V1 filter models

Objectives

Carry out classical physiological characterization of V1 model cells.
Understand how to tell simple from complex cells.
Examine the separability of SF and TF tuning.
Understand how Gabor function parameters influence tuning bandwidth.
Classical characacterization with drifting gratings
There are many ways to characterize the physiological properties of visual neurons. Here we describe one method that has been standardized across many labs and that involves the use of sinusoidal grating stimuli to characterize the receptive field (RF) in terms of preferences for direction, spatial frequency (SF), temporal frequency (TF) and size.
The goal is to find the optimal patch of drifting sinusoidal grating that defines the classical receptive field (CRF) of the neuron. The patch of grating should end up approximating the Gabor function that is commonly drawn to represent the RF of a V1 neuron.
We will characterize the GaborSimp model. It is standard practice to begin with direction tuning, so the first experiment to run is,

Model: GaborSimp
Response: std.rsp
Stimulus: sine_dir
tn: 1024

If you are not yet familiar with how to run this modeling experiment, please go carefully through the instructions in Lesson 1.
When the results are available, launch the nData Viewer from the results page (by clicking on the "View ..." button), and plot the tuning curve. Your goal is simply to identify the preferred direction for the neuron. (Remember to change the "contrast" box to "1" in the nData Viewer.)
By the way, if you want to run more repeats of the stimulus to get better signal-to-noise on the tuning curves, just add the following in the Custom Parameter list:
  stim_nrpt 4
to request 4 repeats of each stimulus.
SF tuning
Now that you have identified the preferred direction (let us say that you found it to be 180 deg), use this setting when running the next experiment - spatial frequency (SF) tuning, as follows,

Model: GaborSimp
Response: std.rsp
Stimulus: sine_sf
tn: 1024
Params: stim_nrpt 4 direction 180

Plot the tuning curve, and estimate the preferred SF.
A widely used definition to distintuish Simple cells from Complex cells is the following: A cell is called a simple cell if its F1 response is greater than its DC response at the peak of its spatial frequency tuning currve. Note, the F1 to DC ratio is used as an index of simpleness, and this ratio can vary substantially with stimulus parameters.
If you look at the raster plot in the nData viewer, you notice the burst of spikes that occur at about 8 per second. This corresponds to the temporal frequency (TF) of the stimulus, which was held constant at 8 Hz so far.
TF tuning
Having identfied the best direction and SF, we will now use those values to run a temporal frequency (TF) tuning curve. One difference here is the duration of the simulation. When we present a low TF value, for example, 0.5 cyc/s, it takes two full seconds for the stimulus to travel 1 cycle. Therefore, we will let the stimulus run longer by setting tn to 2048 (to run for 4096 ms). In the experiments above, the default TF in the stimulus files was relatively high (e.g. 8 Hz); therefore, a shorter stimulus duration (smaller 'tn') was sufficient.
Let's say you have identified the preferred SF as being 3.5 cyc/deg, then add it to the list of parameters (you should use your own result in place of "3.5"), and run the TF tuning.

Model: GaborSimp
Response: std.rsp
Stimulus: sine_tf
tn: 2048
Params: stim_nrpt 4 direction 180 sf 3.5

When you view the results in the nData Viewer, note the patterning in the rasters that results as TF varies. When the F1 tuning curve is computed, the F1 amplitude will be computed at the TF that is appropriate for each group of rasters. Plot the resulting tuning curve and identify the preferred TF.
Size tuning
Now use all of the parameters that you have found so far to run a size tuning curve on the model. The size tuning stimulus is simply a set of gratings in which the diameter of the patch varies. We have skipped an important step, which is to be sure that the stimulus is centered on the RF. In this model, the RF is centered in the simulated patch of visual field, and all of the stimuli that we have used so far have been centered in the patch of simulated visual field.
It is worth taking a moment to view the size stimulus (click on the button in the Stimulus: row of the Model Execution table). Notice that you cannot really see the grating in space for the small aperture sizes. Does this matter?
(Remember to use your own custom parameter values, which probably differ from the ones listed below.)

Model: GaborSimp
Response: std.rsp
Stimulus: sine_size
tn: 1024
Params: stim_nrpt 4 direction 180 sf 3.5 tf 6.0

Analyze the results by plotting the tuning curve. What is the preferred size for this model unit? Not all tuning curves have distinct peaks. For size tuning, it is customary to define the preferred size of the classical receptive field to be the smallest diameter that achieves 95% of the maximum response. This method is intended to avoid problems created by having to choose a peak from somewhere along a noisy, relatively flat tuning curve.
Congratulations! At this point, you have run the basic experiments that a neurophysiologist would use to characterize the spiking response of a V1 cell and to identify an optimal stimulus among the set of drifting sine wave gratings. To convince yourself that you have found a better stimulus than the ones that we started with, compare the maximum firing rates (both F1 and DC) in the output of the last tuning curve (from the size tuning experiment) to the maximal firing rates in the first experiment (the direction tuning curve). How do these rates compare? One could even go back and re-run the direction tuning experiment, but with the optimal stimulus parameters (for SF, TF and size).
The separability of SF and TF tuning
The success of the above characterization depends on the independence of tuning for direction, SF, TF and size. In most V1 cells, the preferred direction does not depend strongly on the stimulus SF or TF. Nor is there a strong trend for SF and TF tuning to depend on each other.
To test whether this holds for the GaborSimp model above, you can run SF tuning curves at high and low values of TF (chosen from the flanks of the TF tuning curve), and likewise, run TF tuning for values of SF near the flanks of the SF tuning curve. Compare how the peaks vary for these different parameter combinations, and conclude for yourself whether these parameters are independent.
From a theoretical point of view, do you expect these parameters to be independent for a Gabor filer model?

Tuning bandwidth
In the Gabor filter model, it is obvious that the preferred direction and the preferred SF, measured from the tuning curves, are set by the parameters of the model file. However, it is less obvious what sets the bandwidth of these parameters. Here, bandwidth refers to the width of the peaks in the tuning curves, which for example could be measured as the full-width at half-maximum. You should experiment with the model filter parameters to see how you can change the bandwidth of the tuning curves. Here are some parameters that you might try to change:

filter.spatial/sd_orth
filter.spatial/sd_par
filter.spatial/sf

Which parameters have the greatest influence on orientation bandwidth? Which ones influence SF bandwidth? Why does this happen from the Fourier (frequency domain) perspective?

Characterizing a mystery model.
To demonstrate your mastery of characterizing V1 simple cells, use the techniques above to find the parameters for the optimal grating patch for the following model:

Model: GaborSimp.hid.01
Response: std.rsp
Stimulus: [... multiple ...]
tn: 1024
Params: stim_nrpt 4 [...]

This model has its RF parameters hidden. In addition, the model RF may not be centered in the visual field. Can you figure out how to design a stimulus that can characterize the location of the RF?

Simple vs. Complex cells
We will explore complex cell behavior in the next lesson Excerise 3, on the motion energy model.