Maintenance of muscle strength retains a normal metabolic cost in simulated walking after transtibial limb loss

Increasing midtarsal joint stiffness reduces triceps surae metabolic costs in walking simulations but has little effect on total stance limb metabolic cost

The human foot's arch is thought to be beneficial for efficient gait. This study addresses the extent to which arch stiffness changes alter the metabolic energy requirements of human gait. Computational musculoskeletal simulations of steady state walking using direct collocation were performed. Across a range of foot arch stiffnesses, the metabolic cost of transport decreased by less than 1% with increasing foot arch stiffness. Increasing arch stiffness increased the metabolic efficiency of the triceps surae during push-off, but these changes were almost entirely offset by other muscle groups consuming more energy with increasing foot arch stiffness.

Transfemoral limb loss modestly increases the metabolic cost of optimal control simulations of walking

Background

In transtibial limb loss, computer simulations suggest that the maintenance of muscle strength between pre- and post-limb loss can maintain the pre-limb loss metabolic cost. These results are consistent with comparable costs found experimentally in select cases of high functioning military service members with transtibial limb loss. It is unlikely that similar results would be found with transfemoral limb loss, although the theoretical limits are not known. Here we performed optimal control simulations of walking with and without an above-knee prosthesis to determine if transfemoral limb loss per se increases the metabolic cost of walking.

Methods

OpenSim Moco was used to generate optimal control simulations of walking in 15 virtual "subjects" that minimized the weighted sum of (i) deviations from average able-bodied gait mechanics and (ii) the gross metabolic cost of walking, pre-limb loss in models with two intact biological limbs, and post-limb loss with one of the limbs replaced by a prosthetic knee and foot. No other changes were made to the model. Metabolic cost was compared between pre- and post-limb loss simulations in paired t-tests.

Results

Metabolic cost post-limb loss increased by 0.7-9.3% (p < 0.01) depending on whether cost was scaled by total body mass or biological body mass and on whether the prosthetic knee was passive or non-passive.

Conclusions

Given that the post-limb loss model had numerous features that predisposed it to low metabolic cost, these results suggest transfemoral limb loss per se increases the metabolic cost of walking. However, the large differences above able-bodied peers of ∼20-45% in most gait analysis experiments may be avoidable, even when minimizing deviations from able-bodied gait mechanics. Portions of this text were previously published as part of a preprint (https://www.biorxiv.org/content/10.1101/2023.06.26.546515v2.full.pdf).

Walking speeds are lower for short distance and turning locomotion: Experiments and modeling in low-cost prosthesis users

Preferred walking speed is a widely-used performance measure for people with mobility issues, but is usually measured in straight line walking for fixed distances or durations, and without explicitly accounting for turning. However, daily walking involves walking for bouts of different distances and walking with turning, with prior studies showing that short bouts with at most 10 steps could be 40% of all bouts and turning steps could be 8-50% of all steps. Here, we studied walking in a straight line for short distances (4 m to 23 m) and walking in circles (1 m to 3 m turning radii) in people with transtibial amputation or transfemoral amputation using a passive ankle-foot prosthesis (Jaipur Foot). We found that the study participants' preferred walking speeds are lower for shorter straight-line walking distances and lower for circles of smaller radii, which is analogous to earlier results in subjects without amputation. Using inverse optimization, we estimated the cost of changing speeds and turning such that the observed preferred walking speeds in our experiments minimizes the total cost of walking. The inferred costs of changing speeds and turning were larger for subjects with amputation compared to subjects without amputation in a previous study, specifically, being 4x to 8x larger for the turning cost and being highest for subjects with transfemoral amputation. Such high costs inferred by inverse optimization could potentially include non-energetic costs such as due to joint or interfacial stress or stability concerns, as inverse optimization cannot distinguish such terms from true metabolic cost. These experimental findings and models capturing the experimental trends could inform prosthesis design and rehabilitation therapy to better assist changing speeds and turning tasks. Further, measuring the preferred speed for a range of distances and radii could be a more comprehensive subject-specific measure of walking performance than commonly used straight line walking metrics.

After scaling to body size hip strength of the residual limb exceeds that of the intact limb among unilateral lower limb prosthesis users

BACKGROUND

Hip muscles play a prominent role in compensating for the loss of ankle and/or knee muscle function after lower limb amputation. Despite contributions to walking and balance, there is no consensus regarding hip strength deficits in lower limb prosthesis (LLP) users. Identifying patterns of hip muscle weakness in LLP users may increase the specificity of physical therapy interventions (i.e., which muscle group(s) to target), and expedite the search for modifiable factors associated with deficits in hip muscle function among LLP users. The purpose of this study was to test whether hip strength, estimated by maximum voluntary isometric peak torque, differed between the residual and intact limbs of LLP users, and age- and gender-matched controls.

METHODS

Twenty-eight LLP users (14 transtibial, 14 transfemoral, 7 dysvascular, 13.5 years since amputation), and 28 age- and gender-matched controls participated in a cross-sectional study. Maximum voluntary isometric hip extension, flexion, abduction, and adduction torque were measured with a motorized dynamometer. Participants completed 15 five-second trials with 10-s rest between trials. Peak isometric hip torque was normalized to body mass × thigh length. A 2-way mixed-ANOVA with a between-subject factor of leg (intact, residual, control) and a within-subject factor of muscle group (extensors, flexors, abductors, adductors) tested for differences in strength among combinations of leg and muscle group (α = 0.05). Multiple comparisons were adjusted using Tukey's Honest-Difference.

RESULTS

A significant 2-way interaction between leg and muscle group indicated normalized peak torque differed among combinations of muscle group and leg (p < 0.001). A significant simple main effect of leg (p = 0.001) indicated peak torque differed between two or more legs per muscle group. Post-hoc comparisons revealed hip extensor, flexor, and abductor peak torque was not significantly different between the residual and control legs (p ≥ 0.067) but torques in both legs were significantly greater than in the intact leg (p < 0.001). Peak hip abductor torque was significantly greater in the control and residual legs than the intact leg (p < 0.001), and significantly greater in the residual than control leg (p < 0.001).

CONCLUSIONS

Our results suggest that it is the intact, rather than the residual limb, that is weaker. These findings may be due to methodological choices (e.g., normalization), or biomechanical demands placed on residual limb hip muscles. Further research is warranted to both confirm, expand upon, and elucidate possible mechanisms for the present findings; and clarify contributions of intact and residual limb hip muscles to walking and balance in LLP users.

CLINICAL TRIAL REGISTRATION

N/A.

Acquisition of bipedal locomotion in a neuromusculoskeletal model with unilateral transtibial amputation

Adaptive locomotion is an essential behavior for animals to survive. The central pattern generator in the spinal cord is responsible for the basic rhythm of locomotion through sensory feedback coordination, resulting in energy-efficient locomotor patterns. Individuals with symmetrical body proportions exhibit an energy-efficient symmetrical gait on flat ground. In contrast, individuals with lower limb amputation, who have morphologically asymmetrical body proportions, exhibit asymmetrical gait patterns. However, it remains unclear how the nervous system adjusts the control of the lower limbs. Thus, in this study, we investigated how individuals with unilateral transtibial amputation control their left and right lower limbs during locomotion using a two-dimensional neuromusculoskeletal model. The model included a musculoskeletal model with 7 segments and 18 muscles, as well as a neural model with a central pattern generator and sensory feedback systems. Specifically, we examined whether individuals with unilateral transtibial amputation acquire prosthetic gait through a symmetric or asymmetric feedback control for the left and right lower limbs. After acquiring locomotion, the metabolic costs of transport and the symmetry of the spatiotemporal gait factors were evaluated. Regarding the metabolic costs of transportation, the symmetric control model showed values approximately twice those of the asymmetric control model, whereas both scenarios showed asymmetry of spatiotemporal gait patterns. Our results suggest that individuals with unilateral transtibial amputation can reacquire locomotion by modifying sensory feedback parameters. In particular, the model reacquired reasonable locomotion for activities of daily living by re-searching asymmetric feedback parameters for each lower limb. These results could provide insight into effective gait assessment and rehabilitation methods to reacquire locomotion in individuals with unilateral transtibial amputation.

Residual limb strength and functional performance measures in individuals with unilateral transtibial amputation

BACKGROUND

Individuals with lower limb amputation exhibit lower residual limb strength compared to their sound limb. Deficits in residual limb knee flexion and extension strength may impact functional performance during tasks relevant to daily living.

RESEARCH QUESTION

Does knee flexor and extensor strength in the residual limb impact functional outcome measures, such as walking energetics and performance metrics, in individuals with unilateral transtibial amputation?

METHODS

Fourteen individuals with traumatic unilateral transtibial amputation were recruited for this observational study. Participants completed metabolic testing at three standardized speeds based on leg length, as well maximum isokinetic knee flexion and extension strength for both residual and sound limbs. Participants also completed a series of functional outcome tests, including a two-minute walk test, timed stair ascent test, and four-square step test. Walking energetics (metabolic cost, heart rate, and rating of perceived exertion) and performance metrics were compared to percent deficit of residual limb to sound limb knee flexion and extension muscle strength. A linear regression assessed significant relationships (p < 0.05).

RESULTS

A significant relationship was observed between percent deficit of knee extension strength and heart rate (p = 0.024) at a fast walking speed. Additionally, percent deficit knee flexion strength related to rating of perceived exertion at slow and moderate walking speeds (p = 0.038, p = 0.024). Percent deficit knee extension strength related to two-minute walk time performance (p = 0.035) and percent deficit knee flexion strength related to timed stair ascent time (p = 0.025).

SIGNIFICANCE

These findings suggest the importance of strength retention of the residual limb knee flexion and extension musculature to improve certain functional outcomes in individuals with unilateral transtibial amputation.

A Computational Gait Model With a Below-Knee Amputation and a Semi-Active Variable-Stiffness Foot Prosthesis

INTRODUCTION

Simulations based on computational musculoskeletal models are powerful tools for evaluating the effects of potential biomechanical interventions, such as implementing a novel prosthesis. However, the utility of simulations to evaluate the effects of varied prosthesis design parameters on gait mechanics has not been fully realized due to the lack of a readily-available limb loss-specific gait model and methods for efficiently modeling the energy storage and return dynamics of passive foot prostheses. The purpose of this study was to develop and validate a forward simulation-capable gait model with lower-limb loss and a semi-active variable-stiffness foot (VSF) prosthesis.

METHODS

A seven-segment 28-DoF gait model was developed and forward kinematics simulations, in which experimentally observed joint kinematics were applied and the resulting contact forces under the prosthesis evolved accordingly, were computed for four subjects with unilateral below-knee amputation walking with a VSF.

RESULTS

Model-predicted resultant ground reaction force (GRFR) matched well under trial-specific optimized parameter conditions (mean R2: 0.97, RMSE: 7.7% body weight (BW)) and unoptimized (subject-specific, but not trial-specific) parameter conditions (mean R2: 0.93, RMSE: 12% BW). Simulated anterior-posterior center of pressure demonstrated a mean R2 = 0.64 and RMSE = 14% foot length. Simulated kinematics remained consistent with input data (0.23 deg RMSE, R2 > 0.99) for all conditions.

CONCLUSIONS

These methods may be useful for simulating gait among individuals with lower-limb loss and predicting GRFR arising from gait with novel VSF prostheses. Such data are useful to optimize prosthesis design parameters on a user-specific basis.

Transtibial limb loss does not increase metabolic cost in three-dimensional computer simulations of human walking

Loss of a lower limb below the knee, i.e., transtibial limb loss, and subsequently walking with a prosthesis, is generally thought to increase the metabolic cost of walking vs. able-bodied controls. However, high-functioning individuals with limb loss such as military service members often walk with the same metabolic cost as controls. Here we used a 3-D computer model and optimal control simulation approach to test the hypothesis that transtibial limb loss in and of itself causes an increase in metabolic cost of walking. We first generated N = 36 simulations of walking at 1.45 m/s using a “pre-limb loss” model, with two intact biological legs, that minimized deviations from able-bodied experimental walking mechanics with minimum muscular effort. We then repeated these simulations using a “post-limb loss” model, with the right leg’s ankle muscles and joints replaced with a simple model of a passive transtibial prosthesis. No other changes were made to the post-limb loss model’s remaining muscles or musculoskeletal parameters compared to the pre-limb loss case. Post-limb loss, the gait deviations on average increased by only 0.17 standard deviations from the experimental means, and metabolic cost did not increase (3.58 ± 0.10 J/m/kg pre-limb loss vs. 3.59 ± 0.12 J/m/kg post-limb loss, p = 0.65). The results suggest that transtibial limb loss does not directly lead to an increase in metabolic cost, even when deviations from able-bodied gait mechanics are minimized. High metabolic costs observed in individuals with transtibial limb loss may be due to secondary changes in strength or general fitness after limb loss, modifiable prosthesis issues, or to prioritization of factors that affect locomotor control other than gait deviations and muscular effort.

A Reduced-Order Computational Model of a Semi-Active Variable-Stiffness Foot Prosthesis

Passive energy storage and return (ESR) feet are current performance standard in lower limb prostheses. A recently developed semi-active variable-stiffness foot (VSF) prosthesis balances the simplicity of a passive ESR device with the adaptability of a powered design. The purpose of this study was to model and simulate the ESR properties of the VSF prosthesis. The ESR properties of the VSF were modeled as a lumped parameter overhung beam. The overhung length is variable, allowing the model to exhibit variable ESR stiffness. Foot-ground contact was modeled using sphere-to-plane contact models. Contact parameters were optimized to represent the geometry and dynamics of the VSF and its foam base. Static compression tests and gait were simulated. Simulation outcomes were compared to corresponding experimental data. Stiffness of the model matched that of the physical VSF (R2: 0.98, root-mean-squared error (RMSE): 1.37 N/mm). Model-predicted resultant ground reaction force (GRFR) matched well under optimized parameter conditions (R2: 0.98, RMSE: 5.3% body weight,) and unoptimized parameter conditions (R2: 0.90, mean RMSE: 13% body weight). Anterior-posterior center of pressure matched well with R2 > 0.94 and RMSE < 9.5% foot length in all conditions. The ESR properties of the VSF were accurately simulated under benchtop testing and dynamic gait conditions. These methods may be useful for predicting GRFR arising from gait with novel prostheses. Such data are useful to optimize prosthesis design parameters on a user-specific basis.

Knee extensor power predicts six-minute walk test performance in people with transfemoral amputations

BACKGROUND

Lower-limb amputees have increased metabolic costs during walking that may be mitigated by maintaining quadriceps strength and power following amputation. However, there are no current studies investigating the relationship between thigh strength and walking performance in individuals with transfemoral amputation.

OBJECTIVE

To quantify the relationship between intact limb quadriceps strength in transfemoral amputees and six-minute walk test (6MWT) performance.

DESIGN

Descriptive laboratory study.

SETTING

Laboratory.

PARTICIPANTS

Eleven participants with unilateral transfemoral amputations from trauma or osteosarcoma (4 women/7 men, 46.21 ± 12.68 years old, 28.24 ± 20.57 years following amputation).

INTERVENTIONS

Strength and power testing on the intact limb followed by 6MWT with a flowmeter to measure oxygen uptake (VO₂ ).

MAIN OUTCOME MEASURES

Strength included mass-normalized peak torque, average torque, and average power. 6MWT measures included total distance traveled and VO₂ normalized to distance and mass. Significant correlations (P ≤ .05) were retained for a regression analysis.

RESULTS

Peak isokinetic knee extensor torque was correlated with total VO₂ (r = -.60, P = .05) and distance traveled (r = .84, P = .001). Average isokinetic knee extensor torque was correlated with total VO₂ (r = -.61, P = .046) and distance traveled (r = .85, P = .001). Average knee extensor power was correlated with total VO₂ (r = -.67, P = .026) and distance traveled (r = .88, P < .001). Peak isometric knee extensor torque was correlated with distance traveled (r = .69, P = .019). Average power explained 77.2% of the variance in distance traveled during the 6MWT (P < .001) and average power explained 44.2% of the variance in total VO₂ during the 6MWT (P = .026).

CONCLUSIONS

Knee extensor strength was correlated with performance on the 6MWT in individuals with unilateral transfemoral amputation. The strongest relationship was between isokinetic quadriceps power and distance traveled, which suggests that developing quadriceps power in the intact limb following amputation may be an important factor to reduce metabolic cost of walking and support a return to an active lifestyle.

Video Game-Based Rehabilitation Approach for Individuals Who Have Undergone Upper Limb Amputation: Case-Control Study

Background

Brain plasticity is an important factor in prosthesis usage. This plasticity helps with brain adaptation to learn new movement and coordination patterns needed to control a prosthetic hand. It can be achieved through repetitive muscle training that is usually very exhausting and often results in considerable reduction in patient motivation. Previous studies have shown that a playful concept in rehabilitation can increase patient engagement and perseverance.

Objective

This study investigated whether the inclusion of video games in the upper limb amputee rehabilitation protocol could have a beneficial impact for muscle preparation, coordination, and patient motivation among individuals who have undergone transradial upper limb amputation.

Methods

Ten participants, including five amputee participants and five able-bodied participants, were enrolled in 10 1-hour sessions within a 4-week rehabilitation program. In order to investigate the effects of the rehabilitation protocol used in this study, virtual reality box and block tests and electromyography (EMG) assessments were performed. Maximum voluntary contraction was measured before, immediately after, and 2 days after interacting with four different EMG-controlled video games. Participant motivation was assessed with the Intrinsic Motivation Inventory (IMI) questionnaire and user evaluation survey.

Results

Survey analysis showed that muscle strength and coordination increased at the end of training for all the participants. The results of Pearson correlation analysis indicated that there was a significant positive association between the training period and the box and block test score (r₈=0.95, P<.001). The maximum voluntary contraction increment was high before training (6.8%) and in the follow-up session (7.1%), but was very small (2.1%) shortly after the training was conducted. The IMI assessment showed high scores for the subscales of interest, perceived competence, choice, and usefulness, but low scores for pressure and tension.

Conclusions

This study demonstrated that video games enhance motivation and adherence in an upper limb amputee rehabilitation program. The use of video games could be seen as a complementary approach for physical training in upper limb amputee rehabilitation.

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.

Strength deficits in lower limb prosthesis users: A scoping review

BACKGROUND

Strength deficits may play a central role in the severity of balance, mobility, and endurance impairments in lower limb prosthesis users. A body of literature detailing the scope and specifics of muscle weakness in lower limb prosthesis users is emerging, but has yet to be summarized. A synopsis of strength deficits, and their impact on functional abilities in lower limb prosthesis users, may inform rehabilitation and research needs.

OBJECTIVES

Synthesize reported strength deficits in lower limb prosthesis users, and discuss possible causes, consequences, and solutions.

STUDY DESIGN

Scoping review.

METHODS

A search of biomedical databases was performed, and inclusion/exclusion criteria were applied to identify publications relevant to the purpose of the review.

RESULTS

In all, 377 publications were identified, of which 12 met the inclusion/exclusion criteria. When compared with the controls and the intact limb, the primary strength outcome, peak torque, was lower in transtibial residual limb knee flexors and extensors, as well as transfemoral residual limb hip muscles.

CONCLUSIONS

The reviewed studies provide evidence of strength deficits in lower limb prosthesis users. These deficits appear to be consequential, as they may contribute to balance, mobility, and endurance impairments. Additional research exploring alternative strength metrics, clinical tests, and causal links to functional impairments is required.

CLINICAL RELEVANCE

Evidence of muscle weakness among lower limb prosthesis users, and its influence on balance, mobility, and endurance, suggests that greater clinical attention and scientific inquiry into physical conditioning of lower limb prosthesis users is merited and required.

Video Game–Based Rehabilitation Approach for Individuals Who Have Undergone Upper Limb Amputation: Case-Control Study (Preprint).. [DOI: 10.2196/preprints.17017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

BACKGROUND

Brain plasticity is an important factor in prosthesis usage. This plasticity helps with brain adaptation to learn new movement and coordination patterns needed to control a prosthetic hand. It can be achieved through repetitive muscle training that is usually very exhausting and often results in considerable reduction in patient motivation. Previous studies have shown that a playful concept in rehabilitation can increase patient engagement and perseverance.

OBJECTIVE

This study investigated whether the inclusion of video games in the upper limb amputee rehabilitation protocol could have a beneficial impact for muscle preparation, coordination, and patient motivation among individuals who have undergone transradial upper limb amputation.

METHODS

Ten participants, including five amputee participants and five able-bodied participants, were enrolled in 10 1-hour sessions within a 4-week rehabilitation program. In order to investigate the effects of the rehabilitation protocol used in this study, virtual reality box and block tests and electromyography (EMG) assessments were performed. Maximum voluntary contraction was measured before, immediately after, and 2 days after interacting with four different EMG-controlled video games. Participant motivation was assessed with the Intrinsic Motivation Inventory (IMI) questionnaire and user evaluation survey.

RESULTS

Survey analysis showed that muscle strength and coordination increased at the end of training for all the participants. The results of Pearson correlation analysis indicated that there was a significant positive association between the training period and the box and block test score (<i>r</i>₈=0.95, <i>P</i>&lt;.001). The maximum voluntary contraction increment was high before training (6.8%) and in the follow-up session (7.1%), but was very small (2.1%) shortly after the training was conducted. The IMI assessment showed high scores for the subscales of interest, perceived competence, choice, and usefulness, but low scores for pressure and tension.

CONCLUSIONS

This study demonstrated that video games enhance motivation and adherence in an upper limb amputee rehabilitation program. The use of video games could be seen as a complementary approach for physical training in upper limb amputee rehabilitation.

Rapid predictive simulations with complex musculoskeletal models suggest that diverse healthy and pathological human gaits can emerge from similar control strategies

Physics-based predictive simulations of human movement have the potential to support personalized medicine, but large computational costs and difficulties to model control strategies have limited their use. We have developed a computationally efficient optimal control framework to predict human gaits based on optimization of a performance criterion without relying on experimental data. The framework generates three-dimensional muscle-driven simulations in 36 min on average—more than 20 times faster than existing simulations—by using direct collocation, implicit differential equations and algorithmic differentiation. Using this framework, we identified a multi-objective performance criterion combining energy and effort considerations that produces physiologically realistic walking gaits. The same criterion also predicted the walk-to-run transition and clinical gait deficiencies caused by muscle weakness and prosthesis use, suggesting that diverse healthy and pathological gaits can emerge from the same control strategy. The ability to predict the mechanics and energetics of a broad range of gaits with complex three-dimensional musculoskeletal models will allow testing novel hypotheses about gait control and hasten the development of optimal treatments for neuro-musculoskeletal disorders.

Dynamic optimization of Gait with a Generalized Lower-Limb Prosthesis Model

Predictive simulation of gait is a promising tool for robotic lower limb prosthesis design, but has been limited in its application to models of existing design types. We propose a modeling approach to find optimal prosthesis dynamics in gait simulations without constraining the prosthesis to follow kinematics allowed by a specific joint mechanism. To accomplish this, we render a transtibial prosthetic device as the composition of its resultant forces and moments as they act upon the prosthetic foot and socket and allow3 degree-of-freedom planar motion. The model is implemented into a human musculoskeletal model and used to solve dynamic optimizations of muscle and prosthesis controls to minimize muscle effort and loading on the residual limb during walking. The emphasis on muscle effort vs. limb loading is varied in the minimization objective and the resulting optimal prosthesis dynamics are compared. We found that muscle effort and socket loading measures were reduced for our prosthesis model compared to a revolute joint prosthesis model. We interpret large displacements in the linear axes to transfer energy to the plantarflexion action before toe-off and reduce loading at the socket-limb interface. Our results suggest this approach could assist in the design of non-biomimetic prostheses but requires experimental validation to assess our modeling assumptions, as well as progress toward increased fidelity of predictive simulation approaches more generally.

Optimal control simulation predicts effects of midsole materials on energy cost of running

Testing sports equipment with athletes is costly, time-consuming, hazardous and sometimes impracticable. We propose a method for virtual testing of running shoes and predict how midsoles made of BOOST^TM affect energy cost of running. We contribute a visco-elastic contact model and identified model parameters based on load-displacement measurements. We propose a virtual study using optimal control simulation of musculoskeletal models. The predicted reduction in energy cost of ∼1% for BOOST^TM in comparison to conventional materials is consistent with experimental studies. This indicates that the proposed method is capable of replacing experimental studies in the future.