Analytical stiffness prediction method for idealized passive dynamic ankle-foot orthoses under standardized bench test conditions

Abstract

Passive dynamic ankle-foot orthoses (PD-AFOs) are used to stabilize the foot and reduce muscle load in patients with neuromuscular impairments. A PD-AFO is characterized by its stiffness - the relationship between its resistive torque and its deflection angle. AFO stiffness plays a decisive role in the quality of patient care. To date, only a few approaches for predicting the stiffness of non-experimental and non-articulated PD-AFOs prior to manufacturing can be found in the literature. All these approaches use finite element analysis. Therefore, the objective of this work was to develop and evaluate a simplified analytical method for predicting the stiffness of idealized PD-AFOs on a standardized test bench prior to manufacture, providing an alternative to finite element analysis. This is particularly relevant in the context of additive manufacturing, where geometry can be freely adapted. The proposed calculation method is based on Castigliano's energy theorem and was demonstrated for PD-AFO designs featuring posterior leaf springs or posterior struts made from plastic (3D-printed) or carbon composite. The calculations can be performed with pen and paper. Validation was performed by comparing calculated stiffness values with measurements on a test bench. On average, the method yields deviations of less than 5% between the calculated and measured stiffness values for PD-AFOs with posterior leaf springs. However, due to deformations of the test bench, the calculated results for PD-AFOs with posterior struts deviate significantly from the measured results. This can be accounted for by a simple adjustment and calibration of the model. For the calibrated model, the calculated values deviate by less than 15% on average from the measured values. This simplified analytical approach offers a practical tool for designers to estimate PD-AFO stiffness during the development phase, enabling stiffness prediction prior to manufacture and thereby supporting patient-specific design decisions.