Entropy-based coregistration for DT-MR images using an efficient tensor shape preserving reorientation strategy

A. Leemans, J. Sijbers, M. Verhoye, A. Van der Linden Physics, University of Antwerp, Antwerp, Belgium, Biomedical Sciences, University of Antwerp, Antwerp, Belgium Introduction and Purpose Diffusion tensor magnetic resonance imaging (DT-MRI) is becoming an important diagnostic tool for various neuropathological diseases [1, 2]. It is often desirable to combine multiple DT-MRI data sets of the same patient (follow up), or even to merge intersubject information (control versus pathology). Only then, diffusion tensor abnormalities can be quantified based on a statistical analysis of these multiple data sets. Therefore, spatial normalization or image coregistration is indispensable to align the data sets in a common reference frame. In this work, we developed a three-dimensional (3D) affine (rotation, translation, scale, and skew) DT-MRI coregistration technique based on the work of Maes et al. [3] using mutual information as a similarity measure. To preserve the orientational information of the diffusion tensor D after affine transformation, D must be reoriented in order to remain consistent with the alignment of the underlying anatomical structures. Current reorientation strategies (RS) for such an affine transformation, e.g. preservation of principal direction (PPD), require calculating several rotation matrices to reorient D [4]. Here, a direct diffusion tensor reconstruction approach is developed without the need to calculate these rotation matrices, resulting in a lower computational cost. Theory Consider the diffusion weighted (DW) images Sk and Rk (here, k = 1,...,7) of two different acquisitions that need to be coregistered. Maximizing the mutual information (MI) of corresponding DW images according to these k channels allows to determine the optimal transformations Φk , i.e. Φk = arg maxφ MI [φ(Sk), Rk], where φ represents the affine transformation. From these transformations Φk , the final registration transformation Φ is estimated. The diffusion tensor shape preserving RS is based on the eigenvalue decomposition, i.e. D = E⋅Λ⋅E, where the matrix E defines the orthonormal eigenvectors ei and the diagonal matrix Λ represents the eigenvalues λi. Extracting the linear transformation matrix ΦL of Φ , the new eigenvectors ni are calculated as follows: n1 is defined by normalizing ΦL⋅e1, n2 is constructed by normalizing [ΦL⋅e2 (n1⋅ΦL⋅e2)n1] and n3 is determined by n3 = n1 × n2. The reoriented diffusion tensor DΦ can now be reconstructed as DΦ = N⋅Λ⋅N, where the matrix N defines the transformed eigenvectors ni. Methods First, the coregistration accuracy and the proposed RS are evaluated by means of a simulated DT-MRI phantom [5]. Next, the proposed coregistration technique is tested on experimental data. In-vivo DT-MRI on a starling brain (N=2) was performed on a 7T MR system. Sagittal slices (thickness 0.4mm) were obtained covering one hemisphere of the starling brain. DW-SE images were obtained with diffusion gradients applied in 7 non-collinear directions. The b-matrices were calculated using analytical expressions incorporating both diffusion gradients (70mT/m, δ=12ms, ∆=20ms) and image gradients [6]. Additional image parameters are FOV=25mm, TE=43ms, TR=2200ms, acquisition matrix=(256x128), 14 averages. Results Simulated DT-MRI phantom: Fig. 1 shows the 3D synthetic reference data set DR and the source data set DS, with DR=φ(DS) and φ : {θx = θy = 0, θz = 45°; tx = ty = tz = 0; sx = 0.7, sy = sz = 0; gx = 0.5, gy = gz = 0} where θi, ti, si, and gi (i=x,y,z) represent the rotation angles, translations, scaling factors, and skew factors respectively (the color encoding provides directional information of the first eigenvector and the slices represent fractional anisotropy (FA) maps). Here, it is important to note that the transformation of the fiber pathways is performed prior to the simulation of the corresponding diffusion tensor data, for then, ground-truth orientational diffusion tensor information will be preserved. Fig. 2 demonstrates the coregistration solution for the slice indicated in Fig. 1, both with (DΦ) and without (DΨ) the RS. Notice that the similarity is significantly higher between DΦ and DR than between DΨ and DR. Experimental DT-MRI data: In Fig. 3, the coregistration technique is applied to the experimental DT-MRI data. As shown, a higher correspondence (quantified by the average Mean Squared Difference (MSD) of corresponding tensor components) between the registered images is obtained when the RS is taken into account. Conclusions A new 3D affine DT-MRI coregistration technique has been developed using a direct diffusion tensor reconstruction approach to preserve the underlying orientational information. 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