Computational modelling of ankle-foot orthosis to evaluate spatially asymmetric structural stiffness: Importance of geometric nonlinearity.

An ankle-foot orthosis (AFO) constructed as a single piece of isotropic elastic material is a commonly used assistive device that provides stability to the ankle joint of patients with spastic diplegic cerebral palsy. The AFO has asymmetric stiffness that restricts plantarflexion during the swing phase while it is flexible to allow dorsiflexion during the stance phase with a large deflection, including buckling originating from geometric nonlinearity. However, its mechanical implications have not been sufficiently investigated. This study aims to develop a computational model of an AFO considering geometric nonlinearity and examine AFO stiffness asymmetry during plantarflexion and dorsiflexion using physical experiments. Three-dimensional AFO mechanics with geometric nonlinearities were expressed using corotational triangle-element formulations that obeyed Kirchhoff-Love plate theory. Computational load tests for plantarflexion and dorsiflexion, using idealised AFOs with two different ankle-region designs (covering or not covering the apexes of the malleoli), showed that plantarflexion moment-ankle angle relationships were linear and dorsiflexion moment-ankle angle relationships were nonlinear; increases in dorsiflexion led to negative apparent stiffness of the AFO. Both ankle-region designs resisted both plantarflexion and dorsiflexion, and out-of-plane elastic energy was locally concentrated on the lateral side, resulting in large deflections during dorsiflexion. These findings give insight into appropriate AFO design from a mechanical viewpoint by characterising three-dimensional structural asymmetry and geometric nonlinearity.