Minimization of metabolic cost of transport predicts changes in gait mechanics over a range of ankle-foot orthosis stiffnesses in individuals with bilateral plantar flexor weakness

Abstract

Neuromuscular disorders often lead to ankle plantar flexor muscle weakness, which impairs ankle push-off power and forward propulsion during gait. To improve walking speed and reduce metabolic cost of transport (mCoT), patients with plantar flexor weakness are provided dorsal-leaf spring ankle-foot orthoses (AFOs). It is widely believed that mCoT during gait depends on the AFO stiffness and an optimal AFO stiffness that minimizes mCoT exists. The biomechanics behind why and how an optimal stiffness exists and benefits individuals with plantar flexor weakness are not well understood. We hypothesized that the AFO would reduce the required support moment and, hence, metabolic cost contributions of the ankle plantar flexor and knee extensor muscles during stance, and reduce hip flexor metabolic cost to initiate swing. To test these hypotheses, we generated neuromusculoskeletal simulations to represent gait of an individual with bilateral plantar flexor weakness wearing an AFO with varying stiffness. Predictions were based on the objective of minimizing mCoT, loading rates at impact and head accelerations at each stiffness level, and the motor patterns were determined via dynamic optimization. The predictive gait simulation results were compared to experimental data from subjects with bilateral plantar flexor weakness walking with varying AFO stiffness. Our simulations demonstrated that reductions in mCoT with increasing stiffness were attributed to reductions in quadriceps metabolic cost during midstance. Increases in mCoT above optimum stiffness were attributed to the increasing metabolic cost of both hip flexor and hamstrings muscles. The insights gained from our predictive gait simulations could inform clinicians on the prescription of personalized AFOs. With further model individualization, simulations based on mCoT minimization may sufficiently predict adaptations to an AFO in individuals with plantar flexor weakness.

Keywords: CMA-ES; ankle-foot orthosis (AFO); musculoskeletal simulation; opensim; plantar flexor weakness; predictive simulation; reflex-based neuromuscular controller; scone.

FIGURE 1

Musculoskeletal model of an individual with bilateral plantar flexor weakness equipped with AFOs. The stiffness (range 0–7 Nm/deg) of the dorsal leaf spring is modeled in OpenSim as a torsional spring between the calf-casing and footplate of each AFO (black). Contact between the foot and the ground are modeled by forces generated by compliant contact spheres (cyan).

FIGURE 2

Ankle, AFO, knee and hip angles, internal moments and powers from the predictive gait simulations. Simulation data of an individual patient (Waterval et al., 2019) model with bilateral plantar flexor muscle weakness wearing an AFO with varying stiffness levels (range 0–7 Nm/deg, colored lines). Gray curves and shading represent patient data without AFO (mean ± 1 SD) (Waterval et al., 2019). Vertical dashed line with SW text marks the beginning of swing. After initial contact, the ankle, knee and hip joints became more extended as AFO stiffness increased.

FIGURE 3

Predicted, and mean and SD of experimental slopes of peak total, biological and AFO-provided ankle joint power and internal moment in stance, peak ankle dorsiflexion angle in stance, peak knee extension angle in stance and peak internal knee flexion moment in late stance (between 35%–50% of the gait cycle). Lines were fitted to the individual experimental and predictive gait simulation data across 1–7 Nm/deg AFO stiffness levels. The bars and the error bars represent the mean and SD of the slope of the lines fitted to the individual experimental data of the 24 patients (Waterval et al., 2019). The diamond shaped markers show the slope of the lines fitted to the predictive gait simulation data. Negative and positive directions are defined the same as in Figure 2. Negative slope means change into absorption direction by ankle/AFO powers, change into internal dorsiflexion moment direction by ankle/AFO moments, change into plantarflexion angle direction by ankle angles, change into knee extension direction by knee angles, and change into knee flexion moment direction by knee moments. The slope, SD and goodness of fit (Rsq) values can be found in the Supplementary Table S1.

FIGURE 4

The mCoT in predictive gait simulation and individual experiments wearing an AFO with varying stiffness. The individual experiments included the condition without an AFO and wearing shoes for 21 subjects (Waterval et al., 2019). A quadratic curve was fitted to the data points for each subject dataset and the minimum of the fitted curve was taken for each subject as their individual minimum mCoT value which is happening at their individual optimal stiffness. The mCoT values of the subjects were shifted by their minimum mCoT value and the AFO stiffness values were shifted by the subject’s optimal stiffness value. The shifted individual experimental subject data is shown in different shades of gray. One quadratic curve was fitted to all shifted experimental subject data (dotted line), the goodness of fit is indicated by the Rsq number on the plot (Rsq = 0.634). The same was done for the predictive gait simulation results (solid line, Rsq = 0.836). Both the experimental (EXP–shaded dots) and predictive gait simulation data (SIM–open circles) show quadratic trends (Rsq >0.63).

FIGURE 5

The mean mCoT, and mean metabolic cost of the top five muscle contributors in the predictive gait simulations. Metabolic cost data for the mean was taken during one whole gait cycle as AFO stiffness was varied from 0–7 Nm/deg. Quadratic curves were fitted to the data-points and the Rsq values represent the goodness-of-fit of the curves. Values of the mean metabolic cost for the whole model and for each muscle group of the model can be found in the S2 Table.

FIGURE 6

Vasti, hamstrings, iliopsoas, soleus and gastrocnemius metabolic power from the predictive gait simulations. AFO stiffness was varied from 0 to 7 Nm/deg. Abbreviations: VAS: vasti muscle group, HAM: hamstrings muscle group, ILIO: iliopsoas muscle group, SOL: soleus muscle, GAS: gastrocnemius muscle, LR: loading response, MS: midstance, PO: push-off, SW: swing, k: AFO stiffness. The gray arrows show the change direction in metabolic cost as AFO stiffness was increased. The size of the arrows is in approximate relation to the size of the metabolic cost changes. The metabolic cost of transport values of each muscle group calculated with integration for each gait phase can be found in Supplementary Table S4.