The 3D visuomotor transformation of reaching depth in a neural network model
Gunnar Blohm, Gerald P. Keith, J. Douglas Crawford
Centre for Vision Research, York University, Toronto, Canada
 
To reach out for a target, the brain needs information about the target’s three-dimensional (3‑D) location in space. Classically, the analysis of artificial or real neural networks involved in reaching has focused on the angular position of the target with respect to the observer, therefore reducing 3‑D space to two dimensions. However, information about initial hand and target egocentric distance is essential to performing the reaching task. It is unclear how depth-related computations would be performed by a neural network and what properties one should expect in real neurons involved in reaching into depth.
To gain insight into the visuomotor transformation that includes distance, we trained a 3‑layer feed-forward artificial neural network. For the training we used the exact 3‑D geometrical relationship between the gaze-centered movement vector and the shoulder-centered motor plan. For the gaze-centered inputs we used: two retinotopic maps providing hand and target direction, two maps of retinal disparity (= right – left eye position), 3-D head and (cyclopean) eye position, and an ocular vergence signal. The output of the network consisted of a 3‑D cosine-tuned population (125 units having uniformly distributed preferred directions) encoding the shoulder-centered movement plan.

We analyzed how the reaching depth was computed and specifically investigated two aspects of this. First, does the network use relative or absolute depth? A correlation analysis between the location of the retinal disparity receptive field (RF) and fixation distance (associated with vergence) showed that the hidden-layer units in the network preferably used absolute distances but there were also units that were biased towards relative distance, while the output-layer units showed a continuum between relative and absolute distance coding. In addition, retinal disparity and vergence signals gain-modulated the hidden-layer unit motor fields whereas this was not the case in the output layer. Second, when the eyes / head rotate, fixed gaze-centered movements plans rotate as well, resulting in a change of the depth component of the shoulder-centered motor plan. The network did this through eye-head position gain-modulation of the units’ retinal disparity RF and also the vergence gain-modulation of the retinal position RF. This gain-modulation resulted in different weights when summing up activity of units with different RF and motor field properties.

As with the angular position, the visuomotor transformation of depth seemed to take place at the individual unit level. Units with different input-output relationships (i.e. RF and motor field) were combined at the population level in a gain-like fashion. Our model predicts that neurons in the visuomotor transformation pathway show both relative and absolute depth coding, that retinal disparity RFs are gain-modulated by eye and head position signals and that angular position RFs are also gain-modulated by vergence.

Supported by Marie Curie (EU) and CIHR (Canada)