def run_model(subj, run):
"""
Single subject fitting of FIAC model
"""
#----------------------------------------------------------------------
# Set initial parameters of the FIAC dataset
#----------------------------------------------------------------------
# Number of volumes in the fMRI data
nvol = 121
# The TR of the experiment
TR = 2.5
# The time of the first volume
Tstart = 0.0
# The array of times corresponding to each volume in the fMRI data
volume_times = np.arange(nvol) * TR + Tstart
# This recarray of times has one column named 't'. It is used in the
# function design.event_design to create the design matrices.
volume_times_rec = make_recarray(volume_times, 't')
# Get a path description dictionary that contains all the path data relevant
# to this subject/run
path_info = futil.path_info_run(subj,run)
#----------------------------------------------------------------------
# Experimental design
#----------------------------------------------------------------------
# Load the experimental description from disk. We have utilities in futil
# that reformat the original FIAC-supplied format into something where the
# factorial structure of the design is more explicit. This has already
# been run once, and get_experiment_initial() will simply load the
# newly-formatted design description files (.csv) into record arrays.
experiment = futil.get_experiment(path_info)
# Create design matrices for the "initial" and "experiment" factors, saving
# the default contrasts.
# The function event_design will create design matrices, which in the case
# of "experiment" will have num_columns = (# levels of speaker) * (# levels
# of sentence) * len(delay.spectral) = 2 * 2 * 2 = 8. For "initial", there
# will be (# levels of initial) * len([hrf.glover]) = 1 * 1 = 1.
# Here, delay.spectral is a sequence of 2 symbolic HRFs that are described
# in:
#
# Liao, C.H., Worsley, K.J., Poline, J-B., Aston, J.A.D., Duncan, G.H.,
# Evans, A.C. (2002). \'Estimating the delay of the response in fMRI
# data.\' NeuroImage, 16:593-606.
# The contrast definitions in ``cons_exper`` are a dictionary with keys
# ['constant_0', 'constant_1', 'speaker_0', 'speaker_1', 'sentence_0',
# 'sentence_1', 'sentence:speaker_0', 'sentence:speaker_1'] representing the
# four default contrasts: constant, main effects + interactions, each
# convolved with 2 HRFs in delay.spectral. For example, sentence:speaker_0
# is the interaction of sentence and speaker convolved with the first (=0)
# of the two HRF basis functions, and sentence:speaker_1 is the interaction
# convolved with the second (=1) of the basis functions.
# XXX use the hrf __repr__ for naming contrasts
X_exper, cons_exper = design.block_design(experiment, volume_times_rec,
hrfs=delay.spectral,
level_contrasts=True)
# In addition to factors, there is typically a "drift" term. In this case,
# the drift is a natural cubic spline with a not at the midpoint
# (volume_times.mean())
vt = volume_times # shorthand
drift = np.array( [vt**i for i in range(4)] +
[(vt-vt.mean())**3 * (np.greater(vt, vt.mean()))] )
for i in range(drift.shape[0]):
drift[i] /= drift[i].max()
# We transpose the drift so that its shape is (nvol,5) so that it will have
# the same number of rows as X_exper.
drift = drift.T
# There are helper functions to create these drifts: design.fourier_basis,
# design.natural_spline. Therefore, the above is equivalent (except for
# the normalization by max for numerical stability) to
#
# >>> drift = design.natural_spline(t, [volume_times.mean()])
# Stack all the designs, keeping the new contrasts which has the same keys
# as cons_exper, but its values are arrays with 15 columns, with the
# non-zero entries matching the columns of X corresponding to X_exper
X, cons = design.stack_designs((X_exper, cons_exper),
(drift, {}))
# Sanity check: delete any non-estimable contrasts
for k in cons.keys():
if not isestimable(cons[k], X):
del(cons[k])
warnings.warn("contrast %s not estimable for this run" % k)
# The default contrasts are all t-statistics. We may want to output
# F-statistics for 'speaker', 'sentence', 'speaker:sentence' based on the
# two coefficients, one for each HRF in delay.spectral
# We reproduce the same constrasts as in the data base
# outputting an F using both HRFs, as well as the
# t using only the first HRF
for obj1, obj2 in [('face', 'scrambled'),
('house', 'scrambled'),
('chair', 'scrambled'),
('face', 'house')]:
cons['%s_vs_%s_F' % (obj1, obj2)] = \
np.vstack([cons['object_%s_0' % obj1] -
cons['object_%s_0' % obj2],
cons['object_%s_1' % obj1] -
cons['object_%s_1' % obj2]])
cons['%s_vs_%s_t' % (obj1, obj2)] = (cons['object_%s_0' % obj1] -
cons['object_%s_0' % obj2])
#----------------------------------------------------------------------
# Data loading
#----------------------------------------------------------------------
# Load in the fMRI data, saving it as an array. It is transposed to have
# time as the first dimension, i.e. fmri[t] gives the t-th volume.
fmri_im = futil.get_fmri(path_info) # an Image
fmri_im = rollimg(fmri_im, 't')
fmri = fmri_im.get_data() # now, it's an ndarray
nvol, volshape = fmri.shape[0], fmri.shape[1:]
nx, sliceshape = volshape[0], volshape[1:]
#----------------------------------------------------------------------
# Model fit
#----------------------------------------------------------------------
# The model is a two-stage model, the first stage being an OLS (ordinary
# least squares) fit, whose residuals are used to estimate an AR(1)
# parameter for each voxel.
m = OLSModel(X)
ar1 = np.zeros(volshape)
# Fit the model, storing an estimate of an AR(1) parameter at each voxel
for s in range(nx):
d = np.array(fmri[:,s])
flatd = d.reshape((d.shape[0], -1))
result = m.fit(flatd)
ar1[s] = ((result.resid[1:] * result.resid[:-1]).sum(0) /
(result.resid**2).sum(0)).reshape(sliceshape)
# We round ar1 to nearest one-hundredth and group voxels by their rounded
# ar1 value, fitting an AR(1) model to each batch of voxels.
# XXX smooth here?
# ar1 = smooth(ar1, 8.0)
ar1 *= 100
ar1 = ar1.astype(np.int) / 100.
# We split the contrasts into F-tests and t-tests.
# XXX helper function should do this
fcons = {}; tcons = {}
for n, v in cons.items():
v = np.squeeze(v)
if v.ndim == 1:
tcons[n] = v
else:
fcons[n] = v
# Setup a dictionary to hold all the output
# XXX ideally these would be memmap'ed Image instances
output = {}
for n in tcons:
tempdict = {}
for v in ['sd', 't', 'effect']:
tempdict[v] = np.memmap(NamedTemporaryFile(prefix='%s%s.nii'
% (n,v)), dtype=np.float,
shape=volshape, mode='w+')
output[n] = tempdict
for n in fcons:
output[n] = np.memmap(NamedTemporaryFile(prefix='%s%s.nii'
% (n,v)), dtype=np.float,
shape=volshape, mode='w+')
# Loop over the unique values of ar1
for val in np.unique(ar1):
armask = np.equal(ar1, val)
m = ARModel(X, val)
d = fmri[:,armask]
results = m.fit(d)
# Output the results for each contrast
for n in tcons:
resT = results.Tcontrast(tcons[n])
output[n]['sd'][armask] = resT.sd
output[n]['t'][armask] = resT.t
output[n]['effect'][armask] = resT.effect
for n in fcons:
output[n][armask] = results.Fcontrast(fcons[n]).F
# Dump output to disk
odir = futil.output_dir(path_info,tcons,fcons)
# The coordmap for a single volume in the time series
vol0_map = fmri_im[0].coordmap
for n in tcons:
for v in ['t', 'sd', 'effect']:
im = Image(output[n][v], vol0_map)
save_image(im, pjoin(odir, n, '%s.nii' % v))
for n in fcons:
im = Image(output[n], vol0_map)
save_image(im, pjoin(odir, n, "F.nii"))
# Inter-stimulus intervals (time between events)
dt = np.random.uniform(low=0, high=2.5, size=(50,))
# Onset times from the ISIs
t = np.cumsum(dt)
# We're going to model the amplitudes ('a') by dt (the time between events)
a = sympy.Symbol('a')
linear = utils.define('linear', utils.events(t, dt, f=hrf.glover))
quadratic = utils.define('quad', utils.events(t, dt, f=hrf.glover, g=a**2))
cubic = utils.define('cubic', utils.events(t, dt, f=hrf.glover, g=a**3))
f1 = Formula([linear, quadratic, cubic])
# Evaluate this time-based formula at specific times to make the design matrix
tval = make_recarray(np.linspace(0,100, 1001), 't')
X1 = f1.design(tval, return_float=True)
# Now we make a model where the relationship of time between events and signal
# is an exponential with a time constant tau
l = sympy.Symbol('l')
exponential = utils.events(t, dt, f=hrf.glover, g=sympy.exp(-l*a))
f3 = Formula([exponential])
# Make a design matrix by passing in time and required parameters
params = make_recarray([(4.5, 3.5)], ('l', '_b0'))
X3 = f3.design(tval, params, return_float=True)
# the columns or d/d_b0 and d/dl
tt = tval.view(np.float)
v1 = np.sum([hrf.glovert(tt - s)*np.exp(-4.5*a) for s,a in zip(t, dt)], 0)
def run_model(subj, run):
"""
Single subject fitting of OpenfMRI ds105 model
"""
#----------------------------------------------------------------------
# Set initial parameters of the OpenfMRI ds105 dataset
#----------------------------------------------------------------------
# Number of volumes in the fMRI data
nvol = 121
# The TR of the experiment
TR = 2.5
# The time of the first volume
Tstart = 0.0
# The array of times corresponding to each volume in the fMRI data
volume_times = np.arange(nvol) * TR + Tstart
# This recarray of times has one column named 't'. It is used in the
# function design.event_design to create the design matrices.
volume_times_rec = make_recarray(volume_times, 't')
# Get a path description dictionary that contains all the path data relevant
# to this subject/run
path_info = futil.path_info_run(subj, run)
#----------------------------------------------------------------------
# Experimental design
#----------------------------------------------------------------------
# Load the experimental description from disk. We have utilities in futil
# that reformat the original OpenfMRI ds105-supplied format into something
# where the factorial structure of the design is more explicit. This has
# already been run once, and get_experiment_initial() will simply load the
# newly-formatted design description files (.csv) into record arrays.
experiment = futil.get_experiment(path_info)
# Create design matrices for the "initial" and "experiment" factors, saving
# the default contrasts.
# The function event_design will create design matrices, which in the case
# of "experiment" will have num_columns = (# levels of speaker) * (# levels
# of sentence) * len(delay.spectral) = 2 * 2 * 2 = 8. For "initial", there
# will be (# levels of initial) * len([hrf.glover]) = 1 * 1 = 1.
# Here, delay.spectral is a sequence of 2 symbolic HRFs that are described
# in:
#
# Liao, C.H., Worsley, K.J., Poline, J-B., Aston, J.A.D., Duncan, G.H.,
# Evans, A.C. (2002). \'Estimating the delay of the response in fMRI
# data.\' NeuroImage, 16:593-606.
# The contrast definitions in ``cons_exper`` are a dictionary with keys
# ['constant_0', 'constant_1', 'speaker_0', 'speaker_1', 'sentence_0',
# 'sentence_1', 'sentence:speaker_0', 'sentence:speaker_1'] representing the
# four default contrasts: constant, main effects + interactions, each
# convolved with 2 HRFs in delay.spectral. For example, sentence:speaker_0
# is the interaction of sentence and speaker convolved with the first (=0)
# of the two HRF basis functions, and sentence:speaker_1 is the interaction
# convolved with the second (=1) of the basis functions.
# XXX use the hrf __repr__ for naming contrasts
X_exper, cons_exper = design.block_design(experiment,
volume_times_rec,
hrfs=delay.spectral,
level_contrasts=True)
# In addition to factors, there is typically a "drift" term. In this case,
# the drift is a natural cubic spline with a not at the midpoint
# (volume_times.mean())
vt = volume_times # shorthand
drift = np.array([vt**i for i in range(4)] + [(vt - vt.mean())**3 *
(np.greater(vt, vt.mean()))])
for i in range(drift.shape[0]):
drift[i] /= drift[i].max()
# We transpose the drift so that its shape is (nvol,5) so that it will have
# the same number of rows as X_exper.
drift = drift.T
# There are helper functions to create these drifts: design.fourier_basis,
# design.natural_spline. Therefore, the above is equivalent (except for
# the normalization by max for numerical stability) to
#
# >>> drift = design.natural_spline(t, [volume_times.mean()])
# Stack all the designs, keeping the new contrasts which has the same keys
# as cons_exper, but its values are arrays with 15 columns, with the
# non-zero entries matching the columns of X corresponding to X_exper
X, cons = design.stack_designs((X_exper, cons_exper), (drift, {}))
# Sanity check: delete any non-estimable contrasts
for k in cons.keys():
if not isestimable(cons[k], X):
del (cons[k])
warnings.warn("contrast %s not estimable for this run" % k)
# The default contrasts are all t-statistics. We may want to output
# F-statistics for 'speaker', 'sentence', 'speaker:sentence' based on the
# two coefficients, one for each HRF in delay.spectral
# We reproduce the same constrasts as in the data base
# outputting an F using both HRFs, as well as the
# t using only the first HRF
for obj1, obj2 in [('face', 'scrambled'), ('house', 'scrambled'),
('chair', 'scrambled'), ('face', 'house')]:
cons['%s_vs_%s_F' % (obj1, obj2)] = \
np.vstack([cons['object_%s_0' % obj1] -
cons['object_%s_0' % obj2],
cons['object_%s_1' % obj1] -
cons['object_%s_1' % obj2]])
cons['%s_vs_%s_t' % (obj1, obj2)] = (cons['object_%s_0' % obj1] -
cons['object_%s_0' % obj2])
#----------------------------------------------------------------------
# Data loading
#----------------------------------------------------------------------
# Load in the fMRI data, saving it as an array. It is transposed to have
# time as the first dimension, i.e. fmri[t] gives the t-th volume.
fmri_im = futil.get_fmri(path_info) # an Image
fmri_im = rollimg(fmri_im, 't')
fmri = fmri_im.get_data() # now, it's an ndarray
nvol, volshape = fmri.shape[0], fmri.shape[1:]
nx, sliceshape = volshape[0], volshape[1:]
#----------------------------------------------------------------------
# Model fit
#----------------------------------------------------------------------
# The model is a two-stage model, the first stage being an OLS (ordinary
# least squares) fit, whose residuals are used to estimate an AR(1)
# parameter for each voxel.
m = OLSModel(X)
ar1 = np.zeros(volshape)
# Fit the model, storing an estimate of an AR(1) parameter at each voxel
for s in range(nx):
d = np.array(fmri[:, s])
flatd = d.reshape((d.shape[0], -1))
result = m.fit(flatd)
ar1[s] = ((result.resid[1:] * result.resid[:-1]).sum(0) /
(result.resid**2).sum(0)).reshape(sliceshape)
# We round ar1 to nearest one-hundredth and group voxels by their rounded
# ar1 value, fitting an AR(1) model to each batch of voxels.
# XXX smooth here?
# ar1 = smooth(ar1, 8.0)
ar1 *= 100
ar1 = ar1.astype(np.int) / 100.
# We split the contrasts into F-tests and t-tests.
# XXX helper function should do this
fcons = {}
tcons = {}
for n, v in cons.items():
v = np.squeeze(v)
if v.ndim == 1:
tcons[n] = v
else:
fcons[n] = v
# Setup a dictionary to hold all the output
# XXX ideally these would be memmap'ed Image instances
output = {}
for n in tcons:
tempdict = {}
for v in ['sd', 't', 'effect']:
tempdict[v] = np.memmap(NamedTemporaryFile(prefix='%s%s.nii' %
(n, v)),
dtype=np.float,
shape=volshape,
mode='w+')
output[n] = tempdict
for n in fcons:
output[n] = np.memmap(NamedTemporaryFile(prefix='%s%s.nii' % (n, v)),
dtype=np.float,
shape=volshape,
mode='w+')
# Loop over the unique values of ar1
for val in np.unique(ar1):
armask = np.equal(ar1, val)
m = ARModel(X, val)
d = fmri[:, armask]
results = m.fit(d)
# Output the results for each contrast
for n in tcons:
resT = results.Tcontrast(tcons[n])
output[n]['sd'][armask] = resT.sd
output[n]['t'][armask] = resT.t
output[n]['effect'][armask] = resT.effect
for n in fcons:
output[n][armask] = results.Fcontrast(fcons[n]).F
# Dump output to disk
odir = futil.output_dir(path_info, tcons, fcons)
# The coordmap for a single volume in the time series
vol0_map = fmri_im[0].coordmap
for n in tcons:
for v in ['t', 'sd', 'effect']:
im = Image(output[n][v], vol0_map)
save_image(im, pjoin(odir, n, '%s.nii' % v))
for n in fcons:
im = Image(output[n], vol0_map)
save_image(im, pjoin(odir, n, "F.nii"))
c1 = utils.events([3,7,10], f=hrf.glover) # Symbolic function of time
c2 = utils.events([1,3,9], f=hrf.glover) # Symbolic function of time
c3 = utils.events([3,4,6], f=delay.spectral[0]) # Symbolic function of time
# We can also use a Fourier basis for some other onsets - again making symbolic
# functions of time
d = utils.fourier_basis([3,5,7]) # Formula
# Make a formula for all four sets of onsets
f = Formula([c1,c2,c3]) + d
# A contrast is a formula expressed on the elements of the design formula
contrast = Formula([c1-c2, c1-c3])
# Instantiate actual values of time at which to create the design matrix rows
t = make_recarray(np.linspace(0,20,50), 't')
# Make the design matrix, and get contrast matrices for the design
X, c = f.design(t, return_float=True, contrasts={'C':contrast})
# c is a dictionary, containing a 2 by 9 matrix - the F contrast matrix for our
# contrast of interest
assert X.shape == (50, 9)
assert c['C'].shape == (2, 9)
# In this case the contrast matrix is rather obvious.
np.testing.assert_almost_equal(c['C'],
[[1,-1, 0, 0, 0, 0, 0, 0, 0],
[1, 0, -1, 0, 0, 0, 0, 0, 0]])
# We can get the design implied by our contrast at our chosen times
c1 = utils.events([3, 7, 10], f=hrf.glover) # Symbolic function of time
c2 = utils.events([1, 3, 9], f=hrf.glover) # Symbolic function of time
c3 = utils.events([3, 4, 6], f=delay.spectral[0]) # Symbolic function of time
# We can also use a Fourier basis for some other onsets - again making symbolic
# functions of time
d = utils.fourier_basis([3, 5, 7]) # Formula
# Make a formula for all four sets of onsets
f = Formula([c1, c2, c3]) + d
# A contrast is a formula expressed on the elements of the design formula
contrast = Formula([c1 - c2, c1 - c3])
# Instantiate actual values of time at which to create the design matrix rows
t = make_recarray(np.linspace(0, 20, 50), 't')
# Make the design matrix, and get contrast matrices for the design
X, c = f.design(t, return_float=True, contrasts={'C': contrast})
# c is a dictionary, containing a 2 by 9 matrix - the F contrast matrix for our
# contrast of interest
assert X.shape == (50, 9)
assert c['C'].shape == (2, 9)
# In this case the contrast matrix is rather obvious.
np.testing.assert_almost_equal(
c['C'], [[1, -1, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 0, 0, 0, 0, 0]])
# We can get the design implied by our contrast at our chosen times
preC = contrast.design(t, return_float=True)