예제 #1
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def test_split_dki_param():
    dkiM = dki.DiffusionKurtosisModel(gtab_2s, fit_method="OLS")
    dkiF = dkiM.fit(DWI)
    evals, evecs, kt = dki.split_dki_param(dkiF.model_params)

    assert_array_almost_equal(evals, dkiF.evals)
    assert_array_almost_equal(evecs, dkiF.evecs)
    assert_array_almost_equal(kt, dkiF.kt)
예제 #2
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def test_split_dki_param():
    dkiM = dki.DiffusionKurtosisModel(gtab_2s, fit_method="OLS")
    dkiF = dkiM.fit(DWI)
    evals, evecs, kt = dki.split_dki_param(dkiF.model_params)

    assert_array_almost_equal(evals, dkiF.evals)
    assert_array_almost_equal(evecs, dkiF.evecs)
    assert_array_almost_equal(kt, dkiF.kt)
예제 #3
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    def run(self,
            input_files,
            bvalues_files,
            bvectors_files,
            mask_files,
            b0_threshold=50.0,
            save_metrics=[],
            out_dir='',
            out_dt_tensor='dti_tensors.nii.gz',
            out_fa='fa.nii.gz',
            out_ga='ga.nii.gz',
            out_rgb='rgb.nii.gz',
            out_md='md.nii.gz',
            out_ad='ad.nii.gz',
            out_rd='rd.nii.gz',
            out_mode='mode.nii.gz',
            out_evec='evecs.nii.gz',
            out_eval='evals.nii.gz',
            out_dk_tensor="dki_tensors.nii.gz",
            out_mk="mk.nii.gz",
            out_ak="ak.nii.gz",
            out_rk="rk.nii.gz"):
        """ Workflow for Diffusion Kurtosis reconstruction and for computing
        DKI metrics. Performs a DKI reconstruction on the files by 'globing'
        ``input_files`` and saves the DKI metrics in a directory specified by
        ``out_dir``.

        Parameters
        ----------
        input_files : string
            Path to the input volumes. This path may contain wildcards to
            process multiple inputs at once.
        bvalues_files : string
            Path to the bvalues files. This path may contain wildcards to use
            multiple bvalues files at once.
        bvectors_files : string
            Path to the bvalues files. This path may contain wildcards to use
            multiple bvalues files at once.
        mask_files : string
            Path to the input masks. This path may contain wildcards to use
            multiple masks at once. (default: No mask used)
        b0_threshold : float, optional
            Threshold used to find b0 volumes.
        save_metrics : variable string, optional
            List of metrics to save.
            Possible values: fa, ga, rgb, md, ad, rd, mode, tensor, evec, eval
        out_dir : string, optional
            Output directory. (default current directory)
        out_dt_tensor : string, optional
            Name of the tensors volume to be saved.
        out_dk_tensor : string, optional
            Name of the tensors volume to be saved.
        out_fa : string, optional
            Name of the fractional anisotropy volume to be saved.
        out_ga : string, optional
            Name of the geodesic anisotropy volume to be saved.
        out_rgb : string, optional
            Name of the color fa volume to be saved.
        out_md : string, optional
            Name of the mean diffusivity volume to be saved.
        out_ad : string, optional
            Name of the axial diffusivity volume to be saved.
        out_rd : string, optional
            Name of the radial diffusivity volume to be saved.
        out_mode : string, optional
            Name of the mode volume to be saved.
        out_evec : string, optional
            Name of the eigenvectors volume to be saved.
        out_eval : string, optional
            Name of the eigenvalues to be saved.
        out_mk : string, optional
            Name of the mean kurtosis to be saved.
        out_ak : string, optional
            Name of the axial kurtosis to be saved.
        out_rk : string, optional
            Name of the radial kurtosis to be saved.

        References
        ----------

        .. [1] Tabesh, A., Jensen, J.H., Ardekani, B.A., Helpern, J.A., 2011.
           Estimation of tensors and tensor-derived measures in diffusional
           kurtosis imaging. Magn Reson Med. 65(3), 823-836

        .. [2] Jensen, Jens H., Joseph A. Helpern, Anita Ramani, Hanzhang Lu,
           and Kyle Kaczynski. 2005. Diffusional Kurtosis Imaging: The
           Quantification of Non-Gaussian Water Diffusion by Means of Magnetic
           Resonance Imaging. MRM 53 (6):1432-40.
        """
        io_it = self.get_io_iterator()

        for (dwi, bval, bvec, mask, otensor, ofa, oga, orgb, omd, oad, orad,
             omode, oevecs, oevals, odk_tensor, omk, oak, ork) in io_it:

            logging.info('Computing DKI metrics for {0}'.format(dwi))
            data, affine = load_nifti(dwi)

            if mask is not None:
                mask = load_nifti_data(mask).astype(bool)

            dkfit, _ = self.get_fitted_tensor(data, mask, bval, bvec,
                                              b0_threshold)

            if not save_metrics:
                save_metrics = [
                    'mk', 'rk', 'ak', 'fa', 'md', 'rd', 'ad', 'ga', 'rgb',
                    'mode', 'evec', 'eval', 'dt_tensor', 'dk_tensor'
                ]

            evals, evecs, kt = split_dki_param(dkfit.model_params)
            FA = fractional_anisotropy(evals)
            FA[np.isnan(FA)] = 0
            FA = np.clip(FA, 0, 1)

            if 'dt_tensor' in save_metrics:
                tensor_vals = lower_triangular(dkfit.quadratic_form)
                correct_order = [0, 1, 3, 2, 4, 5]
                tensor_vals_reordered = tensor_vals[..., correct_order]
                save_nifti(otensor, tensor_vals_reordered.astype(np.float32),
                           affine)

            if 'dk_tensor' in save_metrics:
                save_nifti(odk_tensor, dkfit.kt.astype(np.float32), affine)

            if 'fa' in save_metrics:
                save_nifti(ofa, FA.astype(np.float32), affine)

            if 'ga' in save_metrics:
                GA = geodesic_anisotropy(dkfit.evals)
                save_nifti(oga, GA.astype(np.float32), affine)

            if 'rgb' in save_metrics:
                RGB = color_fa(FA, dkfit.evecs)
                save_nifti(orgb, np.array(255 * RGB, 'uint8'), affine)

            if 'md' in save_metrics:
                MD = mean_diffusivity(dkfit.evals)
                save_nifti(omd, MD.astype(np.float32), affine)

            if 'ad' in save_metrics:
                AD = axial_diffusivity(dkfit.evals)
                save_nifti(oad, AD.astype(np.float32), affine)

            if 'rd' in save_metrics:
                RD = radial_diffusivity(dkfit.evals)
                save_nifti(orad, RD.astype(np.float32), affine)

            if 'mode' in save_metrics:
                MODE = get_mode(dkfit.quadratic_form)
                save_nifti(omode, MODE.astype(np.float32), affine)

            if 'evec' in save_metrics:
                save_nifti(oevecs, dkfit.evecs.astype(np.float32), affine)

            if 'eval' in save_metrics:
                save_nifti(oevals, dkfit.evals.astype(np.float32), affine)

            if 'mk' in save_metrics:
                save_nifti(omk, dkfit.mk().astype(np.float32), affine)

            if 'ak' in save_metrics:
                save_nifti(oak, dkfit.ak().astype(np.float32), affine)

            if 'rk' in save_metrics:
                save_nifti(ork, dkfit.rk().astype(np.float32), affine)

            logging.info('DKI metrics saved in {0}'.format(
                os.path.dirname(oevals)))
예제 #4
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def diffusion_components(dki_params,
                         sphere='repulsion100',
                         awf=None,
                         mask=None):
    """ Extracts the restricted and hindered diffusion tensors of well aligned
    fibers from diffusion kurtosis imaging parameters [1]_.

    Parameters
    ----------
    dki_params : ndarray (x, y, z, 27) or (n, 27)
        All parameters estimated from the diffusion kurtosis model.
        Parameters are ordered as follows:
            1) Three diffusion tensor's eigenvalues
            2) Three lines of the eigenvector matrix each containing the first,
               second and third coordinates of the eigenvector
            3) Fifteen elements of the kurtosis tensor
    sphere : Sphere class instance, optional
        The sphere providing sample directions to sample the restricted and
        hindered cellular diffusion tensors. For more details see Fieremans
        et al., 2011.
    awf : ndarray (optional)
        Array containing values of the axonal water fraction that has the shape
        dki_params.shape[:-1]. If not given this will be automatically computed
        using :func:`axonal_water_fraction`" with function's default precision.
    mask : ndarray (optional)
        A boolean array used to mark the coordinates in the data that should be
        analyzed that has the shape dki_params.shape[:-1]

    Returns
    -------
    edt : ndarray (x, y, z, 6) or (n, 6)
        Parameters of the hindered diffusion tensor.
    idt : ndarray (x, y, z, 6) or (n, 6)
        Parameters of the restricted diffusion tensor.

    Notes
    -----
    In the original article of DKI microstructural model [1]_, the hindered and
    restricted tensors were definde as the intra-cellular and extra-cellular
    diffusion compartments respectively.

    References
    ----------
    .. [1] Fieremans E, Jensen JH, Helpern JA, 2011. White matter
           characterization with diffusional kurtosis imaging.
           Neuroimage 58(1):177-88. doi: 10.1016/j.neuroimage.2011.06.006
    """
    shape = dki_params.shape[:-1]

    # load gradient directions
    if not isinstance(sphere, dps.Sphere):
        sphere = get_sphere(sphere)

    # select voxels where to apply the single fiber model
    if mask is None:
        mask = np.ones(shape, dtype='bool')
    else:
        if mask.shape != shape:
            raise ValueError("Mask is not the same shape as dki_params.")
        else:
            mask = np.array(mask, dtype=bool, copy=False)

    # check or compute awf values
    if awf is None:
        awf = axonal_water_fraction(dki_params, sphere=sphere, mask=mask)
    else:
        if awf.shape != shape:
            raise ValueError("awf array is not the same shape as dki_params.")

    # Initialize hindered and restricted diffusion tensors
    edt_all = np.zeros(shape + (6, ))
    idt_all = np.zeros(shape + (6, ))

    # Generate matrix that converts apparent diffusion coefficients to tensors
    B = np.zeros((sphere.x.size, 6))
    B[:, 0] = sphere.x * sphere.x  # Bxx
    B[:, 1] = sphere.x * sphere.y * 2.  # Bxy
    B[:, 2] = sphere.y * sphere.y  # Byy
    B[:, 3] = sphere.x * sphere.z * 2.  # Bxz
    B[:, 4] = sphere.y * sphere.z * 2.  # Byz
    B[:, 5] = sphere.z * sphere.z  # Bzz
    pinvB = np.linalg.pinv(B)

    # Compute hindered and restricted diffusion tensors for all voxels
    evals, evecs, kt = split_dki_param(dki_params)
    dt = lower_triangular(vec_val_vect(evecs, evals))
    md = mean_diffusivity(evals)

    index = ndindex(mask.shape)
    for idx in index:
        if not mask[idx]:
            continue
        # sample apparent diffusion and kurtosis values
        di = directional_diffusion(dt[idx], sphere.vertices)
        ki = directional_kurtosis(dt[idx],
                                  md[idx],
                                  kt[idx],
                                  sphere.vertices,
                                  adc=di,
                                  min_kurtosis=0)
        edi = di * (1 + np.sqrt(ki * awf[idx] / (3.0 - 3.0 * awf[idx])))
        edt = np.dot(pinvB, edi)
        edt_all[idx] = edt

        # We only move on if there is an axonal water fraction.
        # Otherwise, remaining params are already zero, so move on
        if awf[idx] == 0:
            continue
        # Convert apparent diffusion and kurtosis values to apparent diffusion
        # values of the hindered and restricted diffusion
        idi = di * (1 - np.sqrt(ki * (1.0 - awf[idx]) / (3.0 * awf[idx])))
        # generate hindered and restricted diffusion tensors
        idt = np.dot(pinvB, idi)
        idt_all[idx] = idt

    return edt_all, idt_all
예제 #5
0
파일: reconst.py 프로젝트: arokem/dipy
    def run(self, input_files, bvalues_files, bvectors_files, mask_files,
            b0_threshold=50.0, save_metrics=[],
            out_dir='', out_dt_tensor='dti_tensors.nii.gz', out_fa='fa.nii.gz',
            out_ga='ga.nii.gz', out_rgb='rgb.nii.gz', out_md='md.nii.gz',
            out_ad='ad.nii.gz', out_rd='rd.nii.gz', out_mode='mode.nii.gz',
            out_evec='evecs.nii.gz', out_eval='evals.nii.gz',
            out_dk_tensor="dki_tensors.nii.gz",
            out_mk="mk.nii.gz", out_ak="ak.nii.gz", out_rk="rk.nii.gz"):
        """ Workflow for Diffusion Kurtosis reconstruction and for computing
        DKI metrics. Performs a DKI reconstruction on the files by 'globing'
        ``input_files`` and saves the DKI metrics in a directory specified by
        ``out_dir``.

        Parameters
        ----------
        input_files : string
            Path to the input volumes. This path may contain wildcards to
            process multiple inputs at once.
        bvalues_files : string
            Path to the bvalues files. This path may contain wildcards to use
            multiple bvalues files at once.
        bvectors_files : string
            Path to the bvalues files. This path may contain wildcards to use
            multiple bvalues files at once.
        mask_files : string
            Path to the input masks. This path may contain wildcards to use
            multiple masks at once. (default: No mask used)
        b0_threshold : float, optional
            Threshold used to find b=0 directions (default 0.0)
        save_metrics : variable string, optional
            List of metrics to save.
            Possible values: fa, ga, rgb, md, ad, rd, mode, tensor, evec, eval
            (default [] (all))
        out_dir : string, optional
            Output directory (default input file directory)
        out_dt_tensor : string, optional
            Name of the tensors volume to be saved
            (default: 'dti_tensors.nii.gz')
        out_dk_tensor : string, optional
            Name of the tensors volume to be saved
            (default 'dki_tensors.nii.gz')
        out_fa : string, optional
            Name of the fractional anisotropy volume to be saved
            (default 'fa.nii.gz')
        out_ga : string, optional
            Name of the geodesic anisotropy volume to be saved
            (default 'ga.nii.gz')
        out_rgb : string, optional
            Name of the color fa volume to be saved (default 'rgb.nii.gz')
        out_md : string, optional
            Name of the mean diffusivity volume to be saved
            (default 'md.nii.gz')
        out_ad : string, optional
            Name of the axial diffusivity volume to be saved
            (default 'ad.nii.gz')
        out_rd : string, optional
            Name of the radial diffusivity volume to be saved
            (default 'rd.nii.gz')
        out_mode : string, optional
            Name of the mode volume to be saved (default 'mode.nii.gz')
        out_evec : string, optional
            Name of the eigenvectors volume to be saved
            (default 'evecs.nii.gz')
        out_eval : string, optional
            Name of the eigenvalues to be saved (default 'evals.nii.gz')
        out_mk : string, optional
            Name of the mean kurtosis to be saved (default: 'mk.nii.gz')
        out_ak : string, optional
            Name of the axial kurtosis to be saved (default: 'ak.nii.gz')
        out_rk : string, optional
            Name of the radial kurtosis to be saved (default: 'rk.nii.gz')

        References
        ----------

        .. [1] Tabesh, A., Jensen, J.H., Ardekani, B.A., Helpern, J.A., 2011.
           Estimation of tensors and tensor-derived measures in diffusional
           kurtosis imaging. Magn Reson Med. 65(3), 823-836

        .. [2] Jensen, Jens H., Joseph A. Helpern, Anita Ramani, Hanzhang Lu,
           and Kyle Kaczynski. 2005. Diffusional Kurtosis Imaging: The
           Quantification of Non-Gaussian Water Diffusion by Means of Magnetic
           Resonance Imaging. MRM 53 (6):1432-40.
        """
        io_it = self.get_io_iterator()

        for (dwi, bval, bvec, mask, otensor, ofa, oga, orgb, omd, oad, orad,
             omode, oevecs, oevals, odk_tensor, omk, oak, ork) in io_it:

            logging.info('Computing DKI metrics for {0}'.format(dwi))
            data, affine = load_nifti(dwi)

            if mask is not None:
                mask = nib.load(mask).get_data().astype(np.bool)

            dkfit, _ = self.get_fitted_tensor(data, mask, bval, bvec,
                                              b0_threshold)

            if not save_metrics:
                save_metrics = ['mk', 'rk', 'ak', 'fa', 'md', 'rd', 'ad', 'ga',
                                'rgb', 'mode', 'evec', 'eval', 'dt_tensor',
                                'dk_tensor']

            evals, evecs, kt = split_dki_param(dkfit.model_params)
            FA = fractional_anisotropy(evals)
            FA[np.isnan(FA)] = 0
            FA = np.clip(FA, 0, 1)

            if 'dt_tensor' in save_metrics:
                tensor_vals = lower_triangular(dkfit.quadratic_form)
                correct_order = [0, 1, 3, 2, 4, 5]
                tensor_vals_reordered = tensor_vals[..., correct_order]
                save_nifti(otensor, tensor_vals_reordered.astype(np.float32),
                           affine)

            if 'dk_tensor' in save_metrics:
                save_nifti(odk_tensor, dkfit.kt.astype(np.float32), affine)

            if 'fa' in save_metrics:
                save_nifti(ofa, FA.astype(np.float32), affine)

            if 'ga' in save_metrics:
                GA = geodesic_anisotropy(dkfit.evals)
                save_nifti(oga, GA.astype(np.float32), affine)

            if 'rgb' in save_metrics:
                RGB = color_fa(FA, dkfit.evecs)
                save_nifti(orgb, np.array(255 * RGB, 'uint8'), affine)

            if 'md' in save_metrics:
                MD = mean_diffusivity(dkfit.evals)
                save_nifti(omd, MD.astype(np.float32), affine)

            if 'ad' in save_metrics:
                AD = axial_diffusivity(dkfit.evals)
                save_nifti(oad, AD.astype(np.float32), affine)

            if 'rd' in save_metrics:
                RD = radial_diffusivity(dkfit.evals)
                save_nifti(orad, RD.astype(np.float32), affine)

            if 'mode' in save_metrics:
                MODE = get_mode(dkfit.quadratic_form)
                save_nifti(omode, MODE.astype(np.float32), affine)

            if 'evec' in save_metrics:
                save_nifti(oevecs, dkfit.evecs.astype(np.float32), affine)

            if 'eval' in save_metrics:
                save_nifti(oevals, dkfit.evals.astype(np.float32), affine)

            if 'mk' in save_metrics:
                save_nifti(omk, dkfit.mk().astype(np.float32), affine)

            if 'ak' in save_metrics:
                save_nifti(oak, dkfit.ak().astype(np.float32), affine)

            if 'rk' in save_metrics:
                save_nifti(ork, dkfit.rk().astype(np.float32), affine)

            logging.info('DKI metrics saved in {0}'.
                         format(os.path.dirname(oevals)))
예제 #6
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def dki_prediction(dki_params, gtab, S0=150):
    """
    In Dipy versions < 0.12, there is a bug in DKI prediction, that doesn't
    allow using volumes of S0. This is temporary fix until the bug is fixed
    upstream. See: https://github.com/nipy/dipy/pull/1028

    For now, we provide this as a fix, to monkey-patch into dipy.reconst.dki

    Parameters
    ----------
    dki_params : ndarray (x, y, z, 27) or (n, 27)
        All parameters estimated from the diffusion kurtosis model.
        Parameters are ordered as follows:
            1) Three diffusion tensor's eigenvalues
            2) Three lines of the eigenvector matrix each containing the first,
               second and third coordinates of the eigenvector
            3) Fifteen elements of the kurtosis tensor
    gtab : a GradientTable class instance
        The gradient table for this prediction
    S0 : float or ndarray (optional)
        The non diffusion-weighted signal in every voxel, or across all
        voxels. Default: 150

    Returns
    --------
    S : (..., N) ndarray
        Simulated signal based on the DKI model:

    .. math::

        S=S_{0}e^{-bD+\frac{1}{6}b^{2}D^{2}K}
    """
    evals, evecs, kt = dki.split_dki_param(dki_params)

    # Define DKI design matrix according to given gtab
    A = dki.design_matrix(gtab)

    # Flat parameters and initialize pred_sig
    fevals = evals.reshape((-1, evals.shape[-1]))
    fevecs = evecs.reshape((-1,) + evecs.shape[-2:])
    fkt = kt.reshape((-1, kt.shape[-1]))
    pred_sig = np.zeros((len(fevals), len(gtab.bvals)))
    if isinstance(S0, np.ndarray):
        S0_vol = np.reshape(S0, (len(fevals)))
    else:
        S0_vol = S0
    # looping for all voxels
    for v in range(len(pred_sig)):
        DT = np.dot(np.dot(fevecs[v], np.diag(fevals[v])), fevecs[v].T)
        dt = dki.lower_triangular(DT)
        MD = (dt[0] + dt[2] + dt[5]) / 3
        if isinstance(S0_vol, np.ndarray):
            this_S0 = S0_vol[v]
        else:
            this_S0 = S0_vol
        X = np.concatenate((dt, fkt[v] * MD * MD,
                            np.array([np.log(this_S0)])),
                           axis=0)
        pred_sig[v] = np.exp(np.dot(A, X))

    # Reshape data according to the shape of dki_params
    pred_sig = pred_sig.reshape(dki_params.shape[:-1] + (pred_sig.shape[-1],))

    return pred_sig
예제 #7
0
파일: dki_micro.py 프로젝트: MarcCote/dipy
def diffusion_components(dki_params, sphere='repulsion100', awf=None,
                         mask=None):
    """ Extracts the restricted and hindered diffusion tensors of well aligned
    fibers from diffusion kurtosis imaging parameters [1]_.

    Parameters
    ----------
    dki_params : ndarray (x, y, z, 27) or (n, 27)
        All parameters estimated from the diffusion kurtosis model.
        Parameters are ordered as follows:
            1) Three diffusion tensor's eigenvalues
            2) Three lines of the eigenvector matrix each containing the first,
               second and third coordinates of the eigenvector
            3) Fifteen elements of the kurtosis tensor
    sphere : Sphere class instance, optional
        The sphere providing sample directions to sample the restricted and
        hindered cellular diffusion tensors. For more details see Fieremans
        et al., 2011.
    awf : ndarray (optional)
        Array containing values of the axonal water fraction that has the shape
        dki_params.shape[:-1]. If not given this will be automatically computed
        using :func:`axonal_water_fraction`" with function's default precision.
    mask : ndarray (optional)
        A boolean array used to mark the coordinates in the data that should be
        analyzed that has the shape dki_params.shape[:-1]

    Returns
    --------
    edt : ndarray (x, y, z, 6) or (n, 6)
        Parameters of the hindered diffusion tensor.
    idt : ndarray (x, y, z, 6) or (n, 6)
        Parameters of the restricted diffusion tensor.

    Note
    ----
    In the original article of DKI microstructural model [1]_, the hindered and
    restricted tensors were definde as the intra-cellular and extra-cellular
    diffusion compartments respectively.

    References
    ----------
    .. [1] Fieremans E, Jensen JH, Helpern JA, 2011. White matter
           characterization with diffusional kurtosis imaging.
           Neuroimage 58(1):177-88. doi: 10.1016/j.neuroimage.2011.06.006
    """
    shape = dki_params.shape[:-1]

    # load gradient directions
    if not isinstance(sphere, dps.Sphere):
        sphere = get_sphere(sphere)

    # select voxels where to apply the single fiber model
    if mask is None:
        mask = np.ones(shape, dtype='bool')
    else:
        if mask.shape != shape:
            raise ValueError("Mask is not the same shape as dki_params.")
        else:
            mask = np.array(mask, dtype=bool, copy=False)

    # check or compute awf values
    if awf is None:
        awf = axonal_water_fraction(dki_params, sphere=sphere, mask=mask)
    else:
        if awf.shape != shape:
            raise ValueError("awf array is not the same shape as dki_params.")

    # Initialize hindered and restricted diffusion tensors
    edt_all = np.zeros(shape + (6,))
    idt_all = np.zeros(shape + (6,))

    # Generate matrix that converts apparant diffusion coefficients to tensors
    B = np.zeros((sphere.x.size, 6))
    B[:, 0] = sphere.x * sphere.x  # Bxx
    B[:, 1] = sphere.x * sphere.y * 2.  # Bxy
    B[:, 2] = sphere.y * sphere.y   # Byy
    B[:, 3] = sphere.x * sphere.z * 2.  # Bxz
    B[:, 4] = sphere.y * sphere.z * 2.  # Byz
    B[:, 5] = sphere.z * sphere.z  # Bzz
    pinvB = np.linalg.pinv(B)

    # Compute hindered and restricted diffusion tensors for all voxels
    evals, evecs, kt = split_dki_param(dki_params)
    dt = lower_triangular(vec_val_vect(evecs, evals))
    md = mean_diffusivity(evals)

    index = ndindex(mask.shape)
    for idx in index:
        if not mask[idx]:
            continue
        # sample apparent diffusion and kurtosis values
        di = directional_diffusion(dt[idx], sphere.vertices)
        ki = directional_kurtosis(dt[idx], md[idx], kt[idx], sphere.vertices,
                                  adc=di, min_kurtosis=0)
        edi = di * (1 + np.sqrt(ki * awf[idx] / (3.0 - 3.0 * awf[idx])))
        edt = np.dot(pinvB, edi)
        edt_all[idx] = edt

        # We only move on if there is an axonal water fraction.
        # Otherwise, remaining params are already zero, so move on
        if awf[idx] == 0:
            continue
        # Convert apparent diffusion and kurtosis values to apparent diffusion
        # values of the hindered and restricted diffusion
        idi = di * (1 - np.sqrt(ki * (1.0 - awf[idx]) / (3.0 * awf[idx])))
        # generate hindered and restricted diffusion tensors
        idt = np.dot(pinvB, idi)
        idt_all[idx] = idt

    return edt_all, idt_all