A hitchhiker's guide to diffusion tensor imaging

Diffusion Tensor Imaging (DTI) studies are increasingly popular among clinicians and researchers as they provide unique insights into brain network connectivity. However, in order to optimize the use of DTI, several technical and methodological aspects must be factored in. These include decisions on: acquisition protocol, artifact handling, data quality control, reconstruction algorithm, and visualization approaches, and quantitative analysis methodology. Furthermore, the researcher and/or clinician also needs to take into account and decide on the most suited software tool(s) for each stage of the DTI analysis pipeline. Herein, we provide a straightforward hitchhiker's guide, covering all of the workflow's major stages. Ultimately, this guide will help newcomers navigate the most critical roadblocks in the analysis and further encourage the use of DTI.The work was supported by SwitchBox-FP7-HEALTH-2010-grant 259772-2. The authors acknowledge Nadine Santos for her help in editing the manuscript

Space-Varying Coefficient Models for Brain Imaging

The methodological development and the application in this paper originate from diffusion tensor imaging (DTI), a powerful nuclear magnetic resonance technique enabling diagnosis and monitoring of several diseases as well as reconstruction of neural pathways. We reformulate the current analysis framework of separate voxelwise regressions as a 3d space-varying coefficient model (VCM) for the entire set of DTI images recorded on a 3d grid of voxels. Hence by allowing to borrow strength from spatially adjacent voxels, to smooth noisy observations, and to estimate diffusion tensors at any location within the brain, the three-step cascade of standard data processing is overcome simultaneously. We conceptualize two VCM variants based on B-spline basis functions: a full tensor product approach and a sequential approximation, rendering the VCM numerically and computationally feasible even for the huge dimension of the joint model in a realistic setup. A simulation study shows that both approaches outperform the standard method of voxelwise regressions with subsequent regularization. Due to major efficacy, we apply the sequential method to a clinical DTI data set and demonstrate the inherent ability of increasing the rigid grid resolution by evaluating the incorporated basis functions at intermediate points. In conclusion, the suggested fitting methods clearly improve the current state-of-the-art, but ameloriation of local adaptivity remains desirable

Single- and Multiple-Shell Uniform Sampling Schemes for Diffusion MRI Using Spherical Codes

In diffusion MRI (dMRI), a good sampling scheme is important for efficient acquisition and robust reconstruction. Diffusion weighted signal is normally acquired on single or multiple shells in q-space. Signal samples are typically distributed uniformly on different shells to make them invariant to the orientation of structures within tissue, or the laboratory coordinate frame. The Electrostatic Energy Minimization (EEM) method, originally proposed for single shell sampling scheme in dMRI, was recently generalized to multi-shell schemes, called Generalized EEM (GEEM). GEEM has been successfully used in the Human Connectome Project (HCP). However, EEM does not directly address the goal of optimal sampling, i.e., achieving large angular separation between sampling points. In this paper, we propose a more natural formulation, called Spherical Code (SC), to directly maximize the minimal angle between different samples in single or multiple shells. We consider not only continuous problems to design single or multiple shell sampling schemes, but also discrete problems to uniformly extract sub-sampled schemes from an existing single or multiple shell scheme, and to order samples in an existing scheme. We propose five algorithms to solve the above problems, including an incremental SC (ISC), a sophisticated greedy algorithm called Iterative Maximum Overlap Construction (IMOC), an 1-Opt greedy method, a Mixed Integer Linear Programming (MILP) method, and a Constrained Non-Linear Optimization (CNLO) method. To our knowledge, this is the first work to use the SC formulation for single or multiple shell sampling schemes in dMRI. Experimental results indicate that SC methods obtain larger angular separation and better rotational invariance than the state-of-the-art EEM and GEEM. The related codes and a tutorial have been released in DMRITool.Comment: Accepted by IEEE transactions on Medical Imaging. Codes have been released in dmritool https://diffusionmritool.github.io/tutorial_qspacesampling.htm

Scanner Invariant Representations for Diffusion MRI Harmonization

Purpose: In the present work we describe the correction of diffusion-weighted MRI for site and scanner biases using a novel method based on invariant representation. Theory and Methods: Pooled imaging data from multiple sources are subject to variation between the sources. Correcting for these biases has become very important as imaging studies increase in size and multi-site cases become more common. We propose learning an intermediate representation invariant to site/protocol variables, a technique adapted from information theory-based algorithmic fairness; by leveraging the data processing inequality, such a representation can then be used to create an image reconstruction that is uninformative of its original source, yet still faithful to underlying structures. To implement this, we use a deep learning method based on variational auto-encoders (VAE) to construct scanner invariant encodings of the imaging data. Results: To evaluate our method, we use training data from the 2018 MICCAI Computational Diffusion MRI (CDMRI) Challenge Harmonization dataset. Our proposed method shows improvements on independent test data relative to a recently published baseline method on each subtask, mapping data from three different scanning contexts to and from one separate target scanning context. Conclusion: As imaging studies continue to grow, the use of pooled multi-site imaging will similarly increase. Invariant representation presents a strong candidate for the harmonization of these data

Modeling high resolution MRI: Statistical issues with low SNR

Noise is a common issue for all Magnetic Resonance Imaging (MRI) techniques and obviously leads to variability of the estimates in any model describing the data. A number of special MR sequences as well as increasing spatial resolution in MR experiments further diminish the signal-to-noise ratio (SNR). However, with low SNR the expected signal deviates from its theoretical value. Common modeling approaches therefore lead to a bias in estimated model parameters. Adjustments require an analysis of the data generating process and a characterization of the resulting distribution of the imaging data. We provide an adequate quasi-likelihood approach that employs these characteristics. We elaborate on the effects of typical data preprocessing and analyze the bias effects related to low SNR for the example of the diffusion tensor model in diffusion MRI. We then demonstrate that the problem is relevant even for data from the Human Connectome Project, one of the highest quality diffusion MRI data available so far

Modeling high resolution MRI: Statistical issues with low SNR

Noise is a common issue for all Magnetic Resonance Imaging (MRI) techniques and obviously leads to variability of the estimates in any model describing the data. A number of special MR sequences as well as increasing spatial resolution in MR experiments further diminish the signal-to-noise ratio (SNR). However, with low SNR the expected signal deviates from its theoretical value. Common modeling approaches therefore lead to a bias in estimated model parameters. Adjustments require an analysis of the data generating process and a characterization of the resulting distribution of the imaging data. We provide an adequate quasi-likelihood approach that employs these characteristics. We elaborate on the effects of typical data preprocessing and analyze the bias effects related to low SNR for the example of the diffusion tensor model in diffusion MRI. We then demonstrate that the problem is relevant even for data from the Human Connectome Project, one of the highest quality diffusion MRI data available so far

Persistent Homology in Sparse Regression and its Application to Brain Morphometry

Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in speeding up the computation using the proposed soft-thresholding technique. The topological structures are further used as multivariate features in the tensor-based morphometry (TBM) in characterizing white matter alterations in children who have experienced severe early life stress and maltreatment. These analyses reveal that stress-exposed children exhibit more diffuse anatomical organization across the whole white matter region.Comment: submitted to IEEE Transactions on Medical Imagin

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