Sharpening Improves Clinically Feasible Q-Ball Imaging Reconstructions

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

2. dODF 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)?

3. = 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]

4. Sketch of the method = Convolution assumption

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

6. Laplace-Beltrami regularized estimation of the HARDI signal [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]

7. [Tuch MRM 2004 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

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

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. ~20 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

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 [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. b a a b dODFs fODFs diffusion tensors Real data - Crossing between the cc, cst, slf

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: • 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