Virtual trajectories, joint stiffness, and changes in the limb natural frequency during single-joint oscillatory movements

Abstract

In the framework of the equilibrium-point hypothesis, virtual trajectories and patterns of joint stiffness were reconstructed during voluntary single-joint oscillatory movements in the elbow joint at a variety of frequencies and against two inertial loads. At low frequencies, virtual trajectories were in-phase with the actual joint trajectories. Joint stiffness changed at a doubled frequency. An increase in movement frequency and/or inertial load led to an increase in the difference between the peaks of the actual and virtual trajectories and in both peak and averaged values of joint stiffness. At a certain, critical frequency, virtual trajectory was nearly flat. Further increase in movement frequency led to a 180° phase shift between the actual and virtual trajectories. The assessed values of the natural frequency of the system “limb + manipulandum” were close to the critical frequencies for both low and high inertial loads. Peak levels and integrals of the electromyograms of two flexor and two extensor muscles changed monotonically with movement frequency without any special behavior at the critical frequencies. Nearly flat virtual trajectories at the natural frequency make physical sense as hypothetical control signals, unlike the electromyographic recordings, since a system at its natural frequency requires minimal central interference. Modulation of joint stiffness is assumed to be an important adaptive mechanism attenuating difference between the system's natural frequency and desired movement frequency. Virtual trajectory is considered a behavioral observable. Phase transitions between the virtual and actual trajectories are illustrations of behavioral discontinuities introduced by slow changes in a higher level control parameter, movement frequency. Relative phase shift between these two trajectories may be considered an order parameter.