Theoretical Analysis and Practical Insights on EAP Estimation via a Unified HARDI Framework

International audienceSince Diffusion Tensor Imaging (DTI) cannot describe complex non-Gaussian diffusion process, many techniques, called as single shell High Angular Resolution Diffusion Imaging (sHARDI) methods, reconstruct the Ensemble Average Propagator (EAP) or its feature Orientation Distribution Function (ODF) from diffusion weighted signals only in single shell. Q-Ball Imaging (QBI) and Diffusion Orientation Transform (DOT) are two famous sHARDI methods. However, these sHARDI methods have some intrinsic modeling errors or need some unreal assumptions. Moreover they are hard to deal with signals from different q-shells. Most recently several novel multiple shell HARDI (mHARDI) methods, including Diffusion Propagator Imaging (DPI), Spherical Polar Fourier Imaging (SPFI) and Simple Harmonic Oscillator based Reconstruction and Estimation (SHORE), were proposed to analytically estimate EAP or ODF from multiple shell (or arbitrarily sampled) signals. These three methods all represent diffusion signal with some basis functions in spherical coordinate and use plane wave formula to analytically solve the Fourier transform. To our knowledge, there is no theoretical analysis and practical comparison among these sHARDI and mHARDI methods. In this paper, we propose a unified computational framework, named Analytical Fourier Transform in Spherical Coordinate (AFT-SC), to perform such theoretical analysis and practical comparison among all these five state-of-the-art diffusion MRI methods. We compare these five methods in both theoretical and experimental aspects. With respect to the theoretical aspect, some criteria are proposed for evaluation and some differences together with some similarities among the methods are highlighted. Regarding the experimental aspect, all the methods are compared in synthetic, phantom and real data. The shortcomings and advantages of each method are highlighted from which SPFI appears to be among the best because it uses an orthonormal basis that completely separates the spherical and radial information

Spherical deconvolution of multichannel diffusion MRI data with non-Gaussian noise models and spatial regularization

Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on the methodology used to combine multichannel signals. Indeed, the two prevailing methods for multichannel signal combination lead to Rician and noncentral Chi noise distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in brain data

Insight into the fundamental trade-offs of diffusion MRI from polarization-sensitive optical coherence tomography in ex vivo human brain

In the first study comparing high angular resolution diffusion MRI (dMRI) in the human brain to axonal orientation measurements from polarization-sensitive optical coherence tomography (PSOCT), we compare the accuracy of orientation estimates from various dMRI sampling schemes and reconstruction methods. We find that, if the reconstruction approach is chosen carefully, single-shell dMRI data can yield the same accuracy as multi-shell data, and only moderately lower accuracy than a full Cartesian-grid sampling scheme. Our results suggest that current dMRI reconstruction approaches do not benefit substantially from ultra-high b-values or from very large numbers of diffusion-encoding directions. We also show that accuracy remains stable across dMRI voxel sizes of 1 ​mm or smaller but degrades at 2 ​mm, particularly in areas of complex white-matter architecture. We also show that, as the spatial resolution is reduced, axonal configurations in a dMRI voxel can no longer be modeled as a small set of distinct axon populations, violating an assumption that is sometimes made by dMRI reconstruction techniques. Our findings have implications for in vivo studies and illustrate the value of PSOCT as a source of ground-truth measurements of white-matter organization that does not suffer from the distortions typical of histological techniques.Published versio

Nonparametric tests of structure for high angular resolution diffusion imaging in Q-space

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.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS441 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multi-Shell Hybrid Diffusion Imaging (HYDI) at 7 Tesla in TgF344-AD Transgenic Alzheimer Rats

Diffusion weighted imaging (DWI) is widely used to study microstructural characteristics of the brain. Diffusion tensor imaging (DTI) and high-angular resolution imaging (HARDI) are frequently used in radiology and neuroscience research but can be limited in describing the signal behavior in composite nerve fiber structures. Here, we developed and assessed the benefit of a comprehensive diffusion encoding scheme, known as hybrid diffusion imaging (HYDI), composed of 300 DWI volumes acquired at 7-Tesla with diffusion weightings at b = 1000, 3000, 4000, 8000 and 12000 s/mm^2 and applied it in transgenic Alzheimer rats (line TgF344-AD) that model the full clinico-pathological spectrum of the human disease. We studied and visualized the effects of the multiple concentric “shells” when computing three distinct anisotropy maps–fractional anisotropy (FA), generalized fractional anisotropy (GFA) and normalized quantitative anisotropy (NQA). We tested the added value of the multi-shell q-space sampling scheme, when reconstructing neural pathways using mathematical frameworks from DTI and q-ball imaging (QBI). We show a range of properties of HYDI, including lower apparent anisotropy when using high b-value shells in DTI-based reconstructions, and increases in apparent anisotropy in QBI-based reconstructions. Regardless of the reconstruction scheme, HYDI improves FA-, GFA- and NQA-aided tractography. HYDI may be valuable in human connectome projects and clinical research, as well as magnetic resonance research in experimental animals

Fast Fiber Orientation Estimation in Diffusion MRI from kq-Space Sampling and Anatomical Priors

High spatio-angular resolution diffusion MRI (dMRI) has been shown to provide accurate identification of complex fiber configurations, albeit at the cost of long acquisition times. We propose a method to recover intra-voxel fiber configurations at high spatio-angular resolution relying on a kq-space under-sampling scheme to enable accelerated acquisitions. The inverse problem for reconstruction of the fiber orientation distribution (FOD) is regularized by a structured sparsity prior promoting simultaneously voxelwise sparsity and spatial smoothness of fiber orientation. Prior knowledge of the spatial distribution of white matter, gray matter and cerebrospinal fluid is also assumed. A minimization problem is formulated and solved via a forward-backward convex optimization algorithmic structure. Simulations and real data analysis suggest that accurate FOD mapping can be achieved from severe kq-space under-sampling regimes, potentially enabling high spatio-angular dMRI in the clinical setting.Comment: 10 pages, 5 figures, Supplementary Material

Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI

We develop a general analytical and numerical framework for estimating intra- and extra-neurite water fractions and diffusion coefficients, as well as neurite orientational dispersion, in each imaging voxel. By employing a set of rotational invariants and their expansion in the powers of diffusion weighting, we analytically uncover the nontrivial topology of the parameter estimation landscape, showing that multiple branches of parameters describe the measurement almost equally well, with only one of them corresponding to the biophysical reality. A comprehensive acquisition shows that the branch choice varies across the brain. Our framework reveals hidden degeneracies in MRI parameter estimation for neuronal tissue, provides microstructural and orientational maps in the whole brain without constraints or priors, and connects modern biophysical modeling with clinical MRI.Comment: 25 pages, 12 figures, elsarticle two-colum