Persistent Homology in Sparse Regression and its Application to Brain Morphometry

Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in speeding up the computation using the proposed soft-thresholding technique. The topological structures are further used as multivariate features in the tensor-based morphometry (TBM) in characterizing white matter alterations in children who have experienced severe early life stress and maltreatment. These analyses reveal that stress-exposed children exhibit more diffuse anatomical organization across the whole white matter region.Comment: submitted to IEEE Transactions on Medical Imagin

Estimation of Fiber Orientations Using Neighborhood Information

Data from diffusion magnetic resonance imaging (dMRI) can be used to reconstruct fiber tracts, for example, in muscle and white matter. Estimation of fiber orientations (FOs) is a crucial step in the reconstruction process and these estimates can be corrupted by noise. In this paper, a new method called Fiber Orientation Reconstruction using Neighborhood Information (FORNI) is described and shown to reduce the effects of noise and improve FO estimation performance by incorporating spatial consistency. FORNI uses a fixed tensor basis to model the diffusion weighted signals, which has the advantage of providing an explicit relationship between the basis vectors and the FOs. FO spatial coherence is encouraged using weighted l1-norm regularization terms, which contain the interaction of directional information between neighbor voxels. Data fidelity is encouraged using a squared error between the observed and reconstructed diffusion weighted signals. After appropriate weighting of these competing objectives, the resulting objective function is minimized using a block coordinate descent algorithm, and a straightforward parallelization strategy is used to speed up processing. Experiments were performed on a digital crossing phantom, ex vivo tongue dMRI data, and in vivo brain dMRI data for both qualitative and quantitative evaluation. The results demonstrate that FORNI improves the quality of FO estimation over other state of the art algorithms.Comment: Journal paper accepted in Medical Image Analysis. 35 pages and 16 figure

Diffeomorphic Metric Mapping and Probabilistic Atlas Generation of Hybrid Diffusion Imaging based on BFOR Signal Basis

We 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), denoted as LDDMM-HYDI. We then propose a Bayesian 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 thus 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

Voxel-wise comparisons of cellular microstructure and diffusion-MRI in mouse hippocampus using 3D Bridging of Optically-clear histology with Neuroimaging Data (3D-BOND)

A key challenge in medical imaging is determining a precise correspondence between image properties and tissue microstructure. This comparison is hindered by disparate scales and resolutions between medical imaging and histology. We present a new technique, 3D Bridging of Optically-clear histology with Neuroimaging Data (3D-BOND), for registering medical images with 3D histology to overcome these limitations. Ex vivo 120 × 120 × 200 μm resolution diffusion-MRI (dMRI) data was acquired at 7 T from adult C57Bl/6 mouse hippocampus. Tissue was then optically cleared using CLARITY and stained with cellular markers and confocal microscopy used to produce high-resolution images of the 3D-tissue microstructure. For each sample, a dense array of hippocampal landmarks was used to drive registration between upsampled dMRI data and the corresponding confocal images. The cell population in each MRI voxel was determined within hippocampal subregions and compared to MRI-derived metrics. 3D-BOND provided robust voxel-wise, cellular correlates of dMRI data. CA1 pyramidal and dentate gyrus granular layers had significantly different mean diffusivity (p > 0.001), which was related to microstructural features. Overall, mean and radial diffusivity correlated with cell and axon density and fractional anisotropy with astrocyte density, while apparent fibre density correlated negatively with axon density. Astrocytes, axons and blood vessels correlated to tensor orientation