Abstract in English below.
Diffusion MRI (dMRI) is a unique modality of MRI which allows one to indirectly examine the microstructure and integrity of the cerebral white matter in vivo and non-invasively. Its success lies in its capacity to reconstruct the axonal connectivity of the neurons, albeit at a coarser resolution, without having to operate on the patient, which...
International audience
Generalized Diffusion Tensor Imaging (GDTI) was developed to model complex Apparent Diffusivity Coefficient (ADC) using Higher Order Tensors (HOT) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile doesn't correspond to the underlying structure of fibers. This tissue geometry can be...
Spherical Functions (SF) play a pivotal role in Diffusion MRI (dMRI) in representing sub-voxel-resolution micro- architectural information of the underlying tissue. This in- formation is encoded in the geometric shape of the SF. In this paper we use a polynomial approach to extract geometric characteristics from SFs in dMRI such as the maxima,...
High Order Cartesian Tensors (HOTs) were introduced in Generalized DTI (GDTI) to overcome the limitations of DTI. HOTs can model the apparent diffusion coefficient (ADC) with greater accuracy than DTI in regions with fiber heterogeneity. Although GDTI HOTs were designed to model positive diffusion, the straightforward least square (LS)...
Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be...
Diffusion MRI, which is sensitive to the Brownian motion of molecules, has become today an excellent medical tool for probing the tissue micro-structure of cerebral white matter in vivo and non-invasively. It makes it possible to reconstruct fiber pathways and segment major fiber bundles that reflect the structures in the brain which are not...
In this paper, we review the state of the art in diffusion magnetic resonance imaging (dMRI) and we present current trends in modelling the brainʼs tissue microstructure and the human connectome. dMRI is today the only tool that can probe the brainʼs axonal architecture in vivo and non-invasively, and has grown in leaps and bounds in the last...
In this paper, we explore the theory of tensor invariants as a mathematical framework for computing new biomarkers for HARDI. We present and explain the integrity basis, basic in- variants and principal invariants of 2nd & 4th order tensors to expand on a recently proposed paper on 4th order tensor invariants. We present the mathematical...
We present a ternary quartic based approach with an improved gradient based optimization scheme for diffusion kurtosis imaging to estimate constrained and physically realistic diffusion and kurtosis tensors. We account for the signal noise by considering a maximum likelihood estimation based on the Rician noise model. Diffusion kurtosis imaging...
Generalized Diffusion Tensor Imaging (GDTI) [1] is one of the few methods that estimate the ensemble average diffusion propagator from the diffusion weighted signal. It has a statistical approach and views the signal, which under the q-space formalism is the Fourier transform of the propagator, as the characteristic function of the propagator....
DTI is an important tool to investigate the brain in vivo and non-invasively in spite of its shortcomings in regions of fiber-crossings. HARDI models such as QBI and Higher Order Tensors (HOT) were in- vented to overcome this shortcoming. HOTs, however, have not been explored extensively even though sophisticated estimation schemes were...
Invariants play a crucial role in Diffusion MRI. In DTI (2 nd order tensors), invariant scalars (FA, MD) have been successfully used in clinical applications. But DTI has limitations and HARDI models (e.g. 4 th order tensors) have been proposed instead. These, however, lack invariant features and computing them systematically is challenging. We...
This paper presents a general and complete (up to degree 4) set of invariants of 3D 4th order tensors with respect to SO3. The invariants to SO3 for the 2nd order diffusion tensor are well known and play a crucial role in deriving important biomarkers for DTI, e.g. MD, FA, RA, etc. But DTI is limited in regions with fiber heterogeneity and DTI...
In Diffusion Magnetic Resonance Imaging (D-MRI), the 2nd order diffusion tensor has given rise to a widely used tool – Diffusion Tensor Imaging (DTI). However, it is known that DTI is limited to a single prominent diffusion direction and is inaccurate in regions of complex fiber structures such as crossings. Various other approaches have been...
Historically 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...
Purpose: Diffusion kurtosis imaging (DKI) is a recent improvement over diffusion tensor imaging that characterizes tissue by quantifying non-gaussian diffusion using a 3D fourth-order kurtosis tensor. DKI needs to consider three constraints to be physically relevant. Further, it can be improved by considering the Rician signal noise model. A...
A number of non-parametrically represented High Angular Resolution Diffusion Imaging (HARDI) spherical diffusion functions have been proposed to infer more and more accurately the heterogeneous and complex tissue microarchitecture of the cerebral white-matter. These spherical functions overcome the limitation of Diffusion Tensor Imaging (DTI)...
In diffusion magnetic resonance imaging (dMRI), the Ensemble Average Propagator (EAP), also known as the propagator, describes completely the water molecule diffusion in the brain white matter without any prior knowledge about the tissue shape. In this paper, we describe a new and efficient method to accurately reconstruct the EAP in terms of...
High Angular Resolution Imaging (HARDI) can better explore the complex micro-structure of white matter compared to Diffusion Tensor Imaging (DTI). Orientation Distribution Function (ODF) in HARDI is used to describe the probability of the fiber direction. There are two type definitions of the ODF, which were respectively proposed in Q-Ball...
In this work, we propose an approach to exploit the ability of compressive sensing to recover diffusion MRI signal and its characteristics from a limited number of samples. Our approach is threefold. First, we learn and design a parametric dictionary from a set of training diffusion data. This provides a highly sparse representation of the...
Compared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information...
Background: In Diffusion Tensor Imaging (DTI), Riemannian framework based on Information Geometry theory has been proposed for processing tensors on estimation, interpolation, smoothing, regularization, segmentation, statistical test and so on. Recently Riemannian framework has been generalized to Orientation Distribution Function (ODF) and it...
The geometric median is a classic robust estimator of centrality for data in Euclidean spaces, and it has been generalized in analytical manifold in [1]. Recently, an intrinsic Riemannian framework for Orientation Distribution Function (ODF) was proposed for the calculation in ODF field [2]. In this work, we prove the unique existence of the...