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"""
=========================================
Seed correlation/coherence with fMRI data
=========================================
Seed-based analysis is the analysis of a bivariate measure (such as correlation
or coherence) between one time-series (termed the 'seed') and many other
time-series (termed the 'targets'). This is a rather typical strategy in the
analysis of fMRI data where one might look for all the areas of the brain that
exhibit high level of connectivity to a particular region of interest.
We start by importing the needed modules. First modules from the standard lib
and from 3rd parties:
"""
import os
import numpy as np
import matplotlib.pyplot as plt
"""
Notice that nibabel (http://nipy.org.nibabel) is required in order to run this
example, so we test whether the user has that installed and throw an
informative error if not:
"""
try:
from nibabel import load
except ImportError:
raise ImportError('You need nibabel (http:/nipy.org/nibabel/) in order to run this example')
"""
The following are nitime modules:
"""
import nitime
import nitime.analysis as nta
import nitime.fmri.io as io
"""
We define the TR of the analysis and the frequency band of interest:
"""
TR = 1.35
f_lb = 0.02
f_ub = 0.15
"""
An fMRI data file with some actual fMRI data is shipped as part of the
distribution, the following line will find the path to this data on the
specific setup:
"""
data_path = test_dir_path = os.path.join(nitime.__path__[0], 'data')
fmri_file = os.path.join(data_path, 'fmri1.nii.gz')
"""
Read in the data, using nibabel:
"""
fmri_data = load(fmri_file)
"""
Notice that 'fmri_data' is not an array, but rather a NiftiImage
object. Nibabel cleverly delays the actual allocation of memory and reading
from file as long as possible. In this case, we only want information that is
available through the header of the nifti file, namely the dimensions of the
data.
We extract only the spatial dimensions of the data, excluding the last
dimension which is the time-dimension and generate a coords list:
"""
volume_shape = fmri_data.shape[:-1]
coords = list(np.ndindex(volume_shape))
"""
We choose some number of random voxels to serve as seed voxels:
"""
n_seeds = 3
# Choose n_seeds random voxels to be the seed voxels
seeds = np.random.randint(0, len(coords), n_seeds)
coords_seeds = np.array(coords)[seeds].T
"""
The entire volume is chosen to be the target:
"""
coords_target = np.array(coords).T
"""
We use nitime.fmri.io in order to generate TimeSeries objects from spatial
coordinates in the data file:
"""
# Make the seed time series:
time_series_seed = io.time_series_from_file(fmri_file,
coords_seeds,
TR=TR,
normalize='percent',
filter=dict(lb=f_lb,
ub=f_ub,
method='boxcar'))
# Make the target time series:
time_series_target = io.time_series_from_file(fmri_file,
coords_target,
TR=TR,
normalize='percent',
filter=dict(lb=f_lb,
ub=f_ub,
method='boxcar'))
"""
The SeedCoherencAnalyzer receives as input both of these TimeSeries and
calculates the coherence of each of the channels in the seed TimeSeries to
*all* the channels in the target TimeSeries. Here we initialize it with these
and with a method dict, which specifies the parameters of the spectral analysis
used for the coherence estimation:
"""
A = nta.SeedCoherenceAnalyzer(time_series_seed, time_series_target,
method=dict(NFFT=20))
"""
Similarly, the SeedCorrelationAnalyzer receives as input seed and target
time-series:
"""
B = nta.SeedCorrelationAnalyzer(time_series_seed, time_series_target)
"""
For the coherence, we are only interested in the physiologically relevant
frequency band:
"""
freq_idx = np.where((A.frequencies > f_lb) * (A.frequencies < f_ub))[0]
"""
The results in both analyzer objects are arrays of dimensions: (number of seeds
x number of targets). For the coherence, there is an additional last dimension
of: number of frequency bands, which we will average over. For the
visualization, we extract the coherence and correlation values for each one of
the seeds separately:
"""
cor = []
coh = []
for this_seed in range(n_seeds):
# Extract the coherence and average across these frequency bands:
coh.append(np.mean(A.coherence[this_seed][:, freq_idx], -1)) # Averaging on the
# last dimension
cor.append(B.corrcoef[this_seed]) # No need to do any additional
# computation
"""
We then put the coherence/correlation values back into arrays that have the
original shape of the volume from which the data was extracted:
"""
#For numpy fancy indexing into volume arrays:
coords_indices = list(coords_target)
vol_coh = []
vol_cor = []
for this_vol in range(n_seeds):
vol_coh.append(np.empty(volume_shape))
vol_coh[-1][coords_indices] = coh[this_vol]
vol_cor.append(np.empty(volume_shape))
vol_cor[-1][coords_indices] = cor[this_vol]
"""
We visualize this by choosing a random slice from the data:
"""
#Choose a random slice to display:
random_slice = np.random.randint(0, volume_shape[-1], 1)
"""
We display the coherence and correlation values for each seed voxel in this slice:
"""
fig01 = plt.figure()
fig02 = plt.figure()
ax_coh = []
ax_cor = []
for this_vox in range(n_seeds):
ax_coh.append(fig01.add_subplot(1, n_seeds, this_vox + 1))
ax_coh[-1].matshow(vol_coh[this_vox][:, :, random_slice].squeeze())
ax_coh[-1].set_title('Seed coords: %s' % coords_seeds[:, this_vox])
ax_cor.append(fig02.add_subplot(1, n_seeds, this_vox + 1))
ax_cor[-1].matshow(vol_cor[this_vox][:, :, random_slice].squeeze())
ax_cor[-1].set_title('Seed coords: %s' % coords_seeds[:, this_vox])
for x in zip(['Coherence', 'Correlation'], [fig01, fig02]):
suptit = '%s between all the voxels in slice: ' % x[0]
suptit += '%i and seed voxels' % random_slice
x[1].suptitle(suptit)
"""
We can now compare the results in the coherence:
.. image:: fig/seed_analysis_01.png
And the correlation:
.. image:: fig/seed_analysis_02.png
We call plt.show() in order to display the figure:
"""
plt.show()
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