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This volume gathers papers presented at the Workshop on Computational Diffusion MRI (CDMRI’18), which was held under the auspices of the International Conference on Medical Image Computing and Computer Assisted Intervention in Granada, Spain on September 20, 2018.
It presents the latest developments in the highly active and rapidly growing field of diffusion MRI. The reader will find papers on a broad range of topics, from the mathematical foundations of the diffusion process and signal generation, to new computational methods and estimation techniques for the in-vivo recovery of microstructural and connectivity features, as well as harmonisation and frontline applications in research and clinical practice. The respective papers constitute invited works from high-profile researchers with a specific focus on three topics that are now gaining momentum within the diffusion MRI community: i) machine learning for diffusion MRI; ii) diffusion MRI outside the brain (e.g. in the placenta); and iii) diffusion MRI for multimodal imaging.
The book shares new perspectives on the latest research challenges for those currently working in the field, but also offers a valuable starting point for anyone interested in learning computational techniques in diffusion MRI. It includes rigorous mathematical derivations, a wealth of full-colour visualisations, and clinically relevant results. As such, it will be of interest to researchers and practitioners in the fields of computer science, MRI physics and applied mathematics alike.

Inhaltsverzeichnis

Towards Optimal Sampling in Diffusion MRI

Abstract
The methodology outlined in this chapter is intended to provide a tool for the generation of sets of MRI diffusion encoding waveforms that are optimal for tissue micro-structure estimation. The methodology presented has five distinct components: 1. Defining the class of waveforms allowed, i.e. defining the measurement space. 2. Specifying the expected distribution of microstructure features present in the targeted tissue. 3. Learning the metric in the chosen measurement space. 4. Designing a continuous parametric functional suitable for approximation of the estimated metric. 5. Finding a distribution of a chosen number of waveforms that is optimal given the continuous metric. The tissue is modeled as a collection of simple elliptical compartments with varying size and shape. Two waveform classes are tested: The classical Stejskal-Tanner waveform and an idealized Laun long-short waveform. The estimation of the metric is based on correlations between measurements obtained at given points in the measurement space using an information theoretical approach. Optimal sets of waveforms are found using a simulated annealing inspired energy minimizing approach. The superior performance of the methodology is demonstrated for a number of different cases by means of simulations.
Hans Knutsson

Joint Image Reconstruction and Phase Corruption Maps Estimation in Multi-shot Echo Planar Imaging

Abstract
Multishot echo-planar imaging is a common strategy in diffusion Magnetic Resonance Imaging to reduce the artifacts caused by the long echo-trains in single-shot acquisitions. However, it suffers from shot-to-shot phase discrepancies associated to subject motion, which can notably degrade the quality of the reconstructed image. Consequently, some type of motion-induced phases error correction needs to be incorporated into the reconstruction process. In this paper we focus on ridig motion induced errors, which have proved to corrupt the shots with linear phase maps. By incorporating this prior knowledge, we propose a maximum likelihood formulation that estimates both the parameters that characterize the linear phase maps and the reconstructed image. In order to make the problem tractable, we follow a greedy iterative procedure that alternates between the estimation of each of them. Simulation data are used to illustrate the performance of the method against state-of-the-art alternatives.
Iñaki Rabanillo, Santiago Sanz-Estébanez, Santiago Aja-Fernández, Joseph Hajnal, Carlos Alberola-López, Lucilio Cordero-Grande

Return-to-Axis Probability Calculation from Single-Shell Acquisitions

Abstract
The Ensemble Average diffusion Propagator (EAP) provides relevant microstructural information and meaningful descriptive maps of the white matter previously obscured by traditional techniques like the Diffusion Tensor. The direct estimation of the EAP requires a dense sampling of the $${\mathbf {q}}$$-space data. Although alternative techniques have been proposed, all of them require a high number of gradients and several b-values to be calculated. Once the EAP is calculated scalar measures must be directly derived. In this work, we propose a method to drastically reduce the number of points needed for the estimation of one of the measures, the return-to-axis probability (RTAP), efficiently estimating the $${\mathbf {q}}$$-space diffusion measure from a single shell acquisition. The proposal avoids the calculation of the EAP assuming that the diffusion does not depend on the radial direction. By applying this assumption locally, we achieve closed-form expressions of the measure using information from only one b-value, compatible with acquisitions protocols used for HARDI. Results have shown that the measures are highly correlated with the same measures calculated with state-of-the-art EAP estimators and highly accelerated execution times.
Santiago Aja-Fernández, Antonio Tristán-Vega, Malwina Molendowska, Tomasz Pieciak, Rodrigo de Luis-García

A Novel Spatial-Angular Domain Regularisation Approach for Restoration of Diffusion MRI

Abstract
In this paper we tackle the problem of regularisation for inverse problems in single shell diffusion weighted image restoration. Our aim is to recover a high-resolution and denoised DWI signal, prior to any model fitting. The main contribution of our method is the combination of two regularization terms, one using the information arising from the spatial domain, hence analysing the single image, while the other uses information coming from the angular domain, thus using the relationships between the values along different directions within a single voxel. We show that our novel regularization method outperforms widely used and recent DWI denoising algorithms. Additionally we demonstrate that the proposed regularisation technique can be successfully applied to the super-resolution reconstruction of high-resolution volume from thick-slice data. Both scenarios are tested on simulated phantom and real DWI data.
Alessandro Mella, Alessandro Daducci, Giandomenico Orlandi, Jean-Philippe Thiran, Maria Deprez, Merixtell Bach Cuadra

Dmipy, A Diffusion Microstructure Imaging Toolbox in Python to Improve Research Reproducibility

Abstract
Non-invasive estimation of brain white matter microstructure features using diffusion MRI—otherwise known as Microstructure Imaging—has become an increasingly diverse and complicated field over the last decade. Multi-compartment-based models have been a popular approach to estimate these features. In this work, we present Diffusion Microstructure Imaging in Python (Dmipy), a diffusion MRI toolbox which allows accessing any multi-compartment-based model and robustly estimates these important features from single-shell, multi-shell, and multi-diffusion time, and multi-TE data. Dmipy follows a building block-based philosophy to microstructure imaging, meaning a multi-compartment model can be constructed and fitted to dMRI data using any combination of underlying tissue models, axon dispersion-or diameter distributions, and optimization algorithms using less than 10 lines of code, thus helps improve research reproducibility. In describing the toolbox, we show how Dmipy enables to easily design microstructure models and offers to the users the freedom to choose among different optimization strategies. We finally present three advanced examples of highly complex modeling approaches which are made easy using Dmipy.
Abib Alimi, Rutger Fick, Demian Wassermann, Rachid Deriche

Tissue Segmentation Using Sparse Non-negative Matrix Factorization of Spherical Mean Diffusion MRI Data

Abstract
In this paper, we present a method based on sparse non-negative matrix factorization (NMF) for brain tissue segmentation using diffusion MRI (DMRI) data. Unlike existing NMF-based approaches, in our method NMF is applied to the spherical mean data, computed on a per-shell basis, instead of the original diffusion-weighted images. This is motivated by the fact that the spherical mean is independent of the fiber orientation distribution and is only dependent on tissue microstructure. Applying NMF to the spherical mean data will hence allow tissue signal separation based solely on the microstructural properties, unconfounded by factors such as fiber dispersion and crossing. We show results explaining why applying NMF directly on the diffusion-weighted images fails and why our method is able to yield the expected outcome, producing tissue segmentation with greater accuracy.
Peng Sun, Ye Wu, Geng Chen, Jun Wu, Dinggang Shen, Pew-Thian Yap

A Closed-Form Solution of Rotation Invariant Spherical Harmonic Features in Diffusion MRI

Abstract
Rotation invariant features are an indispensable tool for characterizing diffusion Magnetic Resonance Imaging (MRI) and in particular for brain tissue microstructure estimation. In this work, we propose a new mathematical framework for efficiently calculating a complete set of such invariants from any spherical function. Specifically, our method is based on the spherical harmonics series expansion of a given function of any order and can be applied directly to the resulting coefficients by performing a simple integral operation analytically. This enable us to derive a general closed-form equation for the invariants. We test our invariants on the diffusion MRI fiber orientation distribution function obtained from the diffusion signal both in-vivo and in synthetic data. Results show how it is possible to use these invariants for characterizing the white matter using a small but complete set of features.
Mauro Zucchelli, Samuel Deslauriers-Gauthier, Rachid Deriche

Orientation-Dispersed Apparent Axon Diameter via Multi-Stage Spherical Mean Optimization

Abstract
The estimation of the apparent axon diameter (AAD) via diffusion MRI is affected by the incoherent alignment of single axons around its axon bundle direction, also known as orientational dispersion. The simultaneous estimation of AAD and dispersion is challenging and requires the optimization of many parameters at the same time. We propose to reduce the complexity of the estimation with an multi-stage approach, inspired to alternate convex search, that separates the estimation problem into simpler ones, thus avoiding the estimation of all the relevant model parameters at once. The method is composed of three optimization stages that are iterated, where we separately estimate the volume fractions, diffusivities, dispersion, and mean AAD, using a Cylinder and Zeppelin model. First, we use multi-shell data to estimate the undispersed axon micro-environment’s signal fractions and diffusivities using the spherical mean technique; then, to account for dispersion, we use the obtained micro-environment parameters to estimate a Watson axon orientation distribution; finally, we use data acquired perpendicularly to the axon bundle direction to estimate the mean AAD and updated signal fractions, while fixing the previously estimated diffusivity and dispersion parameters. We use the estimated mean AAD to initiate the following iteration. We show that our approach converges to good estimates while being more efficient than optimizing all model parameters at once. We apply our method to ex-vivo spinal cord data, showing that including dispersion effects results in mean apparent axon diameter estimates that are closer to their measured histological values.
Marco Pizzolato, Demian Wassermann, Rachid Deriche, Jean-Philippe Thiran, Rutger Fick

Current Applications and Future Promises of Machine Learning in Diffusion MRI

Abstract
Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI) explores the random motion of diffusing water molecules in biological tissue and can provide information on the tissue structure at a microscopic scale. DW-MRI in used in many applications both in the brain and other parts of the body such as the breast and prostate, and novelcomputational methods are at the core of advancements in DW-MRI, both in terms of research and its clinical translation. This article reviews the ways in whichmachine learning anddeep learning is currently applied in DW-MRI. We will also discuss the more traditional methods used for processing diffusion MRI and the potential of deep learning in augmenting these existing methods in the future.
Daniele Ravi, Nooshin Ghavami, Daniel C. Alexander, Andrada Ianus

q-Space Learning with Synthesized Training Data

Abstract
q-Space learning has been developed to improve tissue microstructure estimation on diffusion magnetic resonance imaging (dMRI) scans when only a limited number of diffusion gradients are applied. However, the training samples for q-space learning are obtained from high-quality diffusion signals densely sampled in the q-space, which are acquired on the same scanner of the test scans with a large number of diffusion gradients, and they may not be available for existing or ongoing datasets. In this work, we explore q-space learning with synthesized training data so that it can be applied to datasets where training signals are not available. We seek to synthesize diffusion signals densely sampled in the q-space, whose corresponding undersampled signals should match the distribution of observed undersampled diffusion signals. Specifically, by drawing samples from a simple distribution and feeding them into a generator defined by a multiple layer perceptron, we synthesize the continuous SHORE signal representation, from which both densely sampled and undersampled synthesized diffusion signals can be computed. The weights in the generator are learned by minimizing the distribution difference, which is measured by the maximum mean discrepancy, between the synthesized and observed undersampled signals. In addition, regularization terms are added to discourage unrealistic synthetic signals. With the learned generator, densely sampled diffusion signals can be synthesized for q-space learning. The proposed approach was applied to microstructure estimation on dMRI scans acquired with a limited number of diffusion gradients. The results demonstrate the benefit of using synthetic training signals for q-space learning when actual training data are not acquired.
Chuyang Ye, Yue Cui, Xiuli Li

Graph-Based Deep Learning for Prediction of Longitudinal Infant Diffusion MRI Data

Abstract
Diffusion MRI affords great value for studying brain development, owing to its capability in assessing brain microstructure in association with myelination. With longitudinally acquired pediatric diffusion MRI data, one can chart the temporal evolution of microstructure and white matter connectivity. However, due to subject dropouts and unsuccessful scans, longitudinal datasets are often incomplete. In this work, we introduce a graph-based deep learning approach to predict diffusion MRI data. The relationships between sampling points in spatial domain (x-space) and diffusion wave-vector domain (q-space) are harnessed jointly (x-q space) in the form of a graph. We then implement a residual learning architecture with graph convolution filtering to learn longitudinal changes of diffusion MRI data along time. We evaluate the effectiveness of the spatial and angular components in data prediction. We also investigate the longitudinal trajectories in terms of diffusion scalars computed based on the predicted datasets.
Jaeil Kim, Yoonmi Hong, Geng Chen, Weili Lin, Pew-Thian Yap, Dinggang Shen

Supervised Classification of White Matter Fibers Based on Neighborhood Fiber Orientation Distributions Using an Ensemble of Neural Networks

Abstract
White matter fibers constitute the main information transfer network of the brain and their accurate digital representation and classification is an important goal of neuroscience image computing. In current clinical practice, the reconstruction of desired fibers generally involves manual selection of regions of interest by an expert, which is time-consuming and subject to user bias, expertise and fatigue. Hence, automation of the process is desired. To that end, we propose a supervised classification approach that utilizes an ensemble of neural networks. Each streamline is represented by the fiber orientation distributions in its neighborhood, while the resolved fiber orientations are obtained by generalized q-sampling imaging (GQI) and a subsequent diffusion decomposition method. In order to make the supervised fiber classification succeed in a real scenario where a substantial portion of reconstructed fiber tracts contain spurious fibers, we present a way to create an “invalid” class label through a dedicated training set creation scheme with an ensemble of networks. The performance of the proposed classification method is demonstrated on major fiber pathways in the brainstem. 30 subjects from Human Connectome Project (HCP)’s publicly available “WU-Minn 500 Subjects + MEG2 dataset” are used as the dataset.
Devran Ugurlu, Zeynep Firat, Ugur Ture, Gozde Unal

Challenges and Opportunities in dMRI Data Harmonization

Abstract
Advances in diffusion MRI (dMRI) have led to discoveries of factors that affect brain microstructure and connectivity in health and disease. The small size of many neuroimaging studies led to concerns about poor reproducibility of research findings, and calls for the comparison and pooling of multi-cohort datasets to establish the consistency of reported effects. Across studies diffusion MRI protocols vary in spatial, angular and q-space resolution, b-value, as well as hardware used—all of which affect measured diffusion parameters. Efforts to compare and pool dMRI measures use meta- or mega- analytical techniques to compensate for these sources of variance. Meta-analytical methods gauge the consistency of effects, and mega-analytical methods involve mathematical or statistical transformations of the data. Here, we review some recent advances that allowed the diffusion community to create large scale population studies with greater rigor and generalizability than was previously attainable by individual studies.
Alyssa H. Zhu, Daniel C. Moyer, Talia M. Nir, Paul M. Thompson, Neda Jahanshad

Spherical Harmonic Residual Network for Diffusion Signal Harmonization

Abstract
Diffusion imaging is an important method in the field of neuroscience, as it is sensitive to changes within the tissue microstructure of the human brain. However, a major challenge when using MRI to derive quantitative measures is that the use of different scanners, as used in multi-site group studies, introduces measurement variability. This can lead to an increased variance in quantitative metrics, even if the same brain is scanned. Contrary to the assumption that these characteristics are comparable and similar, small changes in these values are observed in many clinical studies, hence harmonization of the signals is essential. In this paper, we present a method that does not require additional preprocessing, such as segmentation or registration, and harmonizes the signal based on a deep learningresidual network. For this purpose, a training database is required, which consist of the same subjects, scanned on different scanners. The results show that harmonized signals are significantly more similar to the ground truth signal compared to no harmonization, but also improve in comparison to another deep learning method. The same effect is also demonstrated in commonly used metrics derived from the diffusion MRI signal.
Simon Koppers, Luke Bloy, Jeffrey I. Berman, Chantal M. W. Tax, J. Christopher Edgar, Dorit Merhof

Longitudinal Harmonization for Improving Tractography in Baby Diffusion MRI

Abstract
The human brain develops very rapidly in the first years of life, resulting in significant changes in water diffusion anisotropy. Developmental changes pose significant challenges to longitudinally consistent white matter tractography. In this paper, we will introduce a method to harmonize infant diffusion MRI data longitudinally across time. Specifically, we harmonize diffusion MRI data collected at an earlier time point to data collected at a later time point. This will promote longitudinal consistency and allow sharpening of fiber orientation distribution functions (ODFs) based on information available at the later time point. For this purpose, we will introduce an approach that is based on the method of moments, which allows harmonization to be performed directly on the diffusion-attenuated signal without the need to fit any diffusion models to the data. Given two diffusion MRI datasets, our method harmonizes them voxel-wise using well-behaving mapping functions (i.e., monotonic, diffeomorphic, etc.), parameters of which are determined by matching the spherical moments (i.e., mean, variance, skewness, etc.) of signal measurements on each shell. The mapping functions we use is isotropic and does not introduce new orientations that are not already in the original data. Our analysis indicates that longitudinal harmonization sharpens ODFs and improves tractography in infant diffusion MRI.
Khoi Minh Huynh, Jaeil Kim, Geng Chen, Ye Wu, Dinggang Shen, Pew-Thian Yap

Inter-Scanner Harmonization of High Angular Resolution DW-MRI Using Null Space Deep Learning

Abstract
Diffusion-weighted magnetic resonance imaging (DW-MRI) allows for non-invasive imaging of the local fiber architecture of the human brain at a millimetric scale. Multiple classical approaches have been proposed to detect both single (e.g., tensors) and multiple (e.g., constrained spherical deconvolution, CSD) fiber population orientations per voxel. However, existing techniques generally exhibit low reproducibility across MRI scanners. Herein, we propose a data-driven technique using a neural network design which exploits two categories of data. First, training data were acquired on three squirrel monkey brains using ex-vivo DW-MRI and histology of the brain. Second, repeated scans of human subjects were acquired on two different scanners to augment the learning of the network proposed. To use these data, we propose a new network architecture, the null space deep network (NSDN), to simultaneously learn on traditional observed/truth pairs (e.g., MRI-histology voxels) along with repeated observations without a known truth (e.g., scan-rescan MRI). The NSDN was tested on twenty percent of the histology voxels that were kept completely blind to the network. NSDN significantly improved absolute performance relative to histology by 3.87% over CSD and 1.42% over a recently proposed deep neural network approach. More-over, it improved reproducibility on the paired data by 21.19% over CSD and 10.09% over a recently proposed deep approach. Finally, NSDN improved generalizability of the model to a third in-vivo human scanner (which was not used in training) by 16.08% over CSD and 10.41% over a recently proposed deep learning approach. This work suggests that data-driven approaches for local fiber reconstruction are more reproducible, informative, precise and offer a novel, practical method for determining these models.
Vishwesh Nath, Prasanna Parvathaneni, Colin B. Hansen, Allison E. Hainline, Camilo Bermudez, Samuel Remedios, Justin A. Blaber, Kurt G. Schilling, Ilwoo Lyu, Vaibhav Janve, Yurui Gao, Iwona Stepniewska, Baxter P. Rogers, Allen T. Newton, L. Taylor Davis, Jeff Luci, Adam W. Anderson, Bennett A. Landman

Effects of Diffusion MRI Model and Harmonization on the Consistency of Findings in an International Multi-cohort HIV Neuroimaging Study

Abstract
HIV-related white matter (WM) differences reported across studies are inconsistent. This is due to clinical and demographic heterogeneity of HIV infected populations, and variations in diffusion MRI (dMRI) acquisition, processing, and analysis methods across studies. Therefore, reliable neuroanatomical consequences of infection and therapeutic targets are difficult to identify. Here, we pooled data from six existing HIV studies from around the world as part of the ENIGMA-HIV consortium to evaluate (1) the effects of harmonization of dMRI measures across sites using ComBat, and (2) whether an improved, higher-order tensor dMRI model, the tensor distribution function (TDF), and derived scalar index (FATDF) conferred higher sensitivity across heterogeneous sites to understand the effect of HIV on WM microstructure. This study suggests that improved dMRI indices and harmonization of these measures across cohorts, may be helpful for detecting consistent effects of disease on the brain in international multi-site studies, while preserving biological differences.
Talia M. Nir, Hei Y. Lam, Jintanat Ananworanich, Jasmina Boban, Bruce J. Brew, Lucette Cysique, J. P. Fouche, Taylor Kuhn, Eric S. Porges, Meng Law, Robert H. Paul, April Thames, Adam J. Woods, Victor G. Valcour, Paul M. Thompson, Ronald A. Cohen, Dan J. Stein, Neda Jahanshad

Muti-shell Diffusion MRI Harmonisation and Enhancement Challenge (MUSHAC): Progress and Results

Abstract
We present a summary of competition results in the multi-shell diffusion MRI harmonisation and enhancement challenge (MUSHAC). MUSHAC is an open competition intended to stimulate the development of computational methods that reduce scanner- and protocol-related variabilities in multi-shell diffusion MRI data across multi-site studies. Twelve different methods from seven research groups have been tested in this challenge. The results show that cross-vendor harmonization and enhancement can be performed by using suitable computational algorithms such as deep convolutional neural networks. Moreover, parametric models for multi-shell diffusion MRI signals also provide reliable performances.
Lipeng Ning, Elisenda Bonet-Carne, Francesco Grussu, Farshid Sepehrband, Enrico Kaden, Jelle Veraart, Stefano B. Blumberg, Can Son Khoo, Marco Palombo, Jaume Coll-Font, Benoit Scherrer, Simon K. Warfield, Suheyla Cetin Karayumak, Yogesh Rathi, Simon Koppers, Leon Weninger, Julia Ebert, Dorit Merhof, Daniel Moyer, Maximilian Pietsch, Daan Christiaens, Rui Teixeira, Jacques-Donald Tournier, Andrey Zhylka, Josien Pluim, Greg Parker, Umesh Rudrapatna, John Evans, Cyril Charron, Derek K. Jones, Chantal W. M. Tax

Diffusion MRI Outside the Brain

Abstract
This manuscript provides an overview of recent developments in Diffusion-Weighted Imaging (DWI) outside the brain, focusing on liver, breast, prostate, muskuloskeletal (MSK) and cardiac applications. A general introduction to cross-cutting acquisition and image processing challenges is first provided. These often include short $$T_2$$ relaxation times, the need to image a large field-of-view with the resulting complications in shimming the B0 field and achieving good fat suppression. Some of the strategies developed for dealing with motion, namely cardiac and respiratory motion are described. Specific sections are then presented for each of the aforementioned organs. A motivation for the clinical applicability of DWI is first provided, followed by specific image acquisition and processing considerations. Quantitative imaging is becoming standard in clinical practice, and the Apparent Diffusion Coefficient is routinely estimated in the liver, breast and prostate. Application of alternative signal models in these organs is being explored, including both the Intravoxel Incoherent Motion and Diffusion Kurtosis models. Ongoing efforts are focused on evaluating the potential clinical added value of the extra parameters and on improving their repeatability. MSK and cardiac DWI have shown potential for assessing pathological changes in fiber architecture, but further validation is required to enable application in the clinical setting.
Rita G. Nunes, Luísa Nogueira, Andreia S. Gaspar, Nuno Adubeiro, Sofia Brandão

A Framework for Calculating Time-Efficient Diffusion MRI Protocols for Anisotropic IVIM and An Application in the Placenta

Abstract
We develop a framework for calculating clinically-viable diffusion MRI (dMRI) protocols for anisotropic IVIM modelling. The proposed multi-stage framework combines previous approaches to dMRI protocol optimisation: first optimising b-values by minimizing Cramer-Rao lower bounds on parameter variances, and subsequently optimising gradient directions jointly to provide maximum angular coverage across all shells. This removes unnecessary measurements of closely spaced b-values with the same gradient directions, which encode very similar information, and hence reduces the total number of dMRI measurements. We applied the framework to establish an organ-specific, data-driven, set of optimised b-values and gradient directions for dMRI of the placenta. The optimised protocol leads to higher contrast-to-noise ratios in parameter maps compared to a naive protocol of comparable scan time. Applying this framework in other organs has the potential to reduce scanning times required for anisotropic IVIM modelling.
Paddy J. Slator, Jana Hutter, Andrada Ianus, Eleftheria Panagiotaki, Mary A. Rutherford, Joseph V. Hajnal, Daniel C. Alexander

Spatial Characterisation of Fibre Response Functions for Spherical Deconvolution in Multiple Sclerosis

Abstract
Brain tractography based on diffusion-weighted (DW) MRI data has been increasingly used to investigate crucial pathophysiological aspects of several neurological conditions, including multiple sclerosis (MS). The advent of fibre tracking methods based on constrained spherical deconvolution (CSD), which recovers the fibre orientation distribution function (fODF) by performing a single-kernel (or uniform-kernel) deconvolution of the measured DW signals with non-negativity constraints, has meant an important breakthrough. However, it is unclear whether using a uniform kernel deconvolution of the measured DW signals for the whole brain is appropriate, especially in pathology. In this study, our main aim was to explore the validity of using a uniform fibre kernel for spherical deconvolution in a cohort of 19 patients with a first inflammatory-demyelinating attack of the central nervous system suggestive of MS and 12 age-matched healthy controls. In particular, considering that the number of peaks is a key feature the fODF and is known to impact directly on downstream fibre tracking, we assessed the association between patient-wise mean number of (fODF) peaks in the non-lesional white matter obtained with a uniform kernel and the bias or differences in the estimation of local diffusion properties when a uniform kernel (instead of a locally-fitted voxel-wise kernel) was used. Finally, in order to support our in-vivo results, we performed a simulation analysis to further assess the theoretical impact of using a uniform kernel. Our in-vivo results showed non-significant trends towards an influence of the bias in the estimation of the local diffusion properties when a uniform kernel was used on the number of peaks. In the simulation analysis, a clear association was observed between such bias and the number of peaks. All this suggests that the use of a uniform kernel to estimate the fODFs at the voxel level may not be adequate. However, we acknowledge that the approach followed here has some limitations, mainly derived from the methods used to estimate the voxel-wise local diffusion properties. Further investigations using larger in-vivo data sets and performing more comprehensive simulation analyses are therefore warranted.
Carmen Tur, Francesco Grussu, Ferran Prados, Sara Collorone, Claudia A. M. Gandini Wheeler-Kingshott, Olga Ciccarelli

Edge WeightsEdge weight and NetworkNetwork Properties in Multiple SclerosisMultiple sclerosis

Abstract
Graph theory is able to provide quantitative parameters that describe structural and functional characteristics of human brain networks. Comparisons between subject populations have demonstrated topological disruptions in many neurological disorders; however interpreting network parameters and assessing the extent of the damage is challenging. The abstraction of brain connectivity to a set of nodes and edges in a graph is non-trivial, and factors from image acquisition, post-processing and network construction can all influence derived network parameters. We consider here the impact of edge weighting schemes in a comparative analysis of structural brain networks, using healthy control and relapsing-remitting multiple sclerosis subjects as test groups. We demonstrate that the choice of edge property can substantially affect inferences of network disruptions in disease, ranging from ‘primarily intact connectivity’ to ‘complete disruption’. Although study design should predominantly dictate the choice of edge weight, it is important to consider how study outcomes may be affected.
Elizabeth Powell, Ferran Prados, Declan Chard, Ahmed Toosy, Jonathan D. Clayden, Claudia Gandini A. M. Wheeler-Kingshott

Measures of Tractography Convergence

Abstract
In the present work, we use information theory to understand the empirical convergence rate of tractography, a widely-used approach to reconstruct anatomical fiber pathways in the living brain. Based on diffusion MRI data, tractography is the starting point for many methods to study brain connectivity. Of the available methods to perform tractography, most reconstruct a finite set of streamlines, or 3D curves, representing probable connections between anatomical regions, yet relatively little is known about how the sampling of this set of streamlines affects downstream results, and how exhaustive the sampling should be. Here we provide a method to measure the information theoretic surprise (self-cross entropy) for tract sampling schema. We then empirically assess four streamline methods. We demonstrate that the relative information gain is very low after a moderate number of streamlines have been generated for each tested method. The results give rise to several guidelines for optimal sampling in brain connectivity analyses.
Daniel C. Moyer, Paul Thompson, Greg Ver Steeg

Brain Connectivity Measures via Direct Sub-Finslerian Front Propagation on the 5D Sphere Bundle of Positions and Directions

Abstract
We propose a novel connectivity measure between brain regions using diffusion-weighted MRI. This connectivity measure is based on optimal sub-Finslerian geodesic front propagation on the 5D base manifold of (3D) positions and (2D) directions, the so-called sphere bundle. The advantage over spatial front propagations is that it prevents leakage at omnipresent crossings. Our optimal fronts on the sphere bundle are geodesically equidistant w.r.t. an asymmetric Finsler metric, and can be computed with existing anisotropic fast-marching methods. Comparisons to ground truth connectivities provided by the ISBI-HARDI challenge reveal promising results, both quantitatively and qualitatively. We also apply the connectivity measures to real data from the Human Connectome Project.
Jorg Portegies, Stephan Meesters, Pauly Ossenblok, Andrea Fuster, Luc Florack, Remco Duits

Inference of an Extended Short Fiber Bundle Atlas Using Sulcus-Based Constraints for a Diffeomorphic Inter-subject Alignment

Abstract
We present a new framework for the creation of an extended atlas of short fiber bundles between 20 and 80 mm length. This method uses a Diffeomorphic inter-subject alignment procedure including information of cortical foldings and forces the accurate match of the sulci that have to be circumvented by the U-bundles. Then, a clustering is performed to extract the most reproducible bundles across subjects. First results show an increased number of U-bundles consistently mapped in the general population compared with previous atlases created from the same database. Future analysis over this new extended Brain atlas may improve our understanding of the relationship between the folding pattern and the U-bundle variability. The ultimate aim will be the possibility to detect abnormal configurations induced by developmental issues.
Nicole Labra Avila, Jessica Lebenberg, Denis Rivière, Guillaume Auzias, Clara Fischer, Fabrice Poupon, Pamela Guevara, Cyril Poupon, Jean-François Mangin

Resolving the Crossing/Kissing Fiber Ambiguity Using Functionally Informed COMMIT

Abstract
The architecture of the white matter is endowed with kissing and crossing bundles configurations. When these white matter tracts are reconstructed using diffusion MRI tractography, this systematically induces the reconstruction of many fiber tracts that are not coherent with the structure of the brain. The question on how to discriminate between true positive connections and false positive connections is the one addressed in this work. State-of-the-art techniques provide a partial solution to this problem by considering anatomical priors in the false positives detection process. We propose a novel model that tackles the same issue but takes into account both structural and functional information by combining them in a convex optimization problem. We validate it on two toy phantoms that reproduce the kissing and the crossing bundles configurations, showing that through this approach we are able to correctly distinguish true positives and false positives.
Matteo Frigo, Isa Costantini, Rachid Deriche, Samuel Deslauriers-Gauthier

Voxel-Wise Clustering of Tractography Data for Building Atlases of Local Fiber Geometry

Abstract
This paper aims at proposing a method to generate atlases of white matter fibers’ geometry that consider local orientation and curvature of fibers extracted from tractography data. Tractography was performed on diffusion magnetic resonance images from a set of healthy subjects and each tract was characterized voxel-wise by its curvature and Frenet–Serret frame, based on which similar tracts could be clustered separately for each voxel and each subject. Finally, the centroids of the clusters identified in all subjects were clustered to create the final atlas. The proposed clustering technique showed promising results in identifying voxel-wise distributions of curvature and orientation. Two tractography algorithms (one deterministic and one probabilistic) were tested for the present work, obtaining two different atlases. A high agreement between the two atlases was found in several brain regions. This suggests that more advanced tractography methods might only be required for some specific regions in the brain. In addition, the probabilistic approach resulted in the identification of a higher number of fiber orientations in various white matter areas, suggesting it to be more adequate for investigating complex fiber configurations in the proposed framework as compared to deterministic tractography.
Irene Brusini, Daniel Jörgens, Örjan Smedby, Rodrigo Moreno

Obtaining Representative Core Streamlines for White Matter Tractometry of the Human Brain

Abstract
Diffusion MRI infers information about the micro-structural architecture of the brain by probing the diffusion of water molecules. The process of virtually reconstructing brain pathways based on these measurements is called tractography. Various metrics can be mapped onto pathways to study their micro-structural properties. Tractometry is an along-tract profiling technique that often requires the extraction of a representative streamline for a given bundle. This is traditionally computed by local averaging of the spatial coordinates of the vertices, and constructing a single streamline through those averages. However, the resulting streamline can end up being highly non-representative of the shape of the individual streamlines forming the bundle. In particular, this occurs when there is variation in the topology of streamlines within a bundle (e.g., differences in length, shape or branching). We propose an envelope-based method to compute a representative streamline that is robust to these individual differences. We demonstrate that this method produces a more representative core streamline, which in turn should lead to more reliable and interpretable tractometry analyses.
Maxime Chamberland, Samuel St-Jean, Chantal M. W. Tax, Derek K. Jones

Improving Graph-Based Tractography Plausibility Using Microstructure Information

Abstract
Tractography is a unique tool to study neurological disorders for its ability to infer the major neural tracts from diffusion MRI data, thus allowing the investigation of the connectivity of the brain in-vivo. Tractography has seen a remarkable interest over the years and a large number of algorithms have been proposed. The choice of which method to use in a given application is usually a trade-off between its computational complexity and the quality of the reconstructions. So-called “shortest path” methods represent an interesting option, as they are computationally efficient, robust to noise and their formulation is very flexible. However, they also come with limitations. For instance, the reconstructed streamlines tend to be collapsed and to share part of their path, especially in regions with highly curved fiber bundles. This can introduce voxels with incorrectly high or low streamline density, which does not correspond to the underlying fiber geometry. To mitigate this problem, we propose an iterative procedure that uses microstructure information and provides feedback to the shortest path tractography algorithm about the plausibility of the reconstructions. We evaluated our method on a synthetic phantom and show that the spatial distribution of streamlines is in closer agreement with the ground truth.
Matteo Battocchio, Gabriel Girard, Muhamed Barakovic, Mario Ocampo, Jean-Philippe Thiran, Simona Schiavi, Alessandro Daducci

Deterministic Group Tractography with Local Uncertainty Quantification

Abstract
While tractography is routinely used to trace the white-matter connectivity in individual subjects, the population analysis of tractography output is hampered by the difficulty of comparing populations of curves. As a result, analysis is often reduced to population summaries such as TBSS, or made pointwise with similar interaction of remote and nearby tracts. As an easy-to-use alternative, we propose population-wide tractography in MNI space, by simultaneously considering diffusion data from the entire population, registered to MNI. We include voxel-wise quantification of population variability as a measure of uncertainty. The group tractography algorithm is illustrated on a population of subjects from the Human Connectome Project, obtaining robust population estimates of the white matter tracts.
Andreas Nugaard Holm, Aasa Feragen, Tom Dela Haije, Sune Darkner

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