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

Connectivity-enhanced diffusion analysis reveals white matter density disruptions in first episode and chronic schizophrenia.

Reduced fractional anisotropy (FA) is a well-established correlate of schizophrenia, but it remains unclear whether these tensor-based differences are the result of axon damage and/or organizational changes and whether the changes are progressive in the adult course of illness. Diffusion MRI data were collected in 81 schizophrenia patients (54 first episode and 27 chronic) and 64 controls. Analysis of FA was combined with "fixel-based" analysis, the latter of which leverages connectivity and crossing-fiber information to assess both fiber bundle density and organizational complexity (i.e., presence and magnitude of off-axis diffusion signal). Compared with controls, patients with schizophrenia displayed clusters of significantly lower FA in the bilateral frontal lobes, right dorsal centrum semiovale, and the left anterior limb of the internal capsule. All FA-based group differences overlapped substantially with regions containing complex fiber architecture. FA within these clusters was positively correlated with principal axis fiber density, but inversely correlated with both secondary/tertiary axis fiber density and voxel-wise fiber complexity. Crossing fiber complexity had the strongest (inverse) association with FA (r = -0.82). When crossing fiber structure was modeled in the MRtrix fixel-based analysis pipeline, patients exhibited significantly lower fiber density compared to controls in the dorsal and posterior corpus callosum (central, postcentral, and forceps major). Findings of lower FA in patients with schizophrenia likely reflect two inversely related signals: reduced density of principal axis fiber tracts and increased off-axis diffusion sources. Whereas the former confirms at least some regions where myelin and or/axon count are lower in schizophrenia, the latter indicates that the FA signal from principal axis fiber coherence is broadly contaminated by macrostructural complexity, and therefore does not necessarily reflect microstructural group differences. These results underline the need to move beyond tensor-based models in favor of acquisition and analysis techniques that can help disambiguate different sources of white matter disruptions associated with schizophrenia

Nonparametric tests of structure for high angular resolution diffusion imaging in Q-space

High angular resolution diffusion imaging data is the observed characteristic function for the local diffusion of water molecules in tissue. This data is used to infer structural information in brain imaging. Nonparametric scalar measures are proposed to summarize such data, and to locally characterize spatial features of the diffusion probability density function (PDF), relying on the geometry of the characteristic function. Summary statistics are defined so that their distributions are, to first-order, both independent of nuisance parameters and also analytically tractable. The dominant direction of the diffusion at a spatial location (voxel) is determined, and a new set of axes are introduced in Fourier space. Variation quantified in these axes determines the local spatial properties of the diffusion density. Nonparametric hypothesis tests for determining whether the diffusion is unimodal, isotropic or multi-modal are proposed. More subtle characteristics of white-matter microstructure, such as the degree of anisotropy of the PDF and symmetry compared with a variety of asymmetric PDF alternatives, may be ascertained directly in the Fourier domain without parametric assumptions on the form of the diffusion PDF. We simulate a set of diffusion processes and characterize their local properties using the newly introduced summaries. We show how complex white-matter structures across multiple voxels exhibit clear ellipsoidal and asymmetric structure in simulation, and assess the performance of the statistics in clinically-acquired magnetic resonance imaging data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS441 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fuzzy Fibers: Uncertainty in dMRI Tractography

Fiber tracking based on diffusion weighted Magnetic Resonance Imaging (dMRI) allows for noninvasive reconstruction of fiber bundles in the human brain. In this chapter, we discuss sources of error and uncertainty in this technique, and review strategies that afford a more reliable interpretation of the results. This includes methods for computing and rendering probabilistic tractograms, which estimate precision in the face of measurement noise and artifacts. However, we also address aspects that have received less attention so far, such as model selection, partial voluming, and the impact of parameters, both in preprocessing and in fiber tracking itself. We conclude by giving impulses for future research

Insight into the fundamental trade-offs of diffusion MRI from polarization-sensitive optical coherence tomography in ex vivo human brain

In the first study comparing high angular resolution diffusion MRI (dMRI) in the human brain to axonal orientation measurements from polarization-sensitive optical coherence tomography (PSOCT), we compare the accuracy of orientation estimates from various dMRI sampling schemes and reconstruction methods. We find that, if the reconstruction approach is chosen carefully, single-shell dMRI data can yield the same accuracy as multi-shell data, and only moderately lower accuracy than a full Cartesian-grid sampling scheme. Our results suggest that current dMRI reconstruction approaches do not benefit substantially from ultra-high b-values or from very large numbers of diffusion-encoding directions. We also show that accuracy remains stable across dMRI voxel sizes of 1 ​mm or smaller but degrades at 2 ​mm, particularly in areas of complex white-matter architecture. We also show that, as the spatial resolution is reduced, axonal configurations in a dMRI voxel can no longer be modeled as a small set of distinct axon populations, violating an assumption that is sometimes made by dMRI reconstruction techniques. Our findings have implications for in vivo studies and illustrate the value of PSOCT as a source of ground-truth measurements of white-matter organization that does not suffer from the distortions typical of histological techniques.Published versio

Probing white-matter microstructure with higher-order diffusion tensors and susceptibility tensor MRI.

Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility tensor imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion tensor model and also with the higher order tensor model based on the cumulant expansion. Frequency shift and susceptibility tensor were measured with quantitative susceptibility mapping and susceptibility tensor imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains

Beyond fractional anisotropy: Extraction of bundle-specific structural metrics from crossing fiber models

Diffusion MRI (dMRI) measurements are used for inferring the microstructural properties of white matter and to reconstruct fiber pathways. Very often voxels contain complex fiber configurations comprising multiple bundles, rendering the simple diffusion tensor model unsuitable. Multi-compartment models deliver a convenient parameterization of the underlying complex fiber architecture, but pose challenges for fitting and model selection. Spherical deconvolution, in contrast, very economically produces a fiber orientation density function (fODF) without any explicit model assumptions. Since, however, the fODF is represented by spherical harmonics, a direct interpretation of the model parameters is impossible. Based on the fact that the fODF can often be interpreted as superposition of multiple peaks, each associated to one relatively coherent fiber population (bundle), we offer a solution that seeks to combine the advantages of both approaches: first the fiber configuration is modeled as fODF represented by spherical harmonics and then each of the peaks is parameterized separately in order to characterize the underlying bundle. In this work, the fODF peaks are approximated by Bingham distributions, capturing first and second-order statistics of the fiber orientations, from which we derive metrics for the parametric quantification of fiber bundles. We propose meaningful relationships between these measures and the underlying microstructural properties. We focus on metrics derived directly from properties of the Bingham distribution, such as peak length, peak direction, peak spread, integral over the peak, as well as a metric derived from the comparison of the largest peaks, which probes the complexity of the underlying microstructure. We compare these metrics to the conventionally used fractional anisotropy (FA) and show how they may help to increase the specificity of the characterization of microstructural properties. While metric relying on the first moments of the Bingham distributions provide relatively robust results, second-order metrics representing the peak spread are only meaningful, if the SNR is very high and no fiber crossings are present in the voxel

Development of Advanced, Clinically Feasible Neuroimaging Methodology with Diffusional Kurtosis Imaging

Diffusion MRI (dMRI) is a powerful, non-invasive tool for probing the structural organization of the human brain. Quantitative dMRI analyses provide unique capabilities for the characterization of tissue microstructure as well as imaging contrast that is not available to other modalities. White matter tractography relies on dMRI and is currently the only non-invasive technique for mapping structural connections in the human brain. In this chapter, we will describe diffusional kurtosis imaging, an effective and versatile dMRI technique, and discuss a clinical problem in temporal lobe epilepsy (TLE) which is insurmountable with current diagnostic approaches. Subsequent chapters will further develop the capabilities of DKI and demonstrate how it may be particularly well suited to overcome current barriers to care in the clinical management of TLE