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

Mapping neuronal fiber crossings in the human brain

International audienceNew magnetic resonance imaging processing tools allow white-matter fiber bundles to be segmented and tracked in regions of high complexity

The frontotemporal organization of the arcuate fasciculus and its relationship with speech perception in young and older amateur singers and non-singers

The ability to perceive speech in noise (SPiN) declines with age. Although the etiology of SPiN decline is not well understood, accumulating evidence suggests a role for the dorsal speech stream. While age-related decline within the dorsal speech stream would negatively affect SPiN performance, experience-induced neuroplastic changes within the dorsal speech stream could positively affect SPiN performance. Here, we investigated the relationship between SPiN performance and the structure of the arcuate fasciculus (AF), which forms the white matter scaffolding of the dorsal speech stream, in aging singers and non-singers. Forty-three non-singers and 41 singers aged 20 to 87 years old completed a hearing evaluation and a magnetic resonance imaging session that included High Angular Resolution Diffusion Imaging. The groups were matched for sex, age, education, handedness, cognitive level, and musical instrument experience. A subgroup of participants completed syllable discrimination in the noise task. The AF was divided into 10 segments to explore potential local specializations for SPiN. The results show that, in carefully matched groups of singers and nonsingers (a) myelin and/or axonal membrane deterioration within the bilateral frontotemporal AF segments are associated with SPiN difficulties in aging singers and non-singers; (b) the structure of the AF is different in singers and non-singers; (c) these differences are not associated with a benefit on SPiN performance for singers. This study clarifies the etiology of SPiN difficulties by supporting the hypothesis for the role of aging of the dorsal speech stream

Spectral Clustering en IRM de diffusion pour Retrouver les Faisceaux de la Matière Blanche

White matter fiber clustering allows to get insight about anatomical structures in order to generate atlases, perform clear visualizations and compute statistics across subjects, all important and current neuroimaging problems. In this work, we present a Diffusion Maps clustering method applied to diffusion MRI in order to cluster and segment complex white matter fiber bundles. It is well-known that Diffusion Tensor Imaging (DTI) is restricted in complex fiber regions with crossings and this is why recent High Angular Resolution Diffusion Imaging (HARDI) such has Q-Ball Imaging (QBI) have been introduced to overcome these limitations. QBI reconstructs the diffusion orientation distribution function (ODF), a spherical function that has its maxima agreeing with the underlying fiber populations. In this paper, we introduce the usage of the Diffusion Maps technique and show how it can be used to directly cluster set of fiber tracts, that could be obtained through a streamline tractography for instance, and how it can also help in segmenting fields of ODF images, obtained through a linear and regularized ODF estimation algorithm based on a spherical harmonics representation of the Q-Ball data. We first show the advantage of using Diffusion Maps clustering over classical methods such as N-Cuts and Laplacian Eigenmaps in both cases. In particular, our Diffusion Maps requires a smaller number of hypothesis from the input data, reduces the number of artifacts in fiber tract clustering and ODF image segmentation and automatically exhibits the number of clusters in both cases by using an adaptive scale-space parameter. We also show that our ODF Diffusion Maps clustering can reproduce published results using the diffusion tensor (DT) clustering with N-Cuts on simple synthetic images without crossings. On more complex data with crossings, we show that our ODF-based method succeeds to separate fiber bundles and crossing regions whereas the DT-based methods generate artifacts and exhibit wrong number of clusters. Finally, we illustrate the potential of our approach on a real brain dataset where we successfully segment well-known fiber bundles

Diffusion Maps Clustering for Magnetic Resonance Q-Ball Imaging Segmentation

International audienceWhite matter fiber clustering aims to get insight about anatomical structures in order to generate atlases, perform clear visualizations, and compute statistics across subjects, all important and current neuroimaging problems. In this work, we present a diffusion maps clustering method applied to diffusion MRI in order to segment complex white matter fiber bundles. It is well known that diffusion tensor imaging (DTI) is restricted in complex fiber regions with crossings and this is why recent high-angular resolution diffusion imaging (HARDI) such as Q-Ball imaging (QBI) has been introduced to overcome these limitations. QBI reconstructs the diffusion orientation distribution function (ODF), a spherical function that has its maxima agreeing with the underlying fiber populations. In this paper, we use a spherical harmonic ODF representation as input to the diffusion maps clustering method.We first show the advantage of using diffusion maps clustering over classical methods such as N-Cuts and Laplacian eigenmaps. In particular, our ODF diffusion maps requires a smaller number of hypothesis from the input data, reduces the number of artifacts in the segmentation, and automatically exhibits the number of clusters segmenting the Q-Ball image by using an adaptive scalespace parameter.We also show that our ODF diffusion maps clustering can reproduce published results using the diffusion tensor (DT) clustering with N-Cuts on simple synthetic images without crossings. On more complex data with crossings, we show that our ODF-based method succeeds to separate fiber bundles and crossing regions whereas the DT-based methods generate artifacts and exhibit wrong number of clusters. Finally, we show results on a real-brain dataset where we segment well-known fiber bundles

Optimal Real-Time QBI using Regularized Kalman Filtering with Incremental Orientation Sets

Diffusion MRI has become an established research tool for the investigation of tissue structure and orientation from which has stemmed a number of variations, such as Diffusion Tensor Imaging (DTI), Diffusion Spectrum Imaging (DSI) and Q-Ball Imaging (QBI). The acquisition and analysis of such data is very challenging due to its complexity. Recently, an exciting new Kalman filtering framework has been proposed for DTI and QBI reconstructions in real time during the repetition time (TR) of the acquisition sequence \cite{Miccai:2007,Med. Image Analysis -Vol 12, Issue 5, June 2008}. In this article, we first revisite and thoroughly analyze this approach and show it is actually sub-optimal and not recursively minimizing the intended criterion due to the Laplace-Beltrami regularization term. Then, we propose a new approach that implements the QBI reconstruction algorithm in real-time using a fast and robust Laplace-Beltrami regularization without sacrificing the optimality of the Kalman filter. We demonstrate that our method solves the correct minimization problem at each iteration and recursively provides the optimal QBI solution. We validate with real QBI data that our proposed real-time method is equivalent in terms of QBI estimation accuracy to the standard off-line processing techniques and outperforms the existing solution. Last, we propose a fast algorithm to recursively compute gradient orientation sets whose partial subsets are almost uniform and show that it can also be applied to the problem of efficiently ordering an existing point-set of any size. Our work allows to start an acquisition just with the minimum number of gradient directions and an initial estimate of the q-ball and then all the rest, including the next gradient directions and the q-ball estimates, are recursively and optimally determined, allowing the acquisition to be stopped as soon as desired or at any iteration with the optimal q-ball estimate. This opens new and interesting opportunities for real-time feedback for clinicians during an acquisition and also for researchers investigating into optimal diffusion orientation sets and, real-time fiber tracking and connectivity mapping

4TH ORDER DIFFUSION TENSOR ESTIMATION AND APPLICATION

International audienceHistorically Diffusion MRI started with Diffusion Tensor Imaging (DTI), which boosted the development of schemes for estimating positive definite tensors but were limited by their inability to detect fiber-crossings. Recent HARDI techniques have overcome that shortcoming with a plethora of new reconstruction schemes such as radial basis functions, Spherical Harmonics (SH), Higher Order Tensors (HOT), etc. It is appropriate, therefore, to explore HOT while leveraging the extensive framework already established for classical DTI. In this work, we propose a review and a comparison of the existing methods and an extension to the Riemannian framework to the space of 4 th order diffusion tensors

Denoising and fast diffusion imaging with physically constrained sparse dictionary learning

International audienceDiffusion-weighted imaging (DWI) allows imaging the geometry of water diffusion in biological tissues. However, DW images are noisy at high b-values and acquisitions are slow when using a large number of measurements, such as in Diffusion Spectrum Imaging (DSI). This work aims to denoise DWI and reduce the number of required measurements, while maintaining data quality. To capture the structure of DWI data, we use sparse dictionary learning constrained by the physical properties of the signal: symmetry and positivity. The method learns a dictionary of diffusion profiles on all the DW images at the same time and then scales to full brain data. Its performance is investigated with simulations and two real DSI datasets. We obtain better signal estimates from noisy measurements than by applying mirror symmetry through the q-space origin, Gaussian denoising or state-of- the-art non-local means denoising. Using a high-resolution dictionary learnt on another subject, we show that we can reduce the number of images acquired while still generating high resolution DSI data. Using dictionary learning, one can denoise DW images effectively and perform faster acquisitions. Higher b-value acquisitions and DSI techniques are possible with approximately 40 measurements. This opens important perspectives for the connectomics community using DSI

Apparent Diffusion Coefficients from High Angular Resolution Diffusion Images: Estimation and Applications

High angular resolution diffusion imaging (HARDI) has recently been of great interest in characterizing non-Gaussian diffusion processes. In the white matter of the brain, non-Gaussian diffusion occurs when fiber bundles cross, kiss or diverge within the same voxel. One important goal in current research is to obtain more accurate fits of the apparent diffusion processes in these multiple fiber regions, thus overcoming the limitations of classical diffusion tensor imaging (DTI). This paper presents an extensive study of high order models for apparent diffusion coefficient estimation and illustrates some of their applications. In particular, we first develop the appropriate mathematical tools to work on noisy HARDI data. Using a meaningful modified spherical harmonics basis to capture the physical constraints of the problem, we propose a new regularization algorithm to estimate a diffusivity profile smoother and closer to the true diffusivities without noise. We define a smoothing term based on the Laplace-Beltrami operator for functions defined on the unit sphere. The properties of the spherical harmonics are then exploited to derive a closed form implementation of this term into the fitting procedure. We next derive the general linear transformation between the coefficients of a spherical harmonics series of order $\ell$ and the independent elements of the rank-$\ell$ high order diffusion tensor. An additional contribution of the paper is the careful study of the state of the art anisotropy measures for high order formulation models computed from spherical harmonics or tensor coefficients. Their ability to characterize the underlying diffusion process is analyzed. We are able to reproduce published results and also able to recover voxels with isotropic, single fiber anisotropic and multiple fiber anisotropic diffusion. We test and validate the different approaches on apparent diffusion coefficients from synthetic data, from a biological phantom and from a human brain dataset