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These Proceedings of the 2015 MICCAI Workshop “Computational Diffusion MRI” offer a snapshot of the current state of the art on a broad range of topics within the highly active and growing field of diffusion MRI. The topics vary from fundamental theoretical work on mathematical modeling, to the development and evaluation of robust algorithms, new computational methods applied to diffusion magnetic resonance imaging data, and applications in neuroscientific studies and clinical practice.

Over the last decade interest in diffusion MRI has exploded. The technique provides unique insights into the microstructure of living tissue and enables in-vivo connectivity mapping of the brain. Computational techniques are key to the continued success and development of diffusion MRI and to its widespread transfer into clinical practice. New processing methods are essential for addressing issues at each stage of the diffusion MRI pipeline: acquisition, reconstruction, modeling and model fitting, image processing, fiber tracking, connectivity mapping, visualization, group studies and inference.

This volume, which includes both careful mathematical derivations and a wealth of rich, full-color visualizations and biologically or clinically relevant results, offers a valuable starting point for anyone interested in learning about computational diffusion MRI and mathematical methods for mapping brain connectivity, as well as new perspectives and insights on current research challenges for those currently working in the field. It will be of interest to researchers and practitioners in the fields of computer science, MR physics, and applied mathematics.​

### An Efficient Finite Element Solution of the Generalised Bloch-Torrey Equation for Arbitrary Domains

Abstract
Nuclear magnetic resonance (NMR) is an invaluable tool for investigating porous media. Its use allows to study pore size distributions, fiber tortuosity, and permeability as a function of the relaxation time, diffusivity, and flow. This information was shown to be important in many applications, such as medical diagnosis and materials science. A complete NMR analysis involves the solution of the Bloch-Torrey (BT) equation. However, solving this equation analytically becomes intractable for all but the simplest geometries.We present an efficient numerical framework for solving the generalised BT equation. This method allows to obtain computational simulations of the NMR experiment in arbitrarily complex domains. In addition to the standard BT equation, the generalised BT formulation takes into account the flow and relaxation terms, allowing a better representation of the phenomena under scope. This framework is flexible enough to deal parametrically with any order of convergence in the spatial domain. Moreover, we developed a second-order implicit scheme for the temporal discretisation with similar computational demands as the existing explicit methods. This represents a huge step forward for obtaining reliable results with few iterations. Comparisons with analytical solutions and real data show the flexibility and accuracy of the proposed method.
Leandro Beltrachini, Zeike A. Taylor, Alejandro F. Frangi

### Super-Resolution Reconstruction of Diffusion-Weighted Images Using 4D Low-Rank and Total Variation

Abstract
Diffusion-weighted imaging (DWI) provides invaluable information in white matter microstructure and is widely applied in neurological applications. However, DWI is largely limited by its relatively low spatial resolution. In this paper, we propose an image post-processing method, referred to as super-resolution reconstruction, to estimate a high spatial resolution DWI from the input low-resolution DWI, e.g., at a factor of 2. Instead of requiring specially designed DWI acquisition of multiple shifted or orthogonal scans, our method needs only a single DWI scan. To do that, we propose to model both the blurring and downsampling effects in the image degradation process where the low-resolution image is observed from the latent high-resolution image, and recover the latent high-resolution image with the help of two regularizations. The first regularization is four-dimensional (4D) low-rank, proposed to gather self-similarity information from both the spatial domain and the diffusion domain of 4D DWI. The second regularization is total variation, proposed to depress noise and preserve local structures such as edges in the image recovery process. Extensive experiments were performed on 20 subjects, and results show that the proposed method is able to recover the fine details of white matter structures, and outperform other approaches such as interpolation methods, non-local means based upsampling, and total variation based upsampling.
Feng Shi, Jian Cheng, Li Wang, Pew-Thian Yap, Dinggang Shen

### Holistic Image Reconstruction for Diffusion MRI

Abstract
Diffusion MRI provides unique information on the microarchitecture of biological tissues. One of the major challenges is finding a balance between image resolution, acquisition duration, noise level and image artifacts. Recent methods tackle this challenge by performing super-resolution reconstruction in image space or in diffusion space, regularization of the image data or of postprocessed data (such as the orientation distribution function, ODF) along different dimensions, and/or impose data-consistency in the original acquisition space. Each of these techniques has its own advantages; however, it is rare that even a few of them are combined. Here we present a holistic framework for diffusion MRI reconstruction that allows combining the advantages of all these techniques in a single reconstruction step. In proof-of-concept experiments, we demonstrate super-resolution on HARDI shells and in image space, regularization of the ODF and of the images in spatial and angular dimensions, and data consistency in the original acquisition space. Reconstruction quality is superior to standard reconstruction, demonstrating the feasibility of combining advanced techniques into one step.
Vladimir Golkov, Jorg M. Portegies, Antonij Golkov, Remco Duits, Daniel Cremers

### Alzheimer’s Disease Classification with Novel Microstructural Metrics from Diffusion-Weighted MRI

Abstract
Alzheimer’s disease (AD) deficits may be due in part to declining white matter (WM) integrity and disrupted connectivity. Numerous diffusion-weighted MRI (dMRI) studies of AD report WM deficits based on tensor model metrics. New microstructural measures derived from additional dMRI models may carry different information about WM microstructure including the geometry of diffusion anisotropy, diffusivity, complexity, estimated number of distinguishable fiber compartments, number of crossing fibers and neurite dispersion. Here we aimed to find the most helpful dMRI metrics and brain regions from a set of 17 dMRI-derived feature maps, to predict diagnostic group (AD or healthy control). The best metrics for classification were non-tensor metrics in the hippocampus and temporal lobes, areas consistently implicated in AD.
Talia M. Nir, Julio E. Villalon-Reina, Boris A. Gutman, Daniel Moyer, Neda Jahanshad, Morteza Dehghani, Clifford R. Jack, Michael W. Weiner, Paul M. Thompson

### Brain Tissue Micro-Structure Imaging from Diffusion MRI Using Least Squares Variable Separation

Abstract
We introduce a novel data fitting procedure of multi compartment models of the brain white matter for diffusion MRI (dMRI) data. These biophysical models aim to characterize important micro-structure quantities like axonal radius, density and orientations. In order to describe the underlying tissue properties, a variety of models for intra-/extra-axonal diffusion signals have been proposed. Combinations of these analytic models are used to predict the diffusion MRI signal in multi-compartment settings. However, parameter estimation from these multi-compartment models is an ill-posed problem. Consequently, many existing fitting algorithms either rely on an initial grid search to find a good start point, or have strong assumptions like single fiber orientation to estimate some of these parameters from simpler models like the diffusion tensor (DT). In both cases, there is a trade-off between computational complexity and accuracy of the estimated parameters. Here, we describe a novel algorithm based on the separation of the Nonlinear Least Squares (NLLS) fitting problem, via Variable Projection Method , to search for non-linearly and linearly entering parameters independently. We use stochastic global search algorithms to find a global minimum, while estimating non-linearly entering parameters. The approach is independent of any starting point, and does not rely on estimates from simpler models. We show that the suggested algorithm is faster than algorithms involving grid search, and its greater accuracy and robustness are demonstrated on synthetic as well as ex-/in-vivo data.
Hamza Farooq, Junqian Xu, Essa Yacoub, Tryphon Georgiou, Christophe Lenglet

### Multi-Tensor MAPMRI: How to Estimate Microstructural Information from Crossing Fibers

Abstract
Diffusion Magnetic Resonance Imaging (dMRI) is able to detect the properties of tissue microstructure underneath the voxel through the imaging of water molecules diffusion. Many reconstruction methods have been proposed to calculate the Orientation Distribution Function (ODF) from the diffusion signal in order to distinguish between coherent fiber bundles and crossing fibers. The diffusion signal was also used to infer other microstructural information such as the axon diameter, but most often in areas with coherent fiber direction such as the corpus callosum. In this work, we developed a reconstruction model called Multi-Tensor MAPMRI (MT-MAPMRI) that is an extension of the MAPMRI model which improves the performance of MAPMRI for crossing fibers. In particular, it provides (a) enhanced signal fitting; (b) improved ODFs; (c) a more accurate diameter estimation. The model was tested and validated on both simulated and in-vivo data.
Mauro Zucchelli, Lorenza Brusini, C. Andrés Méndez, Gloria Menegaz

### On the Use of Antipodal Optimal Dimensionality Sampling Scheme on the Sphere for Recovering Intra-Voxel Fibre Structure in Diffusion MRI

Abstract
In diffusion magnetic resonance imaging (dMRI), the diffusion signal can be reconstructed from measurements collected on single or multiple spheres in $$\boldsymbol{q}$$-space using a spherical harmonic expansion. The number of measurements that can be acquired is severely limited and should be as small as possible. Previous sampling schemes have focused on using antipodal symmetry to reduce the number of samples and uniform sampling to achieve rotationally invariant reconstruction accuracy, but do not allow for an accurate or computationally efficient spherical harmonic transform (SHT). The recently proposed antipodal optimal dimensionality sampling scheme on the sphere requires the minimum number of samples, equal to the number of degrees of freedom for the representation of the antipodal symmetric band-limited diffusion signal in the spherical harmonic domain. In addition, it allows for the accurate and efficient computation of the SHT. In this work, we evaluate the use of this recently proposed scheme for the reconstruction of the diffusion signal and subsequent intra-voxel fibre structure estimation in dMRI. We show, through numerical experiments, that the use of this sampling scheme allows accurate and computationally efficient reconstruction of the diffusion signal, and improved estimation of intra-voxel fibre structure, in comparison to the antipodal electrostatic repulsion and spherical code sampling schemes with the same number of samples. We also demonstrate that it achieves rotationally invariant reconstruction accuracy to the same extent as the other two sampling schemes.
Alice P. Bates, Zubair Khalid, Rodney A. Kennedy

### Estimation of Fiber Orientations Using Neighborhood Information

Abstract
Diffusion magnetic resonance imaging (dMRI) has been used to noninvasively reconstruct fiber tracts. Fiber orientation (FO) estimation is a crucial step in the reconstruction, especially in the case of crossing fibers. In FO estimation, it is important to incorporate spatial coherence of FOs to reduce the effect of noise. In this work, we propose a method of FO estimation using neighborhood information. The diffusion signal is modeled by a fixed tensor basis. The spatial coherence is enforced in weighted 1-norm regularization terms, which contain the interaction of directional information between neighbor voxels. Data fidelity is ensured by the agreement between raw and reconstructed diffusion signals. The resulting objective function is solved using a block coordinate descent algorithm. Experiments were performed on a digital crossing phantom, ex vivo tongue dMRI data, and in vivo brain dMRI data for qualitative and quantitative evaluation. The results demonstrate that the proposed method improves the quality of FO estimation.
Chuyang Ye, Jiachen Zhuo, Rao P. Gullapalli, Jerry L. Prince

### A Framework for Creating Population Specific Multimodal Brain Atlas Using Clinical T1 and Diffusion Tensor Images

Abstract
Spatial normalization is one of the most important steps in population based statistical analysis of brain images. This involves normalizing all the brain images to a pre-defined template or a population specific template. With multiple emerging imaging modalities, it is quintessential to develop a method for building a joint template that is a statistical representation of the given population across different modalities. It is possible to create different population specific templates in different modalities using existing methods. However, they do not give an opportunity for voxelwise comparison of different modalities. A multimodal brain template with probabilistic region of interest (ROI) definitions will give opportunity for multivariate statistical frameworks for better understanding of brain diseases. In this paper, we propose a methodology for developing such a multimodal brain atlas using the anatomical T1 images and the diffusion tensor images (DTI), along with an automated workflow to probabilistically define the different white matter regions on the population specific multimodal template. The method will be useful to carry out ROI based statistics across different modalities even in the absence of expert segmentation. We show the effectiveness of such a template using voxelwise multivariate statistical analysis on population based group studies on HIV/AIDS patients.
Vikash Gupta, Grégoire Malandain, Nicholas Ayache, Xavier Pennec

### Alignment of Tractograms as Linear Assignment Problem

Abstract
Diffusion magnetic resonance imaging (dMRI) offers a unique approach to study the structural connectivity of the brain. DMRI allows to reconstruct the 3D pathways of axons within the white matter as a set of polylines (streamlines), called the tractogram. Tractograms of different brains need to be aligned in a common representation space for various purposes, such as group-analysis, segmentation or atlas construction. Typically, such alignment is obtained with affine registration, through which tractograms are globally transformed, with the limit of not reconciling local differences. In this paper, we propose to improve registration-based alignment by what we call mapping. The goal of mapping is to find the correspondence between streamlines across brains, i.e. to find the map of which streamline in one tractogram correspond to which streamline in the other tractogram. We frame the mapping problem as a rectangular linear assignment problem (RLAP), a cornerstone of combinatorial optimization. We adopt a variant of the famous Hungarian method to get the optimal solution of the RLAP. We validate the proposed method with a tract alignment application, where we register two tractograms and, given one anatomical tract, we segment the corresponding one in the other tractogram. On dMRI data from the Human Connectome Project, we provide experimental evidence that mapping, implemented as a RLAP, can vastly improve both the true positive rate and false discovery rate of registration-based alignment, establishing a strong argument in favor of what we propose. We conclude by discussing the limitations of the current approach, which gives perspective for future work.
Nusrat Sharmin, Emanuele Olivetti, Paolo Avesani

### Accelerating Global Tractography Using Parallel Markov Chain Monte Carlo

Abstract
Global tractography estimates brain connectivity by determining the optimal configuration of signal-generating fiber segments that best describes the measured diffusion-weighted data, promising better stability than local greedy methods with respect to imaging noise. However, global tractography is computationally very demanding and requires computation times that are often prohibitive for clinical applications. We present here a reformulation of the global tractography algorithm for fast parallel implementation amendable to acceleration using multi-core CPUs and general-purpose GPUs. Our method is motivated by the key observation that each fiber segment is affected by a limited spatial neighborhood. That is, a fiber segment is influenced only by the fiber segments that are (or can potentially be) connected to its both ends and also by the diffusion-weighted signal in its proximity. This observation makes it possible to parallelize the Markov chain Monte Carlo (MCMC) algorithm used in the global tractography algorithm so that updating of independent fiber segments can be done concurrently. The experiments show that the proposed algorithm can significantly speed up global tractography, while at the same time maintain or improve tractography performance.
Haiyong Wu, Geng Chen, Zhongxue Yang, Dinggang Shen, Pew-Thian Yap

### Adaptive Enhancement in Diffusion MRI Through Propagator Sharpening

Abstract
In this short note we consider a method of enhancing diffusion MRI data based on analytically deblurring the ensemble average propagator. Because of the Fourier relationship between the normalized signal and the propagator, this technique can be applied in a straightforward manner to a large class of models. In the case of diffusion tensor imaging, a commonly used ‘ad hoc’ $$\min$$-normalization sharpening method is shown to be closely related to this deblurring approach. The main goal of this manuscript is to give a formal description of the method for (generalized) diffusion tensor imaging and higher order apparent diffusion coefficient-based models. We also show how the method can be made adaptive to the data, and present the effect of our proposed enhancement on scalar maps and tractography output.
Tom Dela Haije, Neda Sepasian, Andrea Fuster, Luc Florack

### Angular Resolution Enhancement of Diffusion MRI Data Using Inter-Subject Information Transfer

Abstract
Diffusion magnetic resonance imaging is widely used to investigate diffusion patterns of water molecules in the human brain. It provides information that is useful for tracing axonal bundles and inferring brain connectivity. Diffusion axonal tracing, namely tractography, relies on local directional information provided by the orientation distribution functions (ODFs) estimated at each voxel. To accurately estimate ODFs, data of good signal-to-noise ratio and sufficient angular samples are desired, but unfortunately, are not always practically available. In this paper, we propose to improve ODF estimation by using inter-subject correlation. Specifically, diffusion-weighted images acquired from different subjects, when transformed to the space of a target subject, can not only provide signal denoising with additional information, but also drastically increase the number of angular samples for better ODF estimation. This is largely because of the incoherence of the angular samples generated when the diffusion signals are reoriented and warped to the target space. Experiments on both synthetic data and real data show that our method can reduce noise-induced artifacts, such as spurious ODF peaks, and yield more coherent orientations.
Geng Chen, Pei Zhang, Ke Li, Chong-Yaw Wee, Yafeng Wu, Dinggang Shen, Pew-Thian Yap

### Crossing Versus Fanning: Model Comparison Using HCP Data

Abstract
This paper assesses the importance of modelling fiber dispersion in brain regions with complex fiber configurations using a model comparison approach. It is well known that DTI, although popular, is insufficient for describing complex fiber configurations that exist in the brain—such as crossings, bendings and fannings. “Higher order” models have been proposed to overcome this limitation by modelling crossings with greater accuracy and recent works have reported that up to 90 % of white matter voxels contain crossings. However, since these models do not account for bending and fanning, i.e. dispersion, it is unknown if some fiber configurations are better explained by dispersion or by crossing (or by both). To address this problem, we take a model comparison approach on the publicly available state-of-the-art HCP dataset. We consider compartment based single fiber, crossing fiber and dispersion models, which are fitted to the data and ranked using several model selection and validation metrics, such as AIC, BIC and k-fold cross-validation. We generate maps of the brain based on these rankings which quantify the voxels where a single fiber or crossing or dispersion is the preferred model. The results show that 45–50 % of the brain’s parenchyma, including the white matter, are better explained by dispersion models, indicating the importance of modelling dispersion in addition to crossings.
Aurobrata Ghosh, Daniel Alexander, Hui Zhang

### White Matter Fiber Set Simplification by Redundancy Reduction with Minimum Anatomical Information Loss

Abstract
Advanced Diffusion Weighted Imaging (DWI) techniques and leading tractography algorithms produce dense fiber sets of hundreds of thousands of fibers, or more. In order to make fiber based analysis more practical, the fiber set needs to be preprocessed to eliminate redundancies and to keep only essential representative fibers. In this paper we evaluate seven commonly used distance metrics for fiber clustering and present a novel approach for comparing the metrics as well as estimating the anatomical information loss as a function of the reduction rate. The framework includes pre-clustering into sub-groups using K-means, followed by further decomposition using Hierarchical Clustering, each time with a different distance metric. Finally, volume histograms comparison is used to compare the reduction quality with the different metrics. The proposed comparison was applied to a dataset containing tractographies of four healthy individuals. Each set contains around 600k fibers.
Gali Zimmerman Moreno, Guy Alexandroni, Hayit Greenspan

### A Temperature Phantom to Probe the Ensemble Average Propagator Asymmetry: An In-Silico Study

Abstract
The detection and quantification of asymmetry in the Ensemble Average Propagator (EAP) obtained from the Diffusion-Weighted (DW) signal has been shown only for theoretical models. EAP asymmetry appears for instance when diffusion occurs within fibers with particular geometries. However the quantification of EAP asymmetry corresponding to such geometries in controlled experimental conditions is limited by the difficulty of designing fiber geometries on a micrometer scale. To overcome this limitation we propose to adopt an alternative paradigm to induce asymmetry in the EAP. We apply a temperature gradient to a spinal cord tract to induce a corresponding diffusivity profile that alters locally the diffusion process to be asymmetric. We simulate the EAP and the corresponding complex DW signal in such a scenario. We quantify EAP asymmetry and investigate its relationship with the applied experimental conditions and with the acquisition parameters of a Pulsed Gradient Spin-Echo sequence. Results show that EAP asymmetry is sensible to the applied temperature-induced diffusivity gradient and that its quantification is influenced by the selected acquisition parameters.
Marco Pizzolato, Demian Wassermann, Tanguy Duval, Jennifer S. W. Campbell, Timothé Boutelier, Julien Cohen-Adad, Rachid Deriche

### Registration Strategies for Whole-Body Diffusion-Weighted MRI Stitching

Abstract
With the development of ultra-fast magnetic resonance imaging sequences, whole-body diffusion-weighted magnetic resonance imaging (WB-DWI) becomes a popular diagnostic tool in patient cancer screening. Modality can improve plenty of clinical investigations such as lymphoma, multiple melanoma or metastatic bone cancer diagnosis. Because of vast body coverage and MR scanner limitations, whole-body image is acquired in blocks, called stations. Precise ‘stitching’ of whole-body stations is essential to ensure correct image formation, yet there are not many commercially available registration algorithms. We developed and investigated several registration methods based on apparent diffusion coefficient (ADC) and diffusion-weighted images (DWI) to improve station-to-station registration and WB-DWI image quality. This paper reports on registration results of 52 whole-body DWI images and compares them with other already existing methods. Proposed registration techniques based on ADC images demonstrated superior performance over other registration methods.
Jakub Ceranka, Mathias Polfliet, Frederic Lecouvet, Nicolas Michoux, Johan de Mey, Jef Vandemeulebroucke

### Using Automatic HARDI Feature Selection, Registration, and Atlas Building to Characterize the Neuroanatomy of Aβ Pathology

Abstract
The detection of white matter microstructural changes using diffusion magnetic resonance imaging (dMRI) often involves extracting a small set of scalar features, such as fractional anisotropy (FA) and mean diffusivity (MD) in diffusion tensor imaging (DTI). With the advent of more advanced dMRI techniques, such as high angular resolution diffusion imaging (HARDI), a number of mathematically inspired new scalar features have been proposed. However, it is unclear how to select the most biologically informative combinations of features for biomarker discovery. This paper proposes an automatic HARDI feature selection algorithm which is based on registering HARDI features to feature atlases for optimal clinical usability in population studies. We apply our framework to the characterization of beta-amyloid (Aβ) pathology for the early detection of Alzheimer’s disease (AD) to better understand the relationship between Aβ pathology and degenerative changes in neuroanatomy.
Evan Schwab, Michael A. Yassa, Michael Weiner, René Vidal

### Reliability of Structural Connectivity Examined with Four Different Diffusion Reconstruction Methods at Two Different Spatial and Angular Resolutions

Abstract
Diffusion magnetic resonance imaging (dMRI) has had a great impact on the study of the human brain connectome. Tractography methods allow for the reconstruction of white matter fiber tracts and bundles across the brain, by tracing the estimated direction of water diffusion across neighboring voxels. The tracts can then be used in conjunction with cortical parcellations to create structural connectivity matrices, to map the pattern and distribution of connections between cortical regions. However, the reliability of connectivity matrices is unclear. Tractography results depend on image resolution, and some reconstruction methods used to resolve the voxel-wise microstructure may be more robust to changes in resolution than others, leading to more stable connectivity estimates. We examined the reliability of structural connectivity matrices in 20 healthy young adults imaged with both high and low-resolution dMRI at two time points. We found that the Constrained Spherical Deconvolution (CSD) model produces the most reliable connections for both lower resolution and high resolution scans.
J. E. Villalon-Reina, T. M. Nir, L. Zhan, K. L. McMahon, G. I. de Zubicaray, M. J. Wright, N. Jahanshad, P. M. Thompson