# Copyright 2016 Intel Corporation

#

# Licensed under the Apache License, Version 2.0 (the "License");

# you may not use this file except in compliance with the License.

# You may obtain a copy of the License at

#

# http://www.apache.org/licenses/LICENSE-2.0

#

# Unless required by applicable law or agreed to in writing, software

# distributed under the License is distributed on an "AS IS" BASIS,

# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.

# See the License for the specific language governing permissions and

# limitations under the License.

"""fMRI Simulator

Simulate fMRI data for a single subject.

This code provides a set of functions necessary to produce realistic

simulations of fMRI data. There are two main steps: characterizing the

signal and generating the noise model, which are then combined to simulate

brain data. Tools are included to support the creation of different types

of signal, such as region specific differences in univariate

activity. To create the noise model the parameters can either be set

manually or can be estimated from real fMRI data with reasonable accuracy (

works best when fMRI data has not been preprocessed)

Functions:

generate_signal

Create a volume with activity, of a specified shape and either multivariate

or univariate pattern, in a specific region to represent the signal in the

neural data.

generate_stimfunction

Create a timecourse of the signal activation. This can be specified using event

onsets and durations from a timing file. This is the time course before

convolution and therefore can be at any temporal precision.

export_3_column:

Generate a three column timing file that can be used with software like FSL

to represent event event onsets and duration

export_epoch_file:

Generate an epoch file from the time course which can be used as an input to

brainiak functions

convolve_hrf

Convolve the signal timecourse with the HRF to model the expected evoked

activity

apply_signal

Combine the signal volume with the HRF, thus giving the signal the temporal

properties of the HRF (such as smoothing and lag)

calc_noise

Estimate the noise properties of a given fMRI volume. Prominently, estimate

the smoothing and SFNR of the data

generate_noise

Create the noise for this run. This creates temporal, spatial task and white

noise. Various parameters can be tuned depending on need

mask_brain

Create a mask volume that has similar contrast as an fMRI image. Defaults to

use an MNI grey matter atlas but any image can be supplied to create an

estimate.

compute_signal_change

Convert the signal function into useful metric units according to metrics

used by others (Welvaert & Rosseel, 2013)

Authors:

Cameron Ellis (Princeton & Yale) 2016-2018

Chris Baldassano (Princeton) 2016-2017

Mingbo Cai (Princeton) 2017

"""

import logging

from itertools import product

from statsmodels.tsa.arima_model import ARMA

import math

import numpy as np

# See pyflakes issue #248

# https://github.com/PyCQA/pyflakes/issues/248

import numpy.matlib # noqa: F401

from numpy.linalg import LinAlgError

from pkg_resources import resource_stream

from scipy import stats

from scipy import signal

import scipy.ndimage as ndimage

import copy

__all__ = [

"apply_signal",

"calc_noise",

"compute_signal_change",

"convolve_hrf",

"export_3_column",

"export_epoch_file",

"generate_signal",

"generate_stimfunction",

"generate_noise",

"mask_brain",

]

logger = logging.getLogger(__name__)

def _generate_feature(feature_type,

feature_size,

signal_magnitude,

thickness=1):

"""Generate features corresponding to signal

Generate a single feature, that can be inserted into the signal volume.

A feature is a region of activation with a specific shape such as cube

or ring

Parameters

----------

feature_type : str

What shape signal is being inserted? Options are 'cube',

'loop' (aka ring), 'cavity' (aka hollow sphere), 'sphere'.

feature_size : int

How big is the signal in diameter?

signal_magnitude : float

Set the signal size, a value of 1 means the signal is one standard

deviation of the noise

thickness : int

How thick is the surface of the loop/cavity

Returns

----------

signal : 3 dimensional array

The volume representing the signal

"""

# If the size is equal to or less than 2 then all features are the same

if feature_size <= 2:

feature_type = 'cube'

# What kind of signal is it?

if feature_type == 'cube':

# Preset the size of the signal

signal = np.ones((feature_size, feature_size, feature_size))

elif feature_type == 'loop':

# First make a cube of zeros

signal = np.zeros((feature_size, feature_size, feature_size))

# Make a mesh grid of the space

seq = np.linspace(0, feature_size - 1,

feature_size)

xx, yy = np.meshgrid(seq, seq)

# Make a disk corresponding to the whole mesh grid

xxmesh = (xx - ((feature_size - 1) / 2)) ** 2

yymesh = (yy - ((feature_size - 1) / 2)) ** 2

disk = xxmesh + yymesh

# What are the limits of the rings being made

outer_lim = disk[int((feature_size - 1) / 2), 0]

inner_lim = disk[int((feature_size - 1) / 2), thickness]

# What is the outer disk

outer = disk <= outer_lim

# What is the inner disk

inner = disk <= inner_lim

# Subtract the two disks to get a loop

loop = outer != inner

# Check if the loop is a disk

if np.all(inner is False):

logger.warning('Loop feature reduces to a disk because the loop '

'is too thick')

# If there is complete overlap then make the signal just the

# outer one

if np.all(loop is False):

loop = outer

# store the loop

signal[0:feature_size, 0:feature_size, int(np.round(feature_size /

2))] = loop

elif feature_type == 'sphere' or feature_type == 'cavity':

# Make a mesh grid of the space

seq = np.linspace(0, feature_size - 1,

feature_size)

xx, yy, zz = np.meshgrid(seq, seq, seq)

# Make a disk corresponding to the whole mesh grid

signal = ((xx - ((feature_size - 1) / 2)) ** 2 +

(yy - ((feature_size - 1) / 2)) ** 2 +

(zz - ((feature_size - 1) / 2)) ** 2)

# What are the limits of the rings being made

outer_lim = signal[int((feature_size - 1) / 2), int((feature_size -

1) / 2), 0]

inner_lim = signal[int((feature_size - 1) / 2), int((feature_size -

1) / 2),

thickness]

# Is the signal a sphere or a cavity?

if feature_type == 'sphere':

signal = signal <= outer_lim

else:

# Get the inner and outer sphere

outer = signal <= outer_lim

inner = signal <= inner_lim

# Subtract the two disks to get a loop

signal = outer != inner

# Check if the cavity is a sphere

if np.all(inner is False):

logger.warning('Cavity feature reduces to a sphere because '

'the cavity is too thick')

# If there is complete overlap then make the signal just the

# outer one

if np.all(signal is False):

signal = outer

# Assign the signal magnitude

signal = signal * signal_magnitude

# Return the signal

return signal

def _insert_idxs(feature_centre, feature_size, dimensions):

"""Returns the indices of where to put the signal into the signal volume

Parameters

----------

feature_centre : list, int

List of coordinates for the centre location of the signal

feature_size : list, int

How big is the signal's diameter.

dimensions : 3 length array, int

What are the dimensions of the volume you wish to create

Returns

----------

x_idxs : tuple

The x coordinates of where the signal is to be inserted

y_idxs : tuple

The y coordinates of where the signal is to be inserted

z_idxs : tuple

The z coordinates of where the signal is to be inserted

"""

# Set up the indexes within which to insert the signal

x_idx = [int(feature_centre[0] - (feature_size / 2)) + 1,

int(feature_centre[0] - (feature_size / 2) +

feature_size) + 1]

y_idx = [int(feature_centre[1] - (feature_size / 2)) + 1,

int(feature_centre[1] - (feature_size / 2) +

feature_size) + 1]

z_idx = [int(feature_centre[2] - (feature_size / 2)) + 1,

int(feature_centre[2] - (feature_size / 2) +

feature_size) + 1]

# Check for out of bounds

# Min Boundary

if 0 > x_idx[0]:

x_idx[0] = 0

if 0 > y_idx[0]:

y_idx[0] = 0

if 0 > z_idx[0]:

z_idx[0] = 0

# Max Boundary

if dimensions[0] < x_idx[1]:

x_idx[1] = dimensions[0]

if dimensions[1] < y_idx[1]:

y_idx[1] = dimensions[1]

if dimensions[2] < z_idx[1]:

z_idx[1] = dimensions[2]

# Return the idxs for data

return x_idx, y_idx, z_idx

def generate_signal(dimensions,

feature_coordinates,

feature_size,

feature_type,

signal_magnitude=[1],

signal_constant=1,

):

"""Generate volume containing signal

Generate signal, of a specific shape in specific regions, for a single

volume. This will then be convolved with the HRF across time

Parameters

----------

dimensions : 1d array, ndarray

What are the dimensions of the volume you wish to create

feature_coordinates : multidimensional array

What are the feature_coordinates of the signal being created.

Be aware of clipping: features far from the centre of the

brain will be clipped. If you wish to have multiple features

then list these as a features x 3 array. To create a feature of

a unique shape then supply all the individual

feature_coordinates of the shape and set the feature_size to 1.

feature_size : list, int

How big is the signal. If feature_coordinates=1 then only one value is

accepted, if feature_coordinates>1 then either one value must be

supplied or m values

feature_type : list, string

What feature_type of signal is being inserted? Options are cube,

loop, cavity, sphere. If feature_coordinates = 1 then

only one value is accepted, if feature_coordinates > 1 then either

one value must be supplied or m values

signal_magnitude : list, float

What is the (average) magnitude of the signal being generated? A

value of 1 means that the signal is one standard deviation from the

noise

signal_constant : list, bool

Is the signal constant across the feature (for univariate activity)

or is it a random pattern of a given magnitude across the feature (for

multivariate activity)

Returns

----------

volume_signal : 3 dimensional array, float

Creates a single volume containing the signal

"""

# Preset the volume

volume_signal = np.zeros(dimensions)

feature_quantity = round(feature_coordinates.shape[0])

# If there is only one feature_size value then make sure to duplicate it

# for all signals

if len(feature_size) == 1:

feature_size = feature_size * feature_quantity

# Do the same for feature_type

if len(feature_type) == 1:

feature_type = feature_type * feature_quantity

if len(signal_magnitude) == 1:

signal_magnitude = signal_magnitude * feature_quantity

# Iterate through the signals and insert in the data

for signal_counter in range(feature_quantity):

# What is the centre of this signal

if len(feature_size) > 1:

feature_centre = np.asarray(feature_coordinates[signal_counter, ])

else:

feature_centre = np.asarray(feature_coordinates)[0]

# Generate the feature to be inserted in the volume

signal = _generate_feature(feature_type[signal_counter],

feature_size[signal_counter],

signal_magnitude[signal_counter],

)

# If the signal is a random noise pattern then multiply these ones by

# a noise mask

if signal_constant == 0:

signal = signal * np.random.random([feature_size[signal_counter],

feature_size[signal_counter],

feature_size[signal_counter]])

# Pull out the idxs for where to insert the data

x_idx, y_idx, z_idx = _insert_idxs(feature_centre,

feature_size[signal_counter],

dimensions)

# Insert the signal into the Volume

volume_signal[x_idx[0]:x_idx[1], y_idx[0]:y_idx[1], z_idx[0]:z_idx[

1]] = signal

return volume_signal

def generate_stimfunction(onsets,

event_durations,

total_time,

weights=[1],

timing_file=None,

temporal_resolution=100.0,

):

"""Return the function for the timecourse events

When do stimuli onset, how long for and to what extent should you

resolve the fMRI time course. There are two ways to create this, either

by supplying onset, duration and weight information or by supplying a

timing file (in the three column format used by FSL).

Parameters

----------

onsets : list, int

What are the timestamps (in s) for when an event you want to

generate onsets?

event_durations : list, int

What are the durations (in s) of the events you want to

generate? If there is only one value then this will be assigned

to all onsets

total_time : int

How long (in s) is the experiment in total.

weights : list, float

What is the weight for each event (how high is the box car)? If

there is only one value then this will be assigned to all onsets

timing_file : string

The filename (with path) to a three column timing file (FSL) to

make the events. Still requires total_time to work

temporal_resolution : float

How many elements per second are you modeling for the

timecourse. This is useful when you want to model the HRF at an

arbitrarily high resolution (and then downsample to your TR later).

Returns

----------

stim_function : 1 by timepoint array, float

The time course of stimulus evoked activation. This has a temporal

resolution of temporal resolution / 1.0 elements per second

"""

# If the timing file is supplied then use this to acquire the

if timing_file is not None:

# Read in text file line by line

with open(timing_file) as f:

text = f.readlines() # Pull out file as a an array

# Preset

onsets = list()

event_durations = list()

weights = list()

# Pull out the onsets, weights and durations, set as a float

for line in text:

onset, duration, weight = line.strip().split()

# Check if the onset is more precise than the temporal resolution

upsampled_onset = float(onset) * temporal_resolution

# Because of float precision, the upsampled values might

# not round as expected .

# E.g. float('1.001') * 1000 = 1000.99

if np.allclose(upsampled_onset, np.round(upsampled_onset)) == 0:

warning = 'Your onset: ' + str(onset) + ' has more decimal ' \

'points than the ' \

'specified temporal ' \

'resolution can ' \

'resolve. This means' \

' that events might' \

' be missed. ' \

'Consider increasing' \

' the temporal ' \

'resolution.'

logger.warning(warning)

onsets.append(float(onset))

event_durations.append(float(duration))

weights.append(float(weight))

# If only one duration is supplied then duplicate it for the length of

# the onset variable

if len(event_durations) == 1:

event_durations = event_durations * len(onsets)

if len(weights) == 1:

weights = weights * len(onsets)

# Check files

if np.max(onsets) > total_time:

raise ValueError('Onsets outside of range of total time.')

# Generate the time course as empty, each element is a millisecond by

# default

stimfunction = np.zeros((int(round(total_time * temporal_resolution)), 1))

# Cycle through the onsets

for onset_counter in list(range(len(onsets))):

# Adjust for the resolution

onset_idx = int(np.floor(onsets[onset_counter] * temporal_resolution))

# Adjust for the resolution

offset_idx = int(np.floor((onsets[onset_counter] + event_durations[

onset_counter]) * temporal_resolution))

# Store the weights

stimfunction[onset_idx:offset_idx, 0] = [weights[onset_counter]]

return stimfunction

def export_3_column(stimfunction,

filename,

temporal_resolution=100.0

):

""" Output a tab separated three column timing file

This produces a three column tab separated text file, with the three

columns representing onset time (s), event duration (s) and weight,

respectively. Useful if you want to run the simulated data through FEAT

analyses. In a way, this is the reverse of generate_stimfunction

Parameters

----------

stimfunction : timepoint by 1 array

The stimulus function describing the time course of events. For

instance output from generate_stimfunction.

filename : str

The name of the three column text file to be output

temporal_resolution : float

How many elements per second are you modeling with the

stimfunction?

"""

# Iterate through the stim function

stim_counter = 0

event_counter = 0

while stim_counter < stimfunction.shape[0]:

# Is it an event?

if stimfunction[stim_counter, 0] != 0:

# When did the event start?

event_onset = str(stim_counter / temporal_resolution)

# The weight of the stimulus

weight = str(stimfunction[stim_counter, 0])

# Reset

event_duration = 0

# Is the event still ongoing?

while stimfunction[stim_counter, 0] != 0 & stim_counter <= \

stimfunction.shape[0]:

# Add one millisecond to each duration

event_duration = event_duration + 1

# Increment

stim_counter = stim_counter + 1

# How long was the event in seconds

event_duration = str(event_duration / temporal_resolution)

# Append this row to the data file

with open(filename, "a") as file:

file.write(event_onset + '\t' + event_duration + '\t' +

weight + '\n')

# Increment the number of events

event_counter = event_counter + 1

# Increment

stim_counter = stim_counter + 1

def export_epoch_file(stimfunction,

filename,

tr_duration,

temporal_resolution=100.0

):

""" Output an epoch file, necessary for some inputs into brainiak

This takes in the time course of stimulus events and outputs the epoch

file used in Brainiak. The epoch file is a way to structure the timing

information in fMRI that allows you to flexibly input different stimulus

sequences. This is a list with each entry a 3d matrix corresponding to a

participant. The dimensions of the 3d matrix are condition by epoch by

time. For the i-th condition, if its k-th epoch spans time points t_m to

t_n-1, then [i, k, t_m:t_n] are 1 in the epoch file.

Parameters

----------

stimfunction : list of timepoint by condition arrays

The stimulus function describing the time course of events. Each

list entry is from a different participant, each row is a different

timepoint (with the given temporal precision), each column is a

different condition. export_epoch_file is looking for differences in

the value of stimfunction to identify the start and end of an

epoch. If epochs in stimfunction are coded with the same weight and

there is no time between blocks then export_epoch_file won't be able to

label them as different epochs

filename : str

The name of the epoch file to be output

tr_duration : float

How long is each TR in seconds

temporal_resolution : float

How many elements per second are you modeling with the

stimfunction?

"""

# Cycle through the participants, different entries in the list

epoch_file = [0] * len(stimfunction)

for ppt_counter in range(len(stimfunction)):

# What is the time course for the participant (binarized)

stimfunction_ppt = np.abs(stimfunction[ppt_counter]) > 0

# Down sample the stim function

stride = tr_duration * temporal_resolution

stimfunction_downsampled = stimfunction_ppt[::int(stride), :]

# Calculates the number of event onsets. This uses changes in value

# to reflect different epochs. This might be false in some cases (the

# weight is non-uniform over an epoch or there is no break between

# identically weighted epochs).

epochs = 0 # Preset

conditions = stimfunction_ppt.shape[1]

for condition_counter in range(conditions):

weight_change = (np.diff(stimfunction_downsampled[:,

condition_counter], 1, 0) != 0)

# If the first or last events are 'on' then make these

# represent a epoch change

if stimfunction_downsampled[0, condition_counter] == 1:

weight_change[0] = True

if stimfunction_downsampled[-1, condition_counter] == 1:

weight_change[-1] = True

epochs += int(np.max(np.sum(weight_change, 0)) / 2)

# Get other information

trs = stimfunction_downsampled.shape[0]

# Make a timing file for this participant

epoch_file[ppt_counter] = np.zeros((conditions, epochs, trs))

# Cycle through conditions

epoch_counter = 0 # Reset and count across conditions

tr_counter = 0

while tr_counter < stimfunction_downsampled.shape[0]:

for condition_counter in range(conditions):

# Is it an event?

if tr_counter < stimfunction_downsampled.shape[0] and \

stimfunction_downsampled[

tr_counter, condition_counter] == 1:

# Add a one for this TR

epoch_file[ppt_counter][condition_counter,

epoch_counter, tr_counter] = 1

# Find the next non event value

end_idx = np.where(stimfunction_downsampled[tr_counter:,

condition_counter] == 0)[

0][0]

tr_idxs = list(range(tr_counter, tr_counter + end_idx))

# Add ones to all the trs within this event time frame

epoch_file[ppt_counter][condition_counter,

epoch_counter, tr_idxs] = 1

# Start from this index

tr_counter += end_idx

# Increment

epoch_counter += 1

# Increment the counter

tr_counter += 1

# Convert to boolean

epoch_file[ppt_counter] = epoch_file[ppt_counter].astype('bool')

# Save the file

np.save(filename, epoch_file)

def _double_gamma_hrf(response_delay=6,

undershoot_delay=12,

response_dispersion=0.9,

undershoot_dispersion=0.9,

response_scale=1,

undershoot_scale=0.035,

temporal_resolution=100.0,

):

"""Create the double gamma HRF with the timecourse evoked activity.

Default values are based on Glover, 1999 and Walvaert, Durnez,

Moerkerke, Verdoolaege and Rosseel, 2011

Parameters

----------

response_delay : float

How many seconds until the peak of the HRF

undershoot_delay : float

How many seconds until the trough of the HRF

response_dispersion : float

How wide is the rising peak dispersion

undershoot_dispersion : float

How wide is the undershoot dispersion

response_scale : float

How big is the response relative to the peak

undershoot_scale :float

How big is the undershoot relative to the trough

scale_function : bool

Do you want to scale the function to a range of 1

temporal_resolution : float

How many elements per second are you modeling for the stimfunction

Returns

----------

hrf : multi dimensional array

A double gamma HRF to be used for convolution.

"""

hrf_length = 30 # How long is the HRF being created

# How many seconds of the HRF will you model?

hrf = [0] * int(hrf_length * temporal_resolution)

# When is the peak of the two aspects of the HRF

response_peak = response_delay * response_dispersion

undershoot_peak = undershoot_delay * undershoot_dispersion

for hrf_counter in list(range(len(hrf) - 1)):

# Specify the elements of the HRF for both the response and undershoot

resp_pow = math.pow((hrf_counter / temporal_resolution) /

response_peak, response_delay)

resp_exp = math.exp(-((hrf_counter / temporal_resolution) -

response_peak) /

response_dispersion)

response_model = response_scale * resp_pow * resp_exp

undershoot_pow = math.pow((hrf_counter / temporal_resolution) /

undershoot_peak,

undershoot_delay)

undershoot_exp = math.exp(-((hrf_counter / temporal_resolution) -

undershoot_peak /

undershoot_dispersion))

undershoot_model = undershoot_scale * undershoot_pow * undershoot_exp

# For this time point find the value of the HRF

hrf[hrf_counter] = response_model - undershoot_model

return hrf

def convolve_hrf(stimfunction,

tr_duration,

hrf_type='double_gamma',

scale_function=True,

temporal_resolution=100.0,

):

""" Convolve the specified hrf with the timecourse.

The output of this is a downsampled convolution of the stimfunction and

the HRF function. If temporal_resolution is 1 / tr_duration then the

output will be the same length as stimfunction. This time course assumes

that slice time correction has occurred and all slices have been aligned

to the middle time point in the TR.

Be aware that if scaling is on and event durations are less than the

duration of a TR then the hrf may or may not come out as anticipated.

This is because very short events would evoke a small absolute response

after convolution but if there are only short events and you scale then

this will look similar to a convolution with longer events. In general

scaling is useful, which is why it is the default, but be aware of this

edge case and if it is a concern, set the scale_function to false.

Parameters

----------

stimfunction : timepoint by feature array

What is the time course of events to be modelled in this

experiment. This can specify one or more timecourses of events.

The events can be weighted or binary

tr_duration : float

How long (in s) between each volume onset

hrf_type : str or list

Takes in a string describing the hrf that ought to be created.

Can instead take in a vector describing the HRF as it was

specified by any function. The default is 'double_gamma' in which

an initial rise and an undershoot are modelled.

scale_function : bool

Do you want to scale the function to a range of 1

temporal_resolution : float

How many elements per second are you modeling for the stimfunction

Returns

----------

signal_function : timepoint by timecourse array

The time course of the HRF convolved with the stimulus function.

This can have multiple time courses specified as different

columns in this array.

"""

# Check if it is timepoint by feature

if stimfunction.shape[0] < stimfunction.shape[1]:

logger.warning('Stimfunction may be the wrong shape')

# How will stimfunction be resized

stride = int(temporal_resolution * tr_duration)

duration = int(stimfunction.shape[0] / stride)

# Generate the hrf to use in the convolution

if hrf_type == 'double_gamma':

hrf = _double_gamma_hrf(temporal_resolution=temporal_resolution)

elif isinstance(hrf_type, list):

hrf = hrf_type

# How many timecourses are there

list_num = stimfunction.shape[1]

# Create signal functions for each list in the stimfunction

for list_counter in range(list_num):

# Perform the convolution

signal_temp = np.convolve(stimfunction[:, list_counter], hrf)

# Down sample the signal function so that it only has one element per

# TR. This assumes that all slices are collected at the same time,

# which is often the result of slice time correction. In other

# words, the output assumes slice time correction

signal_temp = signal_temp[:duration * stride]

signal_vox = signal_temp[int(stride / 2)::stride]

# Scale the function so that the peak response is 1

if scale_function:

signal_vox = signal_vox / np.max(signal_vox)

# Add this function to the stack

if list_counter == 0:

signal_function = np.zeros((len(signal_vox), list_num))

signal_function[:, list_counter] = signal_vox

return signal_function

def apply_signal(signal_function,

volume_signal,

):

"""Combine the signal volume with its timecourse

Apply the convolution of the HRF and stimulus time course to the

volume.

Parameters

----------

signal_function : timepoint by timecourse array, float

The timecourse of the signal over time. If there is only one column

then the same timecourse is applied to all non-zero voxels in

volume_signal. If there is more than one column then each column is

paired with a non-zero voxel in the volume_signal (a 3d numpy array

generated in generate_signal).

volume_signal : multi dimensional array, float

The volume containing the signal to be convolved with the same

dimensions as the output volume. The elements in volume_signal

indicate how strong each signal in signal_function are modulated by

in the output volume

Returns

----------

signal : multidimensional array, float

The convolved signal volume with the same 3d as volume signal and

the same 4th dimension as signal_function

"""

# How many timecourses are there within the signal_function

timepoints = signal_function.shape[0]

timecourses = signal_function.shape[1]

# Preset volume

signal = np.zeros([volume_signal.shape[0], volume_signal.shape[

1], volume_signal.shape[2], timepoints])

# Find all the non-zero voxels in the brain

idxs = np.where(volume_signal != 0)

if timecourses == 1:

# If there is only one time course supplied then duplicate it for

# every voxel

signal_function = np.matlib.repmat(signal_function, 1, len(idxs[0]))

elif len(idxs[0]) != timecourses:

raise IndexError('The number of non-zero voxels in the volume and '

'the number of timecourses does not match. Aborting')

# For each coordinate with a non zero voxel, fill in the timecourse for

# that voxel

for idx_counter in range(len(idxs[0])):

x = idxs[0][idx_counter]

y = idxs[1][idx_counter]

z = idxs[2][idx_counter]

# Pull out the function for this voxel

signal_function_temp = signal_function[:, idx_counter]

# Multiply the voxel value by the function timecourse

signal[x, y, z, :] = volume_signal[x, y, z] * signal_function_temp

return signal

def _calc_fwhm(volume,

mask,

voxel_size=[1.0, 1.0, 1.0],

):

""" Calculate the FWHM of a volume

Estimates the FWHM (mm) of a volume's non-masked voxels

Parameters

----------

volume : 3 dimensional array

Functional data to have the FWHM measured.

mask : 3 dimensional array

A binary mask of the brain voxels in volume

voxel_size : length 3 list, float

Millimeters per voxel for x, y and z.

Returns

-------

fwhm : float, list

Returns the FWHM of each TR in mm

"""

# What are the dimensions of the volume

dimensions = volume.shape

# Iterate through the TRs, creating a FWHM for each TR

# Preset

v_count = 0

v_sum = 0

v_sq = 0