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This volume contains the proceedings from two closely related workshops: Computational Diffusion MRI (CDMRI’13) and Mathematical Methods from Brain Connectivity (MMBC’13), held under the auspices of the 16th International Conference on Medical Image Computing and Computer Assisted Intervention, which took place in Nagoya, Japan, September 2013.

Inside, readers will find contributions ranging from mathematical foundations and novel methods for the validation of inferring large-scale connectivity from neuroimaging data to the statistical analysis of the data, accelerated methods for data acquisition, and the most recent developments on mathematical diffusion modeling.

This volume offers a valuable starting point for anyone interested in learning computational diffusion MRI and mathematical methods for brain connectivity as well as offers new perspectives and insights on current research challenges for those currently in the field. It will be of interest to researchers and practitioners in computer science, MR physics, and applied mathematics.



Acquisition of Diffusion MRI


Comparing Simultaneous Multi-slice Diffusion Acquisitions

Diffusion magnetic resonance imaging (dMRI) is an important tool that allows non-invasive investigation of the neural architecture of the brain. Advanced dMRI protocols typically require a large number of measurements for accurately tracing the fiber bundles and estimating the diffusion properties (such as, FA). However, the acquisition time of these sequences is prohibitively large for pediatric as well as patients with certain types of brain disorders (such as, dementia). Thus, fast echo-planar imaging (EPI) acquisition sequences were proposed by the authors in [6, 16], which acquired multiple slices simultaneously to reduce scan time. The scan time in such cases drops proportionately to the number of simultaneous slice acquisitions (which we denote by R). While preliminary results in [6, 16] showed good reproducibility, yet the effect of simultaneous acquisitions on long range fiber connectivity and diffusion measures such as FA, is not known. In this work, we use multi-tensor based fiber connectivity to compare data acquired on two subjects with different acceleration factors (R = 1, 2, 3). We investigate and report the reproducibility of fiber bundles and diffusion measures between these scans on two subjects with different spatial resolutions, which is quite useful while designing neuroimaging studies.
Yogesh Rathi, Borjan Gagoski, Kawin Setsompop, P. Ellen Grant, C.-F. Westin

Effect of Data Acquisition and Analysis Method on Fiber Orientation Estimation in Diffusion MRI

In this paper we investigate the effect of single-shell q-space diffusion sampling strategies and applicable multiple-fiber analysis methods on fiber orientation estimation in Diffusion MRI. Specifically, we develop a simulation based on an in-vivo data set and compare a two-compartment “ball-and-stick” model, a constrained spherical deconvolution approach, a generalized Fourier transform approach, and three related methods based on transforms of Fourier data on the sphere. We evaluate each method for N = 20, 30, 40, 60, 90 and 120 angular diffusion-weighted samples, at SNR = 18 and diffusion-weighting \(b = 1,000\,\mathrm{s}/\mathrm{{mm}}^{2}\), common to clinical studies. Our results quantitatively show the methods are most distinguished from each other by their fiber detection ability. Overall, the “ball-and-stick” model and spherical deconvolution approach were found to perform best, yielding the least orientation error, and greatest detection rate of fibers.
Bryce Wilkins, Namgyun Lee, Vidya Rajagopalan, Meng Law, Natasha Leporé

Model-Based Super-Resolution of Diffusion MRI

This work introduces a model-based super-resolution reconstruction (SRR) technique for achieving high-resolution diffusion-weighted MRI. Diffusion-weighted imaging (DWI) is a key technique for investigating white matter non-invasively. However, due to hardware and imaging time constraints, the technique offers limited spatial resolution. A SRR technique was recently proposed to address this limitation. This approach is attractive because it can produce high-resolution DWI data without the need for onerously long scan time. However, the technique treats individual DWI data from different diffusion-sensitizing gradients as independent, which in fact are coupled through the common underlying tissue. The proposed technique addresses this issue by explicitly accounting for this intrinsic coupling between DWI scans from different gradients. The key technical advance is in introducing a forward model that predicts the DWI data from all the diffusion gradients by the underpinning tissue microstructure. As a proof-of-concept, we show that the proposed SRR approach provides more accurate reconstruction results than the current SRR technique with synthetic white matter phantoms.
Alexandra Tobisch, Peter F. Neher, Matthew C. Rowe, Klaus H. Maier-Hein, Hui Zhang

A Quantitative Evaluation of Errors Induced by Reduced Field-of-View in Diffusion Tensor Imaging

To obtain a better insight in tissue microstructures using diffusion MRI, a high resolution and dense sampling of q-space is required. In clinical settings, however, this can often not be achieved due to limited acquisition time. Reduced field-of-view (FOV) approaches counteract this limitation but may pose a challenge for the post-processing steps such as motion and artifact correction. We present an evaluation of the potential problems that arise with reduced FOV data during the standard post-processing. The acquisition with reduced FOV is extracted from a full FOV dataset. We select three different registration tools to perform the standard data post-processing pipeline. We first evaluate the spatial error and then measure its impact on the tensor reconstruction as well as on the derived fractional anisotropy (FA). With reduced FOV images, the multi-scale registration methods showed high sensitivity to parameter selection and produced up to 30 % outliers. With an optimized parameter set, all registration methods yielded spatial errors of 1 mm (±0.572). The spatial error resulted in a mean error of 0.03 (±0.013) in the estimated FA values, and was thus of the same magnitude as group differences as they are typically reported in DTI studies. Regions with large FA differences were located especially in the corpus callosum. The evaluation indicates that diffusion-weighted MR acquisitions with reduced FOV require careful selection of registration parameters and also cautious interpretation when quantifying derived indices.
Jan Hering, Ivo Wolf, Hans-Peter Meinzer, Bram Stieltjes, Klaus H. Maier-Hein

Diffusion MRI Modeling


The Diffusion Dictionary in the Human Brain Is Short: Rotation Invariant Learning of Basis Functions

To relate diffusion-weighted MRI-signal to the underlying tissue structure remains one of the major challenges in interpreting experimental data, in particular for reconstruction of the structural connectivity in the human brain. Various ideas to tackle this problem are around, either model-based or model-free. We proceed on a third way by proposing a method that automatically determines the basis components of diffusion-weighted MRI signal without any usage of prior knowledge. The resulted components can be well associated with white matter, gray matter and cerebrospinal fluid, respectively. The performance of our method is demonstrated on two DSI datasets and one multi-shell acquisition.
Marco Reisert, Henrik Skibbe, Valerij G. Kiselev

Diffusion Propagator Estimation Using Radial Basis Functions

The average diffusion propagator (ADP) obtained from diffusion MRI (dMRI) data encapsulates important structural properties of the underlying tissue. Measures derived from the ADP can be potentially used as markers of tissue integrity in characterizing several mental disorders. Thus, accurate estimation of the ADP is imperative for its use in neuroimaging studies. In this work, we propose a simple method for estimating the ADP by representing the acquired diffusion signal in the entire q-space using radial basis functions (RBF). We demonstrate our technique using two different RBF’s (generalized inverse multiquadric and Gaussian) and derive analytical expressions for the corresponding ADP’s. We also derive expressions for computing the solid angle orientation distribution function (ODF) for each of the RBF’s. Estimation of the weights of the RBF’s is done by enforcing positivity constraint on the estimated ADP or ODF. Finally, we validate our method on data obtained from a physical phantom with known fiber crossing of 45 degrees and also show comparison with the solid spherical harmonics method of Descoteaux et al. (Med Image Anal 2010). We also demonstrate our method on in-vivo human brain data.
Yogesh Rathi, Marc Niethammer, Frederik Laun, Kawin Setsompop, Oleg Michailovich, P. Ellen Grant, C.-F. Westin

A Framework for ODF Inference by Using Fiber Tract Adaptive MPG Selection

The authors propose a method that selects a set of motion probing gradient (MPG) directions, which is adapted for measuring fiber tracts in some specific region of interest (ROI) with smaller number of MPGs. Given a training set of diffusion magnetic resonance (MR) images, the method selects the set of MPG directions by minimizing a cost function, which represents the square errors of the reconstructed oriented distribution functions (ODFs). This selection of MPGs is a combinatorial optimization problem, and a simulated annealing scheme is employed for selecting the MPGs. Experimental results demonstrated that the set of MPG directions selected by our proposed method reconstructed the ODFs more accurately than an existing method based on spherical harmonics and on greedy optimization.
Hidekata Hontani, Kazunari Iwamoto, Yoshitaka Masutani

Non-negative Spherical Deconvolution (NNSD) for Fiber Orientation Distribution Function Estimation

In diffusion Magnetic Resonance Imaging (dMRI), Spherical Deconvolution (SD) is a commonly used approach for estimating the fiber Orientation Distribution Function (fODF). As a Probability Density Function (PDF) that characterizes the distribution of fiber orientations, the fODF is expected to be non-negative and to integrate to unity on the continuous unit sphere \({\mathbb{S}}^{2}\). However, many existing approaches, despite using continuous representation such as Spherical Harmonics (SH), impose non-negativity only on discretized points of \({\mathbb{S}}^{2}\). Therefore, non-negativity is not guaranteed on the whole \({\mathbb{S}}^{2}\). Existing approaches are also known to exhibit false positive fODF peaks, especially in regions with low anisotropy, causing an over-estimation of the number of fascicles that traverse each voxel. This paper proposes a novel approach, called Non-Negative SD (NNSD), to overcome the above limitations. NNSD offers the following advantages. First, NNSD is the first SH based method that guarantees non-negativity of the fODF throughout the unit sphere. Second, unlike approaches such as Maximum Entropy SD (MESD), Cartesian Tensor Fiber Orientation Distribution (CT-FOD), and discrete representation based SD (DR-SD) techniques, the SH representation allows closed form of spherical integration, efficient computation in a low dimensional space resided by the SH coefficients, and accurate peak detection on the continuous domain defined by the unit sphere. Third, NNSD is significantly less susceptible to producing false positive peaks in regions with low anisotropy. Evaluations of NNSD in comparison with Constrained SD (CSD), MESD, and DR-SD (implemented using L1-regularized least-squares with non-negative constraint), indicate that NNSD yields improved performance for both synthetic and real data. The performance gain is especially prominent for high resolution \({(1.25\,\text{mm})}^{3}\) data.
Jian Cheng, Rachid Deriche, Tianzi Jiang, Dinggang Shen, Pew-Thian Yap



A Novel Riemannian Metric for Geodesic Tractography in DTI

One of the approaches in diffusion tensor imaging is to consider a Riemannian metric given by the inverse diffusion tensor . Such a metric is used for white matter tractography and connectivity analysis. We propose a modified metric tensor given by the adjugate rather than the inverse diffusion tensor. Tractography experiments on real brain diffusion data show improvement in the vicinity of isotropic diffusion regions compared to results for inverse (sharpened) diffusion tensors.
Andrea Fuster, Antonio Tristan-Vega, Tom Dela Haije, Carl-Fredrik Westin, Luc Florack

Fiberfox: An Extensible System for Generating Realistic White Matter Software Phantoms

We present an open-source system, Fiberfox, for generating synthetic diffusion-weighted datasets. Fiberfox enables (1) definition of artificial white matter fibers, (2) signal generation from those fibers using multi-compartment modeling, and (3) simulation of magnetic resonance artifacts including Gibbs ringing, N∕2 ghosting and susceptibility distortions. With a comparative hardware phantom study we show that the synthetic datasets closely resemble real acquisitions. To demonstrate the relevance of Fiberfox for current research questions, we reveal the adverse effects of anisotropic voxels on the outcome of 11 different fiber tractography algorithms. Fiberfox is openly available and may find application in the validation and further development of diffusion-weighted image processing techniques such as super-resolution, denoising, tractography, diffusion modeling or artifact correction.
Peter F. Neher, Frederik B. Laun, Bram Stieltjes, Klaus H. Maier-Hein

Choosing a Tractography Algorithm: On the Effects of Measurement Noise

Diffusion MRI tractography has evolved into a widely used, important tool within neurosciences, providing the foundation for in-vivo fiber anatomy and hence for mapping of structural connectivity in the human brain. This renders it crucially important to understand the influence of the various MRI imaging artifacts on the tractography results. In this paper, we focus on the thermal noise that is present in all MRI measurements and compare its effect on the output of several established tractography algorithms. We create a reference dataset by denoising with a Non-Local Means filter and evaluate the effect of noise added to the reference on the tractography results with a Monte-Carlo simulation. Our results indicate that among the algorithms tested, the Tensorlines approach is the most robust for tracking white matter fiber bundles and both the Tensorlines and the Bayes DTI approach are good choices for calculating gray matter structural connectivity.
Andre Reichenbach, Mario Hlawitschka, Marc Tittgemeyer, Gerik Scheuermann

Uncertainty in Tractography via Tract Confidence Regions

Tractography allows us to explore white matter connectivity in diffusion MR images of the brain. However, noise, artifacts and limited resolution introduce uncertainty into the results. We propose a statistical model that allows us to quantify and visualize the uncertainty of a neuronal pathway between any two fixed anatomical regions. Given a sample set of tract curves obtained via tractography, we use our statistical model to define a confidence region that exposes the location and magnitude of tract uncertainty. The approach is validated on both synthetic and real diffusion MR data and is shown to highlight uncertain regions that occur due to noise, fiber crossings, or pathology.
Colin J. Brown, Brian G. Booth, Ghassan Hamarneh

Estimating Uncertainty in White Matter Tractography Using Wild Non-local Bootstrap

Statistics derived from diffusion MRI data, especially those related to tractography, are often highly non-linear and non-Gaussian with unknown complex distributions. In estimating the sampling distributions of these statistics, many existing techniques are limited by their reliance on models that assume normality and that are yet to be verified in complex situations where various noise sources, such as physiologic variation, scanner instability, and imaging noise, might be simultaneously present. In complex conditions as such, a viable solution is the bootstrap, which due to its distribution-independent nature is an appealing tool for the estimation of the variability of almost any statistic, without relying on complicated theoretical calculations, but purely on computer simulation. In this paper, we will examine whether a new bootstrap scheme, called the wild non-local bootstrap (W-NLB) , is effective in estimating the uncertainty in tractography data. In contrast to the residual or wild bootstrap , which relies on a predetermined data model, or the repetition bootstrap , which requires repeated signal measurements, W-NLB does not assume a predetermined form of data structure and obviates the need for time-consuming multiple acquisitions. W-NLB hinges on the observation that local imaging information recurs in the image. This self-similarity implies that imaging information coming from spatially distant (non-local) regions can be exploited for more effective estimation of statistics of interest. In silico evaluations indicate that W-NLB produces distribution estimates that are in closer agreement to those generated using Monte Carlo simulations, compared with the conventional residual bootstrap. Evaluations using in vivo data show that W-NLB produces results that are in agreement with our knowledge on the white matter connection architecture.
Pew-Thian Yap, Hongyu An, Yasheng Chen, Dinggang Shen

Group Studies and Statistical Analysis


Groupwise Deformable Registration of Fiber Track Sets Using Track Orientation Distributions

Diffusion-weighted imaging (DWI) and tractography allow to study the macroscopic structure of white matter in vivo. We present a novel method for deformable registration of unsegmented full-brain fiber track sets extracted from DWI data. Our method attempts to align the track orientation distributions (TODs) of multiple subjects, rather than individual tracks. As such, it can handle complex track configurations and allows for multi-resolution registration. We validated the registration method on synthetically deformed DWI data and on data of 15 healthy subjects, and achieved sub-voxel accuracy in dense white matter structures. This work is, to the best of our knowledge, the first demonstration of direct registration of probabilistic tractography data.
Daan Christiaens, Thijs Dhollander, Frederik Maes, Stefan Sunaert, Paul Suetens

Groupwise Registration for Correcting Subject Motion and Eddy Current Distortions in Diffusion MRI Using a PCA Based Dissimilarity Metric

Before starting a diffusion-weighted MRI analysis, it is important to correct any misalignment between the diffusion-weighted images (DWIs) that was caused by subject motion and eddy current induced geometric distortions. Conventional methods adopt a pairwise registration approach, in which the non-DWI, a.k.a. the b = 0 image, is used as a reference. In this work, a groupwise affine registration framework, using a global dissimilarity metric, is proposed, which eliminates the need for selecting a reference image and which does not rely on a specific method that models the diffusion characteristics. The dissimilarity metric is based on principal component analysis (PCA) and is ideally suited for DWIs, in which the signal contrast varies drastically as a function of the applied gradient orientation. The proposed method is tested on synthetic data, with known ground-truth transformation parameters, and real diffusion MRI data, resulting in successful alignment.
W. Huizinga, C. T. Metz, D. H. J. Poot, M. de Groot, W. J. Niessen, A. Leemans, S. Klein

Fiber Based Comparison of Whole Brain Tractographies with Application to Amyotrophic Lateral Sclerosis

A method is proposed for comparison between whole brain white matter tractographies derived from Diffusion Tensor Imaging (DTI) scans. The method performs fiber based comparisons between DTI-derived parameter values sampled along the fibers. The individual tractographies and the parameters sampling are done in each brain’s native space. No non-linear registration to a common space is required. Our method for fiber based comparison is especially useful as a first exploratory step in neurologic population studies. It provides pointers to the locations affected by the pathology of interest in the study. It is fully automatic and does not make any grouping assumptions on the fibers. The results are presented on a single fiber resolution level and any sub-group or tract of interest can be examined. The validation of the method was conducted using a set of scans from an Amyotrophic Lateral Sclerosis (ALS) study and comparing the outcome to previous findings.
Gali Zimmerman-Moreno, Dafna ben Bashat, Moran Artzi, Beatrice Nefussy, Vivian Drory, Orna Aizenstein, Hayit Greenspan

Statistical Analysis of White Matter Integrity for the Clinical Study of Typical Specific Language Impairment in Children

Children affected by Specific Language Impairment (SLI) fail to develop a normal language capability. To date, the etiology of SLI remains largely unknown. It induces difficulties with oral language which cannot be directly attributed to intellectual deficit or other developmental delay. Whereas previous studies on SLI focused on the psychological and genetic aspects of the pathology, few imaging studies investigated defaults in neuroanatomy or brain function. We propose to investigate the integrity of white matter in SLI thanks to diffusion Magnetic Resonance Imaging . An exploratory analysis was performed without a prior on the impaired regions. A region of interest statistical analysis was performed based, first, on regions defined from Catani’s atlas and, then, on tractography-based regions. Both the mean fractional anisotropy and mean apparent diffusion coefficient were compared across groups. To the best of our knowledge, this is the first study focusing on white matter integrity in specific language impairment. Twenty-two children with SLI and 19 typically developing children were involved in this study. Overall, the tractography-based approach to group comparison was more sensitive than the classical ROI-based approach. Group differences between controls and SLI patients included decreases in FA in both the perisylvian and ventral pathways of language, comforting findings from previous functional studies.
Emmanuel Vallée, Olivier Commowick, Camille Maumet, Aymeric Stamm, Elisabeth Le Rumeur, Catherine Allaire, Jean-Christophe Ferré, Clément de Guibert, Christian Barillot

Brain Connectivity


Disrupted Brain Connectivity in Alzheimer’s Disease: Effects of Network Thresholding

Diffusion imaging is accelerating our understanding of the human brain. As brain connectivity analyses become more popular, it is vital to develop reliable metrics of the brain’s connections, and their network properties, to allow statistical study of factors that influence brain ‘wiring’. Here we chart differences in brain structural networks between normal aging and Alzheimer’s disease (AD) using 3-T whole-brain diffusion-weighted images (DWI) from 66 subjects (22 AD/44 normal elderly). We performed whole-brain tractography based on the orientation distribution functions. Connectivity matrices were compiled, representing the proportion of detected fibers interconnecting 68 cortical regions. We found clear disease effects on anatomical network topology in the structural backbone – the so-called ‘k-core’ – of the anatomical network, defined by varying the nodal degree threshold, k. However, the thresholding of the structural networks – based on their nodal degree – affected the pattern and interpretation of network differences discovered between patients and controls.
Madelaine Daianu, Emily L. Dennis, Neda Jahanshad, Talia M. Nir, Arthur W. Toga, Clifford R. Jack, Michael W. Weiner, Paul M. Thompson

Rich Club Analysis of Structural Brain Connectivity at 7 Tesla Versus 3 Tesla

The ‘rich club’ is a relatively new concept in brain connectivity analysis, which identifies a core of densely interconnected high-degree nodes. Establishing normative measures for rich club organization is vital, as is understanding how scanning parameters affect it. We compared the rich club organization in 23 subjects scanned at both 7 and 3 T, with 128-gradient high angular resolution diffusion imaging (HARDI). The rich club coefficient (RCC) did not differ significantly between low and high field scans, but the field strength did affect which nodes were included in the rich club. We also examined 3 subjects with Alzheimer’s disease and 3 healthy elderly controls to see how field strength affected the statistical comparison. RCC did not differ with field strength, but again, which nodes differed between groups did. These results illustrate how one key parameter, scanner field strength, impacts rich club organization – a promising concept in brain connectomics research.
Emily L. Dennis, Liang Zhan, Neda Jahanshad, Bryon A. Mueller, Yan Jin, Christophe Lenglet, Essa Yacoub, Guillermo Sapiro, Kamil Ugurbil, Noam Harel, Arthur W. Toga, Kelvin O. Lim, Paul M. Thompson

Coupled Intrinsic Connectivity: A Principled Method for Exploratory Analysis of Paired Data

We present a novel voxel-based connectivity approach for paired functional magnetic resonance imaging (fMRI) data collected under two different conditions labeled the Coupled Intrinsic Connectivity Distribution (coupled-ICD). Our proposed method jointly models both conditions to incorporate additional spatial information into the connectivity metric. When presented with paired data, conventional voxel-based methods analyze each condition separately. However, nonlinearities introduced during processing can cause this approach to underestimate differences between conditions. We show that commonly used methods can underestimate functional changes and evaluate our coupled-ICD solution using a study comparing cocaine-dependent subjects and healthy controls. Our approach detected differences between paired conditions in similar brain regions as the conventional approaches while revealing additional changes. Follow-up seed-based analysis confirmed, via cross validation, connectivity differences between conditions in regions detected by coupled-ICD that were undetected using conventional methods. This approach of jointly analyzing paired connectivity data provides a new and important tool with many clinically relevant applications.
Dustin Scheinost, Xilin Shen, Emily Finn, Rajita Sinha, R. Todd Constable, Xenophon Papademetris

Power Estimates for Voxel-Based Genetic Association Studies Using Diffusion Imaging

The quest to discover genetic variants that affect the human brain will be accelerated by screening brain images from large populations. Even so, the wealth of information in medical images is often reduced to a single numeric summary, such as a regional volume or an average signal, which is then analyzed in a genome wide association study (GWAS). The high cost and penalty for multiple comparisons often constrains us from searching over the entire image space. Here, we developed a method to compute and boost power to detect genetic associations in brain images. We computed voxel-wise heritability estimates for fractional anisotropy in over 1,100 DTI scans, and used the results to threshold FA images from new studies. We describe voxel selection criteria to optimally boost power, as a function of the sample size and allele frequency cut-off. We illustrate our methods by analyzing publicly-available data from the ADNI2 project.
Neda Jahanshad, Peter Kochunov, David C. Glahn, John Blangero, Thomas E. Nichols, Katie L. McMahon, Greig I. de Zubicaray, Nicholas G. Martin, Margaret J. Wright, Clifford R. Jack, Matt A. Bernstein, Michael W. Weiner, Arthur W. Toga, Paul M. Thompson

Global Changes in the Connectome in Autism Spectrum Disorders

There is an increasing interest in connectomics as means to characterize the brain both in healthy controls and in disease. Connectomics strongly relies on graph theory to derive quantitative network related parameters from data. So far only a limited range of possible parameters have been explored in the literature. In this work, we utilize a broad range of global statistic measures combined with supervised machine learning and apply it to a group of 16 children with autism spectrum disorders (ASD) and 16 typically developed (TD) children, which have been matched for age, gender and IQ. We demonstrate that 86.7 % accuracy is achieved in distinguishing between ASD patients and the TD control using highly discriminative graph features in a supervised machine learning setting.
Caspar J. Goch, Basak Oztan, Bram Stieltjes, Romy Henze, Jan Hering, Luise Poustka, Hans-Peter Meinzer, Bülent Yener, Klaus H. Maier-Hein


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