Beyond Crossing Fibers: Tractography Exploiting Sub-voxel Fibre Dispersion and Neighbourhood Structure

In this paper we propose a novel algorithm which leverages models of white matter fibre dispersion to improve tractography. Tractography methods exploit directional information from diffusion weighted magnetic resonance (DW-MR) imaging to infer connectivity between different brain regions. Most tractography methods use a single direction (e.g. the principal eigenvector of the diffusion tensor) or a small set of discrete directions (e.g. from the peaks of an orientation distribution function) to guide streamline propagation. This strategy ignores the effects of within-bundle orientation dispersion, which arises from fanning or bending at the sub-voxel scale, and can lead to missing connections. Various recent DW-MR imaging techniques estimate the fibre dispersion in each bundle directly and model it as a continuous distribution. Here we introduce an algorithm to exploit this information to improve tractography. The algorithm further uses a particle filter to probe local neighbourhood structure during streamline propagation. Using information gathered from neighbourhood structure enables the algorithm to resolve ambiguities between converging and diverging fanning structures, which cannot be distinguished from isolated orientation distribution functions. We demonstrate the advantages of the new approach in synthetic experiments and in vivo data. Synthetic experiments demonstrate the effectiveness of the particle filter in gathering and exploiting neighbourhood information in recovering various canonical fibre configurations and experiments with in vivo brain data demonstrate the advantages of utilising dispersion in tractography, providing benefits in practical situations. © 2013 Springer-Verlag

NODDI-SH: a computational efficient NODDI extension for fODF estimation in diffusion MRI

Diffusion Magnetic Resonance Imaging (DMRI) is the only non-invasive imaging technique which is able to detect the principal directions of water diffusion as well as neurites density in the human brain. Exploiting the ability of Spherical Harmonics (SH) to model spherical functions, we propose a new reconstruction model for DMRI data which is able to estimate both the fiber Orientation Distribution Function (fODF) and the relative volume fractions of the neurites in each voxel, which is robust to multiple fiber crossings. We consider a Neurite Orientation Dispersion and Density Imaging (NODDI) inspired single fiber diffusion signal to be derived from three compartments: intracellular, extracellular, and cerebrospinal fluid. The model, called NODDI-SH, is derived by convolving the single fiber response with the fODF in each voxel. NODDI-SH embeds the calculation of the fODF and the neurite density in a unified mathematical model providing efficient, robust and accurate results. Results were validated on simulated data and tested on \textit{in-vivo} data of human brain, and compared to and Constrained Spherical Deconvolution (CSD) for benchmarking. Results revealed competitive performance in all respects and inherent adaptivity to local microstructure, while sensibly reducing the computational cost. We also investigated NODDI-SH performance when only a limited number of samples are available for the fitting, demonstrating that 60 samples are enough to obtain reliable results. The fast computational time and the low number of signal samples required, make NODDI-SH feasible for clinical application

Ball and rackets: inferring fiber fanning from diffusion-weighted MRI

A number of methods have been proposed for resolving crossing fibers from diffusion-weighted (DW) MRI. However, other complex fiber geometries have drawn minimal attention. In this study, we focus on fiber orientation dispersion induced by within-voxel fanning. We use a multi-compartment, model-based approach to estimate fiber dispersion. Bingham distributions are employed to represent continuous distributions of fiber orientations, centered around a main orientation, and capturing anisotropic dispersion. We evaluate the accuracy of the model for different simulated fanning geometries, under different acquisition protocols and we illustrate the high SNR and angular resolution needs. We also perform a qualitative comparison between our parametric approach and five popular non-parametric techniques that are based on orientation distribution functions (ODFs). This comparison illustrates how the same underlying geometry can be depicted by different methods. We apply the proposed model on high-quality, post-mortem macaque data and present whole-brain maps of fiber dispersion, as well as exquisite details on the local anatomy of fiber distributions in various white matter regions

Enabling Complex Fibre Geometries Using 3D Printed Axon-Mimetic Phantoms

Purpose: To introduce a method to create 3D-printed axon-mimetic phantoms with complex fibre orientations to characterise the performance of diffusion magnetic resonance imaging (MRI) models and representations in the presence of orientation dispersion. Methods: An extension to an open-source 3D printing package was created to produce a set of five 3D-printed axon-mimetic (3AM) phantoms with various combinations of bending and crossing fibre orientations. A two-shell diffusion MRI scan of the five phantoms in water was performed at 9.4T. Diffusion tensor imaging (DTI), diffusion kurtosis imaging (DKI), the ball and stick model, neurite orientation density and dispersion imaging (NODDI), and Bingham-NODDI were all fit to the resulting diffusion MRI data. A ground truth map of that phantom’s crossing angles and/or arc radius was registered to the diffusion-weighted images. Metrics from each model and representation were compared to the ground-truth maps, and a quadratic regression model was fit to each combination of output metric and ground-truth metric. Results: The mean diffusivity (MD) metric defined by DTI was insensitive to crossing angle but increased with fibre curvature. Axial diffusivity (AD) decreased with increasing crossing angle. DKI’s diffusivity metrics replicated the trends seen in DTI, and its mean kurtosis (MK) metric decreased with fibre curvature, except in regions with high crossing angles. The estimated stick volume fraction in the ball and stick model decreased with increasing fibre curvature and crossing angle. NODDI’s intra-neurite volume fraction was insensitive to crossing angle, and its orientation dispersion index (ODI) was correlated to crossing angle. Bingham-NODDI’s intra-neurite volume fraction was also insensitive to crossing angle, while its primary ODI (ODIP) was also correlated to crossing angle and its secondary ODI (ODIS) was insensitive to crossing angle. For both NODDI models, the volume fractions of the extra-neurite and CSF compartments had low reliability with no clear relationship to crossing angle. Conclusion: Inexpensive 3D-printed axon-mimetic phantoms can be used to investigate the effect of fibre curvature and crossings on diffusion MRI representations and models of diffusion signal. The dependence of several representations and models on fibre dispersion/crossing was investigated. As expected, Bingham-NODDI was best able to characterise planar fibre dispersion in the phantoms

New tractography methods based on parametric models of white matter fibre dispersion

Diffusion weighted magnetic resonance imaging (DW-MRI) is a powerful imaging technique that can probe the complex structure of the body, revealing structural trends which exist at scales far below the voxel resolution. Tractography utilises the information derived from DW-MRI to examine the structure of white matter. Using information derived from DW-MRI, tractography can estimate connectivity between distinct, functional cortical and sub-cortical regions of grey matter. Understanding how seperate functional regions of the brain are connected as part of a network is key to understanding how the brain works. Tractography has been used to deliniate many known white matter structures and has also revealed structures not fully understood from anatomy due to limitations of histological examination. However, there still remain many shortcomings of tractography, many anatomical features for which tractography algorithms are known to fail, which leads to discrepancies between known anatomy and tractography results. With the aim of approaching a complete picture of the human connectome via tractography, we seek to address the shortcomings in current tractography techniques by exploiting new advances in modelling techniques used in DW-MRI, which provide more accurate representation of underlying white matter anatomy. This thesis introduces a methodology for fully utilising new tissue models in DWMRI to improve tractography. It is known from histology that there are regions of white matter where fibres disperse or curve rapidly at length scales below the DW-MRI voxel resolution. One area where dispersion is particularly prominent is the corona radiata. New DW-MRI models capture dispersion utilising specialised parametric probability distributions. We present novel tractography algorithms utilising these parametric models of dispersion in tractography to improve connectivity estimation in areas of dispersing fibres. We first present an algorithm utilising the the new parametric models of dispersion for tractography in a simple Bayesian framework. We then present an extension to this algorithm which introduces a framework to pool neighbourhood information from multiple voxels in the neighbournhood surrounding the tract in order to better estimate connectivity, introducing the new concept of the neighbourhood-informed orientation distribution function (NI-ODF). Specifically, using neighbourhood exploration we address the ambiguity arising in ’fanning polarity’. In regions of dispersing fibres, the antipodal symmetry inherent in DW-MRI makes it impossible to resolve the polarity of a dispersing fibre configuration from a local voxel-wise model in isolation, by pooling information from neighbouring voxels, we show that this issue can be addressed. We evaluate the newly proposed tractography methods using synthetic phantoms simulating canonical fibre configurations and validate the ability to effectively navigate regions of dispersing fibres and resolve fanning polarity. We then validate that the algorithms perform effectively in real in vivo data, using DW-MRI data from 5 healthy subjects. We show that by utilising models of dispersion, we recover a wider range of connectivity compared to other standard algorithms when tracking through an area of the brain known to have significant white fibre dispersion - the corona radiata. We then examine the impact of the new algorithm on global connectivity estimates in the brain. We find that whole brain connectivity networks derived using the new tractography method feature strong connectivity between frontal lobe regions. This is in contrast to networks derived using competing tractography methods which do not account for sub-voxel fibre dispersion. We also compare thalamo-cortical connectivity estimated using the newly proposed tractography method and compare with a compteing tractography method, finding that the recovered connectivity profiles are largely similar, with some differences in thalamo-cortical connections to regions of the frontal lobe. The results suggest that fibre dispersion is an important structural feature to model in the basis of a tractography algorithm, as it has a strong effect on connectivity estimation

Validation of NODDI estimation of dispersion anisotropy in V1 of the human neocortex

This work validates the estimation of neurite dispersion anisotropy in the brain, using Bingham-NODDI [1], an extension of the diffusion MRI technique called NODDI [2]. The original NODDI provides indices of neurite (axons and dendrites) morphology that are sensitive and specific to microstructural changes [3-7]. Bingham-NODDI additionally allows the estimation of neurite dispersion anisotropy, which can enhance the accuracy of tractography algorithms [8]. The in vivo feasibility of Bingham-NODDI has been evaluated in [1]. The present study validates its indices using high-resolution ex vivo imaging data of the human primary visual cortex (V1), a well characterised region of the neocortex known to include fibres that fan or bend into the cortical layers

Estimating uncertainty in multiple fibre reconstructions

Diffusion magnetic resonance imaging (MRI) is a technique that allows us to probe the microstructure of materials. The standard technique in diffusion MRI is diffusion tensor imaging (DTI). However, DTI can only model a single fibre orientation and fails in regions of complex microstructure. Multiple-fibre algorithms aim to overcome this limitation of DTI, but there remain many questions about which multiple-fibre algorithms are most promising and how best to exploit them in tractography. This work focuses on exploring the potential of multiple-fibre reconstructions and preparing them for transfer to the clinical arena. We provide a standardised framework for comparing multiple-fibre algorithms and use it for a robust comparison of standard algorithms, such as persistent angular structure (PAS) MRI, spherical deconvolution (SD), maximum entropy SD (MESD), constrained SD (CSD) and QBall. An output of this framework is the parameter settings of the algorithms that maximise the consistency of reconstructions. We show that non-linear algorithms, and CSD in particular, provide the most consistent reconstructions. Next, we investigate features of the reconstructions that can be exploited to improve tractography. We show that the peak shapes of multiple-fibre reconstructions can be used to predict anisotropy in the uncertainty of fibre-orientation estimates. We design an experiment that exploits this information in the probabilistic index of connectivity (PICo) tractography algorithm. We then compare PICo tractography results using information about peak shape and sharpness to estimate uncertainty with PICo results using only the peak sharpness to estimate uncertainty and show structured differences. The final contribution of this work is a robust algorithm for calibrating PICo that overcomes some of the limitations of the original algorithm. We finish with some early exploratory work that aims to estimate the distribution of fibre-orientations in a voxel using features of the reconstruction