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3 Computational Methods
3.1 Model Composition
The retina is represented by two rectangular layers of 40x40 pixels, the first one
representing the ON type ganglion cells, the second one the OFF type ganglion
cells. The lateral geniculate nucleus is modeled by a rectangular layer with di-
mensions 40x40 pixels, each point in the lattice having two neuron models, one
for the relay neurons and the other for interneurons. The fraction of neurons
per point is 1:4, meaning that for each interneuron there are four neighbor relay
cells (Molano and Martinez, 2009) [14] (see Figure 1).
3.2 Coordinate System and Topology
The retina and the thalamus are simulated by means of a lattice of size 40x40
pixels that represents a patch with a parafoveal visual field of 8
◦
x8
◦
. Each posi-
tion in the layer corresponds to a node, each node can define subnets of neurons.
In our case, each node of the layer of the thalamus have two subnets, one formed
by one interneuron and one consisting of four relay neurons.
3.3 Connectivity
Each relay cell in the thalamus is first connected to its nearest neighbor in the
retinal lattice, i.e. the one from which its polarity is inherited. The probability
of each thalamic cell, re-centered at retinal coordinates at the position of its first
retinal input (X), being connected to another retinal ganglion cell is modeled
as a Gaussian function of their relative distance [4]. The synaptic strength of
the connections is also assumed to follow a Gaussian distribution of the dis-
tance between the receptive-field centers [4]. The function for both connection
probability and strength is as follows (see Figure 1):
P
=
p
max
e
−
(
x−y
)
2
/
2
σ
con
(1)
3.4
Input and Output Models
The stimuli used in our simulations are simple geometric figures as bright circles,
rectangles and bars. Stationary stimuli are mathematically represented by using
bidimensional arrays of size 40x40, where the coecients represent either high
or low light intensity.
The spatial arrangement of the receptive fields of retinal ganglion cells are cap-
tured by a difference-of-Gaussians model (Rodieck, Enroth-Cugell and Robson,
1966) in which the spatial receptive field is expressed as:
1
2
πσ
2
cen
B
2
πσ
2
sur
e
−
(
x−y
)
2
/
2
σ
con
−
e
−
(
x−y
)
2
/
2
σ
sur
)
D
(
x, y
)=(
(2)
The first Gaussian function describes the center and the second one the surround
receptive field, the sizes of both fields being determined by the parameters
σ
cen
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