LGN

Afferent Gain Control

A gain control has been implemented for the LGN-to-cortex inputs. The afferent gain control (AGC) operates by dividing the total conductance (both the AMPA and NMDA, if any, from the LGN) for the input by a signal S(t). The signal S(t) is computed from a signal, h(t):

S(t) = gain_ca + gain_cb * h(t),

where h(t), is a Gaussian weighted average involving the raw filter outputs, r:sub:’i’(t) of the <b>n</b> LGN afferents:

        n
h(t) = SUM w<sub>i</sub> [r<sub>i</sub>(t) - r<sub>H</sub>] / r<sub>Max</sub>
       i=1

where w is a Gaussian weight, r_H is the middle of the response range for any r and r_Max is the maximum possible response. The Gaussian SD is set as the larger of sd_orth and sd_par, and it is applied radially from the center of the V1 RF to define the gain field.

In practice, The signal h(t) has been observed to have a value of about 0.04 for a grating of SF 1 cyc/deg and TF 8 Hz for the Dog.0.0 model. The value 0.04 indicates about 4% of maximal theoretical LGN activation on average across the gain field. The theoretical r_Max is probably never achieved.

To smooth the signal, S(t), it is convolved with a one-sided decaying exponential with time constant gain_tau:

<input>
  type lgn_on_off
   ...
  gainflag   1      # 1-Apply gain control, 0-none
  gain_tau   0.020  # Exponential convolution, time constant (s)
  gain_ca    1.0    # Additive constant
  gain_cb   14.0    # Multiplicative constant (0.0=no gain control)
   ...
  sd_orth    0.125  # (deg) Gaussian SD for Gabor RF orthog to ori
  sd_par     0.215  # (deg) Gaussian SD for Gabor RF parallel to ori
   ...
</input>

LGN Responses

The LGN spike trains may arise from two sources:

  1. Difference of Gaussians (DoG) filter model (mod_dog_util.c)

  2. Retina network (mesh_rgc) model

    (mod_mesh_util.c)

If there is a top-level object, <retina0>, in the .moo file, then it is assumed that the retina network is to be used. In that case, see the section below, Mesh interface, for a description of how the mesh model is coordinated with the pop model.

Otherwise, it will be assumed that the DOG filter is to be used, and the rest of the documentation in this section applies.

If the DOG filter is being used, there needs to be at least one population such as:

<pop>
  name lgn
  type lgn
  ...
  <geometry>
    zn    2          # Depth 2 for OFF and ON cells, use 4 if binocular
  </geometry>

  binocular   0      # 0-monocular, 1-binocular
  ...
</pop>

There may also be a population named lgn_m to create a second LGN population with a different DOG filter.

Density of LGN cells

The following reasoning is used to estimate the number of LGN cells available at different eccentricities.

Wassle et al (1990 Vis Res) Fig 6A shows ganglion cell densities vs. eccentricity for Macaque. At 8 deg, there are about 1000 cells per deg^2 (averaging temporal and nasal estimates):

  • 2 deg, nearly 5000 cells/deg^2
  • 4 deg, 2000 cells/deg^2
  • 5 deg, 1800 cells/deg^2
  • 8 deg, 1000 cells/deg^2

Wassle et al (1990 Vis Res, p1910) state that ‘Recent analysis shows, in contrast to previous estimates (Malpeli & Baker, 1975), that there is a one to one relationship between axons arriving in the optic tract and relay cells in the LGN (Schein & DeMonasterio, 1987). No difference in mapping has been found between M and P pathways (Livingstone & Hubel, 1988).’

The ratio of P to M is roughly 10:1 (e.g., Ahmad and Spear, 1993).

Normalization of LGN filter response

After the spatio-temporal DOG filter is computed, it is scaled so that the sum of all positive values in the filter is 1.0. In other words, the positive area is scaled to 1.0.

The maximum response from the filter is equal to the positive area, and the maximum value can only occur if the stimulus is 1.0 everywhere the filter is positive and 0.0 everywhere it is negative.

The normalized filter is convolved with the visual stimulus and the output is used to drive the excitatory input of an IF-unit, where the inhibitory input has been set to zero.

ON and OFF responses

To generate output spike trains for ON LGN cells, the response, R(t) of the DOG filter is used to control the excitatory conductance of a standard IFC (conductance-based integrate-and-fire) unit. For OFF LGN cells, the excitatory conductance is controlled by R’(t)=A-R(t), where A is the integral of the DOG filter. By linearity, R’(t) is, intuitively, the response of the DOG filter to “one minus the stimulus”, where the visual stimulus has values from 0 to 1.

Correlation between LGN spike trains

Three parameters control the correlation between LGN spike trains:

  1. lgn_corr_distance - (“d”) Distance in terms of cells, 1=no correlation
  2. lgn_corr_ppick - (“p”) probability of adding a spike from a neighbor
  3. lgn_corr_tsd - SD of Gaussian for adding temporal jitter to spikes from neighbors. Time units should be msec.

Correlation is created by starting with the set of raw spike trains (which have only that correlation induced by the stimulus). Each cell (the target cell) then keeps only a fraction, k, of its original spikes and discards the rest. The target cell then adds spikes from neighboring cells (in particular, from their kept spikes) that lie within a square region of side length d centered on the cell. When d is even and centering is impossible, the target cell should lie to the lower left of center, as shown below for d=2 and d=4

::

. c c c c . c c c c c c c X - target cell . c c c X c c X c c c - neighbor cell . X c c c c c c c c

d=2 d=3 d=4

Here is a quantitative description of the algorithm:

  1. Assume every cell has n spikes on average, originally.
  2. Each cell will pick from b neighbors, where b = d*d-1
  3. Let k be the fraction of spikes to be kept by each cell.
  4. The average number of spikes picked from all neighbors is s = b*p*k*n
  5. Maintaining the average number of spikes at the original level requires that s = (1-k)*n
  6. Thus, k = 1/(p*b + 1)

For example, if d=2 and p=1, then b=3 and k = 1/4. Thus, all cells keep 1/4 of their spikes, and receive all of the kept spikes from three neighbors. In this case, two horizontally or vertically adjacent cells will share 50% of their spikes, on average.

Decreasing p will cause each cell to keep more of its spikes and include fewer from its neighbors, thus decreasing the correlation. Increasing d will spread correlation over more cells, and the correlation to the more distant cells within the neigbhorhood will be weaker.

Collisions. Currently, this correlation generation algorthm causes spike collisions that are not removed. This violates the spike refractory period of LGN cells, which in our TF data for both M and P cells can be approximated by an absolute refractory period that varies from about 1 to 2 ms.