Fitts' law as a low-pass filter effect of muscle stiffness

Abstract

It is proposed that the speed of aiming movements is the optimized outcome of a stochastic, oscillatory recruitment signal to the muscles and filtering properties of the effector limb. The filtering characteristic of the limb is seen to be modulated through a stiffness parameter, to be set by the subject, and directly related to the perceived accuracy demand. This filtering is assumed to be a necessary condition to delimit the noisy character of the recruitment signal in accordance with the accuracy demands of the task. Because an increase of limb stiffness, at the same time, decreases the gain of the transfer function of the limb system, Fitts' law may be explained as a decreasing net velocity of the limb with increased accuracy demands that is due to increased filtering in the effector limb. In an experimental aiming task, subjects drew line trajectories with a ballpoint pen on a digitizer tablet to goals of varying width and distance. To estimate the effective noise that was characteristic for each level of accuracy, Power Spectral Density Analysis was applied to the deviation scores of the acceleration profile for each single movement, as compared to the average Power Spectral Density Function (PSDF) for that movement condition. Temporal resolution of the apparatus allowed for analysis of periodic fluctuations of the acceleration signal in spectral bands up to 49 Hz. Increase of movement time with movement difficulty was significantly related to an inhibition of the lower frequencies of the PSDF together with a relative increase of energy in the higher bands of the spectrum. This outcome is analogous to the results of a mathematical simulation of single-joint movements of the human arm in which the effect of increased limb stiffness on the PSDFs was calculated by the algorithm. The results support the theory that limb stiffness is a more probable candidate to modulate Fitts' speed-accuracy trade-off than control processes based on the processing of feedback.