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Register a new userNonparametric tests of structure for high angular resolution diffusion imaging in Q-space
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High angular resolution diffusion imaging data is the observed characteristic function for the local diffusion of water molecules in tissue. This data is used to infer structural information in brain imaging. Nonparametric scalar measures are proposed to summarize such data, and to locally characterize spatial features of the diffusion probability density function (PDF), relying on the geometry of the characteristic function. Summary statistics are defined so that their distributions are, to first-order, both independent of nuisance parameters and also analytically tractable. The dominant direction of the diffusion at a spatial location (voxel) is determined, and a new set of axes are introduced in Fourier space. Variation quantified in these axes determines the local spatial properties of the diffusion density. Nonparametric hypothesis tests for determining whether the diffusion is unimodal, isotropic or multi-modal are proposed. More subtle characteristics of white-matter microstructure, such as the degree of anisotropy of the PDF and symmetry compared with a variety of asymmetric PDF alternatives, may be ascertained directly in the Fourier domain without parametric assumptions on the form of the diffusion PDF. We simulate a set of diffusion processes and characterize their local properties using the newly introduced summaries. We show how complex white-matter structures across multiple voxels exhibit clear ellipsoidal and asymmetric structure in simulation, and assess the performance of the statistics in clinically-acquired magnetic resonance imaging data.
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We present a Bayesian probabilistic model to estimate the brain white matter atlas from high angular resolution diffusion imaging (HARDI) data. This model incorporates a shape prior of the white matter anatomy and the likelihood of individual observed HARDI datasets. We first assume that the atlas is generated from a known hyperatlas through a flow of diffeomorphisms and its shape prior can be constructed based on the framework of large deformation diffeomorphic metric mapping (LDDMM). LDDMM characterizes a nonlinear diffeomorphic shape space in a linear space of initial momentum uniquely determining diffeomorphic geodesic flows from the hyperatlas. Therefore, the shape prior of the HARDI atlas can be modeled using a centered Gaussian random field (GRF) model of the initial momentum. In order to construct the likelihood of observed HARDI datasets, it is necessary to study the diffeomorphic transformation of individual observations relative to the atlas and the probabilistic distribution of orientation distribution functions (ODFs). To this end, we construct the likelihood related to the transformation using the same construction as discussed for the shape prior of the atlas. The probabilistic distribution of ODFs is then constructed based on the ODF Riemannian manifold. We assume that the observed ODFs are generated by an exponential map of random tangent vectors at the deformed atlas ODF. Hence, the likelihood of the ODFs can be modeled using a GRF of their tangent vectors in the ODF Riemannian manifold. We solve for the maximum a posteriori using the Expectation-Maximization algorithm and derive the corresponding update equations. Finally, we illustrate the HARDI atlas constructed based on a Chinese aging cohort of 94 adults and compare it with that generated by averaging the coefficients of spherical harmonics of the ODF across subjects.
In this paper, we propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by orientation distribution functions (ODFs). Our proposed algorithm seeks an optimal diffeomorphism of large deformation between two ODF fields in a spatial volume domain and at the same time, locally reorients an ODF in a manner such that it remains consistent with the surrounding anatomical structure. To this end, we first review the Riemannian manifold of ODFs. We then define the reorientation of an ODF when an affine transformation is applied and subsequently, define the diffeomorphic group action to be applied on the ODF based on this reorientation. We incorporate the Riemannian metric of ODFs for quantifying the similarity of two HARDI images into a variational problem defined under the large deformation diffeomorphic metric mapping (LDDMM) framework. We finally derive the gradient of the cost function in both Riemannian spaces of diffeomorphisms and the ODFs, and present its numerical implementation. Both synthetic and real brain HARDI data are used to illustrate the performance of our registration algorithm.
Tomography has made a radical impact on diverse fields ranging from the study of 3D atomic arrangements in matter to the study of human health in medicine. Despite its very diverse applications, the core of tomography remains the same, that is, a mathematical method must be implemented to reconstruct the 3D structure of an object from a number of 2D projections. In many scientific applications, however, the number of projections that can be measured is limited due to geometric constraints, tolerable radiation dose and/or acquisition speed. Thus it becomes an important problem to obtain the best-possible reconstruction from a limited number of projections. Here, we present the mathematical implementation of a tomographic algorithm, termed GENeralized Fourier Iterative REconstruction (GENFIRE). By iterating between real and reciprocal space, GENFIRE searches for a global solution that is concurrently consistent with the measured data and general physical constraints. The algorithm requires minimal human intervention and also incorporates angular refinement to reduce the tilt angle error. We demonstrate that GENFIRE can produce superior results relative to several other popular tomographic reconstruction techniques by numerical simulations, and by experimentally by reconstructing the 3D structure of a porous material and a frozen-hydrated marine cyanobacterium. Equipped with a graphical user interface, GENFIRE is freely available from our website and is expected to find broad applications across different disciplines.
We present 10 to 18 images of four massive clusters of galaxies through the Sunyaev-Zeldovich Effect (SZE). These measurements, made at 90~GHz with the MUSTANG receiver on the Green Bank Telescope (GBT), reveal pressure sub-structure to the intra-cluster medium (ICM) in three of the four systems. We identify the likely presence of a previously unknown weak shock-front in MACS0744+3927. By fitting the Rankine-Hugoniot density jump conditions in a complementary SZE/X-ray analysis, we infer a Mach number of M = 1.2^{+0.2}_{-0.2} and a shock-velocity of 1827^{+267}_{-195}~km/s. In RXJ1347-1145, we present a new reduction of previously reported data and confirm the presence of a south-east SZE enhancement with a significance of 13.9 sigma when smoothed to 18 resolution. This too is likely caused by shock-heated gas produced in a recent merger. In our highest redshift system, CL1226+3332, we detect sub-structure at a peak significance of 4.6 sigma in the form of a ridge oriented orthogonally to the vector connecting the main mass peak and a sub-clump revealed by weak lensing. We also conclude that the gas distribution is elongated in a south-west direction, consistent with a previously proposed merger scenario. The SZE image of the cool core cluster Abell 1835 is, in contrast, consistent with azimuthally symmetric signal only. This pilot study demonstrates the potential of high-resolution SZE images to complement X-ray data and probe the dynamics of galaxy clusters
We use a Lucky Imaging system to obtain I-band images with much improved angular resolution on a ground-based 2.5m telescope. We present results from a 10-night assessment campaign on the 2.56m Nordic Optical Telescope and quantify the performance of our system in seeings better than 1.0. In good seeing we have acquired near diffraction-limited images; in poorer seeing the angular resolution has been routinely improved by factors of 2.5-4. The system can use guide stars as faint as I=16 with full performance and its useful field of view is consistently larger than 40 diameter. The technique shows promise for a number of science programmes, both galactic (eg. binary candidates, brown dwarfs, globular cluster cores) and extragalactic (eg. quasar host galaxies, damped Lyman-alpha absorbers).
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