def make_local_connectivity_tcorr(func_img, clust_mask_img, thresh):
"""
Constructs a spatially constrained connectivity matrix from a fMRI dataset.
The weights w_ij of the connectivity matrix W correspond to the
temporal correlation between the time series from voxel i and voxel j.
Connectivity is only calculated between a voxel and the 27 voxels in its 3D
neighborhood (face touching and edge touching).
References
----------
.. Adapted from PyClusterROI
Parameters
----------
func_img : Nifti1Image
4D Nifti1Image containing fMRI data.
clust_mask_img : Nifti1Image
3D NIFTI file containing a mask, which restricts the
voxels used in the analysis.
thresh : str
Threshold value, correlation coefficients lower than this value
will be removed from the matrix (set to zero).
Returns
-------
W : Compressed Sparse Matrix
A Scipy sparse matrix, with weights corresponding to the temporal correlation between the time series from
voxel i and voxel j
"""
from scipy.sparse import csc_matrix
from scipy import prod
from itertools import product
from pynets.fmri.clustools import indx_1dto3d, indx_3dto1d
# Index array used to calculate 3D neigbors
neighbors = np.array(sorted(sorted(sorted([list(x) for x in list(set(product({-1, 0, 1}, repeat=3)))],
key=lambda k: (k[0])), key=lambda k: (k[1])), key=lambda k: (k[2])))
# Read in the mask
msz = np.shape(np.asarray(clust_mask_img.dataobj).astype('bool'))
# Convert the 3D mask array into a 1D vector
mskdat = np.reshape(np.asarray(clust_mask_img.dataobj).astype('bool'), prod(msz))
# Determine the 1D coordinates of the non-zero elements of the mask
iv = np.nonzero(mskdat)[0]
m = len(iv)
print("%s%s%s" % ('\nTotal non-zero voxels in the mask: ', m, '\n'))
sz = func_img.shape
# Reshape fmri data to a num_voxels x num_timepoints array
func_data = func_img.get_fdata(dtype=np.float32)
imdat = np.reshape(func_data, (prod(sz[:3]), sz[3]))
del func_data
# Construct a sparse matrix from the mask
msk = csc_matrix((list(range(1, m + 1)), (iv, np.zeros(m))), shape=(prod(sz[:-1]), 1), dtype=np.float32)
sparse_i = []
sparse_j = []
sparse_w = []
negcount = 0
# Loop over all of the voxels in the mask
print('Voxels:')
for i in range(0, m):
if i % 1000 == 0:
print(str(i))
# Calculate the voxels that are in the 3D neighborhood of the center voxel
ndx1d = indx_3dto1d(indx_1dto3d(iv[i], sz[:-1]) + neighbors, sz[:-1])
# Restrict the neigborhood using the mask
ondx1d = msk[ndx1d].todense()
ndx1d = ndx1d[np.nonzero(ondx1d)[0]].flatten()
ondx1d = np.array(ondx1d[np.nonzero(ondx1d)[0]]).flatten()
# Determine the index of the seed voxel in the neighborhood
nndx = np.nonzero(ndx1d == iv[i])[0]
# Extract the timecourses for all of the voxels in the neighborhood
tc = np.array(imdat[ndx1d.astype('int'), :])
# Ensure that the "seed" has variance, if not just skip it
if np.var(tc[nndx, :]) == 0:
continue
# Calculate the correlation between all of the voxel TCs
R = np.corrcoef(tc)
if np.linalg.matrix_rank(R) == 1:
R = np.reshape(R, (1, 1))
# Set nans to 0
R[np.isnan(R)] = 0
# Set values below thresh to 0
R[R < thresh] = 0
if np.linalg.matrix_rank(R) == 0:
R = np.reshape(R, (1, 1))
# Extract just the correlations with the seed TC
R = R[nndx, :].flatten()
# Set NaN values to 0
negcount = negcount + sum(R < 0)
# Determine the non-zero correlations (matrix weights) and add their indices and values to the list
nzndx = np.nonzero(R)[0]
if len(nzndx) > 0:
sparse_i = np.append(sparse_i, ondx1d[nzndx] - 1, 0)
sparse_j = np.append(sparse_j, (ondx1d[nndx] - 1) * np.ones(len(nzndx)))
sparse_w = np.append(sparse_w, R[nzndx], 0)
# Concatenate the i, j and w_ij into a single vector
outlist = sparse_i
outlist = np.append(outlist, sparse_j)
outlist = np.append(outlist, sparse_w)
# Calculate the number of non-zero weights in the connectivity matrix
n = len(outlist) / 3
# Reshape the 1D vector read in from infile in to a 3xN array
outlist = np.reshape(outlist, (3, int(n)))
m = max(max(outlist[0, :]), max(outlist[1, :])) + 1
W = csc_matrix((outlist[2, :], (outlist[0, :], outlist[1, :])), shape=(int(m), int(m)), dtype=np.float32)
del imdat, msk, mskdat, outlist, m, sparse_i, sparse_j, sparse_w
return W
def make_local_connectivity_scorr(func_img, clust_mask_img, thresh):
"""
Constructs a spatially constrained connectivity matrix from a fMRI dataset.
The weights w_ij of the connectivity matrix W correspond to the
spatial correlation between the whole brain FC maps generated from the
time series from voxel i and voxel j. Connectivity is only calculated
between a voxel and the 27 voxels in its 3D neighborhood
(face touching and edge touching).
Parameters
----------
func_img : Nifti1Image
4D Nifti1Image containing fMRI data.
clust_mask_img : Nifti1Image
3D NIFTI file containing a mask, which restricts the voxels used in the analysis.
thresh : str
Threshold value, correlation coefficients lower than this value
will be removed from the matrix (set to zero).
Returns
-------
W : Compressed Sparse Matrix
A Scipy sparse matrix, with weights corresponding to the spatial correlation between the time series from
voxel i and voxel j
References
----------
.. Adapted from PyClusterROI
"""
from scipy.sparse import csc_matrix
from scipy import prod
from itertools import product
from pynets.fmri.clustools import indx_1dto3d, indx_3dto1d
neighbors = np.array(sorted(sorted(sorted([list(x) for x in list(set(product({-1, 0, 1}, repeat=3)))],
key=lambda k: (k[0])), key=lambda k: (k[1])), key=lambda k: (k[2])))
# Read in the mask
msz = clust_mask_img.shape
# Convert the 3D mask array into a 1D vector
mskdat = np.reshape(np.asarray(clust_mask_img.dataobj).astype('bool'), prod(msz))
# Determine the 1D coordinates of the non-zero
# elements of the mask
iv = np.nonzero(mskdat)[0]
sz = func_img.shape
# Reshape fmri data to a num_voxels x num_timepoints array
func_data = func_img.get_fdata(dtype=np.float32)
imdat = np.reshape(func_data, (prod(sz[:3]), sz[3]))
del func_data
# Mask the datset to only the in-mask voxels
imdat = imdat[iv, :]
imdat_sz = imdat.shape
# Z-score fmri time courses, this makes calculation of the
# correlation coefficient a simple matrix product
imdat_s = np.tile(np.std(imdat, 1), (imdat_sz[1], 1)).T
# Replace 0 with really large number to avoid div by zero
imdat_s[imdat_s == 0] = 1000000
imdat_m = np.tile(np.mean(imdat, 1), (imdat_sz[1], 1)).T
imdat = (imdat - imdat_m) / imdat_s
# Set values with no variance to zero
imdat[imdat_s == 0] = 0
imdat[np.isnan(imdat)] = 0
# Remove voxels with zero variance, do this here
# so that the mapping will be consistent across
# subjects
vndx = np.nonzero(np.var(imdat, 1) != 0)[0]
iv = iv[vndx]
m = len(iv)
print(m, ' # of non-zero valued or non-zero variance voxels in the mask')
# Construct a sparse matrix from the mask
msk = csc_matrix((vndx + 1, (iv, np.zeros(m))), shape=(prod(msz), 1), dtype=np.float32)
sparse_i = []
sparse_j = []
sparse_w = [[]]
for i in range(0, m):
if i % 1000 == 0:
print('voxel #', i)
# Convert index into 3D and calculate neighbors, then convert resulting 3D indices into 1D
ndx1d = indx_3dto1d(indx_1dto3d(iv[i], sz[:-1]) + neighbors, sz[:-1])
# Convert 1D indices into masked versions
ondx1d = msk[ndx1d].todense()
# Exclude indices not in the mask
ndx1d = ndx1d[np.nonzero(ondx1d)[0]].flatten()
ondx1d = np.array(ondx1d[np.nonzero(ondx1d)[0]])
ondx1d = ondx1d.flatten() - 1
# Keep track of the index corresponding to the "seed"
nndx = np.nonzero(ndx1d == iv[i])[0]
# Extract the time courses corresponding to the "seed"
# and 3D neighborhood voxels
tc = np.array(imdat[ondx1d.astype('int'), :])
# Ensure that the "seed" has variance, if not just skip it
if np.var(tc[nndx, :]) == 0:
continue
# Calculate functional connectivity maps for "seed"
# and 3D neighborhood voxels
R = np.corrcoef(np.dot(tc, imdat.T) / (sz[3] - 1))
if np.linalg.matrix_rank(R) == 1:
R = np.reshape(R, (1, 1))
# Set nans to 0
R[np.isnan(R)] = 0
# Set values below thresh to 0
R[R < thresh] = 0
# Calculate the spatial correlation between FC maps
if np.linalg.matrix_rank(R) == 0:
R = np.reshape(R, (1, 1))
# Keep track of the indices and the correlation weights
# to construct sparse connectivity matrix
sparse_i = np.append(sparse_i, ondx1d, 0)
sparse_j = np.append(sparse_j, (ondx1d[nndx]) * np.ones(len(ondx1d)))
sparse_w = np.append(sparse_w, R[nndx, :], 1)
# Ensure that the weight vector is the correct shape
sparse_w = np.reshape(sparse_w, prod(np.shape(sparse_w)))
# Concatenate the i, j, and w_ij vectors
outlist = sparse_i
outlist = np.append(outlist, sparse_j)
outlist = np.append(outlist, sparse_w)
# Calculate the number of non-zero weights in the connectivity matrix
n = len(outlist) / 3
# Reshape the 1D vector read in from infile in to a 3xN array
outlist = np.reshape(outlist, (3, int(n)))
m = max(max(outlist[0, :]), max(outlist[1, :])) + 1
W = csc_matrix((outlist[2, :], (outlist[0, :], outlist[1, :])), shape=(int(m), int(m)), dtype=np.float32)
del imdat, msk, mskdat, outlist, m, sparse_i, sparse_j, sparse_w
return W