Modeling of Electrically Induced Floor Reaction Torque during Quiet Standing and Estimation of Ankle Joint Stiffness

Standing posture is stabilized by a control mechanism involving the stiffness of the ankle joint. Ankle joint stiffness has previously been studied by measuring the electrically induced fluctuation of the center of pressure. However, the fluctuation is a complex output of a neuromuscular system and a measurement system, and its mechanism has therefore remained unclear. The purpose of this study was to construct a model of the process leading from electrical stimulation to floor reaction torque and to estimate net ankle joint stiffness. The model consisted of an inverted pendulum with a Hill-type muscle model and was described by a state equation that was solved using the Runge‒Kutta method. Some of the model parameters were derived from the physical characteristics of the participants. Unknown parameters were estimated using a nonlinear least squares method by comparing the model torque with the experimental torque. The experimental torque was well reproduced using the model. The stiffness of the ankle joint (passive and active) was 627–944 Nm/rad, which was able to stabilize the standing posture.