The 3-D eye-head geometry is needed to transform visual inputs into reaching movements

G. Blohm^1* and J.D. Crawford^1,2

¹Centre for Vision Research, York University, Toronto, Ontario, Canada

²CIHR Group on Action and Perception

Reaching movements to visual targets require a sensorimotor transformation of retinal signals into motor commands for the arm. The simplest possible transformation consists of a direct mapping of the retinal desired movement vector onto the same movement vector in motor coordinates (Buneo et al. 2002). However, such a direct transformation (DT) does not account for the complex, non-linear 3-D linkage structure between the retina and the movement effector.

Here, we developed the first 3-D model of reference frame transformations for visually guided reaching. We implemented spherical retinal geometry, Listing’s law for eye rotations, static VOR, and Donder’s law for head movements, and computed the transformation of a retinal input into a shoulder-centered motor command. This allowed us to compare the performance of the DT hypothesis with an optimal 3-D transformation (OT) producing spatially correct movements. Whereas the DT implements no non-linear spatial compensation of gaze position, the OT completely compensates for it.

We tested the model’s predictions for oblique gaze positions, head restrained or unrestrained, as well as for different head rolls. Seven subjects were required to reach out in darkness to the memorized position of a previously presented target while maintaining their gaze in different locations. Subjects compensated on average for 96% of the gaze-position-related non-linearity in the sensorimotor transformation (in both head unrestrained [R = .983, p < .001] and head restrained [R = .976, p < .001]) and accounted for 97% [R = .987, p < .001] of the head roll, indicating that OT rather than DT was used.

These results demonstrate that in 3-D space a sensorimotor transformation for visually guided reaching must incorporate the actual eye and head configuration to compensate for the non-linearity of the linkage between the retina and the arm.

Supported by Marie Curie Fellowships (European Union), FSR (UCL Belgium) and CIHR (Canada)