Torques generated at the human elbow joint in response to constant position errors imposed during voluntary movements

Abstract

The stiffness of the human elbow joint was investigated during targeted, 1.0-rad voluntary flexion movements at speeds ranging from slow (1.5 rad/s) to very fast (6.0 rad/s). A torque motor produced controlled step position errors in the execution of the movements. The steps began at the onset of movement, rose to an amplitude of 0.15 rad in 100 ms, and had a duration equal to movement duration. The net joint torque (muscle torque) resisting the step perturbation was computed from the applied torque, the joint acceleration, and the limb inertia. Subjects resisted the imposed step changes with approximately step changes in the net muscle torque. The mean resistance torque divided by the step amplitude was computed and is referred to as the stiffness. The stiffness increased with the voluntary movement speed, over the range of speeds (1.5-6 rad/s). The stiffness increased linearly with the magnitude of the net muscle torque on the unperturbed trials (referred to as "background torque"). The stiffness changed by only 20% when the step amplitude ranged from 0.05 to 0.15 rad. The mechanical resonant frequency (fr), estimated from the average stiffness estimates, ranged from 0.8 to 3.0 Hz. The resonant frequency approximately equaled the principal frequency component of the movement fm. On average: fr = 0.96 fm +0.46. During the fixed, 100-ms rise time of the step, the resistance was not linearly related to the background torque. At slower speeds the resistance was relatively greater during this rise time. However, when the imposed step perturbation was modified so that its rise time occurred in a time proportional to the movement duration (rather than in the fixed, 100-ms, time), the muscle torque resisting the motor during this rise time was proportional to the background torque. When these modified step responses were plotted on a time scale normalized to the movement duration, they all had approximately the same shape. Apparently the muscle viscosity scaled with the stiffness so as to maintain the constant response shape (constant damping ratio). The observed "tuning" of the mechanical properties to the movement speed is suggested to be important in the robust generation of smooth stereotyped voluntary movements.