What is Deconvolution?

Neuroscientists (amongst others) are often interested in time series that are derived from neural activity, such as fMRI BOLD and pupil dilation. However, for some classes of data (notably, pupil dilation and fMRI BOLD), neural activity gets temporally delayed and dispersed. This means that if the time series is related to some behavioral events that are close together in time, these event-related responses will contaminate each other.

from nideconv import simulate
import matplotlib.pyplot as plt
import seaborn as sns
sns.set_style('white')
sns.set_context('notebook')

Simulate data

Here we simulate fMRI data with a “cue - stimulus” design. There are four cues and stimulus pairs. The cue is always followed by a stimulus in 1, 2, 3, or 4 seconds. The cue leads to a small de-activation (0.5 % signal change), the stimulus a slight activation (1.0 % signal change)

cue_onsets = [5, 15, 25, 35]
stim_onsets = [6, 17, 28, 39]

cue_pars = {'name':'cue',
            'mu_group':-.5,
            'std_group':0,
            'onsets':cue_onsets}

stim_pars = {'name':'stim',
             'mu_group':1,
             'std_group':0,
             'onsets':stim_onsets}

conditions = [cue_pars,
              stim_pars]

data, onsets, parameters = simulate.simulate_fmri_experiment(conditions,
                                                             run_duration=60,
                                                             noise_level=0.1)

Plot simulated data

data.plot()
sns.despine()

for onset in cue_onsets:
    l1 =plt.axvline(onset, c='r')

for onset in stim_onsets:
    l2 =plt.axvline(onset, c='g')

plt.legend([l1, l2], ['Cue', 'Stimulus'])
plt.gcf().set_size_inches(10, 4)

Underlying data-generating model

Because we simulated the data, we know that the event-related responses should exactly follow the canonical Hemodynamic Response Function [1]_are

from nideconv.utils import double_gamma_with_d
import numpy as np

plt.figure(figsize=(12, 4))

t = np.linspace(0, 20, 100)
ax1 = plt.subplot(121)
plt.title('Ground truth cue-related response')
plt.plot(t, double_gamma_with_d(t) * -.5,
         c=sns.color_palette()[0])
plt.xlabel('Time since event (s)')
plt.ylabel('Percent signal change')
plt.axhline(0, c='k', ls='--')

plt.subplot(122, sharey=ax1)
plt.title('Ground truth stimulus-related response')
plt.plot(t, double_gamma_with_d(t),
         c=sns.color_palette()[1])
plt.axhline(0, c='k', ls='--')
plt.xlabel('Time since event (s)')
plt.ylabel('Percent signal change')

sns.despine()

Naive approach: epoched averaging

A simple approach that is more appropriate for fast electrphysiological signals like EEG and MEG would be to select little chunks of the time series, corresponding to the onset of our events-of-interest and the first 20 seconds (“epoching”).

nideconv

References

[1]	Glover et al., 1999

Total running time of the script: ( 0 minutes 1.155 seconds)