"""
=====================================================================
Reconstruction of the diffusion signal with the WMTI model
=====================================================================
DKI can also be used to derive concrete biophysical parameters by applying
microstructural models to DT and KT estimated from DKI. For instance,
Fieremans et al. [Fierem2011]_ showed that DKI can be used to
estimate the contribution of hindered and restricted diffusion for well-aligned
fibers - a model that was later referred to as the white matter tract integrity
WMTI technique [Fierem2013]_. The two tensors of WMTI can be also
interpreted as the influences of intra- and extra-cellular compartments and can
be used to estimate the axonal volume fraction and diffusion extra-cellular
tortuosity. According to previous studies [Fierem2012]_ [Fierem2013]_,
these latter measures can be used to distinguish processes of axonal loss from
processes of myelin degeneration.
In this example, we show how to process a dMRI dataset using
the WMTI model.
First, we import all relevant modules:
"""
import numpy as np
import matplotlib.pyplot as plt
import dipy.reconst.dki as dki
import dipy.reconst.dki_micro as dki_micro
from dipy.core.gradients import gradient_table
from dipy.data import get_fnames
from dipy.io.gradients import read_bvals_bvecs
from dipy.io.image import load_nifti
from dipy.segment.mask import median_otsu
from scipy.ndimage.filters import gaussian_filter
"""
As the standard DKI, WMTI requires multi-shell data, i.e. data acquired from
more than one non-zero b-value. Here, we use a fetcher to download a
multi-shell dataset which was kindly provided by Hansen and Jespersen
(more details about the data are provided in their paper [Hansen2016]_).
"""
fraw, fbval, fbvec, t1_fname = get_fnames('cfin_multib')
data, affine = load_nifti(fraw)
bvals, bvecs = read_bvals_bvecs(fbval, fbvec)
gtab = gradient_table(bvals, bvecs)
"""
For comparison, this dataset is pre-processed using the same steps used in the
example for reconstructing DKI (see :ref:`example_reconst_dki`).
"""
# data masking
maskdata, mask = median_otsu(data, vol_idx=[0, 1], median_radius=4, numpass=2,
autocrop=False, dilate=1)
# Smoothing
fwhm = 1.25
gauss_std = fwhm / np.sqrt(8 * np.log(2))
data_smooth = np.zeros(data.shape)
for v in range(data.shape[-1]):
data_smooth[..., v] = gaussian_filter(data[..., v], sigma=gauss_std)
"""
The WMTI model can be defined in DIPY by instantiating the
'KurtosisMicrostructureModel' object in the following way:
"""
dki_micro_model = dki_micro.KurtosisMicrostructureModel(gtab)
"""
Before fitting this microstructural model, it is useful to indicate the
regions in which this model provides meaningful information (i.e. voxels of
well-aligned fibers). Following Fieremans et al. [Fieremans2011]_, a simple way
to select this region is to generate a well-aligned fiber mask based on the
values of diffusion sphericity, planarity and linearity. Here we will follow
these selection criteria for a better comparison of our figures with the
original article published by Fieremans et al. [Fieremans2011]_. Nevertheless,
it is important to note that voxels with well-aligned fibers can be selected
based on other approaches such as using predefined regions of interest.
"""
# Diffusion Tensor is computed based on the standard DKI model
dkimodel = dki.DiffusionKurtosisModel(gtab)
dkifit = dkimodel.fit(data_smooth, mask=mask)
# Initialize well aligned mask with ones
well_aligned_mask = np.ones(data.shape[:-1], dtype='bool')
# Diffusion coefficient of linearity (cl) has to be larger than 0.4, thus
# we exclude voxels with cl < 0.4.
cl = dkifit.linearity.copy()
well_aligned_mask[cl < 0.4] = False
# Diffusion coefficient of planarity (cp) has to be lower than 0.2, thus
# we exclude voxels with cp > 0.2.
cp = dkifit.planarity.copy()
well_aligned_mask[cp > 0.2] = False
# Diffusion coefficient of sphericity (cs) has to be lower than 0.35, thus
# we exclude voxels with cs > 0.35.
cs = dkifit.sphericity.copy()
well_aligned_mask[cs > 0.35] = False
# Removing nan associated with background voxels
well_aligned_mask[np.isnan(cl)] = False
well_aligned_mask[np.isnan(cp)] = False
well_aligned_mask[np.isnan(cs)] = False
"""
Analogous to DKI, the data fit can be done by calling the ``fit`` function of
the model's object as follows:
"""
dki_micro_fit = dki_micro_model.fit(data_smooth, mask=well_aligned_mask)
"""
The KurtosisMicrostructureFit object created by this ``fit`` function can then
be used to extract model parameters such as the axonal water fraction and
diffusion hindered tortuosity:
"""
AWF = dki_micro_fit.awf
TORT = dki_micro_fit.tortuosity
"""
These parameters are plotted below on top of the mean kurtosis maps:
"""
MK = dkifit.mk(0, 3)
axial_slice = 9
fig1, ax = plt.subplots(1, 2, figsize=(9, 4),
subplot_kw={'xticks': [], 'yticks': []})
AWF[AWF == 0] = np.nan
TORT[TORT == 0] = np.nan
ax[0].imshow(MK[:, :, axial_slice].T, cmap=plt.cm.gray,
interpolation='nearest', origin='lower')
im0 = ax[0].imshow(AWF[:, :, axial_slice].T, cmap=plt.cm.Reds, alpha=0.9,
vmin=0.3, vmax=0.7, interpolation='nearest', origin='lower')
fig1.colorbar(im0, ax=ax.flat[0])
ax[1].imshow(MK[:, :, axial_slice].T, cmap=plt.cm.gray,
interpolation='nearest', origin='lower')
im1 = ax[1].imshow(TORT[:, :, axial_slice].T, cmap=plt.cm.Blues, alpha=0.9,
vmin=2, vmax=6, interpolation='nearest', origin='lower')
fig1.colorbar(im1, ax=ax.flat[1])
fig1.savefig('Kurtosis_Microstructural_measures.png')
"""
.. figure:: Kurtosis_Microstructural_measures.png
:align: center
Axonal water fraction (left panel) and tortuosity (right panel) values
of well-aligned fiber regions overlaid on a top of a mean kurtosis all-brain
image.
References
----------
.. [Fierem2011] Fieremans E, Jensen JH, Helpern JA (2011). White matter
characterization with diffusion kurtosis imaging. NeuroImage
58: 177-188
.. [Fierem2012] Fieremans E, Jensen JH, Helpern JA, Kim S, Grossman RI,
Inglese M, Novikov DS. (2012). Diffusion distinguishes between
axonal loss and demyelination in brain white matter.
Proceedings of the 20th Annual Meeting of the International
Society for Magnetic Resonance Medicine; Melbourne, Australia.
May 5-11.
.. [Fierem2013] Fieremans, E., Benitez, A., Jensen, J.H., Falangola, M.F.,
Tabesh, A., Deardorff, R.L., Spampinato, M.V., Babb, J.S.,
Novikov, D.S., Ferris, S.H., Helpern, J.A., 2013. Novel
white matter tract integrity metrics sensitive to Alzheimer
disease progression. AJNR Am. J. Neuroradiol. 34(11),
2105-2112. doi: 10.3174/ajnr.A3553
.. [Hansen2016] Hansen, B, Jespersen, SN (2016). Data for evaluation of fast
kurtosis strategies, b-value optimization and exploration of
diffusion MRI contrast. Scientific Data 3: 160072
doi:10.1038/sdata.2016.72
.. include:: ../links_names.inc
"""