A Kinematic Information-Theoretic Transmission Scheme for Goal-Directed Movements

We build on the variability of human movements by focusing on how the stochastic variance of the limb position varies over time. This implies analyzing a whole set of trajectories rather than a single one. We show, using real data previously acquired by two independent studies, that two distinct phases appear. The first phase, where the positional variance increases steadily, is followed by a second phase where it decreases toward zero. During the second phase, the problem of aiming can be reduced to a Shannon-like communication problem where information is transmitted from a "source" (determined by the position at the end of the first phase), to a "destination" (the movement's endpoint) over a "channel" perturbed by Gaussian noise, with the presence of a noiseless feedback link. We take advantage of a scheme by Elias, which provides a simple yet optimal solution to this problem and show that the rate C of decrease of variance during the second component is at best exponential. This result is observed on real data and C is found to be constant across instructions and task parameters, resulting in the unambiguously defined throughput that characterizes goal-directed movements via a simple measure in bit/second. The well-know Fitts' law is also derived in the case where the second phase dominates movement time, obtained for movements that require high precision.