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%matplotlib inline

The objective is to show you how to explore spectrally localized effects. For this purpose we adapt the method described in [1]_ and use it on the somato dataset. The idea is to track the band-limited temporal evolution of spatial patterns by using the :term:Global Field Power(GFP) <GFP>.

We first bandpass filter the signals and then apply a Hilbert transform. To reveal oscillatory activity the evoked response is then subtracted from every single trial. Finally, we rectify the signals prior to averaging across trials by taking the magniude of the Hilbert. Then the :term:GFP is computed as described in [2], using the sum of the squares but without normalization by the rank. Baselining is subsequently applied to make the :term:GFPs <GFP> comparable between frequencies. The procedure is then repeated for each frequency band of interest and all :term:GFPs <GFP> are visualized. To estimate uncertainty, non-parametric confidence intervals are computed as described in [3] across channels.

The advantage of this method over summarizing the Space x Time x Frequency output of a Morlet Wavelet in frequency bands is relative speed and, more importantly, the clear-cut comparability of the spectral decomposition (the same type of filter is used across all bands).

We will use this dataset: somato-dataset

References

.. [1] Hari R. and Salmelin R. Human cortical oscillations: a neuromagnetic view through the skull (1997). Trends in Neuroscience 20 (1), pp. 44-49. .. [2] Engemann D. and Gramfort A. (2015) Automated model selection in covariance estimation and spatial whitening of MEG and EEG signals, vol. 108, 328-342, NeuroImage. .. [3] Efron B. and Hastie T. Computer Age Statistical Inference (2016). Cambrdige University Press, Chapter 11.2.



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# Authors: Denis A. Engemann <denis.engemann@gmail.com>
#          Stefan Appelhoff <stefan.appelhoff@mailbox.org>
#
# License: BSD (3-clause)
import os.path as op

import numpy as np
import matplotlib.pyplot as plt

import mne
from mne.datasets import somato
from mne.baseline import rescale
from mne.stats import bootstrap_confidence_interval

Set parameters



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data_path = somato.data_path()
subject = '01'
task = 'somato'
raw_fname = op.join(data_path, 'sub-{}'.format(subject), 'meg',
                    'sub-{}_task-{}_meg.fif'.format(subject, task))

# let's explore some frequency bands
iter_freqs = [
    ('Theta', 4, 7),
    ('Alpha', 8, 12),
    ('Beta', 13, 25),
    ('Gamma', 30, 45)
]

We create average power time courses for each frequency band



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# set epoching parameters
event_id, tmin, tmax = 1, -1., 3.
baseline = None

# get the header to extract events
raw = mne.io.read_raw_fif(raw_fname)
events = mne.find_events(raw, stim_channel='STI 014')

frequency_map = list()

for band, fmin, fmax in iter_freqs:
    # (re)load the data to save memory
    raw = mne.io.read_raw_fif(raw_fname)
    raw.pick_types(meg='grad', eog=True)  # we just look at gradiometers
    raw.load_data()

    # bandpass filter
    raw.filter(fmin, fmax, n_jobs=1,  # use more jobs to speed up.
               l_trans_bandwidth=1,  # make sure filter params are the same
               h_trans_bandwidth=1)  # in each band and skip "auto" option.

    # epoch
    epochs = mne.Epochs(raw, events, event_id, tmin, tmax, baseline=baseline,
                        reject=dict(grad=4000e-13, eog=350e-6),
                        preload=True)
    # remove evoked response
    epochs.subtract_evoked()

    # get analytic signal (envelope)
    epochs.apply_hilbert(envelope=True)
    frequency_map.append(((band, fmin, fmax), epochs.average()))
    del epochs
del raw

Now we can compute the Global Field Power We can track the emergence of spatial patterns compared to baseline for each frequency band, with a bootstrapped confidence interval.

We see dominant responses in the Alpha and Beta bands.



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# Helper function for plotting spread
def stat_fun(x):
    """Return sum of squares."""
    return np.sum(x ** 2, axis=0)


# Plot
fig, axes = plt.subplots(4, 1, figsize=(10, 7), sharex=True, sharey=True)
colors = plt.get_cmap('winter_r')(np.linspace(0, 1, 4))
for ((freq_name, fmin, fmax), average), color, ax in zip(
        frequency_map, colors, axes.ravel()[::-1]):
    times = average.times * 1e3
    gfp = np.sum(average.data ** 2, axis=0)
    gfp = mne.baseline.rescale(gfp, times, baseline=(None, 0))
    ax.plot(times, gfp, label=freq_name, color=color, linewidth=2.5)
    ax.axhline(0, linestyle='--', color='grey', linewidth=2)
    ci_low, ci_up = bootstrap_confidence_interval(average.data, random_state=0,
                                                  stat_fun=stat_fun)
    ci_low = rescale(ci_low, average.times, baseline=(None, 0))
    ci_up = rescale(ci_up, average.times, baseline=(None, 0))
    ax.fill_between(times, gfp + ci_up, gfp - ci_low, color=color, alpha=0.3)
    ax.grid(True)
    ax.set_ylabel('GFP')
    ax.annotate('%s (%d-%dHz)' % (freq_name, fmin, fmax),
                xy=(0.95, 0.8),
                horizontalalignment='right',
                xycoords='axes fraction')
    ax.set_xlim(-1000, 3000)

axes.ravel()[-1].set_xlabel('Time [ms]')

Explore event-related dynamics for specific frequency bands

References