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