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_single_voxel_DKI_stats():
# tests if AK and RK are equal to expected values for a single fiber
# simulate randomly oriented
ADi = 0.00099
ADe = 0.00226
RDi = 0
RDe = 0.00087
# Reference values
AD = fie * ADi + (1 - fie) * ADe
AK = 3 * fie * (1 - fie) * ((ADi - ADe) / AD)**2
RD = fie * RDi + (1 - fie) * RDe
RK = 3 * fie * (1 - fie) * ((RDi - RDe) / RD)**2
ref_vals = np.array([AD, AK, RD, RK])
# simulate fiber randomly oriented
theta = random.uniform(0, 180)
phi = random.uniform(0, 320)
angles = [(theta, phi), (theta, phi)]
mevals = np.array([[ADi, RDi, RDi], [ADe, RDe, RDe]])
frac = [fie * 100, (1 - fie) * 100]
signal, dt, kt = multi_tensor_dki(gtab_2s,
mevals,
S0=100,
angles=angles,
fractions=frac,
snr=None)
evals, evecs = decompose_tensor(from_lower_triangular(dt))
dki_par = np.concatenate((evals, evecs[0], evecs[1], evecs[2], kt), axis=0)
# Estimates using dki functions
ADe1 = dti.axial_diffusivity(evals)
RDe1 = dti.radial_diffusivity(evals)
AKe1 = axial_kurtosis(dki_par)
RKe1 = radial_kurtosis(dki_par)
e1_vals = np.array([ADe1, AKe1, RDe1, RKe1])
assert_array_almost_equal(e1_vals, ref_vals)
# Estimates using the kurtosis class object
dkiM = dki.DiffusionKurtosisModel(gtab_2s)
dkiF = dkiM.fit(signal)
e2_vals = np.array([dkiF.ad, dkiF.ak(), dkiF.rd, dkiF.rk()])
assert_array_almost_equal(e2_vals, ref_vals)
# test MK (note this test correspond to the MK singularity L2==L3)
MK_as = dkiF.mk()
sph = Sphere(xyz=gtab.bvecs[gtab.bvals > 0])
MK_nm = np.mean(dkiF.akc(sph))
assert_array_almost_equal(MK_as, MK_nm, decimal=1)
def test_single_voxel_DKI_stats():
# tests if AK and RK are equal to expected values for a single fiber
# simulate randomly oriented
ADi = 0.00099
ADe = 0.00226
RDi = 0
RDe = 0.00087
# Reference values
AD = fie * ADi + (1 - fie) * ADe
AK = 3 * fie * (1 - fie) * ((ADi-ADe) / AD) ** 2
RD = fie * RDi + (1 - fie) * RDe
RK = 3 * fie * (1 - fie) * ((RDi-RDe) / RD) ** 2
ref_vals = np.array([AD, AK, RD, RK])
# simulate fiber randomly oriented
theta = random.uniform(0, 180)
phi = random.uniform(0, 320)
angles = [(theta, phi), (theta, phi)]
mevals = np.array([[ADi, RDi, RDi], [ADe, RDe, RDe]])
frac = [fie * 100, (1 - fie) * 100]
signal, dt, kt = multi_tensor_dki(gtab_2s, mevals, S0=100, angles=angles,
fractions=frac, snr=None)
evals, evecs = decompose_tensor(from_lower_triangular(dt))
dki_par = np.concatenate((evals, evecs[0], evecs[1], evecs[2], kt), axis=0)
# Estimates using dki functions
ADe1 = dti.axial_diffusivity(evals)
RDe1 = dti.radial_diffusivity(evals)
AKe1 = axial_kurtosis(dki_par)
RKe1 = radial_kurtosis(dki_par)
e1_vals = np.array([ADe1, AKe1, RDe1, RKe1])
assert_array_almost_equal(e1_vals, ref_vals)
# Estimates using the kurtosis class object
dkiM = dki.DiffusionKurtosisModel(gtab_2s)
dkiF = dkiM.fit(signal)
e2_vals = np.array([dkiF.ad, dkiF.ak(), dkiF.rd, dkiF.rk()])
assert_array_almost_equal(e2_vals, ref_vals)
# test MK (note this test correspond to the MK singularity L2==L3)
MK_as = dkiF.mk()
sph = Sphere(xyz=gtab.bvecs[gtab.bvals > 0])
MK_nm = np.mean(dkiF.akc(sph))
assert_array_almost_equal(MK_as, MK_nm, decimal=1)
