1. Sharpening Improves Clinically Feasible Q-Ball Imaging Reconstructions
Maxime Descoteaux & Rachid Deriche
Project Team Odyssee
INRIA Sophia Antipolis, France
Presente-toi
Parle des groupes

2. Improving angular resolution of Q-Ball Imaging
Can we transform the diffusion ODF (dODF) into a sharp fiber ODF (fODF)?
dODF
dODF min-max
fODF
dODF min-max

3. In the literature… Fiber orientation density (FOD) function
Spherical Deconvolution =
HARDI Signal
Fiber response
function
FOD
[Tournier et al , Alexander et al 2005, Anderson 2005, Dell’Acqua et al 2007]

4. Sketch of the method =
Convolution assumption

5. Sketch of the method A deconvolution approach FRT HARDI Signal dODF
sharpening
fODF

6. Step 1: Analytical ODF estimation
[Descoteaux et al MRM 2006 & MRM 2007 accepted]
Laplace-Beltrami regularized estimation of the HARDI signal
[Anderson MRM 05, Hess et al MRM 06, Descoteaux et al RR 05, ISBI 06]

7. 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
Analytical ODF
[Tuch MRM 2004
Descoteaux RR 2005]
where e1 > e2 are e-values of D and t := cos

8. Step 3: Deconvolution with the Funk-Hecke theorem
Final sharp fiber ODF
Linear transformation of the spherical harmonic coefficients describing the signal
[Descoteaux et al Research Report 2005, MRM 2007 accepted.]

9. Summary of the method cj 2 Plj(0) fj Analytical FRT HARDI Signal dODF
Deconvolution
Sharpening
fODF
Analytical
FRT cj
2 Plj(0) fj

10. Separation angle Sharp fiber ODF Min-max normalized ODF
(Two-tensor model, FA1 = FA2 = 0.7, SNR 30, b-value 3000 s/mm2, 60 DWI)

11. Simulation results
Sharpening improves angular resolution and improves fiber detection with small angular error on the detected maxima
Mean angular error 4.5 
~20
improvement

12. Real data acquisition 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
3 Tesla Magnetom Trio scanner (Siemens, Erlangen) equipped with an 8-channel head array coil [47]. The spin-echo EPI sequence, TE = 100 ms, TR = 12 s, 128 x 128 image matrix, FOV = 220 x 220 mm2 , consists of 60 diffusion encoding gradients [56] with a b-value of 1000 s/mm2 and 7 images without any diffusion weightings, which are evenly distributed. The measurement of 72 slices with 1.7mm thickness (no gap), which covered the whole brain, was repeated three times, resulting in an acquisition time of about 45 minutes. Hence, the S0 image is the average of 21 b = 0 images. The SNR in the white matter of the averaged b = 0 image S0 was estimated to approximately 37. Additionally, fat saturation was employed, 6/8 partial Fourier imaging, Hanning window filtering, and parallel GRAPPA imaging with a reduction factor of 2.
[Thanks to Max Planck Institute, Leipzig, Germany]

13. Crossing voxel between motor stripe and SLF
Unequal volume fraction of the 2 fiber compartments
Voxel manually chosen by expert.

14. Real data - Crossing between the cc, cst, slf
fODFs
dODFs
diffusion tensors

15. Take home message
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

16. Current work and perspectives…
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

17. Thank You! Key References: Thanks to:
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
Thanks to:
-A. Anwander & T. Knosche of the Max Planck Institute, Leipzig, Germany
-C. Poupon et al, Neurospin, Saclay, Paris

18. Why is this important? Better fiber detection with QBI
Possible to recover crossings on datasets acquired in clinical setup
Better tracking
Even when b-value is small and we know QBI approximation

19. Step 1: Analytical ODF estimation
[Tuch MRM 04]
HARDI Signal
FRT
->
dODF
Funk-Radon
Transform (FRT)

20. SNR effect Sharp fiber ODF Min-max normalized ODF
(Two-tensor model, FA1 = FA2 = 0.7, seperation angle 60, b-value 3000 s/mm2, 60 DWI)

21. Volume fraction effect
Sharp fiber ODF
Min-max normalized ODF
(Two-tensor model, FA1 = FA2 = 0.7, seperation angle 60, SNR 30, b-value 3000 s/mm2, 60 DWI)