Origins of the power law relation between movement velocity and curvature: modeling the effects of muscle mechanics and limb dynamics

Abstract

1. When subjects trace patterns such as ellipses, the instantaneous velocity of movements is related to the instantaneous curvature of the trajectories according to a power law-movements tend to slow down when curvature is high and speed up when curvature is low. It has been proposed that this relationship is centrally planned. 2. The arm's muscle properties and dynamics can significantly affect kinematics. Even under isometric conditions, muscle mechanical properties can affect the development of muscle forces and torques. Without a model that accounts for these effects, it is difficult to distinguish between kinematic patterns that are attributable to central control and patterns that arise because of dynamics and muscle properties and are not represented in the underlying control signals. 3. In this paper we address the nature of the control signals that underlie movements that obey the power law. We use a numerical simulation of arm movement control based on the lambda version of the equilibrium point hypothesis. We demonstrate that simulated elliptical and circular movements, and elliptical force trajectories generated under isometric conditions, obey the power law even though there was no relation between curvature and speed in the modeled control signals. 4. We suggest that limb dynamics and muscle mechanics-specifically, the springlike properties of muscles-can contribute significantly to the emergence of the power law relationship in kinematics. Thus, without a model that accounts for these effects, care must be taken when making inferences about the nature of neural control.