Network models of V1¶

This project will be used to test implementations in PyNN (and eventually NeuroML) of published models of primary visual cortex (V1) based on spiking point neurons.

An initial focus will be on Lauritzen and Miller, 2003, but other models investigated will include Ozeki et al., 2009 and Sadagopan and Ferster, 2012.

This project is part of the INCF participation in the Google Summer of Code 2014.

Troyer Model¶

Here I will describe briefly the implementation of pubmed:9671678.

In order to run this model is necessary to first install git and PyNN and the appropriate simulator.

After that you can clone directly from git using:

git clone https://github.com/OpenSourceBrain/V1NetworkModels.git

As the project stands at this moment the workflow can be described in two steps: first there are two scripts that implement the spatio-temporal filter in the retina and produce the spike-trains for each cell in the Lateral Geniculate Nucelus (LGN) and stores them for further use. Second, there is a file that loads those spike-trains and runs the simulation of the cortical networks in PyNN using them. The first task is executed by two scripts produce_lgn_spikes_on_cells.py and produce_lgn_spikes_off_cells.py which generates pickled files in the folder './data' with the spike trains and positions for a given contrast that is selected in the parameters of the script. After we have run the file to produce the spikes with a given contrast (which can be adjusted in the scripts mentioned above) we can run the main script full_model.py with the same contrast in order to run the complete model. At the beginning of this files we find the following parameters controlling the simulation:

factor = 1.0  # Reduction factor
Nside_exc = int(factor * Nside_exc)
Nside_inh = int(factor * Nside_inh)

Ncell_lgn = Nside_lgn * Nside_lgn
Ncell_exc = Nside_exc ** 2
Ncell_inh = Nside_inh ** 2

N_lgn_layers = 1

## Main connections
thalamo_cortical_connections = True # If True create connections from the thalamus to the cortex
feed_forward_inhibition = True # If True add feed-forward inhibition ( i -> e )
cortical_excitatory_feedback = True # If True add cortical excitatory feedback (e -> e) and ( e -> i )
background_noise = True  # If True add cortical noise
correlated_noise = False  # Makes the noise coorelated

# Save
save_voltage_and_conductances = False
save_orientation_response = False

# Plot
plot_conductance_analysis = True
plot_spike_analysis = True
plot_orientation_analysis = True

The factor parameter allows us to reduce the overall size of the cortical network by a given percentage (the square of it). We can also choose to use between one and four layers of the LGN in case we want with the parameter N_lgn_layers. Finally we can remove the connections and noise between the different networks with the bolean parameters bellow. We also have the settings here to plot relevant analysis of the data and save the data produced by the simulation here.

After we have run the model with a couple of contrasts and save them in the 'output_data' we can run the script compare_contrasts.py in order to see if contrast invariant orientation tuning holds for our data.

As the model stands, spike-trains and orientation curves are already given for four contrasts and the model can be tested right away.

Here bellow I describe in more detail all of the parts of the model

LGN - spikes¶

In brief, the Retina and the Thalamus part of the model can be represented by a spatio-temporal filter that, when convolved with the stimuli, will produce the firing rate of a given LGN cell. After that, we can use a non-homogeneous Poisson process to produce the corresponding spikes for each cell. We describe this in detail bellow.

Spatio-Temporal Receptive Field (STRF)¶

The file kernel_functions.py contains the code for creating the STRF. The spatial part of the kernel possess a center-surround architecture which is model as a different of Gaussians. The temporal part of the receptive field has a biphasic structure, we use the implementation describe in Cai et al (1998). The details of the implementation are described in detail in the companion blog of this project (link). Down here we present a kernel produce with this classes. The time here runs from left to right and from up to down as usual text, so we can see how the spatial components of the filter change in time with this series of two dimensional maps.

We also include a small script center_surround_plot.py that can be used to visualize the spatial component of the STRF and received immediate feedback on how the overall pattern changes when the parameters and resolutions are changed.

Stimuli¶

The file stimuli_functions.py contains the code for creating the stimuli. In particular we used the implementation of a full field sinusoidal grating with the parameters described in the paper. Down here we show an example of the stimuli at a particular point in time for illustration purposes:

Here we also included a small script sine_grating_plot.py to visualize the sine grating at a particular point in time.

Convolution¶

After we have the stimuli and the STRF we can use the convolution function defined in the file analysis_functions.py to calculate the response of LGN' neurons. The details of how the the convolution is implemented is described in the detail in the following entry of the blog (link). With this in our hand and using the parameters described in the paper we can already reproduce the first plot in Troyer's paper. The file lgn_firing_rate_troyer_plot1.py in the repository does this automatically for us and give us the next plot:

Here we can see the firing rate for an on and for an off cell subjected to the same stimuli. Note that they are off-phase and also the contrast dependent response. The responses are rectified after back ground noise was added.

Producing Spikes¶

After we have the firing rate of a neuron we can use the produce_spikes functions in the file analysis_functions.py. This functions takes the firing rate and using non-homogeneous Poisson process outputs an array with the spikes times. We provide one file produce_lgn_spikes_one.py for testing variations of parameters and as an example showcase.

Storing Spikes¶

Now we have the complete mechanism of spike creation. In the file produce_lgn_spikes.py. This file creates a grid of positions (This should correspond to the grid of LGN cells that we are going to use in PyNN) and produces the list of spikes associated with them as well as the positions. The particular stoage format that we are using is cPickled.

LGN - Network¶