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1079 lines (778 loc) · 31.8 KB
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# 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 neural data.
Steps:
generate_signal
Specify the volume (or volumes) which represent the signal in the neural data.
generate_stimfunction
Create a function to describe the stimulus onsets/durations
double_gamma_hrf
Convolve the stimulus function with the HRF to model when events are expected.
apply_signal
Combine the volume and the HRF
generate_noise
Create the noise for this run. This creates temporal, task and white noise.
Various parameters can be tuned depending on need
mask_brain
Mask the volume to look like a volume. Based on MNI standard space
plot_brain
Show the brain as it unfolds over time with a given opacity.
Authors: Cameron Ellis (Princeton) 2016
"""
import logging
import numpy as np
import scipy.ndimage as ndimage
import math
from scipy import stats
from pkg_resources import resource_stream
__all__ = [
"generate_signal",
"generate_stimfunction",
"double_gamma_hrf",
"apply_signal",
"generate_noise",
"mask_brain",
"plot_brain",
]
logger = logging.getLogger(__name__)
def _generate_feature(feature_type, feature_size, signal_magnitude):
"""Generate features corresponding to signal
Generate signal in specific regions of the brain with for a single
volume. This will then be convolved with the HRF across time
Parameters
----------
feature_type : str
What feature_type of signal is being inserted? Options are cube,
loop, cavity, sphere.
feature_size : int
How big is the signal?
signal_magnitude : float
What is the value of the signal voxels in the feature
Returns
----------
3 dimensional array
The volume representing the signal to be outputed
"""
# What kind of signal is it?
if feature_type == 'cube':
# Preset the size of the signal
signal = np.ones(np.power(feature_size, 3))
# Reorganize the signal into a 3d matrix
signal = signal.reshape([feature_size,
feature_size,
feature_size])
elif feature_type == 'loop':
# First make a cube of zeros
signal = np.zeros(np.power(feature_size,
3)).reshape([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
disk = ((xx - ((feature_size - 1) / 2)) ** 2
+ (yy - ((feature_size - 1) / 2)) ** 2)
# What is the outer disk
outer = disk < (feature_size - 1)
# What is the inner disk
inner = disk < (feature_size - 1) / 2
# Subtract the two disks to get a loop
loop = outer != inner
# 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)
# Is the signal a sphere or a cavity?
if feature_type == 'sphere':
signal = signal < (feature_size - 1)
else:
# Get the inner and outer sphere
outer = signal < (feature_size - 1)
inner = signal < (feature_size - 1) / 2
# Subtract the two disks to get a loop
signal = outer != inner
# 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 indexes of where to put the signal into Volume_Static
Parameters
----------
feature_centre : list, int
List of coordinates for the centre location of the signal
feature_size : list, int
How big is the signal.
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)),
int(feature_centre[0] - (feature_size / 2) +
feature_size)]
y_idx = [int(feature_centre[1] - (feature_size / 2)),
int(feature_centre[1] - (feature_size / 2) +
feature_size)]
z_idx = [int(feature_centre[2] - (feature_size / 2)),
int(feature_centre[2] - (feature_size / 2) +
feature_size)]
# 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,
signal_constant=1,
):
"""Generate volume containing signal
Generate signal in specific regions of the brain with for a single
volume. This will then be convolved with the HRF across time
Parameters
----------
dimensions : 3 length array, int
What are the dimensions of the volume you wish to create
feature_coordinates : multidimensional array, int
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 an features x 3 array. To create a signal of
a specific shape then supply all the individual
feature_coordinates and set the feature_size to 1.
feature_size : list, int
How big is the signal. If m=1 then only one value is accepted,
if m>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 features = 1 then
only one value is accepted, if features > 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?
signal_constant : list, bool
Is the signal constant or is it a random pattern (with the same
average magnitude)
Returns
----------
volume_static : 3 dimensional array, float
Creates a single volume containing the signal
"""
# Preset the volume
volume_static = 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 list(range(0, 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_static[x_idx[0]:x_idx[1], y_idx[0]:y_idx[1], z_idx[0]:z_idx[
1]] = signal
return volume_static
def generate_stimfunction(onsets,
event_durations,
total_time,
tr_duration,
):
"""Return the function for the onset of events
When do stimuli onset, how long for and to what extent should you
resolve the fMRI time course
Parameters
----------
onsets : list, int
What are the timestamps for when an event you want to generate
onsets?
event_durations : list, int
What are the durations 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 is the experiment in total.
tr_duration : float
What is the TR duration, related to the precision of the boxcar.
Returns
----------
Iterable[bool]
The time course of stimulus related activation
"""
# 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 (event_durations[0] / tr_duration).is_integer() is False:
logging.warning('Event durations are not a multiple of the TR '
'duration, rounding down.')
if (onsets[0] / tr_duration).is_integer() is False:
logging.warning('Onsets are not a multiple of the TR duration, '
'rounding down.')
# Generate the time course as empty
stimfunction = [0] * round(total_time / tr_duration)
# Cycle through the onsets
for onset_counter in list(range(0, len(onsets))):
# Adjust for the resolution
onset_idx = int(np.floor(onsets[onset_counter] / tr_duration))
# Adjust for the resolution
offset_idx = int(np.floor((onsets[onset_counter] + event_durations[
onset_counter]) / tr_duration))
# For the appropriate indexes and duration, make this value 1
idx_number = round(event_durations[onset_counter] / tr_duration)
stimfunction[onset_idx:offset_idx] = idx_number * [1]
# Remove any indexes that are too long
if len(stimfunction) > total_time / tr_duration:
stimfunction = stimfunction[0:int(total_time / tr_duration)]
return stimfunction
def double_gamma_hrf(stimfunction,
response_delay=6,
undershoot_delay=12,
response_dispersion=0.9,
undershoot_dispersion=0.9,
undershoot_scale=0.035):
"""Return a double gamma HRF
Parameters
----------
stimfunction : list, bool
What is the time course of events to be modelled in this
experiment
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
undershoot_scale :float
How big is the undershoot relative to the peak
Returns
----------
one dimensional array
The time course of the HRF convolved with the stimulus function
"""
hrf_length = 30 # How long is the HRF being created
hrf = [0] * hrf_length # How many seconds of the HRF will you model?
for hrf_counter in list(range(0, hrf_length - 1)):
# When is the peak of the two aspects of the HRF
response_peak = response_delay * response_dispersion
undershoot_peak = undershoot_delay * undershoot_dispersion
# Specify the elements of the HRF for both the response and undershoot
resp_pow = math.pow(hrf_counter / response_peak, response_delay)
resp_exp = math.exp(-(hrf_counter - response_peak) /
response_dispersion)
response_model = resp_pow * resp_exp
undershoot_pow = math.pow(hrf_counter / undershoot_peak,
undershoot_delay)
undershoot_exp = math.exp(-(hrf_counter - 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
# Convolve the hrf that was created with the boxcar input
signal_function = np.convolve(stimfunction, hrf)
# Cut off the HRF
signal_function = signal_function[0:len(stimfunction)]
return signal_function
def apply_signal(signal_function,
volume_static):
"""Apply the convolution and stimfunction
Apply the convolution of the HRF and stimulus time course to the
volume.
Parameters
----------
signal_function : list, float
The one dimensional timecourse of the signal over time.
Found by convolving the HRF with the stimulus time course.
volume_static : multi dimensional array, float
Returns
----------
multidimensional array, float
Generates the spatial noise volume for these parameters
"""
# Preset volume
signal = np.ndarray([volume_static.shape[0], volume_static.shape[
1], volume_static.shape[2], len(signal_function)])
# Iterate through the brain, multiplying the volume by the HRF
for tr_counter in list(range(0, len(signal_function))):
signal[0:volume_static.shape[0],
0:volume_static.shape[1],
0:volume_static.shape[2],
tr_counter] = signal_function[tr_counter] * volume_static
return signal
def _generate_noise_system(dimensions,
sigma=1.5,
):
"""Generate the scanner noise
Generate the noise that is typical of a scanner. This is comprised
of two types of noise, Rician and Gaussian
Parameters
----------
dimensions : n length array, int
What are the dimensions of the volume you wish to insert
noise into. This can be a volume of any size
sigma : float
What is the standard deviation of this noise?
Returns
----------
system_noise : multidimensional array, float
Create a volume with system noise
"""
# Generate the Rician noise
noise_rician = stats.rice.rvs(1, sigma, size=dimensions)
# Apply the gaussian noise
noise_gaussian = np.random.normal(0, sigma, size=dimensions)
# Combine these two noise types
noise_system = noise_rician + noise_gaussian
return noise_system
def _generate_noise_temporal_task(stimfunction,
motion_sigma,
motion_noise='gaussian',
):
"""Generate the signal dependent noise
This noise depends on things like the signal or the timing of the
experiment.
Parameters
----------
stimfunction : 1 Dimensional array
This is the timecourse of the stimuli in this experiment
motion_sigma : float
How much noise is left over after pre-processing has been
done. This is noise specifically on the task events
motion_noise : str
What type of noise will you generate? Can be gaussian or rician
Returns
----------
one dimensional array, float
Generates the temporal task noise timecourse
"""
noise_task = []
if motion_noise == 'gaussian':
noise_task = stimfunction + (stimfunction *
np.random.normal(0,
motion_sigma,
size=len(stimfunction)))
elif motion_noise == 'rician':
noise_task = stimfunction + (stimfunction *
stats.rice.rvs(0,
motion_sigma,
size=len(stimfunction)))
return noise_task
def _generate_noise_temporal_drift(trs,
tr_duration,
drift_sigma,
timepoints,
):
"""Generate the drift noise
According to AFNI (https://afni.nimh.nih.gov/pub/dist/doc/
program_help/3dDeconvolve.html) the appropriate order of the
polynomial to fit for temporal drift is calculated as follows
Parameters
----------
trs : int
How many TRs are there
tr_duration : float
How long is each TR
drift_sigma : float
How large are the coefficients controlling drift
timepoints : 1 Dimensional array
What time points are sampled by a TR
Returns
----------
one dimensional array, float
Generates the autoregression noise timecourse
"""
# Calculate the coefficients of the drift for a given function
degree = round(trs * tr_duration / 150) + 1
coefficients = np.random.normal(0, drift_sigma, size=degree)
# What are the values of this drift
noise_drift = np.polyval(coefficients, timepoints)
# Return noise
return noise_drift
def _generate_noise_temporal_autoregression(auto_reg_rho,
auto_reg_order,
auto_seg_sigma,
timepoints,
):
"""Generate the autoregression noise
Parameters
----------
auto_reg_sigma : float
auto_reg_order : float
auto_reg_rho : float
timepoints : 1 Dimensional array
What time points are sampled by a TR
Returns
----------
one dimensional array, float
Generates the autoregression noise timecourse
"""
if len(auto_reg_rho) == 1:
auto_reg_rho = auto_reg_rho * auto_reg_order # Duplicate this so that
# there is one
# for each value
noise_autoregression = []
for tr_counter in list(range(0, len(timepoints))):
if tr_counter == 0:
noise_autoregression.append(np.random.normal(0, auto_seg_sigma))
else:
temp = []
for pCounter in list(range(1, auto_reg_order + 1)):
if tr_counter - pCounter >= 0:
past_trs = noise_autoregression[int(tr_counter - pCounter)]
past_reg = auto_reg_rho[pCounter - 1]
random = np.random.normal(0, auto_seg_sigma)
temp.append(past_trs * past_reg + random)
noise_autoregression.append(np.mean(temp))
return noise_autoregression
def _generate_noise_temporal_phys(timepoints,
physiological_sigma,
resp_freq=0.2,
heart_freq=1.17,
):
"""Generate the physiological noise.
Parameters
----------
timepoints : 1 Dimensional array
What time points are sampled by a TR
physiological_sigma : float
How variable is the signal as a result of physiology,
like heart beat and breathing
resp_freq : float
What is the frequency of respiration
heart_freq : float
What is the frequency of heart beat
Returns
----------
one dimensional array, float
Generates the physiological temporal noise timecourse
"""
noise_phys = [] # Preset
for tr_counter in timepoints:
# Calculate the radians for each variable at this given TR
resp_radians = resp_freq * tr_counter * 2 * np.pi
heart_radians = heart_freq * tr_counter * 2 * np.pi
# Combine the two types of noise and append
noise_phys.append(np.cos(resp_radians) + np.sin(heart_radians) +
np.random.normal(0, physiological_sigma))
return noise_phys
def _generate_noise_temporal(stimfunction,
tr_duration,
z_score=1,
motion_sigma=15,
drift_sigma=15,
auto_seg_sigma=15,
auto_reg_order=1,
auto_reg_rho=[1],
physiological_sigma=15,
):
"""Generate the signal dependent noise
This noise depends on things like the signal or the timing of the
experiment.
Parameters
----------
stimfunction : 1 Dimensional array
This is the timecourse of the stimuli in this experiment
tr_duration : int
How long is a TR, in seconds
z_score : bool
Is the data to be normalized
motion_sigma : float
How much noise is left over after pre-processing has been
done. This is noise specifically on the task events
drift_sigma : float
What is the sigma on the distribution that coefficients are
randomly sampled from
auto_reg_sigma : float
auto_reg_order : float
auto_reg_rho : float
physiological_sigma : float
How variable is the signal as a result of physiology,
like heart beat and breathing
Returns
----------
one dimensional array, float
Generates the temporal noise timecourse for these parameters
"""
# Set up common parameters
# How many TRs are there
trs = len(stimfunction)
# What time points are sampled by a TR?
timepoints = list(range(0, trs * tr_duration))[::tr_duration]
# Make each noise type
noise_task = _generate_noise_temporal_task(stimfunction,
motion_sigma,
)
noise_drift = _generate_noise_temporal_drift(trs,
tr_duration,
drift_sigma,
timepoints,
)
noise_phys = _generate_noise_temporal_phys(timepoints,
physiological_sigma,
)
noise_autoregression = _generate_noise_temporal_autoregression(
auto_reg_rho, auto_reg_order, auto_seg_sigma, timepoints, )
# Do you want to z score it?
if z_score == 1:
noise_task = stats.zscore(noise_task)
noise_phys = stats.zscore(noise_phys)
noise_drift = stats.zscore(noise_drift)
noise_autoregression = stats.zscore(noise_autoregression)
# add the noise (it would have been nice to just add all of them in a
# single line but this was causing formatting problems)
noise_temporal = noise_task
noise_temporal = noise_temporal + noise_phys
noise_temporal = noise_temporal + noise_drift
noise_temporal = noise_temporal + noise_autoregression
return noise_temporal
def _generate_noise_spatial(dimensions,
sigma=-4.0,
):
"""Generate code for Gaussian Random Fields.
Adapted from code found here:
http://andrewwalker.github.io/statefultransitions/post/gaussian-fields/
with permission from the author:
https://twitter.com/walkera101/status/785578499440377858. Original code
comes from http://mathematica.stackexchange.com/questions/4829
/efficiently-generating-n-d-gaussian-random-fields with a WTFPL (
http://www.wtfpl.net).
Parameters
----------
dimensions : tuple
What is the shape of the volume to be generated
sigma : float
What is the size of the standard deviation in the gaussian random
fields to generated
Returns
----------
multidimensional array, float
Generates the spatial noise volume for these parameters
"""
# Set up the input to the fast fourier transform
def fftIndgen(n):
a = list(range(0, int(n / 2 + 1)))
b = list(range(1, int(n / 2)))
b.reverse()
b = [-i for i in b]
return a + b
# Take in an array of fft values and determine the amplitude for those
# values
def Pk2(idxs):
# If all the indexes are zero then set the out put to zero
if np.all(idxs == 0):
return 0.0
return np.sqrt((np.sqrt(np.sum(idxs ** 2))) ** sigma)
noise = np.fft.fft2(np.random.normal(size=dimensions))
amplitude = np.zeros(dimensions)
for x, fft_x in enumerate(fftIndgen(dimensions[0])):
for y, fft_y in enumerate(fftIndgen(dimensions[1])):
for z, fft_z in enumerate(fftIndgen(dimensions[2])):
amplitude[x, y, z] = Pk2(np.array([fft_x, fft_y, fft_z]))
# The output
noise_spatial = np.fft.ifft2(noise * amplitude)
return noise_spatial.real
def generate_noise(dimensions,
stimfunction,
tr_duration,
noise_strength=[1]):
""" Generate the noise to be added to the signal
Parameters
----------
dimensions : tuple
What is the shape of the volume to be generated
stimfunction : Iterable, bool
When do the stimuli events occur
tr_duration : float
What is the duration, in seconds, of each TR?
noise_strength : list, float
Either a one element list or a list of length 3 which varies
the size of the noise for temporal noise, spatial noise and
system noise
Returns
----------
multidimensional array, float
Generates the noise volume for these parameters
"""
# Duplicate the noise strength if only one is supplied
if len(noise_strength) == 1:
noise_strength = noise_strength * 3
# What are the dimensions of the volume, including time
dimensions_tr = (dimensions[0],
dimensions[1],
dimensions[2],
len(stimfunction))
# Generate the noise
noise_temporal = _generate_noise_temporal(stimfunction=stimfunction,
tr_duration=tr_duration,
) * noise_strength[0]
noise_spatial = _generate_noise_spatial(dimensions=dimensions,
) * noise_strength[1]
noise_system = _generate_noise_system(dimensions=dimensions_tr,
) * noise_strength[2]
# Find the outer product and add white noise
noise = np.multiply.outer(noise_spatial, noise_temporal) + noise_system
return noise
def mask_brain(volume,
mask_name=None):
""" Mask the simulated volume
Parameters
----------
volume : multidimensional array
The volume that has been simulated
mask_name : str
What is the path to the mask to be loaded?
Returns
----------
brain : multidimensional array, float
The masked brain
"""
# Load in the mask
if mask_name is None:
mask_raw = np.load(resource_stream(__name__, "grey_matter_mask.npy"))
else:
mask_raw = np.load(mask_name)
# If there is only one brain volume then make this a forth dimension
if len(volume.shape) == 3:
temp = np.zeros([volume.shape[0], volume.shape[1], volume.shape[2], 1])
temp[:, :, :, 0] = volume
volume = temp
# Reshape the mask to be the size as the brain
brain_dim = volume.shape
mask_dim = mask_raw.shape
zoom_factor = (brain_dim[0] / mask_dim[0],