def test_unique_bvals_magnitude():
bvals = np.array([1000, 1000, 1000, 1000, 2000, 2000, 2000, 2000, 0])
ubvals_gt = np.array([0, 1000, 2000])
b = unique_bvals_magnitude(bvals)
npt.assert_array_almost_equal(ubvals_gt, b)
bvals = np.array([995, 995, 995, 995, 2005, 2005, 2005, 2005, 0])
# Case that b-values are rounded:
b = unique_bvals_magnitude(bvals)
npt.assert_array_almost_equal(ubvals_gt, b)
# b-values are not rounded if you specific the magnitude of the values
# precision:
b = unique_bvals_magnitude(bvals, bmag=0)
npt.assert_array_almost_equal(b, np.array([0, 995, 2005]))
# Case that b-values are in ms/um2
bvals = np.array(
[0.995, 0.995, 0.995, 0.995, 2.005, 2.005, 2.005, 2.005, 0])
b = unique_bvals_magnitude(bvals)
ubvals_gt = np.array([0, 1, 2])
npt.assert_array_almost_equal(ubvals_gt, b)
# Test case that optional parameter round_bvals is set to true
bvals = np.array([995, 1000, 1004, 1000, 2001, 2000, 1988, 2017, 0])
ubvals_gt = np.array([0, 1000, 2000])
rbvals_gt = np.array([1000, 1000, 1000, 1000, 2000, 2000, 2000, 2000, 0])
ub, rb = unique_bvals_magnitude(bvals, rbvals=True)
npt.assert_array_almost_equal(ubvals_gt, ub)
npt.assert_array_almost_equal(rbvals_gt, rb)
def test_design_matrix():
ub = unique_bvals_magnitude(bvals_3s)
D = msdki.design_matrix(ub)
Dgt = np.ones((4, 3))
Dgt[:, 0] = -ub
Dgt[:, 1] = 1.0 / 6 * ub**2
assert_array_almost_equal(D, Dgt)
def __init__(self, gtab, bmag=None, return_S0_hat=False, *args, **kwargs):
""" Mean Signal Diffusion Kurtosis Model [1]_.
Parameters
----------
gtab : GradientTable class instance
bmag : int
The order of magnitude that the bvalues have to differ to be
considered an unique b-value. Default: derive this value from the
maximal b-value provided: $bmag=log_{10}(max(bvals)) - 1$.
return_S0_hat : bool
If True, also return S0 values for the fit.
args, kwargs : arguments and keyword arguments passed to the
fit_method. See msdki.wls_fit_msdki for details
References
----------
.. [1] Henriques, R.N., 2018. Advanced Methods for Diffusion MRI Data
Analysis and their Application to the Healthy Ageing Brain
(Doctoral thesis). Downing College, University of Cambridge.
https://doi.org/10.17863/CAM.29356
"""
ReconstModel.__init__(self, gtab)
self.return_S0_hat = return_S0_hat
self.ubvals = unique_bvals_magnitude(gtab.bvals, bmag=bmag)
self.design_matrix = design_matrix(self.ubvals)
self.bmag = bmag
self.args = args
self.kwargs = kwargs
self.min_signal = self.kwargs.pop('min_signal', MIN_POSITIVE_SIGNAL)
if self.min_signal is not None and self.min_signal <= 0:
e_s = "The `min_signal` key-word argument needs to be strictly"
e_s += " positive."
raise ValueError(e_s)
# Check if at least three b-values are given
enough_b = check_multi_b(self.gtab, 3, non_zero=False, bmag=bmag)
if not enough_b:
mes = "MSDKI requires at least 3 b-values (which can include b=0)"
raise ValueError(mes)
def test_msdki_statistics():
# tests if MD and MK are equal to expected values of a spherical
# tensors
# Multi-tensors
ub = unique_bvals_magnitude(bvals_3s)
design_matrix = msdki.design_matrix(ub)
msignal, ng = msdki.mean_signal_bvalue(DWI, gtab_3s, bmag=None)
params = msdki.wls_fit_msdki(design_matrix, msignal, ng)
assert_array_almost_equal(params[..., 1], MKgt_multi)
assert_array_almost_equal(params[..., 0], MDgt_multi)
mdkiM = msdki.MeanDiffusionKurtosisModel(gtab_3s)
mdkiF = mdkiM.fit(DWI)
mk = mdkiF.msk
md = mdkiF.msd
assert_array_almost_equal(MKgt_multi, mk)
assert_array_almost_equal(MDgt_multi, md)
# Single-tensors
mdkiF = mdkiM.fit(signal_sph)
mk = mdkiF.msk
md = mdkiF.msd
assert_array_almost_equal(MKgt, mk)
assert_array_almost_equal(MDgt, md)
# Test with given mask
mask = np.ones(DWI.shape[:-1])
v = (0, 0, 0)
mask[1, 1, 1] = 0
mdkiF = mdkiM.fit(DWI, mask=mask)
mk = mdkiF.msk
md = mdkiF.msd
assert_array_almost_equal(MKgt_multi, mk)
assert_array_almost_equal(MDgt_multi, md)
assert_array_almost_equal(MKgt_multi[v], mdkiF[v].msk) # tuple case
assert_array_almost_equal(MDgt_multi[v], mdkiF[v].msd) # tuple case
assert_array_almost_equal(MKgt_multi[0], mdkiF[0].msk) # not tuple case
assert_array_almost_equal(MDgt_multi[0], mdkiF[0].msd) # not tuple case
# Test returned S0
mdkiM = msdki.MeanDiffusionKurtosisModel(gtab_3s, return_S0_hat=True)
mdkiF = mdkiM.fit(DWI)
assert_array_almost_equal(S0gt_multi, mdkiF.S0_hat)
assert_array_almost_equal(MKgt_multi[v], mdkiF[v].msk)
def mean_signal_bvalue(data, gtab, bmag=None):
"""
Computes the average signal across different diffusion directions
for each unique b-value
Parameters
----------
data : ndarray ([X, Y, Z, ...], g)
ndarray containing the data signals in its last dimension.
gtab : a GradientTable class instance
The gradient table containing diffusion acquisition parameters.
bmag : The order of magnitude that the bvalues have to differ to be
considered an unique b-value. Default: derive this value from the
maximal b-value provided: $bmag=log_{10}(max(bvals)) - 1$.
Returns
-------
msignal : ndarray ([X, Y, Z, ..., nub])
Mean signal along all gradient directions for each unique b-value
Note that the last dimension contains the signal means and nub is the
number of unique b-values.
ng : ndarray(nub)
Number of gradient directions used to compute the mean signal for
all unique b-values
Notes
-----
This function assumes that directions are evenly sampled on the sphere or
on the hemisphere
"""
bvals = gtab.bvals.copy()
# Compute unique and rounded bvals
ub, rb = unique_bvals_magnitude(bvals, bmag=bmag, rbvals=True)
# Initialize msignal and ng
nub = ub.size
ng = np.zeros(nub)
msignal = np.zeros(data.shape[:-1] + (nub,))
for bi in range(ub.size):
msignal[..., bi] = np.mean(data[..., rb == ub[bi]], axis=-1)
ng[bi] = np.sum(rb == ub[bi])
return msignal, ng