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

A pitfall in the reconstruction of fibre ODFs using spherical deconvolution of diffusion MRI data

Diffusion weighted ( DW ) MRI facilitates non-invasive quantification of tissue microstructure and, in combination with appropriate signal processing, three-dimensional estimates of fibrous orientation. In recent years, attention has shifted from the diffusion tensor model, which assumes a unimodal Gaussian diffusion displacement profile to recover fibre orientation ( with various well-documented limitations ), towards more complex high angular resolution diffusion imaging ( HARDI ) analysis techniques. Spherical deconvolution ( SD ) approaches assume that the fibre orientation density function ( fODF ) within a voxel can be obtained by deconvolving a ‘common’ single fibre response function from the observed set of DW signals. In practice, this common response function is not known a priori and thus an estimated fibre response must be used. Here the establishment of this single-fibre response function is referred to as ‘calibration’. This work examines the vulnerability of two different SD approaches to inappropriate response function calibration: ( 1 ) constrained spherical harmonic deconvolution ( CSHD )—a technique that exploits spherical harmonic basis sets and ( 2 ) damped Richardson–Lucy ( dRL ) deconvolution—a technique based on the standard Richardson–Lucy deconvolution. Through simulations, the impact of a discrepancy between the calibrated diffusion profiles and the observed ( ‘Target’ ) DW-signals in both single and crossing-fibre configurations was investigated. The results show that CSHD produces spurious fODF peaks ( consistent with well known ringing artefacts ) as the discrepancy between calibration and target response increases, while dRL demonstrates a lower over-all sensitivity to miscalibration ( with a calibration response function for a highly anisotropic fibre being optimal ). However, dRL demonstrates a reduced ability to resolve low anisotropy crossing-fibres compared to CSHD. It is concluded that the range and spatial-distribution of expected single-fibre anisotropies within an image must be carefully considered to ensure selection of the appropriate algorithm, parameters and calibration. Failure to choose the calibration response function carefully may severely impact the quality of any resultant tractography

Computing and visualising intra-voxel orientation-specific relaxation-diffusion features in the human brain

Diffusion MRI techniques are used widely to study the characteristics of the human brain connectome in vivo. However, to resolve and characterise white matter (WM) fibres in heterogeneous MRI voxels remains a challenging problem typically approached with signal models that rely on prior information and constraints. We have recently introduced a 5D relaxation–diffusion correlation framework wherein multidimensional diffusion encoding strategies are used to acquire data at multiple echo‐times to increase the amount of information encoded into the signal and ease the constraints needed for signal inversion. Nonparametric Monte Carlo inversion of the resulting datasets yields 5D relaxation–diffusion distributions where contributions from different sub‐voxel tissue environments are separated with minimal assumptions on their microscopic properties. Here, we build on the 5D correlation approach to derive fibre‐specific metrics that can be mapped throughout the imaged brain volume. Distribution components ascribed to fibrous tissues are resolved, and subsequently mapped to a dense mesh of overlapping orientation bins to define a smooth orientation distribution function (ODF). Moreover, relaxation and diffusion measures are correlated to each independent ODF coordinate, thereby allowing the estimation of orientation‐specific relaxation rates and diffusivities. The proposed method is tested on a healthy volunteer, where the estimated ODFs were observed to capture major WM tracts, resolve fibre crossings, and, more importantly, inform on the relaxation and diffusion features along with distinct fibre bundles. If combined with fibre‐tracking algorithms, the methodology presented in this work has potential for increasing the depth of characterisation of microstructural properties along individual WM pathways

Robust processing of diffusion weighted image data

The work presented in this thesis comprises a proposed robust diffusion weighted magnetic resonance imaging (DW-MRI) pipeline, each chapter detailing a step designed to ultimately transform raw DW-MRI data into segmented bundles of coherent fibre ready for more complex analysis or manipulation. In addition to this pipeline we will also demonstrate, where appropriate, ways in which each step could be optimized for the maxillofacial region, setting the groundwork for a wider maxillofacial modelling project intended to aid surgical planning. Our contribution begins with RESDORE, an algorithm designed to automatically identify corrupt DW-MRI signal elements. While slower than the closest alternative, RESDORE is also far more robust to localised changes in SNR and pervasive image corruptions. The second step in the pipeline concerns the retrieval of accurate fibre orientation distribution functions (fODFs) from the DW-MRI signal. Chapter 4 comprises a simulation study exploring the application of spherical deconvolution methods to `generic' fibre; finding that the commonly used constrained spherical harmonic deconvolution (CSHD) is extremely sensitive to calibration but, if handled correctly, might be able to resolve muscle fODFs in vivo. Building upon this information, Chapter 5 conducts further simulations and in vivo image experimentation demonstrating that this is indeed the case, allowing us to demonstrate, for the first time, anatomically plausible reconstructions of several maxillofacial muscles. To complete the proposed pipeline, Chapter 6 then introduces a method for segmenting whole volume streamline tractographies into anatomically valid bundles. In addition to providing an accurate segmentation, this shape-based method does not require computationally expensive inter-streamline comparisons employed by other approaches, allowing the algorithm to scale linearly with respect to the number of streamlines within the dataset. This is not often true for comparison based methods which in the best case scale in higher linear time but more often by O(N2) complexity

Spatially Regularized Reconstruction of Fibre Orientation Distributions in the Presence of Isotropic Diffusion

The connectivity and structural integrity of the white matter of the brain is known to be implicated in a wide range of brain-related diseases and injuries. However, it is only since the advent of diffusion magnetic resonance imaging (dMRI) that researchers have been able to probe the miscrostructure of white matter in vivo. Presently, among a range of methods of dMRI, high angular resolution diffusion imaging (HARDI) is known to excel in its ability to provide reliable information about the local orientations of neural fasciculi (aka fibre tracts). It preserves the high angular resolution property of diffusion spectrum imaging (DSI) but requires less measurements. Meanwhile, as opposed to the more traditional diffusion tensor imaging (DTI), HARDI is capable of distinguishing the orientations of multiple fibres passing through a given spatial voxel. Unfortunately, the ability of HARDI to discriminate neural fibres that cross each other at acute angles is always limited. The limitation becomes the motivation to develop numerous post-processing tools, aiming at the improvement of the angular resolution of HARDI. Among such methods, spherical deconvolution (SD) is the one which attracts the most attentions. Due to its ill-posed nature, however, standard SD relies on a number of a priori assumptions needed to render its results unique and stable. In the present thesis, we introduce a novel approach to the problem of non-blind SD of HARDI signals, which does not only consider the existence of anisotropic diffusion component of HARDI signal but also explicitly take the isotropic diffusion component into account. As a result of that, in addition to reconstruction of fODFs, our algorithm can also yield a useful estimation of its related IDM, which quantifies a relative contribution of the isotropic diffusion component as well as its spatial pattern. Moreover, one of the principal contributions is to demonstrate the effectiveness of exploiting different prior models for regularization of the spatial-domain behaviours of the reconstructed fODFs and IDMs. Specifically, the fibre continuity model has been used to force the local maxima of the fODFs to vary consistently throughout the brain, whereas the bounded variation model has helped us to achieve piecewise smooth reconstruction of the IDMs. The proposed algorithm is formulated as a convex minimization problem, which admits a unique and stable minimizer. Moreover, using ADMM, we have been able to find the optimal solution via a sequence of simpler optimization problems, which are both computationally efficient and amenable to parallel computations. In a series of both in silico and in vivo experiments, we demonstrate how the proposed solution can be used to successfully overcome the effect of partial voluming, while preserving the spatial coherency of cerebral diffusion at moderate to severe noise levels. The performance of the proposed method is compared with that of several available alternatives, with the comparative results clearly supporting the viability and usefulness of our approach. Moreover, the results illustrate the power of applied spatial regularization terms

Compendio de métodos para caracterizar la geometría de los tejidos cerebrales a partir de imágenes de resonancia magnética por difusión del agua.

221 p.FIDMAG Hermanas Hospitalarias Research Foundation; CIBERSAM:Centro de Investigación Biomédica en Re

Trade-off between angular and spatial resolutions in in vivo fiber tractography

Tractography is becoming an increasingly popular method to reconstruct white matter connections in vivo. The diffusion MRI data that tractography is based on requires a high angular resolution to resolve crossing fibers whereas high spatial resolution is required to distinguish kissing from crossing fibers. However, scan time increases with increasing spatial and angular resolutions, which can become infeasible in clinical settings. Here we investigated the trade-off between spatial and angular resolutions to determine which of these factors is most worth investing scan time in. We created a unique diffusion MRI dataset with 1.0mm isotropic resolution and a high angular resolution (100 directions) using an advanced 3D diffusion-weighted multi-slab EPI acquisition. This dataset was reconstructed to create subsets of lower angular (75, 50, and 25 directions) and lower spatial (1.5, 2.0, and 2.5mm) resolution. Using all subsets, we investigated the effects of angular and spatial resolutions in three fiber bundles-the corticospinal tract, arcuate fasciculus and corpus callosum-by analyzing the volumetric bundle overlap and anatomical correspondence between tracts. Our results indicate that the subsets of 25 and 50 directions provided inferior tract reconstructions compared with the datasets with 75 and 100 directions. Datasets with spatial resolutions of 1.0, 1.5, and 2.0mm were comparable, while the lowest resolution (2.5mm) datasets had discernible inferior quality. In conclusion, we found that angular resolution appeared to be more influential than spatial resolution in improving tractography results. Spatial resolutions higher than 2.0mm only appear to benefit multi-fiber tractography methods if this is not at the cost of decreased angular resolution

New insights into cortico-basal-cerebellar connectome: clinical and physiological considerations

The current model of the basal ganglia system based on the 'direct', 'indirect' and 'hyperdirect' pathways provides striking predictions about basal ganglia function that have been used to develop deep brain stimulation approaches for Parkinson's disease and dystonia. The aim of this review is to challenge this scheme in light of new tract tracing information that has recently become available from the human brain using MRI-based tractography, thus providing a novel perspective on the basal ganglia system. We also explore the implications of additional direct pathways running from cortex to basal ganglia and between basal ganglia and cerebellum in the pathophysiology of movement disorders

Evaluating the accuracy of diffusion MRI models in white matter

Models of diffusion MRI within a voxel are useful for making inferences about the properties of the tissue and inferring fiber orientation distribution used by tractography algorithms. A useful model must fit the data accurately. However, evaluations of model-accuracy of some of the models that are commonly used in analyzing human white matter have not been published before. Here, we evaluate model-accuracy of the two main classes of diffusion MRI models. The diffusion tensor model (DTM) summarizes diffusion as a 3-dimensional Gaussian distribution. Sparse fascicle models (SFM) summarize the signal as a linear sum of signals originating from a collection of fascicles oriented in different directions. We use cross-validation to assess model-accuracy at different gradient amplitudes (b-values) throughout the white matter. Specifically, we fit each model to all the white matter voxels in one data set and then use the model to predict a second, independent data set. This is the first evaluation of model-accuracy of these models. In most of the white matter the DTM predicts the data more accurately than test-retest reliability; SFM model-accuracy is higher than test-retest reliability and also higher than the DTM, particularly for measurements with (a) a b-value above 1000 in locations containing fiber crossings, and (b) in the regions of the brain surrounding the optic radiations. The SFM also has better parameter-validity: it more accurately estimates the fiber orientation distribution function (fODF) in each voxel, which is useful for fiber tracking