Diffeomorphic metric mapping and probabilistic atlas generation of hybrid diffusion imaging based on BFOR signal basis

Abstract

We first propose a large deformation diffeomorphic metric mapping algorithm to align multiple b-value diffusion weighted imaging (mDWI) data, specifically acquired via hybrid diffusion imaging (HYDI).We denote this algorithm as LDDMM-HYDI. We then propose a Bayesian probabilistic model for estimating the white matter atlas from HYDIs. We adopt the work given in Hosseinbor et al. (2012) and represent the q-space diffusion signal with the Bessel Fourier orientation reconstruction (BFOR) signal basis. The BFOR framework provides the representation of mDWI in the q-space and the analytic form of the emsemble average propagator (EAP) reconstructure, as well as reduces memory requirement. In addition, since the BFOR signal basis is orthonormal, the L2 norm that quantifies the differences in the q-space signals of any two mDWI datasets can be easily computed as the sum of the squared differences in the BFOR expansion coefficients. In this work, we show that the reorientation of the q-space signal due to spatial transformation can be easily defined on the BFOR signal basis. We incorporate the BFOR signal basis into the LDDMM framework and derive the gradient descent algorithm for LDDMM-HYDI with explicit orientation optimization. Additionally, we extend the previous Bayesian atlas estimation framework for scalar-valued images to HYDIs and derive the expectation-maximization algorithm for solving the HYDI atlas estimation problem. Using real HYDI datasets, we show the Bayesian model generates the white matter atlas with anatomical details. Moreover, we show that it is important to consider the variation of mDWI reorientation due to a small change in diffeomorphic transformation in the LDDMM-HYDI optimization and to incorporate the full information of HYDI for aligning mDWI. Finally, we show that the LDDMM-HYDI outperforms the LDDMM algorithm with diffusion tensors generated from each shell of HYDI.

Estimating diffeomorphic mappings between templates and noisy data: Variance bounds on the estimated canonical volume form

“…6,[30][31][32][33] The symmetric approaches for large deformations were variants of these methods. [34][35][36][37] The large deformation diffeomorphic metric mapping algorithms (LDDMM) emerged corresponding to Lagrangian and Hamilton's principles applied to the flow fields incrementally generating the diffeomorphic transformations involved [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57] and provide a metric between images and diffeomorphisms. The survey article by Sotiras, Davatzikos, and Paragios 58 places these works in the greater context of deformable registration.…”

Multimodal cross‐registration and quantification of metric distortions in marmoset whole brain histology using diffeomorphic mappings

“…Avants & Gee, 2004;B. B. Avants, Epstein, Grossman, & Gee, 2008;Beg, Miller, Trouvé, & Younes, 2005;Beg & Khan, 2007;Ceritoglu et al, 2009;Ceritoglu et al, 2010;Du, Goh, & Qiu, 2012;Du et al, 2014;Du, Younes, & Qiu, 2011;Khan, Wang, & Beg, 2013;Risser et al, 2011;Risser, Vialard, Baluwala, & Schnabel, 2013;Sommer, Nielsen, Lauze, & Pennec, 2011;Tang, Mori, & Miller, 2012;Tward et al, 2011;D. Tward, Ma, Miller, & Younes, 2013;Vercauteren, Pennec, Perchant, & Ayache, 2008;Vadakkumpadan, Arevalo, Ceritoglu, Miller, & Trayanova, 2012).…”

“…For dense images (i.e., 3D voxelized image volumes) with multiple modalities and tensor fields such as Diffusion track imaging (DTI), these methods were further developed and form the basis of the multiple contrast, multiscale algorithmic framework that is well‐described in the literature, but note that much of this work has focused on MRI volumes as opposed to the LM based teravoxel volumes of interest to the present study (B. Avants & Gee, 2004; B. B. Avants, Epstein, Grossman, & Gee, 2008; Beg, Miller, Trouvé, & Younes, 2005; Beg & Khan, 2007; Ceritoglu et al, 2009; Ceritoglu et al, 2010; Du, Goh, & Qiu, 2012; Du et al, 2014; Du, Younes, & Qiu, 2011; Khan, Wang, & Beg, 2013; Risser et al, 2011; Risser, Vialard, Baluwala, & Schnabel, 2013; Sommer, Nielsen, Lauze, & Pennec, 2011; Tang, Mori, & Miller, 2012; Tward et al, 2011; D. Tward, Ma, Miller, & Younes, 2013; Vercauteren, Pennec, Perchant, & Ayache, 2008; Vadakkumpadan, Arevalo, Ceritoglu, Miller, & Trayanova, 2012).…”

Cerebellar development and its mediation role in cognitive planning in childhood

“…In the Markov Random Field model of FreeSurfer, the prior probability of each structure was computed based on the manual segmentation of 20 subjects randomly selected from the sample of this study. The cerebellum was extracted from the T 1 ‐weighted MRI and was then mapped to the ChroMa cerebellar atlas with the cerebellar anatomical labels (https://www.nitrc.org/frs/shownotes.php?release_id=2748) (Bazin et al, ) via large deformation diffeomorphic metric mapping (LDDMM) (Du et al, ; Du, Younes, & Qiu, ; Tan & Qiu, ; Tan & Qiu, ; Zhong, Phua, & Qiu, ). This ChroMa cerebellar atlas provides detailed cerebellar anatomical labels and cerebellar surfaces for the inner, mid‐cerebellar, and outer surfaces for data visualization.…”