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Sharpening Improves Clinically Feasible Q-Ball Imaging Reconstructions

This study focuses on improving angular resolution in Q-Ball Imaging (QBI) by transforming diffusion Orientation Distribution Functions (dODF) into sharp fiber Orientation Distribution Functions (fODF). We utilize a robust deconvolution methodology based on the Funk-Hecke theorem to enhance fiber detection and reduce angular errors. Through both simulated and real data acquisition, we demonstrate significant improvements in fiber ODF estimation within clinical settings, highlighting the method's efficiency and noise resilience for better neuroimaging outcomes.

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Sharpening Improves Clinically Feasible Q-Ball Imaging Reconstructions

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  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

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