Our simulations show that leg kinematics during the pendulum test in individuals with spastic cerebral palsy could be explained by increased muscle tone and sensory feedback gains if their interactions with muscle short-range stiffness are taken into consideration (De Groote et al., 2018. Plos One: 13(10)).
We simulated the dynamics of a pendulum test based on a torque-driven biomechanical model of the lower leg. Our model consisted of a planar lower leg segment with passive stiffness and damping to simulate non-contractile musculotendon properties. Active joint torques representing muscle contractile behavior consisted of a constant baseline torque to represent increased muscle tone, a short-range stiffness torque dependent on the level of muscle tone, and a delayed sensory feedback torque to simulate reflex activity. Muscle short-range stiffness was scaled as a function of muscle tone. We simulated the reflex contributions to the pendulum test by modeling sensory feedback pathways based on either joint position and velocity to represent muscle length and velocity, or active torque and derivative of active torque to represent muscle fiber force and derivative of force. All model parameter values were held constant over the time course of each simulation. To simulate different degrees of spasticity, we altered both muscle tone and the sensitivity of the simulated reflex pathways, i.e. feedback gain values. Our evaluations of the model were based on published kinematic trajectories of the pendulum test in individuals with CP. We were able to reproduce all three key features of the pendulum test associated with increased spasticity: 1) reduced amplitude of the first swing excursion, 2) reduced number of oscillations, and 3) less vertical resting angle. The simulations are freely available (simtk.org) such that other researchers can reproduce our results and perform additional analyses.