, d = 1.93), Achilles tendon impulse per 1-km (p < 0.001, d = 0.91), peak mTFJ load (p < 0.001, d = 1.33), and mTFJ impulse per 1-km (p < 0.001, d = 1.49) were noted with load carriage while moderate increases were observed for the PFJ (peak: p < 0.001, d = 0.69; impulse per 1-km: p < 0.001, d = 0.69). Shortened steps with load carriage only reduced peak Achilles tendon load (p < 0.001, d = -0.44) but did not reduce Achilles impulse per km due to the resulting extra steps and also did not reduce peak or cumulative PFJ and mTFJ loads (p > 0.05). Longer steps with load carriage increased PFJ loads the most (p < 0.001, d = 0.68-0.75) with moderate increases in mTFJ forces (p < 0.001, d = 0.48-0.63) with no changes in Achilles tendon loads (p = 0.11-0.20).

CONCLUSION

A preferred step length is the safest strategy when walking with load carriage. Taking a shorter step is not an effective strategy to reduce loading on the Achilles tendon, PFJ, and mTFJ.

Metabolic cost calculations of gait using musculoskeletal energy models, a comparison study

This paper compares predictions of metabolic energy expenditure in gait using seven metabolic energy expenditure models to assess their correlation with experimental data. Ground reaction forces, marker data, and pulmonary gas exchange data were recorded for six walking trials at combinations of two speeds, 0.8 m/s and 1.3 m/s, and three inclines, -8% (downhill), level, and 8% (uphill). The metabolic cost, calculated with the metabolic energy models was compared to the metabolic cost from the pulmonary gas exchange rates. A repeated measures correlation showed that all models correlated well with experimental data, with correlations of at least 0.9. The model by Bhargava et al. (J Biomech, 2004: 81-88) and the model by Lichtwark and Wilson (J Exp Biol, 2005: 2831-3843) had the highest correlation, 0.95. The model by Margaria (Int Z Angew Physiol Einschl Arbeitsphysiol, 1968: 339-351) predicted the increase in metabolic cost following a change in dynamics best in absolute terms.

Skipping has lower knee joint contact forces and higher metabolic cost compared to running

BACKGROUND

The health benefits of running based exercise programs are plentiful however the high rate of injury in these programs often reduces or eliminates exercise participation. Skipping has shorter steps, reduced vertical ground reaction forces (GRFs), and lower knee extensor torques, compared to running forming the basis of the present hypothesis that skipping would have lower tibio-femoral and patello-femoral joint contact forces.

RESEARCH QUESTION

The purpose of this study was to compare knee contact forces between skipping and running at the same speed. We also compared metabolic cost of these two gaits to examine the idea that the larger vertical displacement in skipping is a primary factor in its previously reported high metabolic cost.

METHODS

The study evaluated joint contact forces through musculoskeletal modeling with GRF and 3D kinematic data and metabolic cost using oxygen consumption data from 20 young, healthy, trained participants as they skipped and ran on an instrumented treadmill at 2.68 m/s.

RESULTS

Skipping, compared to running, had substantially lower tibio-femoral and patello-femoral joint contact forces and linear impulses on both per-step and per-kilometer (i.e. lower cumulative loads) bases and also 30% higher metabolic cost. The lower joint loads in skipping were directly associated with its shorter steps and the higher metabolic cost was directly associated to its larger vertical displacement through the stride.

SIGNIFICANCE

As joint loads may predispose individuals to running related injuries, skipping presents an attractive alternative exercise modality with additional increased aerobic benefits.

The effect of surface inclination and limb on knee loading measures in transtibial prosthesis users

Background

Osteoarthritis (OA) is a degenerative disease caused by the wearing of joint cartilage and bone. Literature has established that a prosthesis user’s intact limb is at greater risk of developing OA. This study analyzed the effect of commonly encountered surface inclinations on knee joint loading measures in able-bodied and transtibial prosthesis users.

Methods

12 transtibial prosthesis users and 12 able-bodied participants walked across level ground, up slope, down slope, and cross slope (further divided into top and bottom slope depending on the location of the limb being analyzed). First and second peak external knee adduction moment (KAM), external knee adduction moment rate, and external knee adduction moment impulse were extracted from the stance phase of gait. Mixed ANOVA statistics with Bonferonni post hoc analyses were performed.

Results

Significant limb differences were only found for KAM rate and first peak KAM. When compared to all other surfaces up slope had the significantly lowest KAM rate and was not significantly lower for all other tested variables. Down slope had significantly greater KAM rate than all surfaces except bottom slope. KAM second peak and KAM impulse analysis resulted in no significant differences.

Conclusions

Individuals at risk for developing, or currently dealing with, knee OA could avoid walking for extended periods on down slope. Walking up moderate slopes may be considered as a complementary activity to level walking for rehabilitation and delaying OA progression.

The lack of significant limb differences suggests that second peak KAM and KAM impulse may not be appropriate load-related indicators of OA initiation among prosthesis users without OA. KAM rate was the most sensitive joint loading variable and therefore should be investigated further as an appropriate variable for identifying OA risk in individuals with transtibial amputations.

A Novel Optimization Framework to Improve the Computational Cost of Muscle Activation Prediction for a Neuromusculoskeletal System

The high computational cost (CC) of neuromusculoskeletal modeling is usually considered a serious barrier in clinical applications. Different approaches have been developed to lessen CC and amplify the accuracy of muscle activation prediction based on forward and inverse analyses by applying different optimization algorithms. This study is aimed at proposing two novel approaches, inverse muscular dynamics with inequality constraints (IMDIC) and inverse-forward muscular dynamics with inequality constraints (IFMDIC), not only to reduce CC but also to amend the computational errors compared to the well-known approach of extended inverse dynamics (EID). To do that, the equality constraints of optimization problem, which are computationally tough to satisfy, are replaced by inequality constraints, which are easier to satisfy. To verify the practical application of the proposed approaches, the muscle activations of the lower limbs during the half of a gait cycle are quantified. The simulation results of the optimal muscle activations are then compared to the experimental ones. The results reveal that IMDIC requires less CC (87.5%) compared to EID. In addition, CC of IMDIC was about 33.3% improved by the application of IFMDIC. The findings of this study suggest that although the novel approach of IFMDIC decreases CC compared to IMDIC, the convergence of its results is very sensitive to the primary guess of the optimization variables.

Walking velocity and step length adjustments affect knee joint contact forces in healthy weight and obese adults

Knee osteoarthritis is a major public health problem and adults with obesity are particularly at risk. One approach to alleviating this problem is to reduce the mechanical load at the joint during daily activity. Adjusting temporospatial parameters of walking could mitigate cumulative knee joint mechanical loads. The purpose of this study was to determine how adjustments to velocity and step length affects knee joint loading in healthy weight adults and adults with obesity. We collected three-dimensional gait analysis data on 10 adults with a normal body mass index and 10 adults with obesity during over ground walking in nine different conditions. In addition to preferred velocity and step length, we also conducted combinations of 15% increased and decreased velocity and step length. Peak tibiofemoral joint impulse and knee adduction angular impulse were reduced in the decreased step length conditions in both healthy weight adults (main effect) and those with obesity (interaction effect). Peak knee joint adduction moment was also reduced with decreased step length, and with decreased velocity in both groups. We conclude from these results that adopting shorter step lengths during daily activity and when walking for exercise can reduce mechanical stimuli associated with articular cartilage degenerative processes in adults with and without obesity. Thus, walking with reduced step length may benefit adults at risk for disability due to knee osteoarthritis. Clinical Significance: Adopting a shorter step length during daily walking activity may reduce knee joint loading and thus benefit those at risk for knee cartilage degeneration. © 2018 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:2679-2686, 2018.

Searching for strategies to reduce the mechanical demands of the sit-to-stand task with a muscle-actuated optimal control model

BACKGROUND

The sit-to-stand task, which involves rising unassisted from sitting on a chair to standing, is important in daily life. Many people with muscle weakness, reduced range of motion or loading-related pain in a particular joint have difficulty performing the task. How should a person suffering from such impairment best perform the sit-to-stand task and, in the case of pain in a particular joint, with reduced loading of that joint?

METHODS

We developed a musculoskeletal model with reference parameter values based on properties of healthy strong subjects. The model's muscle stimulation-time input was optimized using direct collocation to find strategies that yielded successful sit-to-stand task performance with minimum 'control effort' for the reference set and modified sets of parameter values, and with constraints on tibiofemoral compression force.

FINDINGS

The sit-to-stand task could be performed successfully and realistically by the reference model, by a model with isometric knee extensor forces reduced to 40% of reference, by a model with isometric forces of all muscles reduced to 45% of reference, and by the reference model with the tibiofemoral compression force constrained during optimization to 65% of the peak value in the reference condition.

INTERPRETATION

The strategies found by the model in conditions other than reference could be interpreted well on the basis of cost function and task biomechanics. The question remains whether it is feasible to teach patients with musculoskeletal impairments or joint pain to perform the sit-to-stand task according to strategies that are optimal according to the simulation model.

Reductions in knee joint forces with weight loss are attenuated by gait adaptations in class III obesity

A consensus exists that high knee joint forces are a precursor to knee osteoarthritis and weight loss reduces these forces. Because large weight loss also leads to increased step length and walking velocity, knee contact forces may be reduced less than predicted by the magnitude of weight loss. The purpose was to determine the effects of weight loss on knee muscle and joint loads during walking in Class III obese adults. We determined through motion capture, force platform measures and biomechanical modeling the effects of weight loss produced by gastric bypass surgery over one year on knee muscle and joint loads during walking at a standard, controlled velocity and at self-selected walking velocities. Weight loss equaling 412 N or 34% of initial body weight reduced maximum knee compressive force by 824 N or 67% of initial body weight when walking at the controlled velocity. These changes represent a 2:1 reduction in knee force relative to weight loss when walking velocity is constrained to the baseline value. However, behavioral adaptations including increased stride length and walking velocity in the self-selected velocity condition attenuated this effect by ∼50% leading to a 392 N or 32% initial body weight reduction in compressive force in the knee joint. Thus, unconstrained walking elicited approximately 1:1 ratio of reduction in knee force relative to weight loss and is more indicative of walking behavior than the standard velocity condition. In conclusion, massive weight loss produces dramatic reductions in knee forces during walking but when patients stride out and walk faster, these favorable reductions become substantially attenuated.

Direct Methods for Predicting Movement Biomechanics Based Upon Optimal Control Theory with Implementation in OpenSim

The aim of this study was to compare the computational performances of two direct methods for solving large-scale, nonlinear, optimal control problems in human movement. Direct shooting and direct collocation were implemented on an 8-segment, 48-muscle model of the body (24 muscles on each side) to compute the optimal control solution for maximum-height jumping. Both algorithms were executed on a freely-available musculoskeletal modeling platform called OpenSim. Direct collocation converged to essentially the same optimal solution up to 249 times faster than direct shooting when the same initial guess was assumed (3.4 h of CPU time for direct collocation vs. 35.3 days for direct shooting). The model predictions were in good agreement with the time histories of joint angles, ground reaction forces and muscle activation patterns measured for subjects jumping to their maximum achievable heights. Both methods converged to essentially the same solution when started from the same initial guess, but computation time was sensitive to the initial guess assumed. Direct collocation demonstrates exceptional computational performance and is well suited to performing predictive simulations of movement using large-scale musculoskeletal models.

Residual Elimination Algorithm Enhancements to Improve Foot Motion Tracking During Forward Dynamic Simulations of Gait

Patient-specific gait optimizations capable of predicting post-treatment changes in joint motions and loads could improve treatment design for gait-related disorders. To maximize potential clinical utility, such optimizations should utilize full-body three-dimensional patient-specific musculoskeletal models, generate dynamically consistent gait motions that reproduce pretreatment marker measurements closely, and achieve accurate foot motion tracking to permit deformable foot-ground contact modeling. This study enhances an existing residual elimination algorithm (REA) Remy, C. D., and Thelen, D. G., 2009, “Optimal Estimation of Dynamically Consistent Kinematics and Kinetics for Forward Dynamic Simulation of Gait,” ASME J. Biomech. Eng., 131(3), p. 031005) to achieve all three requirements within a single gait optimization framework. We investigated four primary enhancements to the original REA: (1) manual modification of tracked marker weights, (2) automatic modification of tracked joint acceleration curves, (3) automatic modification of algorithm feedback gains, and (4) automatic calibration of model joint and inertial parameter values. We evaluated the enhanced REA using a full-body three-dimensional dynamic skeletal model and movement data collected from a subject who performed four distinct gait patterns: walking, marching, running, and bounding. When all four enhancements were implemented together, the enhanced REA achieved dynamic consistency with lower marker tracking errors for all segments, especially the feet (mean root-mean-square (RMS) errors of 3.1 versus 18.4 mm), compared to the original REA. When the enhancements were implemented separately and in combinations, the most important one was automatic modification of tracked joint acceleration curves, while the least important enhancement was automatic modification of algorithm feedback gains. The enhanced REA provides a framework for future gait optimization studies that seek to predict subject-specific post-treatment gait patterns involving large changes in foot-ground contact patterns made possible through deformable foot-ground contact models.

Does intact limb loading differ in servicemembers with traumatic lower limb loss?

BACKGROUND

The initiation and progression of knee and hip arthritis have been related to limb loading during ambulation. Although altered gait mechanics with unilateral lower limb loss often result in larger and more prolonged forces through the intact limb, how these forces differ with traumatic limb loss and duration of ambulation have not been well described.

QUESTIONS/PURPOSES

The purpose of this study was to determine whether biomechanical variables of joint and limb loading (external adduction moments, vertical ground reaction force loading rates, and impulses) are larger in the intact limb of servicemembers with versus without unilateral lower limb loss and whether intact limb loading differs between shorter (≤ 6 months) versus longer (≥ 2 years) durations of ambulation with a prosthesis.

METHODS

A retrospective review was conducted of all clinical and research gait evaluations performed in the biomechanics laboratory at Walter Reed Army Medical Center and Walter Reed National Military Medical Center between January 2008 and December 2012. Biomechanical data meeting all inclusion and exclusion criteria were obtained for 32 individuals with unilateral transtibial limb loss, 49 with unilateral transfemoral limb loss, and 28 without limb loss. Individuals with unilateral lower limb loss were separated by their experience ambulating with a prosthesis at the time of the gait collection, ≤ 6 months or ≥ 2 years, to determine the effect of duration of ambulation with a prosthesis.

RESULTS

Intact limb mean and peak vertical ground reaction force loading rates (median [range; 95% confidence interval]) were larger for transtibial subjects with ≤ 6 months of experience ambulating with a prosthesis versus control subjects (mean: 12.13 body weight [BW]/s [4.45-16.79; 10.18-12.81] versus 9.03 BW/s [4.64-14.47; 8.26-9.74]; effect size [ES] = 0.40; p = 0.003; and peak: 17.23 BW/s [6.58-25.25; 15.46-19.01] versus 13.60 BW/s [9.82-19.51; 12.98-15.05]; ES = 0.43; p = 0.001), respectively. Intact limb mean and peak vertical ground reaction force loading rates were also larger in subjects with transfemoral limb loss with ≤ 6 months and ≥ 2 years of experience ambulating with a prosthesis versus control subjects (mean: 12.67 BW/s [5.88-18.15; 11.06-14.47] and 12.59 BW/s [8.08-17.39; 11.83-13.68] versus 9.03 BW/s [4.64-14.47; 8.26-9.74]; ES ≥ 0.53; p < 0.001; peak: 19.82 BW/s [11.93-29.43; 18.35-23.05] and 21.33 BW/s [16.68-36.69; 20.66-24.26] versus 13.60 BW/s [9.82-19.51; 12.98-15.05]; ES ≥ 0.68; p < 0.001, respectively). Similarly, intact limb vertical ground reaction force impulses (0.63 BW·s [0.53-0.81; 0.67-0.69] and 0.62 BW·s [0.55-0.74; 0.60-0.63] versus 0.57 BW·s [0.50-0.66; 0.55-0.58]; ES ≥ 0.53, p < 0.001) were also larger among both groups of transfemoral subjects versus control subjects, respectively. Limb loading variables were not statistically different between times ambulating with a prosthesis within groups with transtibial or transfemoral limb loss.

CONCLUSIONS

Larger intact limb loading in individuals with traumatic transtibial loss were only noted early in the rehabilitation process, but these variables were present early and late in the rehabilitation process for those with transfemoral limb loss. Such evidence suggests an increased risk for early onset and progression of arthritis in the intact limb, especially in those with transfemoral limb loss.

CLINICAL RELEVANCE

Interventions should focus on correcting modifiable gait mechanics associated with arthritis, particularly among individuals with transfemoral limb loss, to potentially mitigate the development and progression in this population.

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% Fmax error in the middle deltoid) to good (6.4% Fmax 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.

A comparison of muscle energy models for simulating human walking in three dimensions

The popular Hill model for muscle activation and contractile dynamics has been extended with several different formulations for predicting the metabolic energy expenditure of human muscle actions. These extended models differ considerably in their approach to computing energy expenditure, particularly in their treatment of active lengthening and eccentric work, but their predictive abilities have never been compared. In this study, we compared the predictions of five different Hill-based muscle energy models in 3D forward dynamics simulations of normal human walking. In a data-tracking simulation that minimized muscle fatigue, the energy models predicted metabolic costs that varied over a three-fold range (2.45-7.15 J/m/kg), with the distinction arising from whether or not eccentric work was subtracted from the net heat rate in the calculation of the muscle metabolic rate. In predictive simulations that optimized neuromuscular control to minimize the metabolic cost, all five models predicted similar speeds, step lengths, and stance phase durations. However, some of the models predicted a hip circumduction strategy to minimize metabolic cost, while others did not, and the accuracy of the predicted knee and ankle angles and ground reaction forces also depended on the energy model used. The results highlights the need to clarify how eccentric work should be treated when calculating muscle energy expenditure, the difficulty in predicting realistic metabolic costs in simulated walking even with a detailed 3D musculoskeletal model, the potential for using such models to predict energetically-optimal gait modifications, and the room for improvement in existing muscle energy models and locomotion simulation frameworks.