Least squares for diffusion tensor estimation revisited: propagation of uncertainty with Rician and non-Rician signals

The impact of diffusion tensor imaging tractography settings on muscle fascicle architecture and diffusion parameter estimates: Tract length, completion, and curvature are most sensitive to tractography settings

Diffusion-tensor (DT)-MRI tractography provides information about properties relevant to muscle health and function, including estimates of architectural properties such as fascicle length, pennation angle, and curvature and diffusion properties such as mean diffusivity (MD) and fractional anisotropy (FA). Tractography settings, including integration algorithms, thresholds for early tract termination, and tract smoothing approaches, impact the accuracy of the muscle property estimates. However, muscle DT-MRI tractography is performed using a variety of these settings, complicating comparisons between different studies. The effects of different tractography settings on muscle architecture estimates have not been fully explored, and optimized settings for muscle tractography have not yet been determined. We examined the influence of integration algorithm and termination check settings combined with a range of step sizes, termination criteria, and smoothing polynomial orders on tract characteristics, completion/reason for termination, and goodness of fit between fiber tracts and smoothing polynomials using 3-T DT-MR images of the lower leg muscles of seven healthy adults. We found that tract length and completion were highly sensitive to strict FA and intersegment angle thresholds (25%-69% reduction in complete fiber tracts from lowest to highest minimum FA threshold and 11%-36% reduction from highest to lowest intersegment angle threshold). Higher order polynomials (third and fourth order vs. second order) better fit the muscle fiber trajectories, but curvature estimates were highly sensitive to smoothing polynomial order (3.9-6.6 m-1 increase for second- vs. fourth-order fitting polynomials). Step size impacted curvature estimates, albeit to a lesser degree. Integration algorithm had little impact, and mean pennation angle, and tract-based FA and MD, were relatively insensitive to all parameters. The results demonstrate which muscle diffusion measures and architectural estimates are most sensitive to varying tractography settings and support the need for consistent reporting of tractography details to aid interpretation and comparison of results between studies.

Validation of deep learning techniques for quality augmentation in diffusion MRI for clinical studies

The objective of this study is to evaluate the efficacy of deep learning (DL) techniques in improving the quality of diffusion MRI (dMRI) data in clinical applications. The study aims to determine whether the use of artificial intelligence (AI) methods in medical images may result in the loss of critical clinical information and/or the appearance of false information. To assess this, the focus was on the angular resolution of dMRI and a clinical trial was conducted on migraine, specifically between episodic and chronic migraine patients. The number of gradient directions had an impact on white matter analysis results, with statistically significant differences between groups being drastically reduced when using 21 gradient directions instead of the original 61. Fourteen teams from different institutions were tasked to use DL to enhance three diffusion metrics (FA, AD and MD) calculated from data acquired with 21 gradient directions and a b-value of 1000 s/mm2. The goal was to produce results that were comparable to those calculated from 61 gradient directions. The results were evaluated using both standard image quality metrics and Tract-Based Spatial Statistics (TBSS) to compare episodic and chronic migraine patients. The study results suggest that while most DL techniques improved the ability to detect statistical differences between groups, they also led to an increase in false positive. The results showed that there was a constant growth rate of false positives linearly proportional to the new true positives, which highlights the risk of generalization of AI-based tasks when assessing diverse clinical cohorts and training using data from a single group. The methods also showed divergent performance when replicating the original distribution of the data and some exhibited significant bias. In conclusion, extreme caution should be exercised when using AI methods for harmonization or synthesis in clinical studies when processing heterogeneous data in clinical studies, as important information may be altered, even when global metrics such as structural similarity or peak signal-to-noise ratio appear to suggest otherwise.

Diffusion tensor imaging pipeline measures of cerebral white matter integrity: An overview of recent advances and prospects

Cerebral small vessel disease (CSVD) is a leading cause of age-related microvascular cognitive decline, resulting in significant morbidity and decreased quality of life. Despite a progress on its key pathophysiological bases and general acceptance of key terms from neuroimaging findings as observed on the magnetic resonance imaging (MRI), key questions on CSVD remain elusive. Enhanced relationships and reliable lesion studies, such as white matter tractography using diffusion-based MRI (dMRI) are necessary in order to improve the assessment of white matter architecture and connectivity in CSVD. Diffusion tensor imaging (DTI) and tractography is an application of dMRI that provides data that can be used to non-invasively appraise the brain white matter connections via fiber tracking and enable visualization of individual patient-specific white matter fiber tracts to reflect the extent of CSVD-associated white matter damage. However, due to a lack of standardization on various sets of software or image pipeline processing utilized in this technique that driven mostly from research setting, interpreting the findings remain contentious, especially to inform an improved diagnosis and/or prognosis of CSVD for routine clinical use. In this minireview, we highlight the advances in DTI pipeline processing and the prospect of this DTI metrics as potential imaging biomarker for CSVD, even for subclinical CSVD in at-risk individuals.

Accuracy and reliability of diffusion imaging models

Diffusion imaging aims to non-invasively characterize the anatomy and integrity of the brain's white matter fibers. We evaluated the accuracy and reliability of commonly used diffusion imaging methods as a function of data quantity and analysis method, using both simulations and highly sampled individual-specific data (927-1442 diffusion weighted images [DWIs] per individual). Diffusion imaging methods that allow for crossing fibers (FSL's BedpostX [BPX], DSI Studio's Constant Solid Angle Q-Ball Imaging [CSA-QBI], MRtrix3's Constrained Spherical Deconvolution [CSD]) estimated excess fibers when insufficient data were present and/or when the data did not match the model priors. To reduce such overfitting, we developed a novel Bayesian Multi-tensor Model-selection (BaMM) method and applied it to the popular ball-and-stick model used in BedpostX within the FSL software package. BaMM was robust to overfitting and showed high reliability and the relatively best crossing-fiber accuracy with increasing amounts of diffusion data. Thus, sufficient data and an overfitting resistant analysis method enhance precision diffusion imaging. For potential clinical applications of diffusion imaging, such as neurosurgical planning and deep brain stimulation (DBS), the quantities of data required to achieve diffusion imaging reliability are lower than those needed for functional MRI.

Fast and accurate initialization of the free-water imaging model parameters from multi-shell diffusion MRI

Cerebrospinal fluid partial volume effect is a known bias in the estimation of Diffusion Tensor Imaging (DTI) parameters from diffusion MRI data. The Free-Water Imaging model for diffusion MRI data adds a second compartment to the DTI model, which explicitly accounts for the signal contribution of extracellular free-water, such as cerebrospinal fluid. As a result the DTI parameters obtained through the free-water model are corrected for partial volume effects, and thus better represent tissue microstructure. In addition, the model estimates the fractional volume of free-water, and can be used to monitor changes in the extracellular space. Under certain assumptions, the model can be estimated from single-shell diffusion MRI data. However, by using data from multi-shell diffusion acquisitions, these assumptions can be relaxed, and the fit becomes more robust. Nevertheless, fitting the model to multi-shell data requires high computational cost, with a non-linear iterative minimization, which has to be initialized close enough to the global minimum to avoid local minima and to robustly estimate the model parameters. Here we investigate the properties of the main initialization approaches that are currently being used, and suggest new fast approaches to improve the initial estimates of the model parameters. We show that our proposed approaches provide a fast and accurate initial approximation of the model parameters, which is very close to the final solution. We demonstrate that the proposed initializations improve the final outcome of non-linear model fitting.

Generalised boundary shift integral for longitudinal assessment of spinal cord atrophy

Spinal cord atrophy measurements obtained from structural magnetic resonance imaging (MRI) are associated with disability in many neurological diseases and serve as in vivo biomarkers of neurodegeneration. Longitudinal spinal cord atrophy rate is commonly determined from the numerical difference between two volumes (based on 3D surface fitting) or two cross-sectional areas (CSA, based on 2D edge detection) obtained at different time-points. Being an indirect measure, atrophy rates are susceptible to variable segmentation errors at the edge of the spinal cord. To overcome those limitations, we developed a new registration-based pipeline that measures atrophy rates directly. We based our approach on the generalised boundary shift integral (GBSI) method, which registers 2 scans and uses a probabilistic XOR mask over the edge of the spinal cord, thereby measuring atrophy more accurately than segmentation-based techniques. Using a large cohort of longitudinal spinal cord images (610 subjects with multiple sclerosis from a multi-centre trial and 52 healthy controls), we demonstrated that GBSI is a sensitive, quantitative and objective measure of longitudinal spinal cord volume change. The GBSI pipeline is repeatable, reproducible, and provides more precise measurements of longitudinal spinal cord atrophy than segmentation-based methods in longitudinal spinal cord atrophy studies.

Scalar diffusion-MRI measures invariant to acquisition parameters: A first step towards imaging biomarkers

An imaging biomarker is a biologic feature in an image that is relevant to a patient's diagnosis or prognosis. In order to qualify as a biomarker, a measure must be robust and reproducible. However, the usual scalar measures derived from diffusion tensor imaging are known to be highly dependent on the variation of the acquisition parameters, which prevents their possible use as biomarkers. In this work, we propose a new set of quantitative measures based on diffusion magnetic resonance imaging from single-shell acquisitions that are designed to be robust to the variations of several acquisition parameters (number of gradient directions, b-value and SNR) while keeping a high discrimination power on differences in the diffusion characteristics of the tissue. These new scalar measures are analytically obtained from a generic diffusion function that does not require the calculation of a diffusion tensor. This way, on one hand, we avoid the use of a specific diffusion model and, on the other hand, we make easier the statistical characterization of the measures. Accordingly, the analysis of the measures bias is carried out and it is used to minimize their dependency with respect to the acquisition noise for different SNRs. The robustness and discrimination power of the measures are tested for different number of gradients, b-values and SNRs using a realistic phantom and three real datasets: (1) 13 control subjects and different acquisition parameters; (2) a public data set from a single subject acquired using multiple shells and (3) 32 schizophrenia patients and 32 age and sex-matched healthy controls with a varying number of gradient directions. The proposed quantitative measures exhibit low variability to the changes of the acquisition parameters, while at the same time they preserve a discrimination power that is able to detect significant changes in the anisotropy of the diffusion.

Bayesian Rician Regression for Neuroimaging

It is well-known that data from diffusion weighted imaging (DWI) follow the Rician distribution. The Rician distribution is also relevant for functional magnetic resonance imaging (fMRI) data obtained at high temporal or spatial resolution. We propose a general regression model for non-central χ (NC-χ) distributed data, with the heteroscedastic Rician regression model as a prominent special case. The model allows both parameters in the Rician distribution to be linked to explanatory variables, with the relevant variables chosen by Bayesian variable selection. A highly efficient Markov chain Monte Carlo (MCMC) algorithm is proposed to capture full model uncertainty by simulating from the joint posterior distribution of all model parameters and the binary variable selection indicators. Simulated regression data is used to demonstrate that the Rician model is able to detect the signal much more accurately than the traditionally used Gaussian model at low signal-to-noise ratios. Using a diffusion dataset from the Human Connectome Project, it is also shown that the commonly used approximate Gaussian noise model underestimates the mean diffusivity (MD) and the fractional anisotropy (FA) in the single-diffusion tensor model compared to the Rician model.

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 many factors such as the number of coils and the methodology used to combine multichannel MRI signals. Indeed, the two prevailing methods for multichannel signal combination lead to noise patterns better described by Rician and noncentral Chi 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 human brain data.

Sexual dimorphic abnormalities in white matter geometry common to schizophrenia and non-psychotic high-risk subjects: Evidence for a neurodevelopmental risk marker?

The characterization of neurodevelopmental aspects of brain alterations require neuroimaging methods that reflect correlates of neurodevelopment, while being robust to other progressive pathological processes. Newly developed neuroimaging methods for measuring geometrical features of the white matter fall exactly into this category. Our recent work shows that such features, measured in the anterior corpus callosum in diffusion MRI data, correlate with psychosis symptoms in patients with adolescent onset schizophrenia and subside a reversal of normal sexual dimorphism. Here, we test the hypothesis that similar developmental deviations will also be present in nonpsychotic subjects at familial high risk (FHR) for schizophrenia, due to genetic predispositions. Demonstrating such changes would provide a strong indication of neurodevelopmental deviation extant before, and independent of pathological changes occurring after disease onset. We examined the macrostructural geometry of corpus callosum white matter in diffusion MRI data of 35 non-psychotic subjects with genetic (familial) risk for schizophrenia, and 26 control subjects, both male and female. We report a reversal of normal sexual dimorphism in callosal white matter geometry consistent with recent results in adolescent onset schizophrenia. This pattern may be indicative of an error in neurogenesis and a possible trait marker of schizophrenia.

Impact of MR Acquisition Parameters on DTI Scalar Indexes: A Tractography Based Approach

Acquisition parameters play a crucial role in Diffusion Tensor Imaging (DTI), as they have a major impact on the values of scalar measures such as Fractional Anisotropy (FA) or Mean Diffusivity (MD) that are usually the focus of clinical studies based on white matter analysis. This paper presents an analysis on the impact of the variation of several acquisition parameters on these scalar measures with a novel double focus. First, a tractography-based approach is employed, motivated by the significant number of clinical studies that are carried out using this technique. Second, the consequences of simultaneous changes in multiple parameters are analyzed: number of gradient directions, b-value and voxel resolution. Results indicate that the FA is most affected by changes in the number of gradients and voxel resolution, while MD is specially influenced by variations in the b-value. Even if the choice of a tractography algorithm has an effect on the numerical values of the final scalar measures, the evolution of these measures when acquisition parameters are modified is parallel.

Comprehensive framework for accurate diffusion MRI parameter estimation

During the last decade, many approaches have been proposed for improving the estimation of diffusion measures. These techniques have already shown an increase in accuracy based on theoretical considerations, such as incorporating prior knowledge of the data distribution. The increased accuracy of diffusion metric estimators is typically observed in well-defined simulations, where the assumptions regarding properties of the data distribution are known to be valid. In practice, however, correcting for subject motion and geometric eddy current deformations alters the data distribution tremendously such that it can no longer be expressed in a closed form. The image processing steps that precede the model fitting will render several assumptions on the data distribution invalid, potentially nullifying the benefit of applying more advanced diffusion estimators. In this work, we present a generic diffusion model fitting framework that considers some statistics of diffusion MRI data. A central role in the framework is played by the conditional least squares estimator. We demonstrate that the accuracy of that particular estimator can generally be preserved, regardless the applied preprocessing steps, if the noise parameter is known a priori. To fulfill that condition, we also propose an approach for the estimation of spatially varying noise levels.

White matter integrity, fiber count, and other fallacies: the do's and don'ts of diffusion MRI

Diffusion-weighted MRI (DW-MRI) has been increasingly used in imaging neuroscience over the last decade. An early form of this technique, diffusion tensor imaging (DTI) was rapidly implemented by major MRI scanner companies as a scanner selling point. Due to the ease of use of such implementations, and the plausibility of some of their results, DTI was leapt on by imaging neuroscientists who saw it as a powerful and unique new tool for exploring the structural connectivity of human brain. However, DTI is a rather approximate technique, and its results have frequently been given implausible interpretations that have escaped proper critique and have appeared misleadingly in journals of high reputation. In order to encourage the use of improved DW-MRI methods, which have a better chance of characterizing the actual fiber structure of white matter, and to warn against the misuse and misinterpretation of DTI, we review the physics of DW-MRI, indicate currently preferred methodology, and explain the limits of interpretation of its results. We conclude with a list of 'Do's and Don'ts' which define good practice in this expanding area of imaging neuroscience.

Axial diffusivity and tensor shape as early markers to assess cerebral white matter damage caused by brain tumors using quantitative diffusion tensor tractography

AIMS

We investigated the usefulness of diffusion tensor tractography (DTT) for differentiating between histological pathologies and evaluating white matter (WM) damage resulting from brain tumors. We also sought to categorize the appearance of brain tumor-related WM tract changes.

METHODS

A total of 18 inpatients with intracranial neoplasms were enrolled. MRI examinations were performed at 3 T using an 8-channel phased array coil. DTT was reconstruction from the raw data of diffusion tensor imaging. WM tract-based analysis of the mean diffusivity (MD), eigenvalues (λ(1) , λ(2) , λ(3) ), and fractional anisotropy (FA) was performed by the manual placement of regions of interest (ROIs) on the color-coded FA maps using DTIStudio software. The axial diffusivity (DA, namely λ(1) ) and the tensor shape (Cl, namely (λ(1) -λ(2) )/3 (λ)) were also compared between groups. P values <0.05 were considered statistically significant.

RESULTS

In cases of low-grade glioma (LGG), the tracts adjacent to the tumors displayed the highest levels of invasion. Tract disruption was mainly observed in cases of high-grade glioma (HGG). We found significant differences regarding the FA, MD, DA, and radial diffusivity between ROIs in patients with LGG or HGG. There were also significant differences in DA and tensor shape (Cl) between patients with LGG and HGG.

CONCLUSION

Axial diffusivity and Cl may be useful early markers for differentiating between LGG and HGG.