Ankle Joint Intrinsic Dynamics is More Complex than a Mass-Spring-Damper Model

This paper describes a new small signal parametric model of ankle joint intrinsic mechanics in normal subjects. We found that intrinsic ankle mechanics is a third-order system and the second-order mass-spring-dampermodel, referred to as IBK, used by many researchers in the literature cannot adequately represent ankle dynamics at all frequencies in a number of important tasks. This was demonstrated using experimental data from five healthy subjects with no voluntary muscle contraction and at seven ankle positions covering the range of motion. We showed that the difference between the new third-order model and the conventional IBK model increased from dorsi to plan-tarflexed position. The new model was obtained using a multi-step identification procedure applied to experimental input/output data of the ankle joint. The procedure first identifies a non-parametricmodel of intrinsic joint stiffness where ankle position is the input and torque is the output. Then, in several steps, the model is converted into a continuous-time transfer function of ankle compliance, which is the inverse of stiffness. Finally, we showed that the third-order model is indeed structurally consistent with agonist-antagonist musculoskeletal structure of human ankle, which is not the case for the IBK model.