ND-Track: Tractography utilising parametric models of white matter fibre orientation dispersion

This work develops a tractography algorithm to leverage fibre dispersion estimates derived from fitting parametric models of orientation dispersion to diffusion data. Tractography techniques are powerful tools to probe white matter (WM) connectivity non-invasively. Most current techniques follow a small number of discrete directions per voxel to identify WM connections. This approach addresses the limitation of traditional DTI-based tractography for regions with crossing fibres. However, it remains an oversimplification for regions with fanning and bending configurations, where the underlying fibre orientation distributions are continuous rather than discrete [2]. Following only a discrete set of directions in this case misrepresents the underlying anatomy and is likely to result in false negative connectivity estimates. Recent parameterized models of fibre dispersion represent such sub-voxel fibre architecture more realistically and provide more accurate estimates of dispersion than non-parametric techniques such as spherical deconvolution, which are vulnerable to noise [3]. Here, we present a new tractography algorithm, hereby referred to as ND-Track (Neurite Dispersion Tracking), that leverages directional information gathered from parametric models of dispersion. We investigate the advantages of tracking with dispersion measures on a simple phantom and in in-vivo data, tracking through the coronal radiata, a region known to exhibit a significant degree of fibre dispersion. We further demonstrate that this approach does not compromise the tracking of the WM pathways for which the standard technique works well

Imaging plus X: multimodal models of neurodegenerative disease

PURPOSE OF REVIEW: This article argues that the time is approaching for data-driven disease modelling to take centre stage in the study and management of neurodegenerative disease. The snowstorm of data now available to the clinician defies qualitative evaluation; the heterogeneity of data types complicates integration through traditional statistical methods; and the large datasets becoming available remain far from the big-data sizes necessary for fully data-driven machine-learning approaches. The recent emergence of data-driven disease progression models provides a balance between imposed knowledge of disease features and patterns learned from data. The resulting models are both predictive of disease progression in individual patients and informative in terms of revealing underlying biological patterns. RECENT FINDINGS: Largely inspired by observational models, data-driven disease progression models have emerged in the last few years as a feasible means for understanding the development of neurodegenerative diseases. These models have revealed insights into frontotemporal dementia, Huntington's disease, multiple sclerosis, Parkinson's disease and other conditions. For example, event-based models have revealed finer graded understanding of progression patterns; self-modelling regression and differential equation models have provided data-driven biomarker trajectories; spatiotemporal models have shown that brain shape changes, for example of the hippocampus, can occur before detectable neurodegeneration; and network models have provided some support for prion-like mechanistic hypotheses of disease propagation. The most mature results are in sporadic Alzheimer's disease, in large part because of the availability of the Alzheimer's disease neuroimaging initiative dataset. Results generally support the prevailing amyloid-led hypothetical model of Alzheimer's disease, while revealing finer detail and insight into disease progression. SUMMARY: The emerging field of disease progression modelling provides a natural mechanism to integrate different kinds of information, for example from imaging, serum and cerebrospinal fluid markers and cognitive tests, to obtain new insights into progressive diseases. Such insights include fine-grained longitudinal patterns of neurodegeneration, from early stages, and the heterogeneity of these trajectories over the population. More pragmatically, such models enable finer precision in patient staging and stratification, prediction of progression rates and earlier and better identification of at-risk individuals. We argue that this will make disease progression modelling invaluable for recruitment and end-points in future clinical trials, potentially ameliorating the high failure rate in trials of, e.g., Alzheimer's disease therapies. We review the state of the art in these techniques and discuss the future steps required to translate the ideas to front-line application.This is an open access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License 4.0 (CCBY-NC-ND), where it is permissible to download and share the work provided it is properly cited. The work cannot be changed in any way or used commercially without permission from the journal. http://creativecommons.org/licenses/by-nc-nd/4.0

Optimising oscillating waveform-shape for pore size sensitivity in diffusion-weighted MR

Optimising the shape of a generalised gradient waveform (GEN) in diffusion-weighted MR has been shown to, in theory, greatly increase sensitivity to pore size. The broad class of optimised shapes takes simple oscillatory forms. To speed up convergence of the optimisation, improve computation times and make the waveforms more practical, here we explore various oscillatory waveforms constructed from trapezoidal and sinusoidal shapes and compare their performance with the optimised GEN waveform. The oscillating waveforms are optimised to maximise sensitivity to parameters, such as axon radius, intra-cellular volume fraction and diffusion constants, of a simple white matter model. Simulation experiments find that all oscillating waveforms we tried perform significantly better than the original generalised waveform due to the improved convergence of the optimisation. Differences among the oscillating shapes however are very small and although a truncated sinusoidal waveform consistently gives the lowest cost function, no significant difference in the estimated model parameters was found. Therefore the simplest choice, i.e. the trapezoidal parametrisation, seems sufficient for most practical purposes

Parametric Probability Distribution Functions for Axon Diameters of Corpus Callosum

Axon diameter is an important neuroanatomical characteristic of the nervous system that alters in the course of neurological disorders such as multiple sclerosis. Axon diameters vary, even within a fiber bundle, and are not normally distributed. An accurate distribution function is therefore beneficial, either to describe axon diameters that are obtained from a direct measurement technique (e.g., microscopy), or to infer them indirectly (e.g., using diffusion-weighted MRI). The gamma distribution is a common choice for this purpose (particularly for the inferential approach) because it resembles the distribution profile of measured axon diameters which has been consistently shown to be non-negative and right-skewed. In this study we compared a wide range of parametric probability distribution functions against empirical data obtained from electron microscopy images. We observed that the gamma distribution fails to accurately describe the main characteristics of the axon diameter distribution, such as location and scale of the mode and the profile of distribution tails. We also found that the generalized extreme value distribution consistently fitted the measured distribution better than other distribution functions. This suggests that there may be distinct subpopulations of axons in the corpus callosum, each with their own distribution profiles. In addition, we observed that several other distributions outperformed the gamma distribution, yet had the same number of unknown parameters; these were the inverse Gaussian, log normal, log logistic and Birnbaum-Saunders distributions

A spatial variation model of white matter microstructure

In this study, we introduce a new technique to model the variation of microstructural parameters across speci c brain regions. We use a simple model of di usion in each voxel, but model the variation of parameters across the region using penalised splines. We t the whole region model directly to the di usion-weighted signals. We test the tech- nique on the mid-sagittal section of the corpus callosum (CC) using a di usion MRI data set with distinct age groups. The method detects di erences and separates the groups

Double oscillating diffusion encoding and sensitivity to microscopic anisotropy

PURPOSE: To introduce a novel diffusion pulse sequence, namely double oscillating diffusion encoding (DODE), and to investigate whether it adds sensitivity to microscopic diffusion anisotropy (µA) compared to the well-established double diffusion encoding (DDE) methodology. METHODS: We simulate measurements from DODE and DDE sequences for different types of microstructures exhibiting restricted diffusion. First, we compare the effect of varying pulse sequence parameters on the DODE and DDE signal. Then, we analyse the sensitivity of the two sequences to the microstructural parameters (pore diameter and length) which determine µA. Finally, we investigate specificity of measurements to particular substrate configurations. RESULTS: Simulations show that DODE sequences exhibit similar signal dependence on the relative angle between the two gradients as DDE sequences, however, the effect of varying the mixing time is less pronounced. The sensitivity analysis shows that in substrates with elongated pores and various orientations, DODE sequences increase the sensitivity to pore diameter, while DDE sequences are more sensitive to pore length. Moreover, DDE and DODE sequence parameters can be tailored to enhance/suppress the signal from a particular range of substrates. CONCLUSIONS: A combination of DODE and DDE sequences maximize sensitivity to µA, compared to using just the DDE method. Magn Reson Med, 2016. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine

The development and sea trials of a subsea holographic camera for large volume in-situ recording of marine organisms

We describe the development, construction and sea testing of an underwater holographic camera (HoloCam) for in situ recording of marine organisms and particles in large volumes of sea water. HoloCam comprises a laser, power supply, holographic recording optics and plate holders, a water-tight housing and a support frame. Added to this are control electronics such that the entire camera is remotely operable and controllable from ship or dock-side. Uniquely the camera can simultaneously record both in-line and off-axis holograms using a pulsed frequency doubled Nd-YAG laser. In-line holography is capable of producing images of organisms with a resolution of better than 10 Pm (at concentrations up to a few thousand per cubic centimetre at the smallest sizes). Off-axis holograms of aquatic systems of up to 50,000 cm3 volume, have been recorded. Following initial laboratory testing, the holo-camera was evaluated in an observation tank and ultimately was tested in Loch Etive, Scotland. In-line and off-axis holograms were recorded to a depth of 100 m. We will present results on the test dives and evaluation of the camera performance

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

Branched Polymers and Hyperplane Arrangements

Original manuscript December 17, 2009We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie (Ann Math, 158:1019–1039, 2003), and Kenyon and Winkler (Am Math Mon, 116(7):612–628, 2009) to any central hyperplane arrangement A A . The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement A A is expressed through the value of the characteristic polynomial of A A at 0. We give a more general definition of the space of branched polymers, where we do not require connectivity, and introduce the notion of q-volume for it, which is expressed through the value of the characteristic polynomial of A A at −q − q . Finally, we relate the volume of the space of branched polymers to broken circuits and show that the cohomology ring of the space of branched polymers is isomorphic to the Orlik–Solomon algebra.National Science Foundation (U.S.) (Grant DMS 6923772)National Science Foundation (U.S.) (CAREER Award DMS 0504629

Data-Driven Sequence of Changes to Anatomical Brain Connectivity in Sporadic Alzheimer's Disease

Model-based investigations of transneuronal spreading mechanisms in neurodegenerative diseases relate the pattern of pathology severity to the brain’s connectivity matrix, which reveals information about how pathology propagates through the connectivity network. Such network models typically use networks based on functional or structural connectivity in young and healthy individuals, and only end-stage patterns of pathology, thereby ignoring/excluding the effects of normal aging and disease progression. Here, we examine the sequence of changes in the elderly brain’s anatomical connectivity over the course of a neurodegenerative disease. We do this in a data-driven manner that is not dependent upon clinical disease stage, by using event-based disease progression modeling. Using data from the Alzheimer’s Disease Neuroimaging Initiative dataset, we sequence the progressive decline of anatomical connectivity, as quantified by graph-theory metrics, in the Alzheimer’s disease brain. Ours is the first single model to contribute to understanding all three of the nature, the location, and the sequence of changes to anatomical connectivity in the human brain due to Alzheimer’s disease. Our experimental results reveal new insights into Alzheimer’s disease: that degeneration of anatomical connectivity in the brain may be a viable, even early, biomarker and should be considered when studying such neurodegenerative diseases