def test_single_fiber_model():
# single fiber simulate (which is the assumption of our model)
fie = 0.49
ADi = 0.00099
ADe = 0.00226
RDi = 0
RDe = 0.00087
# prepare simulation:
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,
angles=angles,
fractions=frac,
snr=None)
# DKI fit
dkiM = dki_micro.DiffusionKurtosisModel(gtab_2s, fit_method="WLS")
dkiF = dkiM.fit(signal)
# Axonal Water Fraction
sphere = get_sphere('symmetric724')
AWF = dki_micro.axonal_water_fraction(dkiF.model_params,
sphere,
mask=None,
gtol=1e-5)
assert_almost_equal(AWF, fie)
# Extra-cellular and intra-cellular components
edt, idt = dki_micro.diffusion_components(dkiF.model_params, sphere)
EDT = eig_from_lo_tri(edt)
IDT = eig_from_lo_tri(idt)
# check eigenvalues
assert_array_almost_equal(EDT[0:3], np.array([ADe, RDe, RDe]))
assert_array_almost_equal(IDT[0:3], np.array([ADi, RDi, RDi]))
# first eigenvalue should be the direction of the fibers
fiber_direction = _check_directions([(theta, phi)])
f_norm = abs(np.dot(fiber_direction, np.array((EDT[3], EDT[6], EDT[9]))))
assert_almost_equal(f_norm, 1.)
f_norm = abs(np.dot(fiber_direction, np.array((IDT[3], IDT[6], IDT[9]))))
assert_almost_equal(f_norm, 1.)
# Test model and fit objects
wmtiM = dki_micro.KurtosisMicrostructureModel(gtab_2s, fit_method="WLS")
wmtiF = wmtiM.fit(signal)
assert_almost_equal(wmtiF.awf, AWF)
assert_array_almost_equal(wmtiF.hindered_evals, np.array([ADe, RDe, RDe]))
assert_array_almost_equal(wmtiF.restricted_evals, np.array([ADi, RDi,
RDi]))
assert_almost_equal(wmtiF.hindered_ad, ADe)
assert_almost_equal(wmtiF.hindered_rd, RDe)
assert_almost_equal(wmtiF.axonal_diffusivity, ADi)
assert_almost_equal(wmtiF.tortuosity, ADe / RDe, decimal=4)
# Test diffusion_components when a kurtosis tensors is associated with
# negative kurtosis values. E.g of this cases is given below:
dkiparams = np.array([
1.67135726e-03, 5.03651205e-04, 9.35365328e-05, -7.11167583e-01,
6.23186820e-01, -3.25390313e-01, -1.75247376e-02, -4.78415563e-01,
-8.77958674e-01, 7.02804064e-01, 6.18673368e-01, -3.51154825e-01,
2.18384153, -2.76378153e-02, 2.22893297, -2.68306546e-01, -1.28411610,
-1.56557645e-01, -1.80850619e-01, -8.33152110e-01, -3.62410766e-01,
1.57775442e-01, 8.73775381e-01, 2.77188975e-01, -3.67415502e-02,
-1.56330984e-01, -1.62295407e-02
])
edt, idt = dki_micro.diffusion_components(dkiparams)
assert_(np.all(np.isfinite(edt)))
non-local means filter :ref:`example-denoise-nlmeans`).
"""
fwhm = 1.25
gauss_std = fwhm / np.sqrt(8 * np.log(2)) # converting fwhm to Gaussian std
data_smooth = np.zeros(data.shape)
for v in range(data.shape[-1]):
data_smooth[..., v] = gaussian_filter(data[..., v], sigma=gauss_std)
"""
Now that we have loaded and pre-processed the data we can go forward
with DKI fitting. For this, the DKI model is first defined for the data's
GradientTable object by instantiating the DiffusionKurtosisModel object in the
following way:
"""
dkimodel = dki.DiffusionKurtosisModel(gtab)
"""
To fit the data using the defined model object, we call the ``fit`` function of
this object:
"""
dkifit = dkimodel.fit(data_smooth)
"""
The fit method creates a DiffusionKurtosisFit object, which contains all the
diffusion and kurtosis fitting parameters and other DKI attributes. For
instance, since the diffusion kurtosis model estimates the diffusion tensor,
all diffusion standard tensor statistics can be computed from the
DiffusionKurtosisFit instance. For example, we show below how to extract the
fractional anisotropy (FA), the mean diffusivity (MD), the axial diffusivity
(AD) and the radial diffusivity (RD) from the DiffusionKurtosisiFit instance.
"""
def test_wmti_model_multi_voxel():
# DKI fit
dkiM = dki_micro.DiffusionKurtosisModel(gtab_2s, fit_method="WLS")
dkiF = dkiM.fit(DWIsim)
# Axonal Water Fraction
sphere = get_sphere()
AWF = dki_micro.axonal_water_fraction(dkiF.model_params,
sphere,
mask=None,
gtol=1e-5)
assert_almost_equal(AWF, FIE)
# Extra-cellular and intra-cellular components
edt, idt = dki_micro.diffusion_components(dkiF.model_params, sphere)
EDT = eig_from_lo_tri(edt)
IDT = eig_from_lo_tri(idt)
# check eigenvalues
assert_array_almost_equal(EDT[..., 0], ADE, decimal=3)
assert_array_almost_equal(EDT[..., 1], RDE, decimal=3)
assert_array_almost_equal(EDT[..., 2], RDE, decimal=3)
assert_array_almost_equal(IDT[..., 0], ADI, decimal=3)
assert_array_almost_equal(IDT[..., 1], RDI, decimal=3)
assert_array_almost_equal(IDT[..., 2], RDI, decimal=3)
# Test methods performance when a signal with all zeros is present
FIEc = FIE.copy()
RDIc = RDI.copy()
ADIc = ADI.copy()
ADEc = ADE.copy()
Torc = Tor.copy()
RDEc = RDE.copy()
DWIsimc = DWIsim.copy()
FIEc[0, 0, 0] = 0
RDIc[0, 0, 0] = 0
ADIc[0, 0, 0] = 0
ADEc[0, 0, 0] = 0
Torc[0, 0, 0] = 0
RDEc[0, 0, 0] = 0
DWIsimc[0, 0, 0, :] = 0
mask = np.ones((2, 2, 2))
mask[0, 0, 0] = 0
dkiF = dkiM.fit(DWIsimc)
awf = dki_micro.axonal_water_fraction(dkiF.model_params, sphere, gtol=1e-5)
assert_almost_equal(awf, FIEc)
# Extra-cellular and intra-cellular components
edt, idt = dki_micro.diffusion_components(dkiF.model_params,
sphere,
awf=awf)
EDT = eig_from_lo_tri(edt)
IDT = eig_from_lo_tri(idt)
assert_array_almost_equal(EDT[..., 0], ADEc, decimal=3)
assert_array_almost_equal(EDT[..., 1], RDEc, decimal=3)
assert_array_almost_equal(EDT[..., 2], RDEc, decimal=3)
assert_array_almost_equal(IDT[..., 0], ADIc, decimal=3)
assert_array_almost_equal(IDT[..., 1], RDIc, decimal=3)
assert_array_almost_equal(IDT[..., 2], RDIc, decimal=3)
# Check when mask is given
dkiF = dkiM.fit(DWIsim)
awf = dki_micro.axonal_water_fraction(dkiF.model_params,
sphere,
gtol=1e-5,
mask=mask)
assert_almost_equal(awf, FIEc, decimal=3)
# Extra-cellular and intra-cellular components
edt, idt = dki_micro.diffusion_components(dkiF.model_params,
sphere,
awf=awf,
mask=mask)
EDT = eig_from_lo_tri(edt)
IDT = eig_from_lo_tri(idt)
assert_array_almost_equal(EDT[..., 0], ADEc, decimal=3)
assert_array_almost_equal(EDT[..., 1], RDEc, decimal=3)
assert_array_almost_equal(EDT[..., 2], RDEc, decimal=3)
assert_array_almost_equal(IDT[..., 0], ADIc, decimal=3)
assert_array_almost_equal(IDT[..., 1], RDIc, decimal=3)
assert_array_almost_equal(IDT[..., 2], RDIc, decimal=3)
# Check class object
wmtiM = dki_micro.KurtosisMicrostructureModel(gtab_2s, fit_method="WLS")
wmtiF = wmtiM.fit(DWIsim, mask=mask)
assert_almost_equal(wmtiF.awf, FIEc, decimal=3)
assert_almost_equal(wmtiF.axonal_diffusivity, ADIc, decimal=3)
assert_almost_equal(wmtiF.hindered_ad, ADEc, decimal=3)
assert_almost_equal(wmtiF.hindered_rd, RDEc, decimal=3)
assert_almost_equal(wmtiF.tortuosity, Torc, decimal=3)