def test_eig_from_lo_tri():
psphere = get_sphere('symmetric362')
bvecs = np.concatenate(([[0, 0, 0]], psphere.vertices))
bvals = np.zeros(len(bvecs)) + 1000
bvals[0] = 0
gtab = grad.gradient_table(bvals, bvecs)
mevals = np.array(([0.0015, 0.0003, 0.0001], [0.0015, 0.0003, 0.0003]))
mevecs = [np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]),
np.array([[0, 0, 1], [0, 1, 0], [1, 0, 0]])]
S = np.array([[single_tensor(gtab, 100, mevals[0], mevecs[0], snr=None),
single_tensor(gtab, 100, mevals[0], mevecs[0], snr=None)]])
dm = dti.TensorModel(gtab, 'LS')
dmfit = dm.fit(S)
lo_tri = lower_triangular(dmfit.quadratic_form)
assert_array_almost_equal(dti.eig_from_lo_tri(lo_tri), dmfit.model_params)
def test_eig_from_lo_tri():
psphere = get_sphere('symmetric362')
bvecs = np.concatenate(([[0, 0, 0]], psphere.vertices))
bvals = np.zeros(len(bvecs)) + 1000
bvals[0] = 0
gtab = grad.gradient_table(bvals, bvecs)
mevals = np.array(([0.0015, 0.0003, 0.0001], [0.0015, 0.0003, 0.0003]))
mevecs = [np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]),
np.array([[0, 0, 1], [0, 1, 0], [1, 0, 0]])]
S = np.array([[single_tensor(gtab, 100, mevals[0], mevecs[0], snr=None),
single_tensor(gtab, 100, mevals[0], mevecs[0], snr=None)]])
dm = dti.TensorModel(gtab, 'LS')
dmfit = dm.fit(S)
lo_tri = lower_triangular(dmfit.quadratic_form)
assert_array_almost_equal(dti.eig_from_lo_tri(lo_tri), dmfit.model_params)
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)
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)))
def initial_fit(dwis,
bvals,
bvecs,
mask,
wm_roi,
csf_roi,
MD,
csf_percentile=95,
wm_percentile=5,
lmin=0.1e-3,
lmax=2.5e-3,
evals_lmin=0.1e-3,
evals_lmax=2.5e-3,
md_value=0.6e-3,
interpolate=True,
fixed_MD=False):
'''
Produce the initial estimate of the volume fraction and the initial tensor image
'''
print(" - Compute baseline image and DW attenuation.")
dim_x, dim_y, dim_z = mask.shape
indices_dwis = (bvals > 0)
nb_dwis = np.count_nonzero(indices_dwis)
indices_b0 = (bvals == 0)
nb_b0 = np.count_nonzero(indices_b0)
# TO DO : address this line for multi-shell dwi
b = bvals.max()
b0 = dwis[..., indices_b0].mean(-1)
# signal attenuation
signal = dwis[..., indices_dwis] / b0[..., None]
np.clip(signal, 1.0e-6, 1 - 1.0e-6, signal)
signal[np.logical_not(mask)] = 0.
# tissue b0 references
csf_b0 = np.percentile(b0[csf_roi], csf_percentile)
print("\t{0:2d}th percentile of b0 signal in CSF: {1}.".format(
csf_percentile, csf_b0))
wm_b0 = np.percentile(b0[wm_roi], wm_percentile)
print("\t{0:2d}th percentile of b0 signal in WM : {1}.".format(
wm_percentile, wm_b0))
print(" - Compute initial volume fraction ...")
# Eq. 7 from Pasternak 2009 MRM
epsi = 1e-12 # only used to prevent log(0)
init_f = 1 - np.log(b0 / wm_b0 + epsi) / np.log(csf_b0 / wm_b0)
np.clip(init_f, 0.0, 1.0, init_f)
alpha = init_f.copy() # exponent for interpolation
print(" - Compute fixed MD VF map")
init_f_MD = (np.exp(-b * MD) - np.exp(-b * d)) / (np.exp(-b * md_value) -
np.exp(-b * d))
np.clip(init_f_MD, 0.01, 0.99, init_f_MD)
print(" - Compute min_f and max_f from lmin, lmax")
### This was following Pasternak 2009 although with an error
### Amin = exp(-b*lmax) and Amax = exp(-b*lmin) in that paper
# min_f = (signal.min(-1)-np.exp(-b*d)) / (np.exp(-b*lmin)-np.exp(-b*d))
# max_f = (signal.max(-1)-np.exp(-b*d)) / (np.exp(-b*lmax)-np.exp(-b*d))
### From Pasternak 2009 method, Amin < At implies that the
### term with signal.min(-1) in numerator is the upper bound of f
### although in that paper the equation 6 has fmin and fmax reversed.
### With lmin, lmax=0.1e-3, 2.5e-3, Amin = 0.08, Awater = 0.04
### and one can see that max_f here will usually be >> 1
min_f = (signal.max(-1) - np.exp(-b * d)) / (np.exp(-b * lmin) -
np.exp(-b * d))
max_f = (signal.min(-1) - np.exp(-b * d)) / (np.exp(-b * lmax) -
np.exp(-b * d))
# If MD of a voxel is > 3.0e-3, min_f and max_f can be negative.
# These voxels should be initialized as 0
np.clip(min_f, 0.0, 1.0, min_f)
np.clip(max_f, 0.0, 1.0, max_f)
np.clip(init_f, min_f, max_f, init_f)
if interpolate:
print(" - Interpolate two estimates of volume fraction")
# f = tissue fraction. with init_f high, alpha will be ~1 and init_f_MD will be weighted
init_f = (np.power(init_f, (1 - alpha))) * (np.power(init_f_MD, alpha))
elif fixed_MD:
print(
" - Using fixed MD value of {0} for inital volume fraction".format(
md_value))
init_f = init_f_MD
else:
print(" - Using lmin and lmax for initial volume fraction")
np.clip(init_f, 0.05, 0.99, init_f) # want minimum 5% of tissue
init_f[np.isnan(init_f)] = 0.5
init_f[np.logical_not(mask)] = 0.5
print(" - Compute initial tissue tensor ...")
signal[np.isnan(signal)] = 0
bvecs = bvecs[indices_dwis]
bvals = bvals[indices_dwis]
signal_free_water = np.exp(-bvals * d)
corrected_signal = (signal - (1 - init_f[..., np.newaxis]) \
* signal_free_water[np.newaxis, np.newaxis, np.newaxis, :]) \
/ (init_f[..., np.newaxis])
np.clip(corrected_signal, 1.0e-3, 1. - 1.0e-3, corrected_signal)
log_signal = np.log(corrected_signal)
gtab = gradient_table_from_bvals_bvecs(bvals, bvecs)
H = dti.design_matrix(gtab)[:, :6]
pseudo_inv = np.dot(np.linalg.inv(np.dot(H.T, H)), H.T)
init_tensor = np.dot(log_signal, pseudo_inv.T)
dti_params = dti.eig_from_lo_tri(init_tensor).reshape(
(dim_x, dim_y, dim_z, 4, 3))
evals = dti_params[..., 0, :]
evecs = dti_params[..., 1:, :]
if evals_lmin > 0.1e-3:
print(" - Fatten tensor to {}".format(evals_lmin))
lower_triangular = clip_tensor_evals(evals, evecs, evals_lmin, evals_lmax)
lower_triangular[np.logical_not(mask)] = [
evals_lmin, 0, evals_lmin, 0, 0, evals_lmin
]
nan_mask = np.any(np.isnan(lower_triangular), axis=-1)
lower_triangular[nan_mask] = [evals_lmin, 0, evals_lmin, 0, 0, evals_lmin]
init_tensor = lower_triangular[:, :, :, np.newaxis, :]
return init_f, init_tensor
def gradient_descent(dwis, bvals, bvecs, mask, init_f, init_tensor, niters=50):
'''
Optimize the volume fraction and the tensor via gradient descent.
'''
dim_x, dim_y, dim_z = mask.shape
indices_dwis = (bvals > 0)
nb_dwis = np.count_nonzero(indices_dwis)
indices_b0 = (bvals == 0)
nb_b0 = np.count_nonzero(indices_b0)
b = bvals.max()
b0 = dwis[..., indices_b0].mean(-1)
signal = dwis[..., indices_dwis] / b0[..., None]
np.clip(signal, 1.0e-6, 1 - 1.0e-6, signal)
bvals = bvals[indices_dwis]
bvecs = bvecs[indices_dwis]
gtab = gradient_table_from_bvals_bvecs(bvals, bvecs)
H = dti.design_matrix(gtab)[:, :6]
signal[np.logical_not(mask)] = 0.
signal = signal[mask]
lower_triangular = init_tensor[mask, 0]
volume_fraction = init_f[mask]
print(" - Begin gradient descent.")
mask_nvoxels = np.count_nonzero(mask)
step_size = 1.0e-7
weight = 100.0
l_min_loop, l_max_loop = 0.1e-3, 2.5e-3
for i in range(niters):
print(" - Iteration {0:d} out of {1:d}.".format(i + 1, niters))
grad1, predicted_signal_tissue, predicted_signal_water = \
grad_data_fit_tensor(lower_triangular, signal, H, bvals,
volume_fraction)
print("\tgrad1 avg: {0:0.4e}".format(np.mean(np.abs(grad1))))
predicted_signal = volume_fraction[..., None] * predicted_signal_tissue + \
(1-volume_fraction[..., None]) * predicted_signal_water
prediction_error = np.sqrt(((predicted_signal - signal)**2).mean(-1))
print("\tpref error avg: {0:0.4e}".format(np.mean(prediction_error)))
gradf = (bvals * (predicted_signal - signal) \
* (predicted_signal_tissue - predicted_signal_water)).sum(-1)
print("\tgradf avg: {0:0.4e}".format(np.mean(np.abs(gradf))))
volume_fraction -= weight * step_size * gradf
grad1[np.isnan(grad1)] = 0
# np.clip(grad1, -1.e5, 1.e5, grad1)
np.clip(volume_fraction, 0.01, 0.99, volume_fraction)
lower_triangular -= step_size * grad1
lower_triangular[np.isnan(lower_triangular)] = 0
dti_params = dti.eig_from_lo_tri(lower_triangular).reshape(
(mask_nvoxels, 4, 3))
evals = dti_params[..., 0, :]
evecs = dti_params[..., 1:, :]
lower_triangular = clip_tensor_evals(evals, evecs, l_min_loop,
l_max_loop)
del dti_params, evals, evecs
final_tensor = np.zeros((dim_x, dim_y, dim_z, 1, 6), dtype=np.float32)
final_tensor[mask, 0] = lower_triangular
final_f = np.zeros((dim_x, dim_y, dim_z), dtype=np.float32)
final_f[mask] = 1 - volume_fraction
return final_f, final_tensor
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)))
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)
def _run_interface(self, runtime):
# Load the 4D image files
img = nb.load(self.inputs.in_file)
data = img.get_data()
affine = img.get_affine()
if self.inputs.lower_triangular_input:
try:
dti_params = dti.eig_from_lo_tri(data)
except:
dti_params = dti.tensor_eig_from_lo_tri(data)
else:
data = np.asarray(data)
data_flat = data.reshape((-1, data.shape[-1]))
dti_params = np.empty((len(data_flat), 4, 3))
for ii in range(len(data_flat)):
tensor = from_upper_triangular(data_flat[ii])
evals, evecs = dti.decompose_tensor(tensor)
dti_params[ii, 0] = evals
dti_params[ii, 1:] = evecs
dti_params.shape = data.shape[:-1] + (12, )
evals = dti_params[..., :3]
evecs = dti_params[..., 3:]
evecs = evecs.reshape(np.shape(evecs)[:3] + (3, 3))
# Estimate electrical conductivity
evals = abs(self.inputs.eigenvalue_scaling_factor * evals)
if self.inputs.volume_normalized_mapping:
# Calculate the cube root of the product of the three eigenvalues (for
# normalization)
denominator = np.power(
(evals[..., 0] * evals[..., 1] * evals[..., 2]), (1 / 3))
# Calculate conductivity and normalize the eigenvalues
evals = self.inputs.sigma_white_matter * evals / denominator
evals[denominator < 0.0001] = self.inputs.sigma_white_matter
# Threshold outliers that show unusually high conductivity
if self.inputs.use_outlier_correction:
evals[evals > 0.4] = 0.4
conductivity_quadratic = np.array(vec_val_vect(evecs, evals))
if self.inputs.lower_triangular_output:
conductivity_data = dti.lower_triangular(conductivity_quadratic)
else:
conductivity_data = upper_triangular(conductivity_quadratic)
# Write as a 4D Nifti tensor image with the original affine
img = nb.Nifti1Image(conductivity_data, affine=affine)
out_file = op.abspath(self._gen_outfilename())
nb.save(img, out_file)
IFLOGGER.info(
'Conductivity tensor image saved as {i}'.format(i=out_file))
return runtime
