Diffeomorphic Image Registration of Diffusion MRI Using Spherical Harmonics

Intramural Res. Program, Nat. Institutes of Health, Baltimore, MD, USA
IEEE Transactions on Medical Imaging (Impact Factor: 3.39). 04/2011; 30(3):747 - 758. DOI: 10.1109/TMI.2010.2095027
Source: IEEE Xplore


Nonrigid registration of diffusion magnetic resonance imaging (MRI) is crucial for group analyses and building white matter and fiber tract atlases. Most current diffusion MRI registration techniques are limited to the alignment of diffusion tensor imaging (DTI) data. We propose a novel diffeomorphic registration method for high angular resolution diffusion images by mapping their orientation distribution functions (ODFs). ODFs can be reconstructed using q-ball imaging (QBI) techniques and represented by spherical harmonics (SHs) to resolve intra-voxel fiber crossings. The registration is based on optimizing a diffeomorphic demons cost function. Unlike scalar images, deforming ODF maps requires ODF reorientation to maintain its consistency with the local fiber orientations. Our method simultaneously reorients the ODFs by computing a Wigner rotation matrix at each voxel, and applies it to the SH coefficients during registration. Rotation of the coefficients avoids the estimation of principal directions, which has no analytical solution and is time consuming. The proposed method was validated on both simulated and real data sets with various metrics, which include the distance between the estimated and simulated transformation fields, the standard deviation of the general fractional anisotropy and the directional consistency of the deformed and reference images. The registration performance using SHs with different maximum orders were compared using these metrics. Results show that the diffeomorphic registration improved the affine alignment, and registration using SHs with higher order SHs further improved the registration accuracy by reducing the shape difference and improving the directional consistency of the registered and reference ODF maps.

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    • "If not degenerated, the affine transformations are also diffeomorphic. Examples of registration algorithms that include diffeomorphic transformations can be found in (Ashburner, 2007; Auzias et al., 2011; Beg et al., 2005; Geng et al., 2011; Joshi and Miller, 2000; Marsland and Twining, 2004; Rao et al., 2004; Vercauteren et al., 2007; 2009; Yeo et al., 2010a; Yeo et al., 2009). "
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    • "In order to overcome known limitations of the diffusion tensor model (Skare et al., 2000; Descoteaux et al., 2006; Zhang et al., 2006; Barmpoutis et al., 2007; Hess and Mukherjee, 2007; Koay et al., 2009), higher order models have been proposed (Barmpoutis et al., 2007; Cheng et al., 2009; Dhollander et al., 2010; Verma and Bloy, 2010; Yap et al., 2010; Du et al., 2011; Geng et al., 2011; Raffelt et al., 2011). Nevertheless, relying on such diffusion models might not completely capture the information contained in the raw data and could therefore affect the registration accuracy. "
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