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Parameters tuning in Virtual
Retina using Gibbs distribution
Introduction
• Development of the Virtual Retina Simulator
(Phd. Adrien Wohrer, 2008).
• The goal was to develop a retina ...
• Question A: Does the virtual retina simulator
accurately reproduce a realistic collective response?
• Answer A :No.
• Qu...
The vertebrate
retina structure
The Vision system
We are interested in the Retina part
Eyes Optic nerves
Retina
[Wikipedia]
The eye
Light Action Potential
Retina
The information goes as action potentials from the retina to the brain
[Wikipedia]
What is an Action potential
-Chemical changes across the membrane under a stimuli (light, pressure, heat …)
-Undergoes to ...
The Retina Structure
A. Wohrer et al, Virtual Retina: a biological retina model and simulator, with
contrast gain control....
Ganglion cells types (10-15 types)
• They are different in morphology.
• Two main types: ON and OFF.
▫ ON: Fire a spike un...
The virtual retina simulator
Introduction
The Retina model
-Feedback Ganglion –
Amacrine has not been
implemented
Input Image
Simulator
The spike train (Ganglion cells)
Then?
Some notes before!
• Allows large scale simulation with low computational
cost (more that 100,000 ganglion cells).
•...
• After doing statistics and comparing the simulator
result with the real data results we got the following
result: The Vi...
Why the ganglion cells in the retina
have correlated spike output?
▫ Overlap of the receptive field.
▫ Dynamical correlati...
Notations
Note
Neuron i
Neuron j
. . .
Spike Block
Set of consecutive spike blocks = word
Correlation
• Measures the synchrony of the cell’s spiking
behavior.
• We see how many times two cells spike together.
(In...
Correlation
• We cannot know the correlation value from one
measure but:
▫ We estimate it for several sample (spike train)...
i
j
Correlation
Raster Length
T
2T 3T
4T
2T 3T 4TT
Comparing statistics between the real and
virtual retina
Experiments
• Real data: Institut de la vision de Paris (Bodgan Kolomiets, serge
picaud – Picaud team).
• B. Kolomiets et ...
Real data
• Acquisition with a standard MEA electrode.
• ~ 30 sec. of spontaneous activity and 60 sec. of
evoked potential...
Correlation outlook – Spontaneous
Correlation outlook – Evoked potential
Virtual retina statistics
Experiment protocol
Image series
(Static)
Virtual
Retina
Simulator
Spike Train
Statistics
Customizing Retina
Interpretation
Simulation with Virtual Retina – ON cells
Simulation with Virtual Retina – OFF cells
Simulation of evoked potential using VR
Correlation – Evoked potential with VR
Which model fits the virtual retina spike train
statistics (vanishing correlation)?
Answer: Independent ganglion cells (Be...
Bernoulli model
Even in the independent case the empirical
correlation is not zero, its tend to 0 as:
The correlation tends to zero very slowly as
Comparison - Evoked
Simulation experiment Real experiment
Comparison – Spontaneous
Virtual Retina
Bernoulli Distribution Real Data
Partial Conclusion – What probably
causes the correlations?
• Taking into account that the VR implement the
effect of “rec...
▫ Overlap of the receptive field.
▫ Dynamical correlation possibly because:
 Feedback effects between the retina layers.
...
Analyzing statistics via Gibbs
distribution
It is:
• A Canonical distribution to analyze statistics of
time series in dynamical systems or stochastic
process. Slightl...
Gibbs Potential
• Fixing a priori constraints to obtain an
approximation of the exact potential (usually
unknown), by maxi...
Ex 1: Bernoulli
• A network of N neurons.
▫ They are independent.
▫ Stationary behavior.
▫ Maximizing entropy under rate c...
Ex 2: Ising (taking into account rates
and spatial correlations)
• In the Ising model, we take the interaction
between the...
How can we compute the effective
connectivity?
• The EnaS (event neural assembly simulation),
developed in INRIA.
• Made f...
Reference
• Entropy-based parametric estimation of spike
train statistics. J.C. Vasquez et al. 2010.
Home Page
Performing statistics with the Ising
model with real data in order to
compute the connectivity
Negative values !!!
Positive values
Firing rate
Gap Junction
• There are two types of neural connections:
▫ Electrical = Direct : The gap junction (between
neighbor cells...
The Gap junction is modeled by a
simple resistor
Gap Junction
Current leakage
Cell 1 Cell 2
What does Negative connectivit...
Now, let’s see what do biologists and
bibliography say!
Brivanlou et al. 1998
• Short term correlation 
Gap junction.
• Medium correlations: gap
junction between the
amacrine cells!
• Broad correlati...
Jang Hee Ye et al. 2008
With synapse blocker (For chemical
connections):
Discussion
• We verified that the virtual retina doesn’t
reproduce the correlations between the ganglion
cells.
• By compa...
• Ising model is just an approximation (just “after”
Bernoulli). What would give more general potential
the propagation de...
Future (known) work
• Search more in the bibliography about the
anatomical connectivity map.
• implement a simple gap junc...
Publications (Submitted in NeuroComp
2010)
• Parametric estimation of Spike train statistics by
Gibbs distributions : an a...
Thanks
• Thanks
Parameters tuning in Virtual Retina using Gibbs distribution
Parameters tuning in Virtual Retina using Gibbs distribution
Parameters tuning in Virtual Retina using Gibbs distribution
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Parameters tuning in Virtual Retina using Gibbs distribution

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Parameters tuning in Virtual Retina using Gibbs distribution

  1. 1. Parameters tuning in Virtual Retina using Gibbs distribution
  2. 2. Introduction • Development of the Virtual Retina Simulator (Phd. Adrien Wohrer, 2008). • The goal was to develop a retina model that allows a large scale simulations (thousands of neurons). • The scientific community is hardly investigating the collective response of the neurons (inferring statistics in a network of cells and not in one cell)  Suspect about the performance of the Virtual Retina in term of the collective answer.
  3. 3. • Question A: Does the virtual retina simulator accurately reproduce a realistic collective response? • Answer A :No. • Question B: How to check it? • Answer B: By inferring statistics. • Question C: If not, how can we improve the virtual retina so that it better reproduces the real collective response. • Answer C: Adding missing circuits (e.g. connections between the retinal ganglion cells). • Goal of the internship: ▫ Make one step toward answering the previous questions.
  4. 4. The vertebrate retina structure
  5. 5. The Vision system We are interested in the Retina part Eyes Optic nerves Retina [Wikipedia]
  6. 6. The eye Light Action Potential Retina The information goes as action potentials from the retina to the brain [Wikipedia]
  7. 7. What is an Action potential -Chemical changes across the membrane under a stimuli (light, pressure, heat …) -Undergoes to the brain to interpret the message. -Order for a function (From the brain to an organ). [Wikipedia]
  8. 8. The Retina Structure A. Wohrer et al, Virtual Retina: a biological retina model and simulator, with contrast gain control. Journal of Computational Neuroscience Volume 26:2, pp. 219-249, 2009 Feedbacks
  9. 9. Ganglion cells types (10-15 types) • They are different in morphology. • Two main types: ON and OFF. ▫ ON: Fire a spike under a stimulation. ▫ OFF: Fire a spike under an inhibition. Alpha (Y) cells Beta (X) cells
  10. 10. The virtual retina simulator
  11. 11. Introduction
  12. 12. The Retina model -Feedback Ganglion – Amacrine has not been implemented
  13. 13. Input Image Simulator
  14. 14. The spike train (Ganglion cells)
  15. 15. Then? Some notes before! • Allows large scale simulation with low computational cost (more that 100,000 ganglion cells). • Reproduces some biological plausibility at the level of individual ganglion cells. Virtual Retina ModelReal cat cells Enroth-cugell & Robson, 66
  16. 16. • After doing statistics and comparing the simulator result with the real data results we got the following result: The Virtual Retina is able to reproduce an accurate single ganglion cell spike train but it’s is unable to reproduce an accurate raster for the whole retina ganglion cells network. Why? What about the collective response?
  17. 17. Why the ganglion cells in the retina have correlated spike output? ▫ Overlap of the receptive field. ▫ Dynamical correlation possibly because:  Feedback effects between the retina layers.  Possible connections (direct/indirect) between the ganglion cells.  Other possibilities?? Retina –Ganglion cells Receptive fields Ganglion cells in Virtual Retina Ganglion cells in Real Retina
  18. 18. Notations Note Neuron i Neuron j . . . Spike Block Set of consecutive spike blocks = word
  19. 19. Correlation • Measures the synchrony of the cell’s spiking behavior. • We see how many times two cells spike together. (Instantaneous) Correlation Correlation N1 N2 N3
  20. 20. Correlation • We cannot know the correlation value from one measure but: ▫ We estimate it for several sample (spike train) lengths. ▫ We see how it evolve with the sample length (T). • Empirical estimation:
  21. 21. i j Correlation Raster Length T 2T 3T 4T 2T 3T 4TT
  22. 22. Comparing statistics between the real and virtual retina
  23. 23. Experiments • Real data: Institut de la vision de Paris (Bodgan Kolomiets, serge picaud – Picaud team). • B. Kolomiets et al. Late histological and functional changes in the P23H rat retina after photoreceptor loss. Neurobiology of Disease 38 (2010) 47–58
  24. 24. Real data • Acquisition with a standard MEA electrode. • ~ 30 sec. of spontaneous activity and 60 sec. of evoked potential. MEA Multi electrode array – Acquire the signal and transmits them to the computer to be processed. Acquired spike train
  25. 25. Correlation outlook – Spontaneous
  26. 26. Correlation outlook – Evoked potential
  27. 27. Virtual retina statistics
  28. 28. Experiment protocol Image series (Static) Virtual Retina Simulator Spike Train Statistics Customizing Retina Interpretation
  29. 29. Simulation with Virtual Retina – ON cells
  30. 30. Simulation with Virtual Retina – OFF cells
  31. 31. Simulation of evoked potential using VR
  32. 32. Correlation – Evoked potential with VR
  33. 33. Which model fits the virtual retina spike train statistics (vanishing correlation)? Answer: Independent ganglion cells (Bernoulli model).
  34. 34. Bernoulli model
  35. 35. Even in the independent case the empirical correlation is not zero, its tend to 0 as:
  36. 36. The correlation tends to zero very slowly as
  37. 37. Comparison - Evoked Simulation experiment Real experiment
  38. 38. Comparison – Spontaneous Virtual Retina Bernoulli Distribution Real Data
  39. 39. Partial Conclusion – What probably causes the correlations? • Taking into account that the VR implement the effect of “receptive field overlapping”, and, with the missing of the correlation in the spikes of VR we can say that: the correlation effect doesn’t come from the overlapping of receptive fields. It comes probably from anatomical connections (between RGC ?).
  40. 40. ▫ Overlap of the receptive field. ▫ Dynamical correlation possibly because:  Feedback effects between the retina layers.  Possible connections (direct/indirect) between the ganglion cells.  Other possibilities??
  41. 41. Analyzing statistics via Gibbs distribution
  42. 42. It is: • A Canonical distribution to analyze statistics of time series in dynamical systems or stochastic process. Slightly different from spatial Gibbs distribution in statistical physics or image deconvolution and denoising (thought with some analogies). • The conditional probability with a spike block that verifies: Past Gibbs Potential Conditional Partition Function
  43. 43. Gibbs Potential • Fixing a priori constraints to obtain an approximation of the exact potential (usually unknown), by maximizing the statistical entropy under these constraints guess Gibbs Potential Observable (ex: correlation)
  44. 44. Ex 1: Bernoulli • A network of N neurons. ▫ They are independent. ▫ Stationary behavior. ▫ Maximizing entropy under rate constraints gives a Bernoulli distribution with potential:
  45. 45. Ex 2: Ising (taking into account rates and spatial correlations) • In the Ising model, we take the interaction between the neurons into account. Effective connections between RGCs S. Cocco, S. Leibler and R. Monasson Neuronal couplings between retinal ganglion cells inferred by efficient inverse statistical physics methods PNAS, 2009
  46. 46. How can we compute the effective connectivity? • The EnaS (event neural assembly simulation), developed in INRIA. • Made for more general models, not limited just to Ising.
  47. 47. Reference • Entropy-based parametric estimation of spike train statistics. J.C. Vasquez et al. 2010. Home Page
  48. 48. Performing statistics with the Ising model with real data in order to compute the connectivity
  49. 49. Negative values !!! Positive values Firing rate
  50. 50. Gap Junction • There are two types of neural connections: ▫ Electrical = Direct : The gap junction (between neighbor cells). ▫ Chemical = Long distance: Synapses. academic.brooklyn.cuny.edu Gap Junction Synapses
  51. 51. The Gap junction is modeled by a simple resistor Gap Junction Current leakage Cell 1 Cell 2 What does Negative connectivity mean? -Negative current? -Inhibition? -Is there another surprising phenomena?
  52. 52. Now, let’s see what do biologists and bibliography say!
  53. 53. Brivanlou et al. 1998
  54. 54. • Short term correlation  Gap junction. • Medium correlations: gap junction between the amacrine cells! • Broad correlations synaptic connections between amacrine and/or bipolar cells. I. H. Brivanlou, D. K. Warland, and M. Meister. Mechanisms of concerted firing among retinal ganglion cells. Neuron, 20:527–529, March 1998.
  55. 55. Jang Hee Ye et al. 2008
  56. 56. With synapse blocker (For chemical connections):
  57. 57. Discussion • We verified that the virtual retina doesn’t reproduce the correlations between the ganglion cells. • By comparison between the different data types statistics, we see a serious need to improve the collective answer of retinal ganglion cells.
  58. 58. • Ising model is just an approximation (just “after” Bernoulli). What would give more general potential the propagation delay (Under current investigation with EnaS). • If we believe that the account for connections, then: ▫ The statistics we have done are not sufficient to add the connections. We need more information about the anatomical maps. ▫ We don’t know yet how to interpret the negative values of connectivity (between two neighbor cells) in the statistics.
  59. 59. Future (known) work • Search more in the bibliography about the anatomical connectivity map. • implement a simple gap junction model between neighbor cells in the virtual retina. • Implement synapses between distant cells.
  60. 60. Publications (Submitted in NeuroComp 2010) • Parametric estimation of Spike train statistics by Gibbs distributions : an application to bio- inspired technologies. J.C. Vasquez, B. Cessac, H. Nasser, T. Vieville, H. Conzalez, A. Palacios. • Spike train statistics in integrate and fire models. B.Cessac, H.Nasser, J.C. Vasquez
  61. 61. Thanks • Thanks

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