NTU-90: A high angular resolution brain atlas constructed by q-space diffeomorphic reconstruction
Highlights
► A diffusion MRI brain atlas is constructed from 90 DSI datasets. ► Q-space diffeomorphic reconstruction is used to conduct the normalization. ► Our method can preserve crossing fiber orientations after spatial normalization. ► The NTU-90 atlas can provide quantitative anisotropy mapping. ► The NTU-90 atlas can resolve individual fiber bundles in crossing regions.
Introduction
Diffusion MRI is a noninvasive imaging method to reveal the underlying white matter structure of the human brain (Merboldt et al., 1992, Moseley et al., 1993). By using the diffusion tensor model, diffusion MRI can be used to reconstruct diffusion tensor imaging (DTI) (Basser et al., 1994), which has been used to study the fiber orientations and the quantitative measurement of the diffusion characteristics (Basser and Pierpaoli, 1996, Pierpaoli and Basser, 1996, Pierpaoli et al., 1996). The axonal connections in the human brain can also be assessed by applying streamline fiber tracking on DTI data (Basser et al., 2000, Conturo et al., 1999, Mori et al., 1999). The application of diffusion MRI has been extended to group studies, which aim to construct an atlas by linearly or nonlinearly transforming individual brains to a template space. This approach offers ensemble information about the human brain and may play an important role in the study of brain connectome (Williams, 2010).
To provide reliable ensemble information, an atlas needs to resolve accurate principal fiber directions and to offer consistent results of the quantitative analysis. To satisfy these purposes, studies have been conducted using affine transform (Jones et al., 2002, Mori et al., 2008, Muller et al., 2007) or nonlinear transformation (Ardekani and Sinha, 2006, Goodlett et al., 2006, Park et al., 2003, Peng et al., 2009, Van Hecke et al., 2008, Xu et al., 2003, Zhang et al., 2006, Zhang et al., 2011). Although these templates have provided various solutions to construct an atlas, they are all based on DTI, which is known to have the following limitations: difficulty in resolving crossing fibers (Alexander et al., 2002, Tuch et al., 2002) and the partial volume effect, which leads to inaccurate estimation of the anisotropy index in the fiber crossing regions (Alexander et al., 2001, Barrick and Clark, 2004, Oouchi et al., 2007).
The crossing fiber limitation could be solved by using an orientation distribution function (ODF) to characterize the diffusion distribution or fiber populations. The diffusion images can be acquired by using a single-shell diffusion sampling scheme, which is also known as high angular resolution diffusion image (HARDI) (Tuch et al., 2002) acquisition, or by using a grid sampling scheme, which is known as diffusion spectrum imaging (DSI) (Wedeen et al., 2005) acquisition. Model-free reconstruction methods include q-ball imaging (QBI) (Tuch, 2004) and DSI, which model diffusion distribution by a probability based approach and calculate diffusion ODFs. Deconvolution methods include spherical deconvolution (Tournier et al., 2004), which calculates the volume fraction of fiber populations and obtains the fiber orientation distribution (FOD). To further apply spatial transformation to these ODF-based methods, a recent study was proposed to obtain the transformed FOD from the high angular resolution diffusion image (HARDI) (Hong et al., 2009). However, this method is limited to linear transformation, and the transformed FOD has not yet been shown to provide an anisotropic index for quantitative analysis.
In addition to the crossing fiber limitation, the partial volume problem is still under active research. Although fiber crossing can be resolved by using HARDI acquisition, one recent study showed that the generalized fractional anisotropy (GFA) offered by QBI is also vulnerable to the partial volume effect of crossing fibers (Fritzsche et al., 2010), indicating that studies using ODF to characterize diffusion distribution may also suffer from the partial volume effect. This result can be understood by the fact that the ODF of the diffusion distribution (e.g. diffusion ODF) or fiber volume fraction (e.g. FOD) are fractional values, not the actual amount of the diffusion spins. The partial occupation of crossing fibers or background diffusion will inevitably change the fractional values, leading to a consequence known as the partial volume effect. This problem is even more challenging when nonlinear transformation is applied to the ODF. The transformation may contain scaling and shearing that alters the fractional measurement of the diffusion spins and causes difficulties in transforming an ODF to the template space. To solve this problem, a possible solution is to use the spin distribution function (SDF), which presents the amount of the spins undergoing diffusion in different orientations. The SDF can be estimated by using generalized q-sampling imaging (GQI) (Yeh et al., 2010), with the expense of an additional spin density scan for calibration.
In this study, we aimed to construct a high angular resolution brain atlas in the ICBM-152 space using the SDF measurement. To obtain the SDFs in the ICBM-152 space (termed transformed SDF in the following texts, as opposed to the original SDF, which is the SDF obtained from GQI without transformation), we propose a novel method called q-space diffeomorphic reconstruction, which can calculate transformed SDFs in any given deformation field that satisfies diffeomorphism. This method can employ linear or non-linear registration, including registration based on diffusion images (Chiang et al., 2008, Hong et al., 2009, Yap et al., 2010, Yap et al., 2011) or registration based on structure images. The q-space diffeomorphic reconstruction aims to preserve fiber orientations so that these orientations can be used to conduct fiber tracking. Moreover, this method aims to satisfy the conservation of diffusion spins, and the transformed SDFs can be used to conduct quantitative analysis.
To demonstrate the performance of this method, we simulated a 90°-crossing phantom and applied nonlinear transformation that models scaling and rotation. The transformed SDFs were examined and compared with the original SDFs to examine their abilities to resolve crossing fibers and to provide quantitative analysis. Streamline fiber tracking was conducted to examine the fiber tracts generated from the resolved fiber orientations.
To construct a high angular resolution brain atlas, we collected a total of 90 DSI datasets, and SPM5 (Wellcome Trust Centre for Neuroimaging, London, UK) was used to obtain the nonlinear transformation that maps each subject space to the ICBM-152 space. The transformed SDFs in the ICBM-152 space were reconstructed using the q-space diffeomorphic reconstruction, and our NTU-90 atlas was constructed by averaging the transformed SDFs of these 90 DSI datasets. The averaged SDFs were examined to confirm the ability to resolve crossing fiber, and streamline fiber tracking was applied to present potential applications of the atlas in brain studies.
Section snippets
Diffeomorphic mapping
Diffeomorphic mapping can be formulated as the following equation: φ(rs) = rt, where φ is the mapping function (φ : R3 → R3), rs is the coordinates in the subject space, and rt is the coordinates in the template space (e.g. the ICBM-152 space). Diffeomorphic mapping satisfies two prerequisites: φ has an invert function φ− 1, and both φ and φ− 1 are differentiable. In other words, for any point rs, there exists a corresponding point φ(rs) in the template space, and the Jacobian matrix Jφ(rs) can be
Simulation
The analysis of the angular error showed that the average angular error of the horizontal fibers was 2.25° on the transformed SDFs, whereas that of the vertical fibers was 2.27°. These two errors are significantly smaller than the angular resolution of an ODF, which is 8.09° (p < 0.001). This result suggests that in our 90°-crossing simulation, the resolved fibers on the transformed SDFs achieved the angular resolution of our ODF sampling. This meets our aim that the transformed SDFs obtained
Discussion
We present a high angular resolution brain atlas, NTU-90, which is constructed by applying our q-space diffeomorphic reconstruction to 90 DSI datasets and averaging the transformed SDFs. The performance of our q-space diffeomorphic reconstruction method was examined by a simulation study. The simulation showed that the transformed SDF can preserve the principle fiber orientations, and the resolved fiber orientations can be used in fiber tracking to generate fiber tracts and to reveal the
Acknowledgments
The work is supported in part by the National Science Council, Taiwan (NSC99-2321-B-002-037 and NSC99-3112-B-002-030).
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