def fractional_anisotropy_std(d,
dperp0,
dperp1,
d_std,
dperp0_std,
dperp1_std,
covariances=None):
"""Calculate the standard deviation of the fractional anisotropy (FA) using error propagation.
Args:
d (ndarray): an 1d array
dperp0 (ndarray): an 1d array
dperp1 (ndarray): an 1d array
d_std (ndarray): an 1d array
dperp0_std (ndarray): an 1d array
dperp1_std (ndarray): an 1d array
covariances (dict): optionally, a matrix holding the covariances. This expects the keys to be like:
'<param_0>_to_<param_1>'. The order of the parameter names does not matter.
Returns:
ndarray: the standard deviation of the fraction anisotropy using error propagation of the diffusivities.
"""
gradient = DTIMeasures._get_fractional_anisotropy_gradient(
d, dperp0, dperp1)
covars = create_covariance_matrix(d.shape[0], {
'd.std': d_std,
'dperp0.std': dperp0_std,
'dperp1.std': dperp1_std
}, ['d', 'dperp0', 'dperp1'], covariances)
return np.nan_to_num(
np.sqrt(
voxelwise_vector_matrix_vector_product(gradient, covars,
gradient)))
def extra_output_maps(results):
np.warnings.filterwarnings('ignore')
Rb, RM0a, fterm, gM0a, T1a_T2a, s0 = [
np.squeeze(results[n])
for n in ('QMT.Rb', 'QMT.RM0a', 'QMT.fterm', 'QMT.gM0a',
'QMT.T1a_T2a', 'S0.s0')
]
Rb_std, RM0a_std, fterm_std, gM0a_std, T1a_T2a_std, s0_std = [
np.squeeze(results.get(n + '.std', 0))
for n in ('QMT.Rb', 'QMT.RM0a', 'QMT.fterm', 'QMT.gM0a',
'QMT.T1a_T2a', 'S0.s0')
]
R_obs = 1. / results.get_input_data('T1')
if len(R_obs.shape) > 1:
R_obs = R_obs[:, 0]
Ra = R_obs / (1.0 + ((RM0a * fterm * (Rb - R_obs)) /
(Rb - R_obs + RM0a)))
f = fterm * Ra / (1.0 + fterm * Ra)
covars = create_covariance_matrix(f.shape[0], results,
['QMT.RM0a', 'QMT.fterm', 'QMT.Rb'],
results.get('covariances', None))
Ra_gradient = get_ra_gradient(R_obs, RM0a, fterm, Rb)
Ra_std = np.nan_to_num(
np.sqrt(
voxelwise_vector_matrix_vector_product(Ra_gradient, covars,
Ra_gradient)))
f_gradient = get_f_gradient(R_obs, RM0a, fterm, Rb)
f_std = np.nan_to_num(
np.sqrt(
voxelwise_vector_matrix_vector_product(f_gradient, covars,
f_gradient)))
values = {
'QMT.PD': gM0a * s0,
'QMT.T1_f': 1.0 / Ra,
'QMT.T2_f': (1.0 / Ra) / T1a_T2a,
'QMT.k_bf': RM0a * f / (1.0 - f),
'QMT.f_b': f,
'QMT.Ra': Ra,
}
values.update({
'QMT.PD.std':
np.nan_to_num(np.sqrt(gM0a**2 * s0_std + s0**2 * gM0a_std)),
'QMT.T1_f.std':
np.nan_to_num(np.sqrt(Ra_std / Ra**4)),
'QMT.T2_f.std':
np.nan_to_num(
np.sqrt((Ra**2 * T1a_T2a_std + Ra_std * T1a_T2a**2) /
(Ra**4 * T1a_T2a**4))),
'QMT.k_bf.std':
np.nan_to_num(
np.sqrt((RM0a**2 * f_std + RM0a_std * f**2 * (f - 1.0)**2) /
(f - 1.0)**4)),
'QMT.f_b.std':
f_std,
'QMT.Ra.std':
Ra_std,
})
return values