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

Increasing the Analytical Accessibility of Multishell and Diffusion Spectrum Imaging Data Using Generalized Q-Sampling Conversion

Many diffusion MRI researchers, including the Human Connectome Project (HCP), acquire data using multishell (e.g., WU-Minn consortium) and diffusion spectrum imaging (DSI) schemes (e.g., USC-Harvard consortium). However, these data sets are not readily accessible to high angular resolution diffusion imaging (HARDI) analysis methods that are popular in connectomics analysis. Here we introduce a scheme conversion approach that transforms multishell and DSI data into their corresponding HARDI representations, thereby empowering HARDI-based analytical methods to make use of data acquired using non-HARDI approaches. This method was evaluated on both phantom and in-vivo human data sets by acquiring multishell, DSI, and HARDI data simultaneously, and comparing the converted HARDI, from non-HARDI methods, with the original HARDI data. Analysis on the phantom shows that the converted HARDI from DSI and multishell data strongly predicts the original HARDI (correlation coefficient > 0.9). Our in-vivo study shows that the converted HARDI can be reconstructed by constrained spherical deconvolution, and the fiber orientation distributions are consistent with those from the original HARDI. We further illustrate that our scheme conversion method can be applied to HCP data, and the converted HARDI do not appear to sacrifice angular resolution. Thus this novel approach can benefit all HARDI-based analysis approaches, allowing greater analytical accessibility to non-HARDI data, including data from the HCP

NODDI-SH: a computational efficient NODDI extension for fODF estimation in diffusion MRI

Diffusion Magnetic Resonance Imaging (DMRI) is the only non-invasive imaging technique which is able to detect the principal directions of water diffusion as well as neurites density in the human brain. Exploiting the ability of Spherical Harmonics (SH) to model spherical functions, we propose a new reconstruction model for DMRI data which is able to estimate both the fiber Orientation Distribution Function (fODF) and the relative volume fractions of the neurites in each voxel, which is robust to multiple fiber crossings. We consider a Neurite Orientation Dispersion and Density Imaging (NODDI) inspired single fiber diffusion signal to be derived from three compartments: intracellular, extracellular, and cerebrospinal fluid. The model, called NODDI-SH, is derived by convolving the single fiber response with the fODF in each voxel. NODDI-SH embeds the calculation of the fODF and the neurite density in a unified mathematical model providing efficient, robust and accurate results. Results were validated on simulated data and tested on \textit{in-vivo} data of human brain, and compared to and Constrained Spherical Deconvolution (CSD) for benchmarking. Results revealed competitive performance in all respects and inherent adaptivity to local microstructure, while sensibly reducing the computational cost. We also investigated NODDI-SH performance when only a limited number of samples are available for the fitting, demonstrating that 60 samples are enough to obtain reliable results. The fast computational time and the low number of signal samples required, make NODDI-SH feasible for clinical application

Evaluating the accuracy of diffusion MRI models in white matter

Models of diffusion MRI within a voxel are useful for making inferences about the properties of the tissue and inferring fiber orientation distribution used by tractography algorithms. A useful model must fit the data accurately. However, evaluations of model-accuracy of some of the models that are commonly used in analyzing human white matter have not been published before. Here, we evaluate model-accuracy of the two main classes of diffusion MRI models. The diffusion tensor model (DTM) summarizes diffusion as a 3-dimensional Gaussian distribution. Sparse fascicle models (SFM) summarize the signal as a linear sum of signals originating from a collection of fascicles oriented in different directions. We use cross-validation to assess model-accuracy at different gradient amplitudes (b-values) throughout the white matter. Specifically, we fit each model to all the white matter voxels in one data set and then use the model to predict a second, independent data set. This is the first evaluation of model-accuracy of these models. In most of the white matter the DTM predicts the data more accurately than test-retest reliability; SFM model-accuracy is higher than test-retest reliability and also higher than the DTM, particularly for measurements with (a) a b-value above 1000 in locations containing fiber crossings, and (b) in the regions of the brain surrounding the optic radiations. The SFM also has better parameter-validity: it more accurately estimates the fiber orientation distribution function (fODF) in each voxel, which is useful for fiber tracking

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

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

Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution

We propose two strategies to improve the quality of tractography results computed from diffusion weighted magnetic resonance imaging (DW-MRI) data. Both methods are based on the same PDE framework, defined in the coupled space of positions and orientations, associated with a stochastic process describing the enhancement of elongated structures while preserving crossing structures. In the first method we use the enhancement PDE for contextual regularization of a fiber orientation distribution (FOD) that is obtained on individual voxels from high angular resolution diffusion imaging (HARDI) data via constrained spherical deconvolution (CSD). Thereby we improve the FOD as input for subsequent tractography. Secondly, we introduce the fiber to bundle coherence (FBC), a measure for quantification of fiber alignment. The FBC is computed from a tractography result using the same PDE framework and provides a criterion for removing the spurious fibers. We validate the proposed combination of CSD and enhancement on phantom data and on human data, acquired with different scanning protocols. On the phantom data we find that PDE enhancements improve both local metrics and global metrics of tractography results, compared to CSD without enhancements. On the human data we show that the enhancements allow for a better reconstruction of crossing fiber bundles and they reduce the variability of the tractography output with respect to the acquisition parameters. Finally, we show that both the enhancement of the FODs and the use of the FBC measure on the tractography improve the stability with respect to different stochastic realizations of probabilistic tractography. This is shown in a clinical application: the reconstruction of the optic radiation for epilepsy surgery planning

Left-Invariant Diffusion on the Motion Group in terms of the Irreducible Representations of SO(3)

In this work we study the formulation of convection/diffusion equations on the 3D motion group SE(3) in terms of the irreducible representations of SO(3). Therefore, the left-invariant vector-fields on SE(3) are expressed as linear operators, that are differential forms in the translation coordinate and algebraic in the rotation. In the context of 3D image processing this approach avoids the explicit discretization of SO(3) or $S_2$, respectively. This is particular important for SO(3), where a direct discretization is infeasible due to the enormous memory consumption. We show two applications of the framework: one in the context of diffusion-weighted magnetic resonance imaging and one in the context of object detection

Fiber Orientation Estimation Guided by a Deep Network

Diffusion magnetic resonance imaging (dMRI) is currently the only tool for noninvasively imaging the brain's white matter tracts. The fiber orientation (FO) is a key feature computed from dMRI for fiber tract reconstruction. Because the number of FOs in a voxel is usually small, dictionary-based sparse reconstruction has been used to estimate FOs with a relatively small number of diffusion gradients. However, accurate FO estimation in regions with complex FO configurations in the presence of noise can still be challenging. In this work we explore the use of a deep network for FO estimation in a dictionary-based framework and propose an algorithm named Fiber Orientation Reconstruction guided by a Deep Network (FORDN). FORDN consists of two steps. First, we use a smaller dictionary encoding coarse basis FOs to represent the diffusion signals. To estimate the mixture fractions of the dictionary atoms (and thus coarse FOs), a deep network is designed specifically for solving the sparse reconstruction problem. Here, the smaller dictionary is used to reduce the computational cost of training. Second, the coarse FOs inform the final FO estimation, where a larger dictionary encoding dense basis FOs is used and a weighted l1-norm regularized least squares problem is solved to encourage FOs that are consistent with the network output. FORDN was evaluated and compared with state-of-the-art algorithms that estimate FOs using sparse reconstruction on simulated and real dMRI data, and the results demonstrate the benefit of using a deep network for FO estimation.Comment: A shorter version is accepted by MICCAI 201