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 n LGN afferents::
n
h(t) = SUM wi [ri(t) - rH] / rMax
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**::
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
...
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, **, 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::
name lgn
type lgn
...
zn 2 # Depth 2 for OFF and ON cells, use 4 if binocular
binocular 0 # 0-monocular, 1-binocular
...
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.