The interaction between muscle pathophysiology, body mass, walking speed and ankle foot orthosis stiffness on walking energy cost: a predictive simulation study

BACKGROUND

The stiffness of a dorsal leaf AFO that minimizes walking energy cost in people with plantarflexor weakness varies between individuals. Using predictive simulations, we studied the effects of plantarflexor weakness, passive plantarflexor stiffness, body mass, and walking speed on the optimal AFO stiffness for energy cost reduction.

METHODS

We employed a planar, nine degrees-of-freedom musculoskeletal model, in which for validation maximal strength of the plantar flexors was reduced by 80%. Walking simulations, driven by minimizing a comprehensive cost function of which energy cost was the main contributor, were generated using a reflex-based controller. Simulations of walking without and with an AFO with stiffnesses between 0.9 and 8.7 Nm/degree were generated. After validation against experimental data of 11 people with plantarflexor weakness using the Root-mean-square error (RMSE), we systematically changed plantarflexor weakness (range 40-90% weakness), passive plantarflexor stiffness (range: 20-200% of normal), body mass (+ 30%) and walking speed (range: 0.8-1.2 m/s) in our baseline model to evaluate their effect on the optimal AFO stiffness for energy cost minimization.

RESULTS

Our simulations had a RMSE < 2 for all lower limb joint kinetics and kinematics except the knee and hip power for walking without AFO. When systematically varying model parameters, more severe plantarflexor weakness, lower passive plantarflexor stiffness, higher body mass and walking speed increased the optimal AFO stiffness for energy cost minimization, with the largest effects for severity of plantarflexor weakness.

CONCLUSIONS

Our forward simulations demonstrate that in individuals with bilateral plantarflexor the necessary AFO stiffness for walking energy cost minimization is largely affected by severity of plantarflexor weakness, while variation in walking speed, passive muscle stiffness and body mass influence the optimal stiffness to a lesser extent. That gait deviations without AFO are overestimated may have exaggerated the required support of the AFO to minimize walking energy cost. Future research should focus on improving predictive simulations in order to implement personalized predictions in usual care. Trial Registration Nederlands Trial Register 5170. Registration date: May 7th 2015.  http://www.trialregister.nl/trialreg/admin/rctview.asp?TC=5170.

Interacting effects of AFO stiffness, neutral angle and footplate stiffness on gait in case of plantarflexor weakness: A predictive simulation study

To maximize effects of dorsal leaf ankle foot orthoses (AFOs) on gait in people with bilateral plantarflexor weakness, the AFO properties should be matched to the individual. However, how AFO properties interact regarding their effect on gait function is unknown. We studied the interaction of AFO bending stiffness with neutral angle and footplate stiffness on the effect of bending stiffness on walking energy cost, gait kinematics and kinetics in people with plantarflexor weakness by employing predictive simulations. Our simulation framework consisted of a planar 11 degrees of freedom model, containing 11 muscles activated by a reflex-based neuromuscular controller. The controller was optimized by a comprehensive cost function, predominantly minimizing walking energy cost. The AFO bending and footplate stiffness were modelled as torsional springs around the ankle and metatarsal joint. The neutral angle of the AFO was defined as the angle in the sagittal plane at which the moment of the ankle torsional spring was zero. Simulations without AFO and with AFO for 9 bending stiffnesses (0-14 Nm/degree), 3 neutral angles (0-3-6 degrees dorsiflexion) and 3 footplate stiffnesses (0-0.5-2.0 Nm/degree) were performed. When changing neutral angle towards dorsiflexion, a higher AFO bending stiffness minimized energy cost of walking and normalized joint kinematics and kinetics. Footplate stiffness mainly affected MTP joint kinematics and kinetics, while no systematic and only marginal effects on energy cost were found. In conclusion, the interaction of the AFO bending stiffness and neutral angle in bilateral plantarflexor weakness, suggests that these should both be considered together when matching AFO properties to the individual patient.

Validation of forward simulations to predict the effects of bilateral plantarflexor weakness on gait

BACKGROUND

Bilateral plantarflexor muscle weakness is a common impairment in many neuromuscular diseases. However, the way in which severity of plantarflexor weakness affects gait in terms of walking energy cost and speed is not fully understood. Predictive simulations are an attractive alternative to human experiments as simulations allow systematic alterations in muscle weakness. However, simulations of pathological gait have not yet been validated against experimental data, limiting their applicability.

RESEARCH QUESTION

Our first aim was to validate a predictive simulation framework for walking with bilateral plantarflexor weakness by comparing predicted gait against experimental gait data of patients with bilateral plantarflexor weakness. Secondly, we aimed to evaluate how incremental levels of bilateral plantarflexor weakness affect gait.

METHODS

We used a planar musculoskeletal model with 9 degrees of freedom and 9 Hill-type muscle-tendon units per leg. A state-dependent reflex-based controller optimized for a function combining energy cost, muscle activation squared and head acceleration was used to simulate gait. For validation, strength of the plantarflexors was reduced by 80 % and simulated gait compared with experimental data of 16 subjects with bilateral plantarflexor weakness. Subsequently, strength of the plantarflexors was reduced stepwise to evaluate its effect on gait kinematics and kinetics, walking energy cost and speed.

RESULTS

Simulations with 80 % weakness matched well with experimental hip and ankle kinematics and kinetics (R > 0.64), but less for knee kinetics (R < 0.55). With incremental strength reduction, especially beyond a reduction of 60 %, the maximal ankle moment and power decreased. Walking energy cost and speed showed a strong quadratic relation (R²>0.82) with plantarflexor strength.

SIGNIFICANCE

Our simulation framework predicted most gait changes due to bilateral plantarflexor weakness, and indicates that pathological gait features emerge especially when bilateral plantarflexor weakness exceeds 60 %. Our framework may support future research into the effect of pathologies or assistive devices on gait.

Evaluating cost function criteria in predicting healthy gait

Accurate predictive simulations of human gait rely on optimisation criteria to solve the system's redundancy. Defining such criteria is challenging, as the objectives driving the optimization of human gait are unclear. This study evaluated how minimising various physiologically-based criteria (i.e., cost of transport, muscle activity, head stability, foot-ground impact, and knee ligament use) affects the predicted gait, and developed and evaluated a combined, weighted cost function tuned to predict healthy gait. A generic planar musculoskeletal model with 18 Hill-type muscles was actuated using a reflex-based, parameterized controller. First, the criteria were applied into the base simulation framework separately. The gait pattern predicted by minimising each criterion was compared to experimental data of healthy gait using coefficients of determination (R²) and root mean square errors (RMSE) averaged over all biomechanical variables. Second, the optimal weighted combined cost function was created through stepwise addition of the criteria. Third, performance of the resulting combined cost function was evaluated by comparing the predicted gait to a simulation that was optimised solely to track experimental data. Optimising for each of the criteria separately showed their individual contribution to distinct aspects of gait (overall R²: 0.37-0.56; RMSE: 3.47-4.63 SD). An optimally weighted combined cost function provided improved overall agreement with experimental data (overall R²: 0.72; RMSE: 2.10 SD), and its performance was close to what is maximally achievable for the underlying simulation framework. This study showed how various optimisation criteria contribute to synthesising gait and that careful weighting of them is essential in predicting healthy gait.

1H-N.m.r. study of enzymically generated wheat-endosperm arabinoxylan oligosaccharides: structures of hepta- to tetradeca-saccharides containing two or three branched xylose residues

The structures of hepta- to tetradeca-saccharides, generated by digestion of wheat-endosperm arabinoxylan with endo-(1----4)-beta-D-xylanase, and isolated by gel-permeation chromatography on Bio-Gel P-6 and high-performance anion-exchange chromatography with pulsed amperometric detection (h.p.a.e.-p.a.d.), were elucidated using monosaccharide and methylation analysis, f.a.b.-m.s., and 1H-n.m.r. spectroscopy. The structures identified had two branching elements, ----4)[alpha-L-Araf-(1----3)]-beta-D-Xylp-(1---- and/or ----4) [alpha-L-Araf-(1----2)][alpha-L-Araf-(1----3)]-beta-D-Xyl p-(1----, directly connected to each other in all four possible combinations. The h.p.a.e.-p.a.d. elution pattern showed that these combinations are not present in equal amounts. Also, compounds containing two 2,3-branched beta-D-Xylp residues separated by one or two unbranched beta-D-Xylp residues were found, and the presence of a tetradecasaccharide containing three 2,3-branched beta-D-Xylp residues was established.