def test_spherical_dki_statistics():
# tests if MK, AK and RK are equal to expected values of a spherical
# kurtosis tensor
# Define multi voxel spherical kurtosis simulations
MParam = np.zeros((2, 2, 2, 27))
MParam[0, 0, 0] = MParam[0, 0, 1] = MParam[0, 1, 0] = params_sph
MParam[0, 1, 1] = MParam[1, 1, 0] = params_sph
# MParam[1, 1, 1], MParam[1, 0, 0], and MParam[1, 0, 1] remains zero
MRef = np.zeros((2, 2, 2))
MRef[0, 0, 0] = MRef[0, 0, 1] = MRef[0, 1, 0] = Kref_sphere
MRef[0, 1, 1] = MRef[1, 1, 0] = Kref_sphere
MRef[1, 1, 1] = MRef[1, 0, 0] = MRef[1, 0, 1] = 0
# Mean kurtosis analytical solution
MK_multi = mean_kurtosis(MParam)
assert_array_almost_equal(MK_multi, MRef)
# radial kurtosis analytical solution
RK_multi = radial_kurtosis(MParam)
assert_array_almost_equal(RK_multi, MRef)
# axial kurtosis analytical solution
AK_multi = axial_kurtosis(MParam)
assert_array_almost_equal(AK_multi, MRef)
def test_spherical_dki_statistics():
# tests if MK, AK and RK are equal to expected values of a spherical
# kurtosis tensor
# Define multi voxel spherical kurtosis simulations
MParam = np.zeros((2, 2, 2, 27))
MParam[0, 0, 0] = MParam[0, 0, 1] = MParam[0, 1, 0] = params_sph
MParam[0, 1, 1] = MParam[1, 1, 0] = params_sph
# MParam[1, 1, 1], MParam[1, 0, 0], and MParam[1, 0, 1] remains zero
MRef = np.zeros((2, 2, 2))
MRef[0, 0, 0] = MRef[0, 0, 1] = MRef[0, 1, 0] = Kref_sphere
MRef[0, 1, 1] = MRef[1, 1, 0] = Kref_sphere
MRef[1, 1, 1] = MRef[1, 0, 0] = MRef[1, 0, 1] = 0
# Mean kurtosis analytical solution
MK_multi = mean_kurtosis(MParam)
assert_array_almost_equal(MK_multi, MRef)
# radial kurtosis analytical solution
RK_multi = radial_kurtosis(MParam)
assert_array_almost_equal(RK_multi, MRef)
# axial kurtosis analytical solution
AK_multi = axial_kurtosis(MParam)
assert_array_almost_equal(AK_multi, MRef)
def test_spherical_dki_statistics():
# tests if MK, AK, RK and MSK are equal to expected values of a spherical
# kurtosis tensor
# Define multi voxel spherical kurtosis simulations
MParam = np.zeros((2, 2, 2, 27))
MParam[0, 0, 0] = MParam[0, 0, 1] = MParam[0, 1, 0] = params_sph
MParam[0, 1, 1] = MParam[1, 1, 0] = params_sph
# MParam[1, 1, 1], MParam[1, 0, 0], and MParam[1, 0, 1] remains zero
MRef = np.zeros((2, 2, 2))
MRef[0, 0, 0] = MRef[0, 0, 1] = MRef[0, 1, 0] = Kref_sphere
MRef[0, 1, 1] = MRef[1, 1, 0] = Kref_sphere
MRef[1, 1, 1] = MRef[1, 0, 0] = MRef[1, 0, 1] = 0
# Mean kurtosis analytical solution
MK_multi = mean_kurtosis(MParam, analytical=True)
assert_array_almost_equal(MK_multi, MRef)
# radial kurtosis analytical solution
RK_multi = radial_kurtosis(MParam, analytical=True)
assert_array_almost_equal(RK_multi, MRef)
# axial kurtosis analytical solution
AK_multi = axial_kurtosis(MParam, analytical=True)
assert_array_almost_equal(AK_multi, MRef)
# mean kurtosis tensor analytical solution
MSK_multi = mean_kurtosis_tensor(MParam)
assert_array_almost_equal(MSK_multi, MRef)
# kurtosis fractional anisotropy (isotropic case kfa=0)
KFA_multi = kurtosis_fractional_anisotropy(MParam)
assert_array_almost_equal(KFA_multi, 0 * MRef)
def test_MK_singularities():
# To test MK in case that analytical solution was a singularity not covered
# by other tests
dkiM = dki.DiffusionKurtosisModel(gtab_2s)
# test singularity L1 == L2 - this is the case of a prolate diffusion
# tensor for crossing fibers at 90 degrees
angles_all = np.array([[(90, 0), (90, 0), (0, 0), (0, 0)],
[(89.9, 0), (89.9, 0), (0, 0), (0, 0)]])
for angles_90 in angles_all:
s_90, dt_90, kt_90 = multi_tensor_dki(gtab_2s,
mevals_cross,
S0=100,
angles=angles_90,
fractions=frac_cross,
snr=None)
dkiF = dkiM.fit(s_90)
MK_an = dkiF.mk(analytical=True)
MK_nm = dkiF.mk(analytical=False)
assert_almost_equal(MK_an, MK_nm, decimal=3)
# test singularity L1 == L3 and L1 != L2
# since L1 is defined as the larger eigenvalue and L3 the smallest
# eigenvalue, this singularity theoretically will never be called,
# because for L1 == L3, L2 have also to be = L1 and L2.
# Nevertheless, I decided to include this test since this singularity
# is relevant for cases that eigenvalues are not ordered
# artificially revert the eigenvalue and eigenvector order
dki_params = dkiF.model_params.copy()
dki_params[1] = dkiF.model_params[2]
dki_params[2] = dkiF.model_params[1]
dki_params[4] = dkiF.model_params[5]
dki_params[5] = dkiF.model_params[4]
dki_params[7] = dkiF.model_params[8]
dki_params[8] = dkiF.model_params[7]
dki_params[10] = dkiF.model_params[11]
dki_params[11] = dkiF.model_params[10]
MK_an = dki.mean_kurtosis(dki_params, analytical=True)
MK_nm = dki.mean_kurtosis(dki_params, analytical=False)
assert_almost_equal(MK_an, MK_nm, decimal=3)
def test_MK_singularities():
# To test MK in case that analytical solution was a singularity not covered
# by other tests
dkiM = dki.DiffusionKurtosisModel(gtab_2s)
# test singularity L1 == L2 - this is the case of a prolate diffusion
# tensor for crossing fibers at 90 degrees
angles_all = np.array([[(90, 0), (90, 0), (0, 0), (0, 0)],
[(89.9, 0), (89.9, 0), (0, 0), (0, 0)]])
for angles_90 in angles_all:
s_90, dt_90, kt_90 = multi_tensor_dki(gtab_2s, mevals_cross, S0=100,
angles=angles_90,
fractions=frac_cross, snr=None)
dkiF = dkiM.fit(s_90)
MK = dkiF.mk()
sph = Sphere(xyz=gtab.bvecs[gtab.bvals > 0])
MK_nm = np.mean(dkiF.akc(sph))
assert_almost_equal(MK, MK_nm, decimal=2)
# test singularity L1 == L3 and L1 != L2
# since L1 is defined as the larger eigenvalue and L3 the smallest
# eigenvalue, this singularity teoretically will never be called,
# because for L1 == L3, L2 have also to be = L1 and L2.
# Nevertheless, I decided to include this test since this singularity
# is revelant for cases that eigenvalues are not ordered
# artificially revert the eigenvalue and eigenvector order
dki_params = dkiF.model_params.copy()
dki_params[1] = dkiF.model_params[2]
dki_params[2] = dkiF.model_params[1]
dki_params[4] = dkiF.model_params[5]
dki_params[5] = dkiF.model_params[4]
dki_params[7] = dkiF.model_params[8]
dki_params[8] = dkiF.model_params[7]
dki_params[10] = dkiF.model_params[11]
dki_params[11] = dkiF.model_params[10]
MK = dki.mean_kurtosis(dki_params)
MK_nm = np.mean(dki.apparent_kurtosis_coef(dki_params, sph))
assert_almost_equal(MK, MK_nm, decimal=2)
