def test_multi_voxel_kurtosis_maximum():
# Multi-voxel simulations parameters
FIE = np.array([[[0.30, 0.32], [0.74, 0.51]], [[0.47, 0.21], [0.80,
0.63]]])
RDI = np.zeros((2, 2, 2))
ADI = np.array([[[1e-3, 1.3e-3], [0.8e-3, 1e-3]],
[[0.9e-3, 0.99e-3], [0.89e-3, 1.1e-3]]])
ADE = np.array([[[2.2e-3, 2.3e-3], [2.8e-3, 2.1e-3]],
[[1.9e-3, 2.5e-3], [1.89e-3, 2.1e-3]]])
Tor = np.array([[[2.6, 2.4], [2.8, 2.1]], [[2.9, 2.5], [2.7, 2.3]]])
RDE = ADE / Tor
# prepare simulation:
DWIsim = np.zeros((2, 2, 2, gtab_2s.bvals.size))
for i in range(2):
for j in range(2):
for k in range(2):
ADi = ADI[i, j, k]
RDi = RDI[i, j, k]
ADe = ADE[i, j, k]
RDe = RDE[i, j, k]
fie = FIE[i, j, k]
mevals = np.array([[ADi, RDi, RDi], [ADe, RDe, RDe]])
frac = [fie * 100, (1 - fie) * 100]
theta = random.uniform(0, 180)
phi = random.uniform(0, 320)
angles = [(theta, phi), (theta, phi)]
signal, dt, kt = multi_tensor_dki(gtab_2s,
mevals,
angles=angles,
fractions=frac,
snr=None)
DWIsim[i, j, k, :] = signal
# Ground truth Maximum kurtosis
RD = FIE * RDI + (1 - FIE) * RDE
RK = 3 * FIE * (1 - FIE) * ((RDI - RDE) / RD)**2
# prepare inputs
dkiM = dki.DiffusionKurtosisModel(gtab_2s, fit_method="WLS")
dkiF = dkiM.fit(DWIsim)
sphere = get_sphere('symmetric724')
# TEST - when no sphere is given
k_max = dki.kurtosis_maximum(dkiF.model_params)
assert_almost_equal(k_max, RK, decimal=4)
# TEST - when sphere is given
k_max = dki.kurtosis_maximum(dkiF.model_params, sphere)
assert_almost_equal(k_max, RK, decimal=4)
# TEST - when mask is given
mask = np.ones((2, 2, 2), dtype='bool')
mask[1, 1, 1] = 0
RK[1, 1, 1] = 0
k_max = dki.kurtosis_maximum(dkiF.model_params, mask=mask)
assert_almost_equal(k_max, RK, decimal=4)
def test_multi_voxel_kurtosis_maximum():
# Multi-voxel simulations parameters
FIE = np.array([[[0.30, 0.32], [0.74, 0.51]],
[[0.47, 0.21], [0.80, 0.63]]])
RDI = np.zeros((2, 2, 2))
ADI = np.array([[[1e-3, 1.3e-3], [0.8e-3, 1e-3]],
[[0.9e-3, 0.99e-3], [0.89e-3, 1.1e-3]]])
ADE = np.array([[[2.2e-3, 2.3e-3], [2.8e-3, 2.1e-3]],
[[1.9e-3, 2.5e-3], [1.89e-3, 2.1e-3]]])
Tor = np.array([[[2.6, 2.4], [2.8, 2.1]],
[[2.9, 2.5], [2.7, 2.3]]])
RDE = ADE / Tor
# prepare simulation:
DWIsim = np.zeros((2, 2, 2, gtab_2s.bvals.size))
for i in range(2):
for j in range(2):
for k in range(2):
ADi = ADI[i, j, k]
RDi = RDI[i, j, k]
ADe = ADE[i, j, k]
RDe = RDE[i, j, k]
fie = FIE[i, j, k]
mevals = np.array([[ADi, RDi, RDi], [ADe, RDe, RDe]])
frac = [fie*100, (1 - fie)*100]
theta = random.uniform(0, 180)
phi = random.uniform(0, 320)
angles = [(theta, phi), (theta, phi)]
signal, dt, kt = multi_tensor_dki(gtab_2s, mevals,
angles=angles,
fractions=frac, snr=None)
DWIsim[i, j, k, :] = signal
# Ground truth Maximum kurtosis
RD = FIE*RDI + (1-FIE)*RDE
RK = 3 * FIE * (1-FIE) * ((RDI-RDE) / RD) ** 2
# prepare inputs
dkiM = dki.DiffusionKurtosisModel(gtab_2s, fit_method="WLS")
dkiF = dkiM.fit(DWIsim)
sphere = get_sphere('symmetric724')
# TEST - when no sphere is given
k_max = dki.kurtosis_maximum(dkiF.model_params)
assert_almost_equal(k_max, RK, decimal=4)
# TEST - when sphere is given
k_max = dki.kurtosis_maximum(dkiF.model_params, sphere)
assert_almost_equal(k_max, RK, decimal=4)
# TEST - when mask is given
mask = np.ones((2, 2, 2), dtype='bool')
mask[1, 1, 1] = 0
RK[1, 1, 1] = 0
k_max = dki.kurtosis_maximum(dkiF.model_params, mask=mask)
assert_almost_equal(k_max, RK, decimal=4)
def axonal_water_fraction(dki_params,
sphere='repulsion100',
gtol=1e-2,
mask=None):
""" Computes the axonal water fraction from DKI [1]_.
Parameters
----------
dki_params : ndarray (x, y, z, 27) or (n, 27)
All parameters estimated from the diffusion kurtosis model.
Parameters are ordered as follows:
1) Three diffusion tensor's eigenvalues
2) Three lines of the eigenvector matrix each containing the first,
second and third coordinates of the eigenvector
3) Fifteen elements of the kurtosis tensor
sphere : Sphere class instance, optional
The sphere providing sample directions for the initial search of the
maximal value of kurtosis.
gtol : float, optional
This input is to refine kurtosis maxima under the precision of the
directions sampled on the sphere class instance. The gradient of the
convergence procedure must be less than gtol before successful
termination. If gtol is None, fiber direction is directly taken from
the initial sampled directions of the given sphere object
mask : ndarray
A boolean array used to mark the coordinates in the data that should be
analyzed that has the shape dki_params.shape[:-1]
Returns
-------
awf : ndarray (x, y, z) or (n)
Axonal Water Fraction
References
----------
.. [1] Fieremans E, Jensen JH, Helpern JA, 2011. White matter
characterization with diffusional kurtosis imaging.
Neuroimage 58(1):177-88. doi: 10.1016/j.neuroimage.2011.06.006
"""
kt_max = kurtosis_maximum(dki_params, sphere=sphere, gtol=gtol, mask=mask)
awf = kt_max / (kt_max + 3)
return awf
def axonal_water_fraction(dki_params, sphere='repulsion100', gtol=1e-2,
mask=None):
""" Computes the axonal water fraction from DKI [1]_.
Parameters
----------
dki_params : ndarray (x, y, z, 27) or (n, 27)
All parameters estimated from the diffusion kurtosis model.
Parameters are ordered as follows:
1) Three diffusion tensor's eigenvalues
2) Three lines of the eigenvector matrix each containing the first,
second and third coordinates of the eigenvector
3) Fifteen elements of the kurtosis tensor
sphere : Sphere class instance, optional
The sphere providing sample directions for the initial search of the
maximal value of kurtosis.
gtol : float, optional
This input is to refine kurtosis maxima under the precision of the
directions sampled on the sphere class instance. The gradient of the
convergence procedure must be less than gtol before successful
termination. If gtol is None, fiber direction is directly taken from
the initial sampled directions of the given sphere object
mask : ndarray
A boolean array used to mark the coordinates in the data that should be
analyzed that has the shape dki_params.shape[:-1]
Returns
--------
awf : ndarray (x, y, z) or (n)
Axonal Water Fraction
References
----------
.. [1] Fieremans E, Jensen JH, Helpern JA, 2011. White matter
characterization with diffusional kurtosis imaging.
Neuroimage 58(1):177-88. doi: 10.1016/j.neuroimage.2011.06.006
"""
kt_max = kurtosis_maximum(dki_params, sphere=sphere, gtol=gtol, mask=mask)
awf = kt_max / (kt_max + 3)
return awf
