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Research Papers

Evaluating the Effects of Ankle-Foot Orthosis Mechanical Property Assumptions on Gait Simulation Muscle Force Results

[+] Author and Article Information
Amy K. Hegarty, Anthony J. Petrella

Department of Mechanical Engineering,
Colorado School of Mines,
Golden, CO 80401

Max J. Kurz

Department of Physical Therapy,
Munroe-Meyer Institute for Genetics
and Rehabilitation,
University of Nebraska Medical Center,
Omaha, NE 68198

Anne K. Silverman

Department of Mechanical Engineering,
Colorado School of Mines,
1500 Illinois Street,
Golden, CO 80401
e-mail: asilverm@mines.edu

1Corresponding author.

Manuscript received July 21, 2016; final manuscript received November 21, 2016; published online January 23, 2017. Assoc. Editor: Tammy L. Haut Donahue.

J Biomech Eng 139(3), 031009 (Jan 23, 2017) (8 pages) Paper No: BIO-16-1308; doi: 10.1115/1.4035472 History: Received July 21, 2016; Revised November 21, 2016

Musculoskeletal modeling and simulation techniques have been used to gain insights into movement disabilities for many populations, such as ambulatory children with cerebral palsy (CP). The individuals who can benefit from these techniques are often limited to those who can walk without assistive devices, due to challenges in accurately modeling these devices. Specifically, many children with CP require the use of ankle-foot orthoses (AFOs) to improve their walking ability, and modeling these devices is important to understand their role in walking mechanics. The purpose of this study was to quantify the effects of AFO mechanical property assumptions, including rotational stiffness, damping, and equilibrium angle of the ankle and subtalar joints, on the estimation of lower-limb muscle forces during stance for children with CP. We analyzed two walking gait cycles for two children with CP while they were wearing their own prescribed AFOs. We generated 1000-trial Monte Carlo simulations for each of the walking gait cycles, resulting in a total of 4000 walking simulations. We found that AFO mechanical property assumptions influenced the force estimates for all the muscles in the model, with the ankle muscles having the largest resulting variability. Muscle forces were most sensitive to assumptions of AFO ankle and subtalar stiffness, which should therefore be measured when possible. Muscle force estimates were less sensitive to estimates of damping and equilibrium angle. When stiffness measurements are not available, limitations on the accuracy of muscle force estimates for all the muscles in the model, especially the ankle muscles, should be acknowledged.

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Figures

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Fig. 3

Average coefficient of variation for muscle force estimates developed from the Monte Carlo simulations. The coefficient of variation was averaged across both legs, both trials, and both subjects, generated by individual Monte Carlo simulations.

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Fig. 4

Average (absolute value) sensitivity factor for AFO model input parameters across all the muscles for each walking trial. High sensitivity factors indicate greater influence on output metrics for an individual input parameter. Average sensitivity factors were averaged across the range of possible output values for each muscle force estimate, across both legs within each walking trial, and across walking trials for both subjects.

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Fig. 5

Ankle dorsiflexion stiffness sensitivity factors for simulation muscle force estimates. A summary of the response of each muscle, for each child and trial, is shown. Sensitivity factors are averaged across both legs for each trial. The sensitivity value for 5% of the outcome distribution (left arrow), 50% of the outcome distribution (median, square), and 95% of the outcome distribution (right arrow) is indicated.

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Fig. 8

Ankle equilibrium angle sensitivity factors for simulation muscle force estimates. The response of each muscle, for each child and trial, is shown. Sensitivity factors are averaged across both legs for each trial. The sensitivity value for 5% of the outcome distribution (left arrow), 50% of the outcome distribution (median, square), and 95% of the outcome distribution (right arrow) is indicated.

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Fig. 6

Subtalar inversion stiffness sensitivity factors for simulation muscle force estimates. The response of each muscle, for each child and trial, is shown. Sensitivity factors are averaged across both legs for each trial. The sensitivity value for 5% of the outcome distribution (left arrow), 50% of the outcome distribution (median, square), and 95% of the outcome distribution (right arrow) is indicated.

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Fig. 7

Subtalar eversion stiffness sensitivity factors for simulation muscle force estimates. The response of each muscle, for each child and trial, is shown. Sensitivity factors are averaged across both legs for each trial. The sensitivity value for 5% of the outcome distribution (left arrow), 50% of the outcome distribution (median, square), and 95% of the outcome distribution (right arrow) is indicated.

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Fig. 2

Methodological diagram for the generation of each Monte Carlo simulation. Eight input parameters including ankle/subtalar joint unidirectional stiffness, damping, and equilibrium angle, defined as random variables, were described by predetermined distributions (a). Values generated from these distributions were used as inputs into the ankle-foot orthosis model to generate an equation for the external torque applied at the ankle and subtalar joints (b). The AFO torque model, perturbed by the random inputs, was applied within a standard musculoskeletal walking simulation for a single gait cycle (c). Muscle force estimates for the simulated gait cycle were recorded, and the average muscle force during stance was calculated (d). This process was repeated 1000 times to generate a distribution of possible muscle force values ((e) and (f)). The cumulative distribution function for each lower-limb muscle was used to calculate the muscles' coefficients of variation and probabilistic sensitivity factors (f).

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Fig. 1

AFO model generated within the generic musculoskeletal model used for each child within the simulation framework. AFO torque development for motion at the ankle is shown for both plantarflexion torque (left) and dorsiflexion torque (right). Unidirectional stiffness terms dependent on the ankle position are shown as dorsiflexion stiffness (left) and plantarflexion stiffness (right).

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