Crossing invariant fiber response function with FORECAST model

Crossing invariant fiber response function with FORECAST model

We show how to obtain a voxel specific response function in the form of axially symmetric tensor and the fODF using the FORECAST model from [Anderson2005] , [Kaden2016] and [Zucchelli2017].

First import the necessary modules:

import numpy as np
import matplotlib.pyplot as plt
from dipy.reconst.forecast import ForecastModel
from dipy.viz import actor, window
from dipy.data import fetch_hbn, get_sphere
import nibabel as nib
import os.path as op
from dipy.core.gradients import gradient_table

Download and read the data for this tutorial. Our implementation of FORECAST requires multi-shell data.fetch_hbn() provides data that was acquired using b-values of 1000 and 2000 as part of the Healthy Brain Network study [Alexander2017] and was preprocessed and quality controlled in the HBN-POD2 dataset [RichieHalford2022].

data_path = fetch_hbn(["NDARAA948VFH"])[1]
dwi_path = op.join(
       data_path, "derivatives", "qsiprep", "sub-NDARAA948VFH",
       "ses-HBNsiteRU", "dwi")

img = nib.load(op.join(
       dwi_path,
       "sub-NDARAA948VFH_ses-HBNsiteRU_acq-64dir_space-T1w_desc-preproc_dwi.nii.gz"))

gtab = gradient_table(
       op.join(dwi_path,
"sub-NDARAA948VFH_ses-HBNsiteRU_acq-64dir_space-T1w_desc-preproc_dwi.bval"),
       op.join(dwi_path,
"sub-NDARAA948VFH_ses-HBNsiteRU_acq-64dir_space-T1w_desc-preproc_dwi.bvec"))

data = np.asarray(img.dataobj)

mask_img = nib.load(
       op.join(dwi_path,
"sub-NDARAA948VFH_ses-HBNsiteRU_acq-64dir_space-T1w_desc-brain_mask.nii.gz"))

brain_mask = mask_img.get_fdata()

Let us consider only a single slice for the FORECAST fitting

data_small = data[:, :, 50:51]
mask_small = brain_mask[:, :, 50:51]

Instantiate the FORECAST Model.

“sh_order” is the spherical harmonics order used for the fODF.

dec_alg is the spherical deconvolution algorithm used for the FORECAST basis fitting, in this case we used the Constrained Spherical Deconvolution (CSD) algorithm.

fm = ForecastModel(gtab, sh_order=6, dec_alg='CSD')

Fit the FORECAST to the data

f_fit = fm.fit(data_small, mask_small)

Calculate the crossing invariant tensor indices [Kaden2016] : the parallel diffusivity, the perpendicular diffusivity, the fractional anisotropy and the mean diffusivity.

d_par = f_fit.dpar
d_perp = f_fit.dperp
fa = f_fit.fractional_anisotropy()
md = f_fit.mean_diffusivity()

Show the indices and save them in FORECAST_indices.png.

fig = plt.figure(figsize=(6, 6))
ax1 = fig.add_subplot(2, 2, 1, title='parallel diffusivity')
ax1.set_axis_off()
ind = ax1.imshow(d_par[:, :, 0].T, interpolation='nearest',
                 origin='lower', cmap=plt.cm.gray)
plt.colorbar(ind, shrink=0.6)
ax2 = fig.add_subplot(2, 2, 2, title='perpendicular diffusivity')
ax2.set_axis_off()
ind = ax2.imshow(d_perp[:, :, 0].T, interpolation='nearest',
                 origin='lower', cmap=plt.cm.gray)
plt.colorbar(ind, shrink=0.6)
ax3 = fig.add_subplot(2, 2, 3, title='fractional anisotropy')
ax3.set_axis_off()
ind = ax3.imshow(fa[:, :, 0].T, interpolation='nearest',
                 origin='lower', cmap=plt.cm.gray)
plt.colorbar(ind, shrink=0.6)
ax4 = fig.add_subplot(2, 2, 4, title='mean diffusivity')
ax4.set_axis_off()
ind = ax4.imshow(md[:, :, 0].T, interpolation='nearest',
                 origin='lower', cmap=plt.cm.gray)
plt.colorbar(ind, shrink=0.6)
plt.savefig('FORECAST_indices.png', dpi=300, bbox_inches='tight')
../../_images/FORECAST_indices.png

FORECAST scalar indices.

Load an ODF reconstruction sphere

sphere = get_sphere('repulsion724')

Compute the fODFs.

odf = f_fit.odf(sphere)
print('fODF.shape (%d, %d, %d, %d)' % odf.shape)

Display a part of the fODFs

odf_actor = actor.odf_slicer(odf[30:60, 30:60, :], sphere=sphere,
                             colormap='plasma', scale=0.6)
scene = window.Scene()
scene.add(odf_actor)
window.record(scene, out_path='fODFs.png', size=(600, 600), magnification=4)
../../_images/fODFs.png

Fiber Orientation Distribution Functions, in a small ROI of the brain.

References

[Anderson2005]

Anderson A. W., “Measurement of Fiber Orientation Distributions Using High Angular Resolution Diffusion Imaging”, Magnetic Resonance in Medicine, 2005.

[Kaden2016] (1,2)

Kaden E. et al., “Quantitative Mapping of the Per-Axon Diffusion Coefficients in Brain White Matter”, Magnetic Resonance in Medicine, 2016.

[Zucchelli2017]

Zucchelli E. et al., “A generalized SMT-based framework for Diffusion MRI microstructural model estimation”, MICCAI Workshop on Computational DIFFUSION MRI (CDMRI), 2017.

[Alexander2017]

Alexander LM, Escalera J, Ai L, et al. An open resource for transdiagnostic research in pediatric mental health and learning disorders. Sci Data. 2017;4:170181.

[RichieHalford2022]

Richie-Halford A, Cieslak M, Ai L, et al. An analysis-ready and quality controlled resource for pediatric brain white-matter research. Scientific Data. 2022;9(1):1-27.

Example source code

You can download the full source code of this example. This same script is also included in the dipy source distribution under the doc/examples/ directory.