demons registration of high angular resolution diffusion images - CBICA

DEMONS REGISTRATION OF HIGH ANGULAR RESOLUTION DIFFUSION IMAGES Luke Bloy1 , Ragini Verma2 Department of Bioengineering1 , Department of Radiology2 , University of Pennsylvania, USA ABSTRACT In this work we present a method for non-rigid registration of high angular resolution diffusion imaging (HARDI) datasets that are modeled by a field of antipodally symmetric spherical functions, represented by their expansion in the real spherical harmonic (RSH) basis. We use a multichannel demons algorithm which utilizes a computationally simple, rotationally invariant similarity function defined in the RSH space. Additionally, we describe a finite strain based algorithm for reorientation of the HARDI data model. We validate our framework on simulated fiber orientation distribution datasets and on human in-vivo data. Index Terms— DIFFUSION IMAGING, REGISTRATION, HARDI 1. INTRODUCTION Diffusion imaging, specifically tensor imaging (DTI), has in the past decade developed into the method of choice for investigating and characterizing white matter neural architecture non invasively. DTI is however limited in its ability to model voxels of complex white matter, i.e. multiple fibers with different orientations, which has prompted the development of high angular resolution diffusion imaging (HARDI) to address these concerns. A necessary step in performing group-based analysis and statistics, is to establish a common spatial coordinate frame rendering data from different subjects comparable, making the development of registration algorithms which utilize the additional information yielded by HARDI, a paramount research interest. Many DTI registration algorithms have been proposed [1, 2, 3, 4, 5], however few are applicable to HARDI data models. The spatial normalization of HARDI datasets is rendered challenging by the fact that the data model possess an orientational component, necessitating the reorientation of the HARDI model when applying a spatial transformation. In order to avoid the computational complexity of differentiating a similarity term incorporating model reorientation, we propose the use of the rotationally invariant objective function and a reorientation scheme based on Finite-Strain (FS) [6]. This work was supported by the National Institute of Health via grants R01-MH-079938 and T32-EB-000814

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While HARDI registration is relatively new there has been some prior work in the field. Barmpoutis et al [7], use a 4th order diffusion tensor model along with the rotationally invariant Hellinger distance and a specialized reorientation scheme. Cheng et al [8], describes a non-rigid registration of images of Gaussian mixture models and in more closely related work, Hong et al [9], performs registration on the b=0 images and utilizes a unique reorientation scheme for fiber orientation distribution (FOD) images. Geng et al [10], performs a linear-elastic registration on images of orientation distribution functions. In this work we present a diffeomorphic demons based registration framework which utilizes a rotationally invariant distance function between spherical functions represented by their expansion in the real spherical harmonic (RSH) basis. The utilization of the RSH expansion makes this a natural fit for a number of the popular HARDI data models, specifically the orientation distribution function (ODF), the fODF [11] and the FOD, ([12, 13]), since these models make explicit use of the RSH in the fitting process. We proceed by discussing the relevant properties of the real spherical harmonic basis followed by a description of the demons registration framework which we utilize for HARDI registration. Finally, we present results on both simulated and in-vivo human data, utilizing the FOD as the HARDI model. 2. PROPERTIES OF REAL SPHERICAL HARMONIC BASIS The foundation of our registration framework is the utilization of the real spherical harmonics as a basis set for our HARDI models. The real spherical harmonics (RSH) form an orthonormal basis for real-valued functions defined on the unit sphere. Because RSH basis functions of odd order, l, are not symmetric, they can be removed from the RSH expansion of most HARDI models, which are antipodally symmetric, yielding the following basis set: ⎧√ i m m m −m ⎪ ⎨ 2 Imag Yl = √2 (−Yl + (−1) Yl ) m > 0 Sl,m = Ylm m=0 ⎪ ⎩√ 2 Real Ylm = √12 (Ylm + (−1)m Yl−m ) m