Continuous and analytical diffusion signal modelling with 3D-SHORE

We show how to model the diffusion signal as a linear combination of continuous functions from the SHORE basis [Merlet2013]. We also compute the analytical Orientation Distribution Function (ODF).

First import the necessary modules:

from dipy.reconst.shore import ShoreModel
from dipy.viz import window, actor
from dipy.data import fetch_isbi2013_2shell, read_isbi2013_2shell, get_sphere

Download and read the data for this tutorial.

fetch_isbi2013_2shell() provides data from the ISBI HARDI contest 2013 acquired for two shells at b-values 1500 \(s/mm^2\) and 2500 \(s/mm^2\).

The six parameters of these two functions define the ROI where to reconstruct the data. They respectively correspond to (xmin,xmax,ymin,ymax,zmin,zmax) with x, y, z and the three axis defining the spatial positions of the voxels.

fetch_isbi2013_2shell()
img, gtab = read_isbi2013_2shell()
data = img.get_data()
data_small = data[10:40, 22, 10:40]

print('data.shape (%d, %d, %d, %d)' % data.shape)

data contains the voxel data and gtab contains a GradientTable object (gradient information e.g. b-values). For example, to show the b-values it is possible to write:

``print(gtab.bvals)``

Instantiate the SHORE Model.

radial_order is the radial order of the SHORE basis.

zeta is the scale factor of the SHORE basis.

lambdaN and lambdaL are the radial and angular regularization constants, respectively.

For details regarding these four parameters see [Cheng2011] and [Merlet2013].

radial_order = 6
zeta = 700
lambdaN = 1e-8
lambdaL = 1e-8
asm = ShoreModel(gtab, radial_order=radial_order,
                 zeta=zeta, lambdaN=lambdaN, lambdaL=lambdaL)

Fit the SHORE model to the data

asmfit = asm.fit(data_small)

Load an odf reconstruction sphere

sphere = get_sphere('symmetric724')

Compute the ODFs

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

Display the ODFs

# Enables/disables interactive visualization
interactive = False

ren = window.Renderer()
sfu = actor.odf_slicer(odf[:, None, :], sphere=sphere, colormap='plasma', scale=0.5)
sfu.RotateX(-90)
sfu.display(y=0)
ren.add(sfu)
window.record(ren, out_path='odfs.png', size=(600, 600))
if interactive:
    window.show(ren)
../_images/odfs.png

Orientation distribution functions.

References

[Merlet2013](1, 2) Merlet S. et al., “Continuous diffusion signal, EAP and ODF estimation via Compressive Sensing in diffusion MRI”, Medical Image Analysis, 2013.
[Cheng2011]Cheng J. et al., “Theoretical Analysis and Pratical Insights on EAP Estimation via Unified HARDI Framework”, MICCAI workshop on Computational Diffusion MRI, 2011.

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.