The document discusses improving the statistical realism of a retina simulator called VirtualRetina by implementing additional retinal circuitry features. While VirtualRetina can accurately model individual retinal ganglion cell responses, it does not capture the synchronization and correlations seen in real retinal data. Implementing gap junction connections between retinal ganglion cells and modeling feedback from amacrine cells could help VirtualRetina better match real data statistics. The goal is to produce a statistically plausible retinal output that can serve as realistic input for models of the visual cortex.

1. Toward a realistic input for visual cortex models
* Pierre Kornprobst, Serge Picaud*
+ + +
Hassan Nasser, Bruno Cessac, Bogdan Kolomiets,
+ NeuroMathComp project team (INRIA, ENS Paris, UNSA, LJAD) Contact: Hassan.Nasser@inria.fr
* Institut de la Vision http://www-sop.inria.fr/members/Hassan.Nasser
The modelling of the visual system needs to provide realistic retinal responses (spike trains) to
visual stimuli. Our team [1] developed a retina simulator that allows a large scale simulation Performing statistics Simulation of biological experiments
(about 100.000 cells) and provides spikes train output as a response to visual stimuli. This model
contains several blocks representing the retina layers. It is able to reproduce realistic individual
A spike train is represented by a set of Dirac
functions for N neurons:
in VirtualRetina
responses of retinal ganglion cell (RGC). However, as emphasized in the present work, we checked We simulated the biological experiment (described before) with VirtualRetina. A 93 sec of image sequence. The spontaneous
Neuron Index
that the collective responses of RGC don't match to real data. Comparing our simulator outputs to activity is simulated with a white noise (dark image), the light flash stimulus with a white noise (lighted image). We respected
real acquisitions data made by B. Kolomiets and S. Picaud (Institut de la Vision) we have shown, the exact time of stimulus (1 sec of light flash followed by 5 sec of rest repeated 10 times) in order to reproduce the experiment
We call observables, the events we observe in this conditions. Fig. 11 and 12 show C(T) respectively in spontaneous and evoked potential activity.
using statistical methods developed by our team (EnaS) [3], that real data show a significant spike train (Ex: Individual spike related with firing
synchronization and correlations between RGC outputs, that is absent from our simulator outputs. rate and doublets related with correlations ...). The Simulation with the VirtualRetina
software shows a decreasing of the
It is commonly believed that those correlations come from the overlap of RGC receptive fields. correlation is given by the following equation:
correlation with the raster length (Both
However, since, our simulator carefully reproduces this overlap this suggests that synchronization Time (s)
in spontaneous and evoked potential
Fig. 3
must be explained by other mechanisms such as long range connections from Amacrine to RGC or activities). The synthetic data (two
electrical connections (gap junctions) between RGC which have not been implemented yet in our Where the first term represents how many times the neurons i fires after a time delay t from the neurons firing independently) show also
simulator. neuron j. is the empirical average of an observable. the same behavior. This is the typical
behavior of two non-correlated firing
We consider the evolving of the correlation value in neurons. Despite the fact that the
Problematic & Background term of the raster length (T) in order to evaluate the
correlation between two neurons. Theoretically, this
receptive fields are implemented in the
software, the correlation outlook for two
correlation tends to zero when T tends to infinity (Plot neurons in the software reflects the
Spike Train in the log scale) as / , Where K is a constant. behavior of non-correlated neurons. Our
Stimulus Retina Visual Cortex first conclusion is that the overlap of
Cortex Response RGC receptive fields in Virtual Retina
Fig. 4 shows C(T) for two neurons that fire
Retinal Cortex doesn't imply correlation between RGC. Fig. 12
independently. Despite the fluctuations on small time Fig. 11
output Input
windows, we see the evolution of C(T):
The modeling of the visual system needs to provide realistic retinal responses (spike trains) to
visual stimuli. Our team (Wohrer et al. 2008) developed a retina simulator that allows a large scale
simulation (about 100.000 cells) and provides spikes train outputs as a response to visual stimuli.
Fig. 4 Raster length (s)
Interaction between RGC cells
This model contains several blocks representing the retina layers. In order to have hints on the RGC circuitry, we Fig. 14 shows the for
Biological experiments are time consuming and expensive. An alternative could be a retina
simulator: The VirtualRetina.
Statistics on real data applied Ising model to analyze statistics of
these data. Ising model is characterized by a
neurons at several distance.
The units are the indexes of
Retinal connection [4] VirtualRetina model [1] Fig. 5
The vertebrate retina Real data acquisition were provided by Bogdan Gibbs distribution whose potential is: neurons in the MEA chip.
Kolmiets and Serge Picaud (Institut de la vision de L0LX coefficients are for .
Paris). Acquisition details: 30 sec of spontaneous The index 0 replaces the
activity followed by 63 sec of evoked potential (1 unit 8, the index X replaces
Ising model is one of the most popular in
sec of light flash followed by 5 sec of rest, repeated neural computation. It is believed that the the other units: 16, 24, 32,
several 10 times) - Acquisition on MEA chip of 54 coefficients are related to connections 39, 47. These units are
electrodes. The activity of these neurons is shown between gap junctions although other located at various distances
interpretations are possible. Fig. 13
in the Fig. 5. from the unit 0. the
Fig. 13 shows the and for a two different coefficient increases and
Fig. 2 Fig. 3
Experiments: sets of 7 neurons (N0-N6). The are the firing
rate (in positive). The are gives an idea
then decrease after a
distance of about 300 um.
Fig. 1 about the RGC interaction. Interaction values How can we interpret this
The diagram of the VirtualRetina. Experiments were done for rats' retina, aged between 13 and 17 months. The electrode (Fig. appear almost in negative. Knowing that RGC bahavior?
The retina contains several layer of Connectivity map 6) size is: 40x40 um. The inter-electrode distance is 200 um. the retina were placed in a
The receptors and horizontal layer are connected with Gap Juction which implies
cells connected through chemical in the retina. full
are implemented as image filters. recording chamber where the MEA and stimulation tools are (Fig. 7). a positive connectivity. Why do these negative
and electrical synapse. More than 50 and empty disks However, bipolar and ganglion Fig. 14
represent values appear?
cell subtypes exists. However, cells are implemented as Fig. 6
scientist believe that less than 50 % respectively conductance based and I&F
of cell functions are known until excitatory and neurons respectively. Amacrine
now. inhibitory. cells are not yet implemented. Fig. 7
Discussion
Fig. 15 [5]
Performance of VirtualRetina Fig. 15 shows cros correlograms for directely
connected RGC and Amacrine connected RGC.
Allows large scale simulation (More than 100,000 cells). The direct connection implies a narrow
Possibility of customizing retina and retina parameters. Fig. 8 [2] correlation. In contrary, broad correlation
+ High biological plausibility at the level of single cell.
Reasonable computational cost.
appears for RGC connected through Amacrine
cells.
Implements the underlying of receptive fields of retinal ganglion cells (RGC).
Amacrine cells are not implemented. The VirtualRetina needs to be improved at the level of RGC cells circuitry. One of our perspectives is to implement gap
- Connections between RGC and Amacrine-RGC are not implemented.
Statistically, the response of a set of RGC doesn't fit to real RGC.
junction connections between RGC in order to approach statistics on real data acquisition.
Amacrine cells provide a negative feedback to RGC cells. The negative connectivity coefficients could be interpreted by these
feedback.
A statistically plausible retinal model is required to produce a realistic retinal input for the visual cortex model.
[3] J.C. Vasquez, T. Vieville, B. Cessac, Entropy-based Fig. 9 Fig. 10 We would like to create image-statistics dictionary. In fact, we believe that the response of the RGC depends statistically on
[1] Adrien Wohrer, Model and large-scale simulator of a the image events (motion, color detection, texture detection., ....). The implementation of retinal circuitry provided in (Gollish et
parametric estimation of spike train statistics. INRIA,
biological retina, with contrast gain control. University of
Nice Sophia-Antipolis, INRIA, 2009.
2009. al. 2009) will help to create this dictionary.
[4] T. Gollisch, M. Meister. Eye Smarter than Scientists
[2] B. Kolomiets, E. Dubus, M Simonutti, S Rosolen, J.A Believed: Neural Computations in Circuits of the Retina.
Fig. 9 and 10 show C(T) in spontaneous activity and evoked potential respectively, for three
Sahel, S.Picaud, Late his-tological and functional changes
in the P23H rat retina afterphotoreceptor loss.
j.neuron. 2009 (volume 65 issue 2 pp.150 - 164) . different pairs of neurons mounted at several distances. The correlation outlook is different than Softwares
Neurobiology of Disease 38 (2010) 47-58.
[5] S. Bloomfield, B. Völgyi. The diverse functional roles for independently firing neurons. This assumption implies that there exist connections within the VirtualRetina: http://www-sop.inria.fr/neuromathcomp/software/virtualretina/index.shtml
and regulation of neuronal gap junctions in the retina.
network of RGC which induces synchronization in firing.
Nature Reviews Neuroscience 10, 495-506 (July 2009). EnaS (Event neural assembly simulator): http://enas.gforge.inria.fr/
.
http://www-sop.inria.fr/neuromathcomp