Pointing with the wrist: a postural model for Donders’ law

Abstract

The central nervous system uses stereotypical combinations of the three wrist/forearm joint angles to point in a given (2D) direction in space. In this paper, we first confirm and analyze this Donders' law for the wrist as well as the distributions of the joint angles. We find that the quadratic surfaces fitting the experimental wrist configurations during pointing tasks are characterized by a subject-specific Koenderink shape index and by a bias due to the prono-supination angle distribution. We then introduce a simple postural model using only four parameters to explain these characteristics in a pointing task. The model specifies the redundancy of the pointing task by determining the one-dimensional task-equivalent manifold (TEM), parameterized via wrist torsion. For every pointing direction, the torsion is obtained by the concurrent minimization of an extrinsic cost, which guarantees minimal angle rotations (similar to Listing's law for eye movements) and of an intrinsic cost, which penalizes wrist configurations away from comfortable postures. This allows simulating the sequence of wrist orientations to point at eight peripheral targets, from a central one, passing through intermediate points. The simulation first shows that in contrast to eye movements, which can be predicted by only considering the extrinsic cost (i.e., Listing's law), both costs are necessary to account for the wrist/forearm experimental data. Second, fitting the synthetic Donders' law from the simulated task with a quadratic surface yields similar fitting errors compared to experimental data.

Ergonomic design of a wrist exoskeleton and its effects on natural motor strategies during redundant tasks

“…The first feature is an offset in the r x component. This bias corresponds to an offset in prono-supination which confirms the findings in [12]. Comparison of the results in Fig.…”

“…The dotted lines illustrate the loci of the equivalent shape index for each experiment. Based on the work presented in [12], the loci in Fig. 8.a suggest shape clustering.…”

“…Similar to [12], a generic quadratic surface, r * i = [r * xi r yi r zi ] T , was fitted to the sequence of the first components r xi :…”

“…By definition −1 ≤ S ≤ 1. Independently of curvature's amount, this index reflects the intuitive notion of shape [12].…”

“…Recent studies have demonstrated that Donders law can be applied to two DOF pointing tasks of the wrist. In such tasks, the 3 DOFs of the wrist become redundant [10], [11], [12].…”