Intro to GLM Analysis: a single-run, single-subject fMRI dataset

In this tutorial, we use a General Linear Model (GLM) to compare the fMRI signal during periods of auditory stimulation versus periods of rest.

Warning

The analysis described here is performed in the native space, directly on the original EPI scans without any spatial or temporal preprocessing. More sensitive results would likely be obtained on the corrected, spatially normalized and smoothed images.

Retrieving the data

Note

In this tutorial, we load the data using a data downloading function. To input your own data, you will need to provide a list of paths to your own files in the subject_data variable. These should abide to the Brain Imaging Data Structure (BIDS) organization.

from nilearn.datasets import fetch_spm_auditory

subject_data = fetch_spm_auditory()
[get_dataset_dir] Dataset found in /home/runner/work/nilearn/nilearn/nilearn_data/spm_auditory

Inspecting the dataset

print dataset descriptions

.. _spm_auditory_dataset:

SPM auditory dataset
====================

Access
------
See :func:`nilearn.datasets.fetch_spm_auditory`.

Notes
-----
These whole brain BOLD/EPI images were acquired on a modified 2T Siemens MAGNETOM Vision system.
Each acquisition consisted of 64 contiguous slices (64x64x64 3mm x 3mm x 3mm voxels).
Acquisition took 6.05 seconds, with the scan to scan repeat time (RT) set arbitrarily to 7 seconds.

96 acquisitions were made (RT= 7 seconds), in blocks of 6, giving 16 blocks of 42 seconds.
The condition for successive blocks alternated between rest and auditory stimulation,
starting with rest.

Auditory stimulation was bi-syllabic words presented binaurally at a rate of 60 per minute.

A structural image was also acquired.

.. warning::

    This dataset is a raw BIDS dataset.
    The data are in the native space
    and no spatial or temporal preprocessing has been performed.

This experiment was conducted by Geriant Rees
under the direction of Karl Friston and the FIL methods group.

See :footcite:t:`spm_auditory`.

Content
-------
    :'func': Paths to functional images
    :'anat': Path to anat image
    :'events': Path to events.tsv
    :'description': Data description

References
----------

.. footbibliography::

License
-------
The purpose was to explore new equipment and techniques.
As such it has not been formally written up,
and is freely available for personal education and evaluation purposes.
Those wishing to use these data for other purposes,
including published evaluation of methods,
should contact the methods group at the Wellcome Department of Cognitive Neurology.

print paths of func image

'/home/runner/work/nilearn/nilearn/nilearn_data/spm_auditory/MoAEpilot/sub-01/func/sub-01_task-auditory_bold.nii'

We can display the mean functional image and the subject’s anatomy:

from nilearn.image import mean_img
from nilearn.plotting import plot_anat, plot_img, plot_stat_map, show

fmri_img = subject_data.func
mean_img = mean_img(subject_data.func[0], copy_header=True)
plot_img(mean_img, colorbar=True, cbar_tick_format="%i", cmap="gray")

plot_anat(subject_data.anat, colorbar=True, cbar_tick_format="%i")

show()
  • plot single subject single run
  • plot single subject single run

Specifying the experimental paradigm

We must now provide a description of the experiment, that is, define the timing of the auditory stimulation and rest periods. This is typically provided in an events.tsv file. The path of this file is provided in the dataset.

onset duration trial_type
0 42 42 listening
1 126 42 listening
2 210 42 listening
3 294 42 listening
4 378 42 listening
5 462 42 listening
6 546 42 listening


Performing the GLM analysis

It is now time to create and estimate a FirstLevelModel object, that will generate the design matrix using the information provided by the events object.

from nilearn.glm.first_level import FirstLevelModel

Parameters of the first-level model

  • t_r=7(s) is the time of repetition of acquisitions

  • noise_model='ar1' specifies the noise covariance model: a lag-1 dependence

  • standardize=False means that we do not want to rescale the time series to mean 0, variance 1

  • hrf_model='spm' means that we rely on the SPM “canonical hrf” model (without time or dispersion derivatives)

  • drift_model='cosine' means that we model the signal drifts as slow oscillating time functions

  • high_pass=0.01 (Hz) defines the cutoff frequency (inverse of the time period).

fmri_glm = FirstLevelModel(
    t_r=7,
    noise_model="ar1",
    standardize=False,
    hrf_model="spm",
    drift_model="cosine",
    high_pass=0.01,
)

Now that we have specified the model, we can run it on the fMRI image

One can inspect the design matrix (rows represent time, and columns contain the predictors).

Formally, we have taken the first design matrix, because the model is implictily meant to for multiple runs.

from nilearn.plotting import plot_design_matrix

plot_design_matrix(design_matrix)

show()
plot single subject single run

Save the design matrix image to disk first create a directory where you want to write the images

from pathlib import Path

output_dir = Path.cwd() / "results" / "plot_single_subject_single_run"
output_dir.mkdir(exist_ok=True, parents=True)
print(f"Output will be saved to: {output_dir}")

plot_design_matrix(design_matrix, output_file=output_dir / "design_matrix.png")
Output will be saved to: /home/runner/work/nilearn/nilearn/examples/00_tutorials/results/plot_single_subject_single_run

The first column contains the expected response profile of regions which are sensitive to the auditory stimulation. Let’s plot this first column

import matplotlib.pyplot as plt

plt.plot(design_matrix["listening"])
plt.xlabel("scan")
plt.title("Expected Auditory Response")

show()
Expected Auditory Response

Detecting voxels with significant effects

To access the estimated coefficients (Betas of the GLM model), we created contrast with a single ‘1’ in each of the columns: The role of the contrast is to select some columns of the model –and potentially weight them– to study the associated statistics. So in a nutshell, a contrast is a weighted combination of the estimated effects. Here we can define canonical contrasts that just consider the effect of the stimulation in isolation.

Note

Here the baseline is implicit, so passing a value of 1 for the first column will give contrast for: listening > rest

Let’s look at it: plot the coefficients of the contrast, indexed by the names of the columns of the design matrix.

plot single subject single run
<Axes: label='conditions'>

Below, we compute the ‘estimated effect’. It is in BOLD signal unit, but has no statistical guarantees, because it does not take into account the associated variance.

eff_map = fmri_glm.compute_contrast(activation, output_type="effect_size")

In order to get statistical significance, we form a t-statistic, and directly convert it into z-scale. The z-scale means that the values are scaled to match a standard Gaussian distribution (mean=0, variance=1), across voxels, if there were no effects in the data.

z_map = fmri_glm.compute_contrast(activation, output_type="z_score")

Plot thresholded z scores map

We display it on top of the average functional image of the series (could be the anatomical image of the subject). We use arbitrarily a threshold of 3.0 in z-scale. We’ll see later how to use corrected thresholds. We will show 3 axial views, with display_mode=’z’ and cut_coords=3.

plotting_config = {
    "bg_img": mean_img,
    "display_mode": "z",
    "cut_coords": 3,
    "black_bg": True,
}
plot_stat_map(
    z_map,
    threshold=3,
    title="listening > rest (|Z|>3)",
    figure=plt.figure(figsize=(10, 4)),
    **plotting_config,
)
show()
plot single subject single run

Note

Notice how the visualisations above shows both ‘activated’ voxels with Z > 3, as well as ‘deactivated’ voxels with Z < -3. In the rest of this example we will show only the activate voxels by using one-sided tests.

Statistical significance testing

One should worry about the statistical validity of the procedure: here we used an arbitrary threshold of 3.0 but the threshold should provide some guarantees on the risk of false detections (aka type-1 errors in statistics). One suggestion is to control the false positive rate (fpr, denoted by alpha) at a certain level, e.g. 0.001: this means that there is 0.1% chance of declaring an inactive voxel, active.

from nilearn.glm import threshold_stats_img

clean_map, threshold = threshold_stats_img(
    z_map,
    alpha=0.001,
    height_control="fpr",
    two_sided=False,  # using a one-sided test
)
# Let's use a sequential colormap as we will only display positive values.
plotting_config["cmap"] = "black_red"
plot_stat_map(
    clean_map,
    threshold=threshold,
    title=(
        "listening > rest (Uncorrected p<0.001; "
        f"threshold: {threshold:.3f})"
    ),
    figure=plt.figure(figsize=(10, 4)),
    **plotting_config,
)
show()
plot single subject single run

The problem is that with this you expect 0.001 * n_voxels to show up while they’re not active — tens to hundreds of voxels. A more conservative solution is to control the family wise error rate, i.e. the probability of making only one false detection, say at 5%. For that we use the so-called Bonferroni correction.

clean_map, threshold = threshold_stats_img(
    z_map, alpha=0.05, height_control="bonferroni", two_sided=False
)
plot_stat_map(
    clean_map,
    threshold=threshold,
    title=(
        "listening > rest (p<0.05 Bonferroni-corrected, "
        f"threshold: {threshold:.3f})"
    ),
    figure=plt.figure(figsize=(10, 4)),
    **plotting_config,
)
show()
plot single subject single run

This is quite conservative indeed! A popular alternative is to control the expected proportion of false discoveries among detections. This is called the False discovery rate.

clean_map, threshold = threshold_stats_img(
    z_map, alpha=0.05, height_control="fdr", two_sided=False
)
plot_stat_map(
    clean_map,
    threshold=threshold,
    title=(
        "listening > rest (p<0.05 FDR-corrected; "
        f"threshold: {threshold:.3f})"
    ),
    figure=plt.figure(figsize=(10, 4)),
    **plotting_config,
)
show()
plot single subject single run

Finally people like to discard isolated voxels (aka “small clusters”) from these images. It is possible to generate a thresholded map with small clusters removed by providing a cluster_threshold argument. Here clusters smaller than 10 voxels will be discarded.

clean_map, threshold = threshold_stats_img(
    z_map,
    alpha=0.05,
    height_control="fdr",
    cluster_threshold=10,
    two_sided=False,
)
plot_stat_map(
    clean_map,
    threshold=threshold,
    title=(
        "listening > rest "
        f"(p<0.05 FDR-corrected; threshold: {threshold:.3f}; "
        "clusters > 10 voxels)"
    ),
    figure=plt.figure(figsize=(10, 4)),
    **plotting_config,
)
show()
plot single subject single run

We can save the effect and zscore maps to the disk.

z_map.to_filename(output_dir / "listening_gt_rest_z_map.nii.gz")
eff_map.to_filename(output_dir / "listening_gt_rest_eff_map.nii.gz")

We can furthermore extract and report the found positions in a table.

from nilearn.reporting import get_clusters_table

table = get_clusters_table(
    z_map, stat_threshold=threshold, cluster_threshold=20
)
table
Cluster ID X Y Z Peak Stat Cluster Size (mm3)
0 1 -60.0 -6.0 42.0 9.341729 3888
1 1a -51.0 -12.0 39.0 7.952826
2 1b -63.0 0.0 42.0 7.595170
3 1c -42.0 -12.0 39.0 7.034967
4 2 60.0 0.0 36.0 8.738699 1620
5 2a 45.0 -12.0 42.0 6.850138
6 2b 69.0 6.0 30.0 4.062676
7 3 66.0 15.0 27.0 7.947193 837
8 3a 51.0 3.0 30.0 6.676518
9 4 36.0 -3.0 15.0 7.945328 1161
10 4a 39.0 -12.0 12.0 5.511866
11 5 51.0 30.0 27.0 6.825038 675
12 5a 48.0 21.0 27.0 6.763636
13 5b 57.0 39.0 27.0 5.631803
14 6 45.0 -18.0 57.0 5.901255 972
15 6a 39.0 -15.0 63.0 5.213951
16 6b 45.0 -21.0 63.0 4.108046
17 6c 36.0 -9.0 66.0 4.090935
18 7 -15.0 -60.0 66.0 5.005065 864
19 7a -15.0 -60.0 57.0 4.546246
20 7b -3.0 -60.0 57.0 4.463430
21 8 -12.0 -69.0 51.0 4.269133 540
22 8a -18.0 -63.0 48.0 4.081260
23 8b -6.0 -69.0 51.0 3.530991


This table can be saved for future use.

table.to_csv(output_dir / "table.csv")

Performing an F-test

“listening > rest” is a typical t test: condition versus baseline. Another popular type of test is an F test in which one seeks whether a certain combination of conditions (possibly two-, three- or higher-dimensional) explains a significant proportion of the signal. Here one might for instance test which voxels are well explained by the combination of more active or less active than rest.

Note

As opposed to t-tests, the beta images produced by of F-tests only contain positive values.

Specify the contrast and compute the corresponding map. Actually, the contrast specification is done exactly the same way as for t-contrasts.

z_map = fmri_glm.compute_contrast(
    activation,
    output_type="z_score",
    stat_type="F",  # set stat_type to 'F' to perform an F test
)

Note that the statistic has been converted to a z-variable, which makes it easier to represent it.

clean_map, threshold = threshold_stats_img(
    z_map,
    alpha=0.05,
    height_control="fdr",
    cluster_threshold=10,
    two_sided=False,
)
plot_stat_map(
    clean_map,
    threshold=threshold,
    title="Effects of interest (fdr=0.05), clusters > 10 voxels",
    figure=plt.figure(figsize=(10, 4)),
    **plotting_config,
)
show()
plot single subject single run

Total running time of the script: (0 minutes 14.853 seconds)

Estimated memory usage: 843 MB

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