"""
Beta-Series Modeling for Task-Based Functional Connectivity and Decoding
========================================================================
This example shows how to run beta series :term:`GLM` models, which are a
common modeling approach for a variety of analyses of task-based :term:`fMRI`
data with an event-related task design, including
:term:`functional connectivity`, :term:`decoding `, and
representational similarity analysis.
Beta series models fit trial-wise conditions, which allow users to create
"time series" of these trial-wise maps, which can be substituted for the
typical time series used in resting-state functional connectivity analyses.
Generally, these models are most useful for event-related task designs,
while other modeling approaches, such as psychophysiological interactions
(PPIs), tend to perform better in block designs, depending on the type of
analysis.
See :footcite:t:`Cisler2014` for more information about this,
in the context of functional connectivity analyses.
Two of the most well-known beta series modeling methods are
Least Squares- All (LSA) :footcite:p:`Rissman2004` and
Least Squares- Separate (LSS)
:footcite:p:`Mumford2012,Turner2012`.
In LSA, a single :term:`GLM` is run, in which each trial of each condition of
interest is separated out into its own condition within the design matrix.
In LSS, each trial of each condition of interest has its own :term:`GLM`,
in which the targeted trial receives its own column within the design matrix,
but everything else remains the same as the standard model.
Trials are then looped across, and many GLMs are fitted,
with the :term:`Parameter Estimate` map extracted from each GLM to build the
LSS beta series.
.. topic:: Choosing the right model for your analysis
We have chosen not to reproduce analyses systematically comparing beta
series modeling approaches in nilearn's documentation;
however, we do incorporate recommendations from the literature.
Rather than taking these recommendations at face value, please refer back
to the original publications and any potential updates to the literature,
when possible.
First, as mentioned above, according to :footcite:t:`Cisler2014`,
beta series models are most appropriate for event-related task designs.
For block designs, a PPI model is better suited- at least for
functional connectivity analyses.
According to :footcite:t:`Abdulrahman2016`,
the decision between LSA and LSS should be based on three factors:
inter-trial variability, scan noise, and stimulus onset timing.
While :footcite:t:`Mumford2012` proposes LSS as a tool
primarily for fast event-related designs (i.e., ones with short inter-trial
intervals), :footcite:t:`Abdulrahman2016` finds, in simulations,
that LSA performs better than LSS when trial variability is greater
than scan noise, even in fast designs.
.. include:: ../../../examples/masker_note.rst
"""
# sphinx_gallery_thumbnail_number = -2
import matplotlib.pyplot as plt
from nilearn import image, plotting
##############################################################################
# Prepare data and analysis parameters
# ------------------------------------
# Download data in :term:`BIDS` format and event information for one subject,
# and create a standard :class:`~nilearn.glm.first_level.FirstLevelModel`.
from nilearn.datasets import fetch_language_localizer_demo_dataset
from nilearn.glm.first_level import FirstLevelModel, first_level_from_bids
data_dir, _ = fetch_language_localizer_demo_dataset()
models, models_run_imgs, events_dfs, models_confounds = first_level_from_bids(
data_dir,
"languagelocalizer",
img_filters=[("desc", "preproc")],
)
# Grab the first subject's model, functional file, and events DataFrame
standard_glm = models[0]
fmri_file = models_run_imgs[0][0]
events_df = events_dfs[0][0]
# We will use first_level_from_bids's parameters for the other models
glm_parameters = standard_glm.get_params()
# We need to override one parameter (signal_scaling)
# with the value of scaling_axis
glm_parameters["signal_scaling"] = standard_glm.scaling_axis
##############################################################################
# Define the standard model
# -------------------------
# Here, we create a basic :term:`GLM` for this run, which we can use to
# highlight differences between the standard modeling approach and beta series
# models.
# We will just use the one created by
# :func:`~nilearn.glm.first_level.first_level_from_bids`.
standard_glm.fit(fmri_file, events_df)
# The standard design matrix has one column for each condition, along with
# columns for the confound regressors and drifts
fig, ax = plt.subplots(figsize=(5, 10))
plotting.plot_design_matrix(standard_glm.design_matrices_[0], ax=ax)
fig.show()
##############################################################################
# Define the LSA model
# --------------------
# We will now create a least squares- all (LSA) model.
# This involves a simple transformation, where each trial of interest receives
# its own unique trial type.
# It's important to ensure that the original trial types can be inferred from
# the updated trial-wise trial types, in order to collect the resulting
# beta maps into condition-wise beta series.
# Transform the DataFrame for LSA
lsa_events_df = events_df.copy()
conditions = lsa_events_df["trial_type"].unique()
condition_counter = {c: 0 for c in conditions}
for i_trial, trial in lsa_events_df.iterrows():
trial_condition = trial["trial_type"]
condition_counter[trial_condition] += 1
# We use a unique delimiter here (``__``) that shouldn't be in the
# original condition names
trial_name = f"{trial_condition}__{condition_counter[trial_condition]:03d}"
lsa_events_df.loc[i_trial, "trial_type"] = trial_name
lsa_glm = FirstLevelModel(**glm_parameters)
lsa_glm.fit(fmri_file, lsa_events_df)
fig, ax = plt.subplots(figsize=(10, 10))
plotting.plot_design_matrix(lsa_glm.design_matrices_[0], ax=ax)
fig.show()
##############################################################################
# Aggregate beta maps from the LSA model based on condition
# `````````````````````````````````````````````````````````
# Collect the :term:`Parameter Estimate` maps
lsa_beta_maps = {cond: [] for cond in events_df["trial_type"].unique()}
trialwise_conditions = lsa_events_df["trial_type"].unique()
for condition in trialwise_conditions:
beta_map = lsa_glm.compute_contrast(condition, output_type="effect_size")
# Drop the trial number from the condition name to get the original name
condition_name = condition.split("__")[0]
lsa_beta_maps[condition_name].append(beta_map)
# We can concatenate the lists of 3D maps into a single 4D beta series for
# each condition, if we want
lsa_beta_maps = {
name: image.concat_imgs(maps) for name, maps in lsa_beta_maps.items()
}
##############################################################################
# Define the LSS models
# ---------------------
# We will now create a separate LSS model for each trial of interest.
# The transformation is much like the LSA approach, except that we only
# relabel *one* trial in the DataFrame.
# We loop through the trials, create a version of the DataFrame where the
# targeted trial has a unique trial type, fit the model to that DataFrame,
# and finally collect the targeted trial's beta map for the beta series.
def lss_transformer(df, row_number):
"""Label one trial for one LSS model.
Parameters
----------
df : pandas.DataFrame
BIDS-compliant events file information.
row_number : int
Row number in the DataFrame.
This indexes the trial that will be isolated.
Returns
-------
df : pandas.DataFrame
Update events information, with the select trial's trial type isolated.
trial_name : str
Name of the isolated trial's trial type.
"""
df = df.copy()
# Determine which number trial it is *within the condition*
trial_condition = df.loc[row_number, "trial_type"]
trial_type_series = df["trial_type"]
trial_type_series = trial_type_series.loc[
trial_type_series == trial_condition
]
trial_type_list = trial_type_series.index.tolist()
trial_number = trial_type_list.index(row_number)
# We use a unique delimiter here (``__``) that shouldn't be in the
# original condition names.
# Technically, all you need is for the requested trial to have a unique
# 'trial_type' *within* the dataframe, rather than across models.
# However, we may want to have meaningful 'trial_type's (e.g., 'Left_001')
# across models, so that you could track individual trials across models.
trial_name = f"{trial_condition}__{trial_number:03d}"
df.loc[row_number, "trial_type"] = trial_name
return df, trial_name
# Loop through the trials of interest and transform the DataFrame for LSS
lss_beta_maps = {cond: [] for cond in events_df["trial_type"].unique()}
lss_design_matrices = []
for i_trial in range(events_df.shape[0]):
lss_events_df, trial_condition = lss_transformer(events_df, i_trial)
# Compute and collect beta maps
lss_glm = FirstLevelModel(**glm_parameters)
lss_glm.fit(fmri_file, lss_events_df)
# We will save the design matrices across trials to show them later
lss_design_matrices.append(lss_glm.design_matrices_[0])
beta_map = lss_glm.compute_contrast(
trial_condition,
output_type="effect_size",
)
# Drop the trial number from the condition name to get the original name
condition_name = trial_condition.split("__")[0]
lss_beta_maps[condition_name].append(beta_map)
# We can concatenate the lists of 3D maps into a single 4D beta series for
# each condition, if we want
lss_beta_maps = {
name: image.concat_imgs(maps) for name, maps in lss_beta_maps.items()
}
##############################################################################
# Show the design matrices for the first few trials
# `````````````````````````````````````````````````
fig, axes = plt.subplots(ncols=3, figsize=(20, 10))
for i_trial in range(3):
plotting.plot_design_matrix(
lss_design_matrices[i_trial],
ax=axes[i_trial],
)
axes[i_trial].set_title(f"Trial {i_trial + 1}")
fig.show()
##############################################################################
# Compare the three modeling approaches
# -------------------------------------
DM_TITLES = ["Standard GLM", "LSA Model", "LSS Model (Trial 1)"]
DESIGN_MATRICES = [
standard_glm.design_matrices_[0],
lsa_glm.design_matrices_[0],
lss_design_matrices[0],
]
fig, axes = plt.subplots(
ncols=3,
figsize=(20, 10),
gridspec_kw={"width_ratios": [1, 2, 1]},
)
for i_ax, ax in enumerate(axes):
plotting.plot_design_matrix(DESIGN_MATRICES[i_ax], ax=axes[i_ax])
axes[i_ax].set_title(DM_TITLES[i_ax])
fig.show()
##############################################################################
# Applications of beta series
# ---------------------------
# Beta series can be used much like resting-state data, though generally with
# vastly reduced degrees of freedom than a typical resting-state run, given
# that the number of trials should always be less than the number of volumes
# in a functional MRI run.
#
# Two common applications of beta series are to functional connectivity and
# decoding analyses.
# For an example of a beta series applied to decoding, see
# :ref:`sphx_glr_auto_examples_02_decoding_plot_haxby_glm_decoding.py`.
# Here, we show how the beta series can be applied to functional connectivity
# analysis.
# In the following section, we perform a quick task-based functional
# connectivity analysis of each of the two task conditions
# ('language' and 'string'), using the LSS beta series.
# This section is based on
# :ref:`sphx_glr_auto_examples_03_connectivity_plot_seed_to_voxel_correlation.py`,
# which goes into more detail about seed-to-voxel functional connectivity
# analyses.
import numpy as np
from nilearn.maskers import NiftiMasker, NiftiSpheresMasker
# Coordinate taken from Neurosynth's 'language' meta-analysis
coords = [(-54, -42, 3)]
# Initialize maskers for the seed and the rest of the brain
seed_masker = NiftiSpheresMasker(
coords,
radius=8,
detrend=True,
standardize="zscore_sample",
low_pass=None,
high_pass=None,
t_r=None,
memory="nilearn_cache",
memory_level=1,
verbose=0,
)
brain_masker = NiftiMasker(
smoothing_fwhm=6,
detrend=True,
standardize="zscore_sample",
low_pass=None,
high_pass=None,
t_r=None,
memory="nilearn_cache",
memory_level=1,
verbose=0,
)
# Perform the seed-to-voxel correlation for the LSS 'language' beta series
lang_seed_beta_series = seed_masker.fit_transform(lss_beta_maps["language"])
lang_beta_series = brain_masker.fit_transform(lss_beta_maps["language"])
lang_corrs = (
np.dot(
lang_beta_series.T,
lang_seed_beta_series,
)
/ lang_seed_beta_series.shape[0]
)
language_connectivity_img = brain_masker.inverse_transform(lang_corrs.T)
# Same but now for the LSS 'string' beta series
string_seed_beta_series = seed_masker.fit_transform(lss_beta_maps["string"])
string_beta_series = brain_masker.fit_transform(lss_beta_maps["string"])
string_corrs = (
np.dot(
string_beta_series.T,
string_seed_beta_series,
)
/ string_seed_beta_series.shape[0]
)
string_connectivity_img = brain_masker.inverse_transform(string_corrs.T)
# Show both correlation maps
fig, axes = plt.subplots(figsize=(10, 8), nrows=2)
display = plotting.plot_stat_map(
language_connectivity_img,
threshold=0.5,
vmax=1,
cut_coords=coords[0],
title="Language",
figure=fig,
axes=axes[0],
)
display.add_markers(
marker_coords=coords,
marker_color="g",
marker_size=300,
)
display = plotting.plot_stat_map(
string_connectivity_img,
threshold=0.5,
vmax=1,
cut_coords=coords[0],
title="String",
figure=fig,
axes=axes[1],
)
display.add_markers(
marker_coords=coords,
marker_color="g",
marker_size=300,
)
fig.suptitle("LSS Beta Series Functional Connectivity")
fig.show()
##############################################################################
# References
# ----------
#
# .. footbibliography::