In [ ]:

```
%matplotlib inline
```

This example shows how to produce seed-to-voxel correlation maps for a single
subject based on movie-watching fMRI scans.
These maps depict the temporal correlation of a **seed region** with the
**rest of the brain**.

This example is an advanced one that requires manipulating the data with numpy. Note the difference between images, that lie in brain space, and the numpy array, corresponding to the data inside the mask.

See also `for a similar example using cortical surface input data

<sphx_glr_auto_examples_01_plotting_plot_surf_stat_map.py>`.

In [ ]:

```
# author: Franz Liem
```

In [ ]:

```
# We will work with the first subject of the brain development fmri data set.
# dataset.func is a list of filenames. We select the 1st (0-based)
# subject by indexing with [0]).
from nilearn import datasets
dataset = datasets.fetch_development_fmri(n_subjects=1)
func_filename = dataset.func[0]
confound_filename = dataset.confounds[0]
```

Note that func_filename and confound_filename are strings pointing to files on your hard drive.

In [ ]:

```
print(func_filename)
print(confound_filename)
```

We are going to extract signals from the functional time series in two
steps. First we will extract the mean signal within the **seed region of
interest**. Second, we will extract the **brain-wide voxel-wise time series**.

We will be working with one seed sphere in the Posterior Cingulate Cortex (PCC), considered part of the Default Mode Network.

In [ ]:

```
pcc_coords = [(0, -52, 18)]
```

We use :class:`nilearn.input_data.NiftiSpheresMasker`

to extract the
**time series from the functional imaging within the sphere**. The
sphere is centered at pcc_coords and will have the radius we pass the
NiftiSpheresMasker function (here 8 mm).

The extraction will also detrend, standardize, and bandpass filter the data. This will create a NiftiSpheresMasker object.

In [ ]:

```
from nilearn import input_data
seed_masker = input_data.NiftiSpheresMasker(
pcc_coords, radius=8,
detrend=True, standardize=True,
low_pass=0.1, high_pass=0.01, t_r=2,
memory='nilearn_cache', memory_level=1, verbose=0)
```

Then we extract the mean time series within the seed region while regressing out the confounds that can be found in the dataset's csv file

In [ ]:

```
seed_time_series = seed_masker.fit_transform(func_filename,
confounds=[confound_filename])
```

Next, we can proceed similarly for the **brain-wide voxel-wise time
series**, using :class:`nilearn.input_data.NiftiMasker`

with the same input
arguments as in the seed_masker in addition to smoothing with a 6 mm kernel

In [ ]:

```
brain_masker = input_data.NiftiMasker(
smoothing_fwhm=6,
detrend=True, standardize=True,
low_pass=0.1, high_pass=0.01, t_r=2,
memory='nilearn_cache', memory_level=1, verbose=0)
```

Then we extract the brain-wide voxel-wise time series while regressing out the confounds as before

In [ ]:

```
brain_time_series = brain_masker.fit_transform(func_filename,
confounds=[confound_filename])
```

We can now inspect the extracted time series. Note that the **seed time
series** is an array with shape n_volumes, 1), while the
**brain time series** is an array with shape (n_volumes, n_voxels).

In [ ]:

```
print("Seed time series shape: (%s, %s)" % seed_time_series.shape)
print("Brain time series shape: (%s, %s)" % brain_time_series.shape)
```

We can plot the **seed time series**.

In [ ]:

```
import matplotlib.pyplot as plt
plt.plot(seed_time_series)
plt.title('Seed time series (Posterior cingulate cortex)')
plt.xlabel('Scan number')
plt.ylabel('Normalized signal')
plt.tight_layout()
```

Exemplarily, we can also select 5 random voxels from the **brain-wide
data** and plot the time series from.

In [ ]:

```
plt.plot(brain_time_series[:, [10, 45, 100, 5000, 10000]])
plt.title('Time series from 5 random voxels')
plt.xlabel('Scan number')
plt.ylabel('Normalized signal')
plt.tight_layout()
```

Now that we have two arrays (**sphere signal**: (n_volumes, 1),
**brain-wide voxel-wise signal** (n_volumes, n_voxels)), we can correlate
the **seed signal** with the **signal of each voxel**. The dot product of
the two arrays will give us this correlation. Note that the signals have
been variance-standardized during extraction. To have them standardized to
norm unit, we further have to divide the result by the length of the time
series.

In [ ]:

```
import numpy as np
seed_to_voxel_correlations = (np.dot(brain_time_series.T, seed_time_series) /
seed_time_series.shape[0]
)
```

The resulting array will contain a value representing the correlation
values between the signal in the **seed region** of interest and **each
voxel's signal**, and will be of shape (n_voxels, 1). The correlation
values can potentially range between -1 and 1.

In [ ]:

```
print("Seed-to-voxel correlation shape: (%s, %s)" %
seed_to_voxel_correlations.shape)
print("Seed-to-voxel correlation: min = %.3f; max = %.3f" % (
seed_to_voxel_correlations.min(), seed_to_voxel_correlations.max()))
```

We can now plot the seed-to-voxel correlation map and perform thresholding to only show values more extreme than +/- 0.5. Before displaying, we need to create an in memory Nifti image object. Furthermore, we can display the location of the seed with a sphere and set the cross to the center of the seed region of interest.

In [ ]:

```
from nilearn import plotting
seed_to_voxel_correlations_img = brain_masker.inverse_transform(
seed_to_voxel_correlations.T)
display = plotting.plot_stat_map(seed_to_voxel_correlations_img,
threshold=0.5, vmax=1,
cut_coords=pcc_coords[0],
title="Seed-to-voxel correlation (PCC seed)"
)
display.add_markers(marker_coords=pcc_coords, marker_color='g',
marker_size=300)
# At last, we save the plot as pdf.
display.savefig('pcc_seed_correlation.pdf')
```

Finally, we can Fisher-z transform the data to achieve a normal distribution. The transformed array can now have values more extreme than +/- 1.

In [ ]:

```
seed_to_voxel_correlations_fisher_z = np.arctanh(seed_to_voxel_correlations)
print("Seed-to-voxel correlation Fisher-z transformed: min = %.3f; max = %.3f"
% (seed_to_voxel_correlations_fisher_z.min(),
seed_to_voxel_correlations_fisher_z.max()
)
)
# Finally, we can transform the correlation array back to a Nifti image
# object, that we can save.
seed_to_voxel_correlations_fisher_z_img = brain_masker.inverse_transform(
seed_to_voxel_correlations_fisher_z.T)
seed_to_voxel_correlations_fisher_z_img.to_filename(
'pcc_seed_correlation_z.nii.gz')
```