A Global Orientation Map in the Primary Visual Cortex (V1): Could a Self Organizing Model Reveal Its Hidden Bias?

Abstract

A remarkable accomplishment of self organizing models is their ability to simulate the development of feature maps in the cortex. Additionally, these models have been trained to tease out the differential causes of multiple feature maps, mapped on to the same output space. Recently, a Laterally Interconnected Synergetically Self Organizing Map (LISSOM) model has been used to simulate the mapping of eccentricity and meridional angle onto orthogonal axes in the primary visual cortex (V1). This model is further probed to simulate the development of the radial bias in V1, using a training set that consists of both radial (rectangular bars of random size and orientation) as well as non-radial stimuli. The radial bias describes the preference of the visual system toward orientations that match the angular position (meridional angle) of that orientation with respect to the point of fixation. Recent fMRI results have shown that there exists a coarse scale orientation map in V1, which resembles the meridional angle map, thereby providing a plausible neural basis for the radial bias. The LISSOM model, trained for the development of the retinotopic map, on probing for orientation preference, exhibits a coarse scale orientation map, consistent with these experimental results, quantified using the circular cross correlation (r_c ). The r_c between the orientation map developed on probing with a thin annular ring containing sinusoidal gratings with a spatial frequency of 0.5 cycles per degree (cpd) and the corresponding meridional map for the same annular ring, has a value of 0.8894. The results also suggest that the radial bias goes beyond the current understanding of a node to node correlation between the two maps.

Keywords: LISSOM; V1; meridional preference; orientation preference; plasticity; radial bias; retinotopy; self-organizing.

Figure 1

A schematic representation of the architecture of the LISSOM model.

Figure 2

Training and probing stimuli used in the LISSOM model. The first 2 stimuli represent training stimuli, while the rest are representative of probing stimuli. (A,B) Rectangular bar with aspect ratio of 0.05, and randomized dilation and rotation; (C) Centered, collinear point stimuli to probe orientation preference; (D,E) Full field sinusoidal gratings with a spatial frequency of 0.75 cpd, 0.5 cpd to probe orientation preference; (F) Full field sinusoidal gratings with random noise added; (G) Annular ring subtending 2° of visual angle masked with a sinusoidal grating of randomized orientation and phase with a spatial frequency of 0.5 cpd; (H) Blurred edge annular ring subtending 2° of visual angle masked with a sinusoidal grating of randomized orientation and phase with a spatial frequency of 0.5 cpd.

Figure 3

The orientation map developed when the trained LISSOM model is probed with gratings having orientation 45° and 135°, respectively, with varying spatial frequencies. The nodes which respond maximally to one of the orientations are color coded appropriately as shown in the colorbar. These results resemble (Sasaki et al., 2006), where the majority of nodes in the upper half of the output map prefer the 45° orientation, while the nodes in the lower half respond to the 135° orientation stimulus. (A) Orientation Preference of the map developed on probing with gratings of 0.5 cpd; (B) Combined Orientation Preference and Selectivity on probing with gratings of 0.5 cpd.

Figure 4

The orientation map developed when the trained LISSOM model is probed with gratings having 12 orientations equally spaced between 0° and 180°, respectively. The nodes which respond to these orientations are color coded appropriately as shown by the colorbar. These results resemble (Freeman et al., 2011) with the orientation map developed resembling the meridional map developed. (A) Meridional preference map developed; (B) Orientation preference map developed on probing with a thin annular ring with spatial frequency of grating set to 0.5 cpd; (C) Orientation preference map developed on probing with a thick annular ring with spatial frequency of gratings set to 0.5 cpd; (D) Orientation preference map developed on probing with a thick annular ring with spatial frequency of the grating set to 0.75 cpd.

Figure 5

Similarity between the meridional preference and orientation preference maps: For a single node the orientation preference is assigned to the y-coordinate where as the meridional preference is assigned the x-coordinate, so as to give the location of a point.

Figure 6

A radial bias is observed even on training with different ratios of radial to non-radial orientation. For the maps shown (A) 1 in 2, (B) 1 in 3, (C) 1 in 5, (D) 1 in 10, (E) 1 in 20 of the orientations given for their training are radial. The cross-correlation values are given the bottom of each map.

Figure 7

The coarse scale orientation map is sufficient in order to achieve orientation discriminability from the output activity of the model. (A) The sufficiency of the orientation map to classify orientations is demonstrated by circular average of the orientation of nodes which have similar meridional preference as opposed to random averaging; (B) The necessity of the radial bias is probed by removing the component corresponding to meridional preference from the orientation preference of each node as opposed to removing a random meridional component.

Figure 8

Development of the meridional preference map and orientation preference maps. Developing meridional preference maps when probed at (A) 200, (B) 400, (C) 600 iterations, respectively; Developing orientation preference maps when probed at (D) 200, (E) 400, (F) 600 iterations respectively with full field orientation gratings having a spatial frequency of 0.5 cpd; Developing orientation preference maps when probed at (G) 200, (H) 400, (I) 600 iterations respectively with full field orientation gratings having spatial frequency of 0.75 cpd.

Figure 9

The blurring of the edge of the annular ring does not seem to affect the radial bias. (A) Orientation map developed on probing with a sharp edged annular ring masked with a sinusoidal grating; (B) Orientation map developed on probing with a blurred edged annular ring masked with a sinusoidal grating.

Figure 10

The phase preference map developed reflects the preferences of individual nodes to that phase of the grating, when the middle peak of the grating matches with radial stimuli. (A–C) represent the phase preferences on testing with sinusoidal gratings of varying orientation for spatial frequency of 0.25, 0.5, and 0.75 cpd, respectively.

Figure 11

The fine-scale orientation map developed at the scale of the hyper-column. (A) The orientation map developed using equi-probable orientations for training and (C) the histogram of the orientations in the map. (B) The orientation map developed when one in 10 orientations used for training are horizontal (here radial) and (D) the histogram of the orientations in the map demonstrating an over-representation of the horizontal (here radial) orientations.