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)