Sharpening improves clinically feasible q ball imaging reconstructions
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Sharpening Improves Clinically Feasible Q-Ball Imaging Reconstructions. Maxime Descoteaux & Rachid Deriche Project Team Odyssee INRIA Sophia Antipolis, France. dODF. dODF min-max. dODF min-max. fODF. Improving angular resolution of Q-Ball Imaging.

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Sharpening improves clinically feasible q ball imaging reconstructions

Sharpening Improves Clinically Feasible Q-Ball Imaging Reconstructions

Maxime Descoteaux & Rachid Deriche

Project Team Odyssee

INRIA Sophia Antipolis, France


Improving angular resolution of q ball imaging

dODF Reconstructions

dODF min-max

dODF min-max

fODF

Improving angular resolution of Q-Ball Imaging

  • Can we transform the diffusion ODF (dODF) into a sharp fiber ODF (fODF)?


In the literature

= Reconstructions

Fiber response

function

HARDI Signal

FOD

In the literature…

  • Fiber orientation density (FOD) function

  • Spherical Deconvolution

[Tournier et al 2004-2005-2006-2007, Alexander et al 2005, Anderson 2005, Dell’Acqua et al 2007]


Sketch of the method
Sketch of the method Reconstructions

=

Convolution assumption


Sketch of the method1

FRT Reconstructions

HARDI Signal

dODF

fODF

Deconvolution

sharpening

Sketch of the method

  • A deconvolution approach


Step 1 analytical odf estimation

Laplace-Beltrami regularized estimation of the HARDI signal Reconstructions

[Descoteaux et al MRM 2006 & MRM 2007 accepted]

Step 1: Analytical ODF estimation

[Anderson MRM 05, Hess et al MRM 06, Descoteaux et al RR 05, ISBI 06]


Step 2 diffusion odf kernel for deconvolution

[Tuch MRM 2004 Reconstructions

Descoteaux RR 2005]

Analytical ODF

where e1 > e2 are e-values of D and t := cos

Step 2: Diffusion ODF kernel for deconvolution

  • Estimate from real data

  • Take 300 voxels with highest FA

    • Assumed to contain a single fiber population

  • Find average prolate tensor D that fits the data

  • Diffusion ODF kernel is


Step 3 deconvolution with the funk hecke theorem
Step 3: Deconvolution with the Funk-Hecke theorem Reconstructions

  • Final sharp fiber ODF

  • Linear transformation of the spherical harmonic coefficients describing the signal

[Descoteaux et al Research Report 2005, MRM 2007 accepted.]


Summary of the method

HARDI Signal Reconstructions

dODF

fODF

Deconvolution

Sharpening

Summary of the method

Analytical

FRT

cj

fj

2 Plj(0)


Separation angle
Separation angle Reconstructions

Sharp fiber ODF

Min-max normalized ODF

(Two-tensor model, FA1 = FA2 = 0.7, SNR 30, b-value 3000 s/mm2, 60 DWI)


Simulation results

~20 Reconstructions

improvement

Mean angular error 4.5 +- 1.23

Simulation results

  • Sharpening improves angular resolution and improves fiber detection with small angular error on the detected maxima


Real data acquisition
Real data acquisition Reconstructions

  • N = 60 directions

  • 72 slices, 128 x 128

  • 1.7 mm3 voxels

  • b-value 1000 s/mm2

  • Sharp fiber ODF estimation of order 4 in less than 20 seconds

[Thanks to Max Planck Institute, Leipzig, Germany]


Crossing voxel between motor stripe and slf
Crossing voxel between motor stripe and SLF Reconstructions

Unequal volume fraction of the 2 fiber compartments

Voxel manually chosen by expert.


Real data crossing between the cc cst slf

b Reconstructions

a

a

b

dODFs

fODFs

diffusion tensors

Real data - Crossing between the cc, cst, slf


Take home message
Take home message Reconstructions

  • It is possible to transform the diffusion ODF into a sharp fiber ODF for clinical QBI acquisitions

  • Method is:

    • Linear, fast, analytic, robust to noise

  • All this possible because of the properties of the spherical harmonics and the Funk-Heck theorem


Current work and perspectives
Current work and perspectives… Reconstructions

  • Compare with spherical deconvolution

    • Study the link between the two approaches

    • Study the negative lobe problem that appears with spherical deconvolution [see Tournier et al 2007, Sakaie et al 2007 and Dell’Acqua et al 2007]

  • Use the fiber ODF for tracking

    • Deterministic

    • Probabilistic


Thank you

Thank You! Reconstructions

Key References:

  • Descoteaux et al, Regularized, Fast and Robust Analytical Q-Ball Imaging, MRM 2007

  • Descoteaux et al, ISBI 2006 & INRIA Research Report 2005

  • D. Tuch, Q-Ball Imaging, MRM 2004

  • Tournier et al, … Spherical Deconvolution…, NeuroImage 2004 & 2007

  • http://www-sop.inria.fr/odyssee

Thanks to:

-A. Anwander & T. Knosche of the Max Planck Institute, Leipzig, Germany

-C. Poupon et al, Neurospin, Saclay, Paris


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