Maxime Descoteaux

Regularized, fast, and robust analytical Q-ball imaging

We propose a regularized, fast, and robust analytical solution for the Q‐ball imaging (QBI) reconstruction of the orientation distribution function (ODF) together with its detailed validation and a discussion on its benefits over the state‐of‐the‐art. Our analytical solution is achieved by modeling the raw high angular resolution diffusion imaging signal with a spherical harmonic basis that incorporates a regularization term based on the Laplace–Beltrami operator defined on the unit sphere. This leads to an elegant mathematical simplification of the Funk–Radon transform which approximates the ODF. We prove a new corollary of the Funk–Hecke theorem to obtain this simplification. Then, we show that the Laplace–Beltrami regularization is theoretically and practically better than Tikhonov regularization. At the cost of slightly reducing angular resolution, the Laplace–Beltrami regularization reduces ODF estimation errors and improves fiber detection while reducing angular error in the ODF maxima detected. Finally, a careful quantitative validation is performed against ground truth from synthetic data and against real data from a biological phantom and a human brain dataset. We show that our technique is also able to recover known fiber crossings in the human brain and provides the practical advantage of being up to 15 times faster than original numerical QBI method. Magn Reson Med 58:497–510, 2007.

Deterministic and Probabilistic Tractography Based on Complex Fibre Orientation Distributions

We propose an integral concept for tractography to describe crossing and splitting fibre bundles based on the fibre orientation distribution function (ODF) estimated from high angular resolution diffusion imaging (HARDI). We show that in order to perform accurate probabilistic tractography, one needs to use a fibre ODF estimation and not the diffusion ODF. We use a new fibre ODF estimation obtained from a sharpening deconvolution transform (SDT) of the diffusion ODF reconstructed from q-ball imaging (QBI). This SDT provides new insight into the relationship between the HARDI signal, the diffusion ODF, and the fibre ODF. We demonstrate that the SDT agrees with classical spherical deconvolution and improves the angular resolution of QBI. Another important contribution of this paper is the development of new deterministic and new probabilistic tractography algorithms using the full multidirectional information obtained through use of the fibre ODF. An extensive comparison study is performed on human brain datasets comparing our new deterministic and probabilistic tracking algorithms in complex fibre crossing regions. Finally, as an application of our new probabilistic tracking, we quantify the reconstruction of transcallosal fibres intersecting with the corona radiata and the superior longitudinal fasciculus in a group of eight subjects. Most current diffusion tensor imaging (DTI)-based methods neglect these fibres, which might lead to incorrect interpretations of brain functions.

Apparent diffusion coefficients from high angular resolution diffusion imaging: estimation and applications.

High angular resolution diffusion imaging has recently been of great interest in characterizing non‐Gaussian diffusion processes. One important goal is to obtain more accurate fits of the apparent diffusion processes in these non‐Gaussian regions, thus overcoming the limitations of classical diffusion tensor imaging. This paper presents an extensive study of high‐order models for apparent diffusion coefficient estimation and illustrates some of their applications. Using a meaningful modified spherical harmonics basis to capture the physical constraints of the problem, a new regularization algorithm is proposed. The new smoothing term is based on the Laplace–Beltrami operator and its closed form implementation is used in the fitting procedure. Next, the linear transformation between the coefficients of a spherical harmonic series of order ℓ and independent elements of a rank‐ℓ high‐order diffusion tensor is explicitly derived. This relation allows comparison of the state‐of‐the‐art anisotropy measures computed from spherical harmonics and tensor coefficients. Published results are reproduced accurately and it is also possible to recover voxels with isotropic, single fiber anisotropic, and multiple fiber anisotropic diffusion. Validation is performed on apparent diffusion coefficients from synthetic data, from a biological phantom, and from a human brain dataset. Magn Reson Med, 2006.

Dipy, a library for the analysis of diffusion MRI data

Diffusion Imaging in Python (Dipy) is a free and open source software project for the analysis of data from diffusion magnetic resonance imaging (dMRI) experiments. dMRI is an application of MRI that can be used to measure structural features of brain white matter. Many methods have been developed to use dMRI data to model the local configuration of white matter nerve fiber bundles and infer the trajectory of bundles connecting different parts of the brain. Dipy gathers implementations of many different methods in dMRI, including: diffusion signal pre-processing; reconstruction of diffusion distributions in individual voxels; fiber tractography and fiber track post-processing, analysis and visualization. Dipy aims to provide transparent implementations for all the different steps of dMRI analysis with a uniform programming interface. We have implemented classical signal reconstruction techniques, such as the diffusion tensor model and deterministic fiber tractography. In addition, cutting edge novel reconstruction techniques are implemented, such as constrained spherical deconvolution and diffusion spectrum imaging (DSI) with deconvolution, as well as methods for probabilistic tracking and original methods for tractography clustering. Many additional utility functions are provided to calculate various statistics, informative visualizations, as well as file-handling routines to assist in the development and use of novel techniques. In contrast to many other scientific software projects, Dipy is not being developed by a single research group. Rather, it is an open project that encourages contributions from any scientist/developer through GitHub and open discussions on the project mailing list. Consequently, Dipy today has an international team of contributors, spanning seven different academic institutions in five countries and three continents, which is still growing.

Multiple q-shell diffusion propagator imaging

Many recent high angular resolution diffusion imaging (HARDI) reconstruction techniques have been introduced to infer an orientation distribution function (ODF) of the underlying tissue structure. These methods are more often based on a single-shell (one b-value) acquisition and can only recover angular structure information contained in the ensemble average propagator (EAP) describing the three-dimensional (3D) average diffusion process of water molecules. The EAP can thus provide richer information about complex tissue microstructure properties than the ODF by also considering the radial part of the diffusion signal. In this paper, we present a novel technique for analytical EAP reconstruction from multiple q-shell acquisitions. The solution is based on a Laplace equation by part estimation between the diffusion signal for each shell acquisition. This simplifies greatly the Fourier integral relating diffusion signal and EAP, which leads to an analytical, linear and compact EAP reconstruction. An important part of the paper is dedicated to validate the diffusion signal estimation and EAP reconstruction on real datasets from ex vivo phantoms. We also illustrate multiple q-shell diffusion propagator imaging (mq-DPI) on a real in vivo human brain and perform a qualitative comparison against state-of-the-art diffusion spectrum imaging (DSI) on the same subject. mq-DPI is shown to reconstruct robust EAP from only several different b-value shells and less diffusion measurements than DSI. This opens interesting perspectives for new q-space sampling schemes and tissue microstructure investigation.

Robust clustering of massive tractography datasets.

This paper presents a clustering method that detects the fiber bundles embedded in any MR-diffusion based tractography dataset. Our method can be seen as a compressing operation, capturing the most meaningful information enclosed in the fiber dataset. For the sake of efficiency, part of the analysis is based on clustering the white matter (WM) voxels rather than the fibers. The resulting regions of interest are used to define subset of fibers that are subdivided further into consistent bundles using a clustering of the fiber extremities. The dataset is reduced from more than one million fiber tracts to about two thousand fiber bundles. Validations are provided using simulated data and a physical phantom. We see our approach as a crucial preprocessing step before further analysis of huge fiber datasets. An important application will be the inference of detailed models of the subdivisions of white matter pathways and the mapping of the main U-fiber bundles.

Towards quantitative connectivity analysis: reducing tractography biases

Diffusion MRI tractography is often used to estimate structural connections between brain areas and there is a fast-growing interest in quantifying these connections based on their position, shape, size and length. However, a portion of the connections reconstructed with tractography is biased by their position, shape, size and length. Thus, connections reconstructed are not equally distributed in all white matter bundles. Quantitative measures of connectivity based on the streamline distribution in the brain such as streamline count (density), average length and spatial extent (volume) are biased by erroneous streamlines produced by tractography algorithms. In this paper, solutions are proposed to reduce biases in the streamline distribution. First, we propose to optimize tractography parameters in terms of connectivity. Then, we propose to relax the tractography stopping criterion with a novel probabilistic stopping criterion and a particle filtering method, both based on tissue partial volume estimation maps calculated from a T1-weighted image. We show that optimizing tractography parameters, stopping and seeding strategies can reduce the biases in position, shape, size and length of the streamline distribution. These tractography biases are quantitatively reported using in-vivo and synthetic data. This is a critical step towards producing tractography results for quantitative structural connectivity analysis.

Tractometer: Towards validation of tractography pipelines

We have developed the Tractometer: an online evaluation and validation system for tractography processing pipelines. One can now evaluate the results of more than 57,000 fiber tracking outputs using different acquisition settings (b-value, averaging), different local estimation techniques (tensor, q-ball, spherical deconvolution) and different tracking parameters (masking, seeding, maximum curvature, step size). At this stage, the system is solely based on a revised FiberCup analysis, but we hope that the community will get involved and provide us with new phantoms, new algorithms, third party libraries and new geometrical metrics, to name a few. We believe that the new connectivity analysis and tractography characteristics proposed can highlight limits of the algorithms and contribute in solving open questions in fiber tracking: from raw data to connectivity analysis. Overall, we show that (i) averaging improves quality of tractography, (ii) sharp angular ODF profiles helps tractography, (iii) seeding and multi-seeding has a large impact on tractography outputs and must be used with care, and (iv) deterministic tractography produces less invalid tracts which leads to better connectivity results than probabilistic tractography.

Diffusion abnormalities in the primary sensorimotor pathways in writer's cramp.

OBJECTIVE To determine whether there are diffusion abnormalities along the fibers connecting sensorimotor regions, including the primary sensorimotor areas and the striatum, in patients with writers cramp using voxel-based diffusion analysis and fiber tracking. Recent studies have shown structural changes in these regions in writers cramp. DESIGN Patient and control group comparison. SETTING Referral center for movement disorders. PARTICIPANTS Twenty-six right-handed patients with writers cramp and 26 right-handed healthy control subjects matched for sex and age. INTERVENTIONS Clinical motor evaluations. MAIN OUTCOME MEASURES Fractional anisotropy changes and results of fiber tracking in writers cramp. RESULTS Diffusion-tensor imaging revealed increased fractional anisotropy bilaterally in the white matter of the posterior limb of the internal capsule and adjacent structures in the patients with writers cramp. Fiber tracking demonstrated that fractional anisotropy changes involve fiber tracts connecting the primary sensorimotor areas with subcortical structures. CONCLUSIONS Diffusion abnormalities are present in fiber tracts connecting the primary sensorimotor areas with subcortical structures in writers cramp. These abnormalities strengthen the role of the corticosubcortical pathways in the pathophysiologic mechanisms of writers cramp.

Quantitative Comparison of Reconstruction Methods for Intra-Voxel Fiber Recovery From Diffusion MRI

Validation is arguably the bottleneck in the diffusion magnetic resonance imaging (MRI) community. This paper evaluates and compares 20 algorithms for recovering the local intra-voxel fiber structure from diffusion MRI data and is based on the results of the “HARDI reconstruction challenge” organized in the context of the “ISBI 2012” conference. Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. To quantitatively compare the methods under controlled conditions, two datasets with known ground-truth were synthetically generated and two main criteria were used to evaluate the quality of the reconstructions in every voxel: correct assessment of the number of fiber populations and angular accuracy in their orientation. This comparative study investigates the behavior of every algorithm with varying experimental conditions and highlights strengths and weaknesses of each approach. This information can be useful not only for enhancing current algorithms and develop the next generation of reconstruction methods, but also to assist physicians in the choice of the most adequate technique for their studies.