Berlin Workshop on Statistics and Neuroimaging 2011

I. Aganj (Martinos Center for Biomedical Imaging, Harvard Medical School and LIDS, MIT, Boston, MA, U.S.A.)

A Hough transform approach to multiple-subject diffusion MRI tractography

Abstract: In this talk, I will introduce a global probabilistic diffusion MRI fiber tracking approach based on the voting process provided by the Hough transform. The proposed framework tests candidate 3D curves in the volume, assigning to each one a score computed from the diffusion images, e.g. from q-ball imaging ODFs which have been proven very successful in resolving multiple intravoxel fiber orientations. It then selects the curves with the highest scores as the potential anatomical connections. I will show experimental results on simulated and real high angular resolution diffusion images (HARDI).

B. Burgeth (Mathematik, Universität Saarbrücken)

PDE-based image processing for matrix fields

Abstract: Matrix fields make their appearance, for example, as the output of diffusion tensor magnetic resonance imaging (DT-MRI). This image acquisition method provides information about the diffusive properties of water molecules in tissue, and as such, knowledge about the tissue structure. Stemming from measurements these data types require tools for filtering and analysis. For scalar images various methods based on partial differential equations (PDEs), ranging from simple linear over nonlinear isotropic to anisotropic adaptive type, are at our disposal. In this talk we propose a generic framework based on the operator-algebraic properties of symmetric matrices that allows us to find the truly matrix-valued counterparts of PDEs used for the processing of scalar images. In order to solve these novel matrix-valued PDEs we extend the scalar numerical solution schemes to the matrix field setting. Numerical experiments with artificial and real DT-MRI data confirm that the matrix-valued processing tools indeed inherit the filtering qualities from their scalar predecessors.

J. Clayden (Neuroscience, University College London, UK)

Imaging connectivity: Statistical modelling and the wiring of the brain

Abstract: Without its complex pattern of connectivity, or "wiring", the information processing abilities of the brain would be substantially compromised. Diffusion magnetic resonance imaging (dMRI) allows us, in principle, to reconstruct the physical connections between brain regions in a living subject, but physiological noise and various imaging limitations make robust reconstruction difficult. In this talk an approach based on prior information and statistical modelling of the shapes of major connective structures will be discussed, along with the scope for applying this technique in clinical and nonclinical neuroscience.

M. Deppe (Universitätsklinikum Münster)

Why the neurologist wants more than one DTI: Quantitative assessment of microstructural brain tissue alterations

Abstract: Post-mortem studies have demonstrated that frequently many more brain structures are altered in neurological diseases than one would expect on the basis of conventional structural magnetic resonance imaging (MRI). This calls for a non-invasive imaging technique that allows detecting brain alterations also in tissue that appears to be normal in classical MRI. By examples of epilepsy syndromes, multiple sclerosis, amyotrophic lateral sclerosis, stroke, and a rare autoimmune disease, the potential use and clinical benefit of diffusion tensor imaging (DTI) as an additional routine MRI sequence will be demonstrated. One special focus is set to the quantitative characteristic, sensitivity, and robustness of DTI measures like the fractional anisotropy (FA) to monitor the progression of a neurological disease. A second focus is set to the functional relevance of microstructural tissue changes as assessed by FA.

R. Duits (Eindhoven University of Technology)

Enhancement of crossing fiber-structures in DW-MRI

Abstract: Diffusion-Weighted MRI (DW-MRI) measures local water diffusion in biological tissue, which reflects the underlying fiber structure. In order to enhance the fiber structure in the DW-MRI data we consider both (convection-)diffusions and Hamilton-Jacobi equations (erosions) on the coupled space R3xS2 of 3D-positions and orientations, embedded as a quotient in the group SE(3) of 3D-rigid body movements. These left-invariant evolutions are expressed in the frame of left-invariant vector fields on SE(3), which serves as a moving frame of reference attached to fiber fragments. The linear (convection-)diffusions are solved by a convolution with the corresponding Green's function, whereas the Hamilton-Jacobi equations are solved by a morphological convolution with the corresponding Green's function. Furthermore, we combine dilation and diffusion in pseudo-linear scale spaces on R3xS2. All methods are tested on DTI-images of the brain. These experiments indicate that our techniques are useful to deal with both the problem of limited angular resolution of DTI and the problem of spurious, non-aligned crossings in HARDI. Finally, we propose new fiber tracking algorithms based on the evolved DW-MRI.

The whole framework is a special case in a larger group theoretical framework. We will briefly highlight other imaging applications of other cases in this group theoretical framework.

References For short LNCS-articles see: [1](overview theory and applications), [2](overview finite difference implementation). For complete IJCV article see: [3]. For short neuro-imaging conference papers see: [4,5]. For large, recent technical report see: [6].

For other instances of our group-theoretical framework see:

• evolutions on invertible orientation scores (the SE(2)-case). [7,8,9,10,11]
• evolutions on Gabor transforms (the H(2d+1)-case) [12,13] and recent preprint.

[1] R. Duits, T. C. J. Dela Haije, A. Ghosh, E. J. Creusen, A. Vilanova, and B. ter Haar Romeny, "Enhancement of DW-MRI," in Scale Space and Variational Methods in Computer Vision (Lecture Notes in Computer Science), vol. 6667, pp. 1-13, September.
[2] E. J. Creusen, R. Duits, and T. C. J. Dela Haije, "Numerical schemes for linear and non-linear enhancement of DW-MRI," in Scale Space and Variational Methods in Computer Vision (Lecture Notes in Computer Science), vol. 6667, (Heidelberg), pp. 14-25, Springer-Verlag, September 2011.
[3] R. Duits and E. M. Franken, "Left-invariant diffusions on the space of positions and orientations and their application to crossing- preserving smoothing of hardi images.," vol. 92, pp. 231-264, March 2011.
[4] V. Prckovska, P. Rodrigues, R. Duits, A. Vilanova, and B. ter Haar Romeny, "Extrapolating fiber crossings from DTI data. can we infer similar fiber crossings as in HARDI ?," in CDMRI'10 MICCAI 2010 workshop on computational diffusion MRI, vol. 1, (Beijing China), pp. 26-37, Springer, august 2010.
[5] P. Rodrigues, R. Duits, A. Vilanova, and B. ter Haar Romeny, "Accelerated diffusion operators for enhancing dw-mri," in Eurographics Workshop on Visual Computing for Biology and Medicine, ISBN 978-3-905674-28-6, (Leipzig Germany), pp. 49-56, Springer, 2010.
[6] R. Duits, E. Creusen, A. Ghosh, and T. Dela Haije, "Diffusion, convection and erosion on SE(3)/({0}xSO(2)) and their application to the enhancement of crossing fibers." ArXiv, March 2011. http://arxiv.org/abs/1103.0656v4.
[7] R. Duits, M. Felsberg, G. Granlund, and B. M. ter Haar Romeny, "Image analysis and reconstruction using a wavelet transform constructed from a reducible representation of the Euclidean motion group," International Journal of Computer Vision, vol. 79, no. 1, pp. 79-102, 2007.
[8] R. Duits and E. M. Franken, "Left invariant parabolic evolution equations on SE(2) and contour enhancement via invertible orientation scores, part I: Linear left-invariant diffusion equations on SE(2)," Quarterly of Applied mathematics, AMS, vol. 68, pp. 255-292, June 2010.
[9] R. Duits and E. Franken, "Left invariant parabolic evolution equations on SE(2) and contour enhancement via invertible orientation scores, part II: Nonlinear left-invariant diffusion equations on invertible orientation scores," Quarterly of Applied mathematics, AMS, vol. 68, pp. 293-331, June 2010.
[10] E. Franken and R. Duits, "Crossing-preserving coherence-enhancing diffusion on invertible orientation scores," International Journal of Computer Vision (IJCV), vol. 85, no. 3, pp. 253-278, 2009.
[11] E. M. Franken, Enhancement of Crossing Elongated Structures in Images. PhD thesis, Department of Biomedical Engineering, Eindhoven University of Technology, The Netherlands, Eindhoven, October 2008. cum laude, http://www.bmia.bmt.tue.nl/people/EFranken/PhDThesisErikFranken.pdf.

Ch. Gaser (FSU Jena)

Computational morphometry for the early detection of brain diseases

Abstract: MR brain morphometry has undergone tremendous changes in the last years with the availability of new computational techniques. These techniques overcome the restriction of regions of interest analyses and allow the analysis of every voxel in the image. Many laboratories have developed sophisticated algorithms and the number of applications to clinical cohorts is growing. However, the current clinical practise is still to qualitatively assess structural alterations by an experienced radiologist. I will present two machine learning approaches to aid diagnosis using computational morphometry. The idea is to use the distribution of anatomical alterations of the brain in a large training database to classify (and diagnose) a given new subject. We demonstrate that early detection of dieseases such as Alzheimer's dementia and schizophrenia is possible up to three years before the onset of the disease with accuracy rates about 90%.

J.-D. Haynes (BCCN Berlin)

Multivariate decoding in neuroimaging

Abstract: Multivariate decoding has recently emerged as a novel and powerful analysis tool in functional neuroimaging. The application of multivariate pattern recognition techniques for the analysis of fMRI and EEG signals has several important advantages over more conventional analyses based on 'mass-univariate' approaches. Pattern recognition can help increase the sensitivity for detecting experimental effects. It can assess the amount of information 'encoded' in a particular brain region under various cognitive tasks, even for fine-grained representations that are often assumed to be inaccessible to current neuroimaging techniques. It provides a more powerful framework for analysing neural representations that takes into account their distributed nature. It can also be extended to reveal the encoding of similarity structures and representational spaces. Furthermore, its increased sensitivity makes simple forms of 'brain reading' possible, where mental states are decoded from neuroimaging signals. This opens up a window for potential applications such as brain-computer-interfacing, biofeedback, clinical diagnostics or even the detection of deception and neuromarketing. After an overview some recent methodological developments will be introduced, such as surface-base searchlight decoding, cortical-cortical-receptive field measurement and surface-wavelet-based pattern analysis. Then the talk will briefly show show the usefulness of decoding techniques for the study of human behavior, clinical diagnostics and neurotechnological applications.

H.-C. Hege (ZIB Berlin)

Light-microscopy-based anatomical reconstruction, simulation and analysis of cortical neural networks

Abstract: One fundamental challenge in neuroscience is to understand how brains process sensory information about their environment and how this can be related to the animals' behavior. A widely used model system is the somatosensory whisker system in rodents. The sensory input from each whisker is processed by neuronal networks organized in a cortical column and a one-to-one correspondence exists between whiskers and barrel columns in the primary somatosensory cortex.
We describe a pipeline for reverse engineering anatomically realistic cortical networks that represent an average cortical column. For this, anatomical data, such as number and morphology of neurons, are acquired using several imaging and reconstruction techniques and registered into a common coordinate system. Then the network wiring is defined using an estimated number of synaptic contacts, based on axo-dendritic overlap. Given realistic input measured in-vivo, the signal flow through the network can be numerically simulated.
The specification of anatomical and functional network properties comprises a high-dimensional parameter space. Of paramount interest is how network output depends on these parameters and what constitutes a valid set of parameters that result in realistic output. Specific tools for visually supported analysis of such networks and their behavior will be presented.

R. Heidemann (Department of Neurophysics, MPI for Human Cognitive and Brain Sciences Leipzig)

Ultra-high spatial and angular resolution in diffusion MRI

Abstract: There is ongoing debate whether using a higher spatial resolution (sampling k-space) or a higher angular resolution (sampling q-space angles) is the better way to improve diffusion MRI (dMRI) based tractography results in living humans. In both cases, the limiting factor is the signal-to-noise ratio (SNR), due to the restricted acquisition time. One possible way to increase the spatial resolution without sacrificing either SNR or angular resolution is to move to a higher magnetic field strength. Nevertheless, dMRI has not been the preferred application for ultra-high field strength (7 Tesla). This is because single-shot echo-planar imaging (EPI) has been the method of choice for human in vivo dMRI. EPI faces several challenges related to the use of a high resolution at high field strength, for example, distortions and image blurring. These problems can easily invalidate the expected SNR gain related to the higher field strength. In this lecture, the basics of dMRI are briefly summarized and a new method is described, which can be used to address the afore mentioned challenges. An adapted EPI sequence is used in conjunction with a combination of ZOOmed imaging and Partially Parallel Acquisition (ZOOPPA). This approach can produce high quality diffusion-weighted images with high spatial and angular resolution at 7 Tesla. Examples of in vivo human dMRI are provided with isotropic resolutions of 1 mm and 800 µm. These data sets are particularly suitable for resolving complex and subtle fiber architectures, including fiber crossings in the white matter, anisotropy in the cortex and, for the first time, fibers entering the cortex.

Ch. Lenglet (CMRR, University of Minnesota, Minneapolis, MN, U.S.A.)

Computational diffusion MRI and subject-specific connectome

Abstract: Diffusion MRI provides unprecedented insights into the organization of the human brain. It also presents numerous mathematical and computational challenges to optimize data acquisition and image reconstruction. In this talk, I will give an introduction to these problems, such as the estimation of white matter fiber orientations and pathways reconstruction. I will also show how these techniques can be leveraged to build subject-specific models of the human brain connectome using high-resolution 7T MRI.

R. Mekle (Medizinische Messtechnik, PTB)

In vivo MR spectroscopy at high fields: Some principles, quantification, and applications

Abstract: Enhanced sensitivity and increased spectral dispersion are the major benefits for magnetic resonance spectroscopy (MRS) at high main magnetic fields Bo (>= 3 Tesla(T)). Recent studies using short echo time (TE) MRS have shown that these benefits can be translated into improved metabolite quantification. With this background in mind, the basic principles of MRS data acquisition and quantification will be briefly described. As method of choice for data analysis, LCModel will be introduced. Results from single volume MRS studies at 3T and 7T, as well as from MR spectroscopic imaging (MRSI) experiments at 3T will be presented. Possible applications to clinical and neuroscience questions will be outlined. In particular, the detection of the neurotransmitter GABA in the human amygdala that is of great interest to psychologists due to its believed central role in the modulation of fear and anxiety will be discussed.

S. Mohammadi (Wellcome Trust Centre for Neuroimaging, UCL, London, UK)

Artefact correction in DTI (ACID)

Abstract: Diffusion tensor imaging (DTI) is widely used in research and clinical applications, but still suffers from substantial artefacts, which bias quantitative DTI indices or reduce their sensitivity. Here, the sources of different DTI artefacts are briefly discussed; retrospective correction methods and their software implementation are presented. One major part of the DTI artefacts is related to the strong diffusion sensitizing gradients, e.g., eddy currents, gradient nonuniformity and miscalibration, as well as vibration of the patient table.

Eddy currents (ECs) lead to image distortions, which differ for different diffusion gradient directions, and can be corrected using image registration methods.

The nonuniformity and miscalibration of gradients and other local perturbation fields (LPF) like the ECs can lead to a local mismatch between the effective and the expected diffusion gradients, resulting in a spatially varying error in the diffusion weighting B matrix and diffusion tensor estimation. A method is presented to measure these LPFs using a water phantom and correct for the error in the B matrix.

Vibrations induced by the strong diffusion gradients in DTI could cause an echo shift in k-space and consequential signal-loss in diffusion weighted images. A model of vibration-induced echo shifts is developed, showing that asymmetric k-space coverage in widely used Partial Fourier acquisitions results in locally differing signal loss in images acquired with reversed phase encoding direction (blip-up/blip-down images). Based on this theory a correction of vibration artefacts in DTI is introduced, using phase-encoding reversal (COVIPER) by combining blip-up and blip-down images, each weighted by a function of its local tensor-fit error.

The brief overview over the different correction methods will be complemented by a discussion of the implications of the different artefacts and their correction with respect to current and future applications in basic and clinical neuroscience.

J. Polzehl (WIAS Berlin)

Modeling the orientation distribution function by mixtures of angular central Gaussian distributions

Abstract: We develop a tensor mixture model for diffusion weighted imaging data using an automatic model order selection criterion for the number of tensor components in a voxel. We show that the weighted orientation distribution function for this model can be expanded into a mixture of angular central Gaussian distributions. We investigate properties of this model in extensive simulations and in a high angular resolution scan of a human brain. The results suggest that the model improves imaging of cerebral fiber tracts. In addition, inference on canonical model parameters could potentially provide novel clinical markers of altered white matter. Software to compute the tensor mixture model from diffusion weighted MRI data is available in the programming language R.

Y. Rosseel (Ghent University, Gent, Belgium)

spmR: an R package for fMRI data analysis

Abstract: spmR is an R package for fMRI data analysis. Although several R packages for fMRI are available, the spmR package is unique in that it is capable to mimic the results of the widely used (Matlab-based) SPM package. For standard fMRI analyses, the spmR package can be used as a plugin replacement for SPM, yielding exactly the same results. This is important if the Matlab environment is not available (for example in high-performance computing environments), yet SPM comparable results are highly desirable. The R environment is ideal to run large-scale simulation studies. If the fMRI analysis is just a part of a larger pipeline, access to a dedicated R package for fMRI is enormously convenient. In this talk, I will discuss the original motives for developing this package, why it was abandoned, and why it is reborn.

V. Schmid (Institut für Statistik, LMU München)

Modelling dynamic images using hierarchical Bayes models

Abstract: Dynamic images, i.e., 2D or 3D images acquired over time, are used in biology and medicine in order to capture rapid kinetic processes in organisms in vivo and can be derived with a variety of technologies, including, amongst others, magnetic resonance imaging (MRI). From a statistical point-of-view dynamic images - independent from the modalities they have been acquired with - share a similar data structure. The signal time curve in each voxel can be described by kinetic models based on the biological processes in the organism. Biological models for dynamic images are often oversimplified to ease parameter fitting. We use Bayesian inference to allow for robust parameter estimation in more realistic biological models. By using contextual prior information, more robust estimators can be obtained. Examples for contextual information are, e.g., spatial structures or patient-specific information. Often, adaptive approaches are necessary. The contextual information can be used via hierarchical Bayes models. In addition, we will explore approaches to determine the best model, e.g., the number of compartments in compartmental models. Applications include DCE-MRI and cardio-vascular perfusion MRI.

M. Tittgemeyer (MPI für neurologische Forschung Köln)

Relating connectional architecture to brain function using diffusion imaging

Abstract: Neuroanatomy places critical constraints on the functional connectivity of the cerebral cortex. Unfortunately, microstructural borders, the individual cytoarchitecture and the distribution of neuroreceptors cannot be visualized in a living brain used for functional studies. However, brain function also strongly depends upon anatomical connectivity, and understanding brain function in terms of connectional architecture is therefore a major goal of neuroimaging. Diffusion-weighted magnetic resonance imaging (dMRI) offers the opportunity to explore the brains connectional architecture in the individual living subject and tractographic methods provide excellent means to extract connectivity information from these data sets.
In the talk, I will address recent approaches to use diffusion-weighted and functional MRI to test structure- function relations directly. Specifically, I focus on diffusion tractography, as an objective tool for parcellation of the human cortex into functionally meaningful (sub-)regions, and as a method to specify anatomically informed priors for dynamic causal models of fMRI data.

H.U. Voss (Citigroup Biomedical Imaging Center, Weill Cornell Medical College, New York, NY, U.S.A.)

Magnetic resonance imaging of structural and functional connectivity of the brain

Abstract: We review the MRI physics behind magnetic resonance diffusion tensor imaging (DTI) used to image structural connectivity of the brain. DTI is sensitive to the thermal diffusion of water protons in the brain parenchyma and allows for mapping parameters influenced by microscopic tissue properties such as main fiber direction and fiber density. Advanced methods like high angular resolution diffusion imaging (HARDI) can also test for crossing, branching, and 'kissing' fibers. A more complete picture of connectivity arises when also functional signatures of connections in the brain are imaged and combined with DTI. In particular, we will briefly review the very recent approach of optogenetic functional MRI that has the potential to reveal more about functional connectivity and its complexities involved than any other functional MRI method.

B. Whitcher (Mango Solutions, Imperial College London, UK)

Quantitative medical image analysis using R

Abstract: The quantitative analysis of medical imaging data is complex and involves a wide variety of mathematical/statistical techniques. Over the last twenty years software packages, whether proprietary or academic or public domain, have been developed. R is a free software environment for statistical computing and graphics. Although R is not the only offering to the field of neuroscience, there are a moderate collection of packages specifically for medical imaging and a community is growing. I believe that open-source programming environments and public-domain medical imaging data sets are key to incrementally improving the quality of the methodology and implementation of algorithms for medical imaging. I will provide an overview of quantitative methods for medical image analysis using specific packages developed in the R community and relevant clinical data.

R. Yotter (FSU Jena)

Surface modeling and analysis of structural MRI data

Abstract: A geometric model of the cortical surface is most often represented using a polygonal mesh. This mesh is constructed from volumetric MRI data, and it facilitates new powerful analysis approaches that are not possible using volumetric data alone. In this introductory talk, we will cover basic topics, including: how to construct a surface mesh from volumetric data; limitations and pitfalls of surface mesh construction; and the motivation for constructing a cortical surface mesh, including a survey of surface analysis methods and what these methods have revealed about cortical anatomy.

S. Becker (WIAS Berlin)

Model-free structural adaptive smoothing of diffusion weighted images

Abstract: In this talk we will present a smoothing method for diffusion weighted imaging data S : R3xS2 -> R using the embedding of R3xS2 into SE(3) as introduced by R. Duits and E. Franken (2010). The algorithm is based on the propagation-separation approach of J. Polzehl and V. Spokoiny (2006) and can be applied without reference to a specific model like the diffusion tensor or higher order modeling. Further, this algorithm is able to reduce noise without blurring the structural borders. We show properties of this structural adaptive method, both for simulated and experimental data.

Bibliography
R. Duits and E. Franken (2010). Left-Invariant Diffusions on the Space of Positions and Orientations and their Application to Crossing-Preserving Smoothing of HARDI images. International Journal of Computer Vision, 1-34.
J. Polzehl and V. Spokoiny (2006). Propagation-separation approach for local likelihood estimation. Probab. Theory and Relat. Fields, 135:335-362.

Y. Chen (MPI for Human Cognitive and Brain Sciences Leipzig)

Multi-scale mapping of fMRI information on the cortical surface: A graph wavelet based approach

Abstract: The power and efficiency of multivariate decoding for functional magnetic resonance imaging (fMRI) data has been demonstrated by numerous studies in recent years. The strength of this methodology lies in the way it jointly analyzes the brain activity across multiple locations (voxels). Importantly, patterning of functional units in the brain occurs at multiple spatial scales, ranging from cortical columns to Brodman areas and entire functional networks. However, most decoding approaches have not yet managed to provide a bias free assessment of pattern information across different spatial scales. To address this question, here we used a bank of wavelet filters to decompose the activity patterns on the cortical surface into components of different spatial scales. Then we assessed and compared the information carried by each band separately. Particularly, we exploited the graph representation of the cortical surface mesh, took the graph analogue of the Fourier domain, namely the eigenspectrum of the mesh graph Laplacian, and defined a graph wavelet function and a series of its dilations on it. The filter bank implemented with these wavelet functions has gradually changing sizes of spatial support, and can be used to extract the informative components of the activity pattern on the cortical surface in different scales. A standard discriminant analysis and statistical test were further conducted to assess the information in the extracted components. We applied the method to the data sets of two real fMRI experiments. Our results show that the distribution of the information can be reconstructed at different spatial scales. The informative scales vary depending on cognitive tasks. In summary, by highlighting the importance of differentiating spatial scale factors, our method actively prompts a new approach for multi-scale multivariate fMRI analysis.

M. Reuter (Mass.General Hospital / Harvard Medical / MIT, Martinos Center for Biomedical Imaging)

Unbiased longitudinal processing of structural MRI in FreeSurfer

Abstract: Automatic longitudinal image analysis has become increasingly important with the availability of large sets of longitudinal imaging data. Longitudinal studies are necessary to distinguish between cross-sectional and longitudinal effects, for example, to analyze change in neurodegenerative diseases or aging and to evaluate disease modifying therapies. Particularly in drug trials where small effect sizes need to be detected, a longitudinal design can provide the necessary power by significantly increasing the reliability of the measures. In this talk we introduce a longitudinal image processing pipeline for the automatic reconstruction and segmentation of brain MRI, available freely within the FreeSurfer software package. The presented methods are based on inverse consistent robust registration and within-subject template creation and are designed to be unbiased with respect to any of the time points. They can significantly increase precision and power while preserving the ability to detect large deviations, as encountered in neurodegeneration.

Ch. Rügge (Institut für Numerische und Angewandte Mathematik, Uni Göttingen)

On the design of regularized Newton-type methods for all-at-once reconstructions from HARDI datasets

Abstract: In High Angular Resolution Diffusion Imaging one tries to reconstruct orientation distribution functions (ODFs) containing information on the directional dependence of water diffusion from a set of diffusion weighted (DW) MR images. Reconstruction methods usually consist of several independent k-space-inversions for each DW image followed by reconstruction of the ODF and possibly by post-processing and smoothing. Each of these steps only uses a part of the available data. In this talk, ODF reconstruction will be modelled as a non-linear inverse problem which is tackled by a constrained Newton-type method. Special emphasis is placed on the design of penalty terms that reflect the structure of the unknown solution. Even though this all-at-once approach is computationally rather challenging, it has the potential to avoid loss of information that may occur in multi-step methods. The performance of the proposed method will be illustrated in numerical examples.

M. Welvaert (Ghent University)

Simulating fMRI data: the R package neuRosim

Abstract: Functional magentic resonance imaging (fMRI) is used as a powerful imaging tool to locate BOLD activation in time and in particular in place. With about 3300 publications in 2010 and heading the same number in 2011, the technique is also very popular in the neuroimaging community. Unfortunately, the ground truth of the data acquired using fMRI is unknown. This is a major problem because the location of activity in the data requires complex analysis processes that need to be validated to ensure that the analysis techniques are working properly. Validation is only possible if the ground truth is known. As a solution, fMRI data are generated artificially. However, simulation studies could be considered as a minority in the fMRI literature (only 100 publications in 2010). Moreover, there is currently no consensus on how to simulate fMRI data, neither is there any attempt made to converge and validate the existing simulation methods. Generally, simulation studies are conducted using ad-hoc methods and in-house software routines.

neuRosim is an R package (http://www.r-project.org) that aims to serve as a general standardized software platform to simulate fMRI data. Currently, the package gathers the functionalities of existing simulation studies with the extension to more biophysically plausible models. The main focus lies on the inclusion of several noise sources (for example system noise, temporally and spatially correlated noise, physiological noise, ...).

neuRosim can be downloaded from CRAN (http://cran.r-project.org) and is released with a GPL licence, meaning that it is completely open-source and can be freely used under almost all platforms (Windows, Mac and Unix). The data generation in neuRosim is fairly fast and, depending on the dimensions of the dataset, can be easily computed on a standard desktop within a few minutes. Therefore, the simulation process can be smoothly incorporated in large simulation studies.

During the presentation, we will stress the importance for validated simulation research and demonstrate how neuRosim can contribute by comparing the differences between implemented simulation methods. Further we will show examples that demonstrate the functionalities of the package and discuss briefly our plans for coming updates.

J. Durnez and B. Moerkerke (Ghent University),

Adaptive thresholding for fMRI data

Abstract: In the analysis of functional MRI-data, several thresholding procedures are available to account for the huge number of volume units or features that are tested simultaneously. The main focus of these methods is to prevent an inflation of false positives. However, this comes with a serious decrease in power and therefore leads to a problematic imbalance between type I and type II errors (Lieberman & Cunningham, 2009).

In this research, we present a method to estimate the number of activated features. The goal is twofold:
-- Given the expected number of active units, widely used methods to control the false discovery rate (FDR) can be made adaptive and more powerful.
-- The type I and type II error rate following such a thresholding technique can be estimated enabling a direct trade-off between sensitivity and specificity.
Chen, Wang, Eberly, Caffo, Schwartz (2009) argue that activation foci in fMRI data are often small and local leading to a large proportion of null voxels. However, task-related activation is expected to occur in clusters of voxels rather than in isolated single voxels. We consider peaks of activation instead of voxels and provide a procedure to estimate the number of active peaks. Concentrating on peaks leads to an enormous data reduction, and the proportion of non-null hypotheses can be expected to be much smaller among peaks than among voxels.

Given an estimate of the number of active and non-active peaks, we demonstrate how an adaptive FDR controlling procedure on peaks can be obtained and how false positive and negative rates associated with this procedure can be estimated. This allows researchers to reconsider the balance between sensitivity and specificity in function of study goals. The method is evaluated and illustrated using simulation studies and a real data example.

References
Lieberman, M. D. and Cunningham, W. A. (2009), Type I and Type II error concerns in fMRI research; re-balancing the scale, Social cognitive and affective neuroscience 4, 423-428
Chen, S., Wang, C., Eberly, L.E., Caffo, B.S. and Schwartz, B.S. (2009), Addaptive control of the false discovery rate in voxel-based morphometry, Human Brain Mapping 30, 2304-2311

T. W. Riffert, A. Anwander and T. R. Knösche (Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany)

Bingham distribution based quantification of fiber bundle properties

Abstract: Introduction In diffusion MRI (dMRI), one method used for modeling multiple fiber orientations in regions with complex microstructure is spherical deconvolution [1]. This produces a fiber orientation density function (fODF).. Most often, this function can be seen as superposition of multiple peaks, each associated to one relatively coherent fiber population (bundle). By parameterizing these peaks one may be able to disentangle and characterize these bundles. In this line, the fODF peaks can be approximated by Bingham distributions [2,3,4], capturing second-order statistics of the fiber orientations. Using a geometric fitting approach we decomposed the fODF into a sum of Bingham distributions.

Methods High resolution dMRI scans were acquired on a Siemens 3T TIM Trio scanner (1.5mm isotropic, 60 directions, b=1000s/mm², 32-channel array head coil, GRAPPA 3, AV=3) from a single healthy subject. We performed a 6th order spherical harmonic approximation of the fODF. Assuming each of the fODF maxima represents a single fiber peak, we estimated the parameters of a scaled Bingham distribution modeling the underlying fiber bundle. The Bingham parameters directly represent statistical properties which were used to estimate properties of fiber compartments such as the peak magnitude and the fiber spread.

Results The Bingham distribution can closely approximate the peaks of the fODF. The scaling parameter of the distribution provides quantifies the relative contribution of the different compartments. The two concentration parameters of the Bingham distribution characterize the peak anisotropy and provide a measure for the spread of fiber compartments with a circular shape of the distribution e.g. in the corpus callosum and a strong fanning of the fibers of the major peak in the internal capsule.

Conclusions The approximation of single-fiber peaks using a Bingham distribution supplies a powerful tool for parametric quantification of fiber bundle properties which might replace measures derived from the diffusion tensor (e.g. FA) in areas of crossing fibers. Combination with tractography will enable the estimation of parameters along single fiber tracts.

References
[1] Tournier et al, Neuroimage 23, 2004.
[2] Seunarine et al, ICCV, 2008.
[3] Kaden et al, Neuroimage, 2007.
[4] Bingham, Ann Stat, 1974.

S. Roels, T. Loeys and B. Moerkerke (Ghent University)

Evaluating bootstrap procedures for fMRI data

Abstract: Over the last decade the bootstrap procedure is gaining popularity in the statistical analysis of neuro-imaging data. This powerful procedure can be used for example in the non-parametric analysis of neuro-imaging data. As fMRI data are complexly structured with both temporal and spatial dependencies, such bootstrap procedures may indeed offer an elegant solution. However, a thorough investigation on the most appropriate bootstrapping procedure for fMRI data has to our knowledge never been performed. Friman and Westin (2005) showed that a bootstrap procedure based on pre-whitening the temporal structure of fMRI time series is superior to procedures based on wavelets or Fourier decomposition of the signal, especially in the case of blocked fMRI designs. For time-series, several bootstrap schemes can be exploited though (see e.g. Lahiri, 2003). For the re-sampling of residuals from general linear models fitted on fMRI data, we examine more specifically here the differences between 1) bootstrapping pre-whitened residuals which are based on parametric assumptions of the temporal structure, 2) a blocked bootstrapping which avoids making such assumptions (with several variants like the circular bootstrap, ...), and 3) a combination of both bootstrap procedures. We furthermore explore whether the bootstrap procedures is best applied before or after smoothing the volume of interest. Based on real data and simulation studies, we discuss the temporal and spatial properties of the bootstrapped volumes for all possible combinations and find interesting differences.

References
Friman, O. and Westin, F.-J. (2005). Resampling fmri time series. NeuroImage, 25, 859-867.
Lahiri, S. N. (2003). Resampling Methods for Dependent Data. Springer series in statistics. Springer-Verlag.

B. Roelstraete and Y. Rosseel (Ghent University)

Can partial Granger causality really eliminate the influence of exogenous inputs and latent variables? A reply to Guo et al. 2008.

Abstract: Introduction In the 2008 paper by Guo and collaborators, conditional and partial G-causality were compared using an extensively applied toy model in Granger tests containing an exogenous input and a latent variable. The influence of these exogenous inputs and latent variables was examined on the performance of conditional and partial G-causality in retrieving the true underlying causal network. The conclusion of the authors was that, although partial G-causality could only theoretically fully eliminate the influence of latent variables and exogenous inputs in the case where this influence is equal over all variables, it outperformed conditional G-causality in many other cases. Based on the numerical results it was stated that, in contrast to the conditional G-causality statistic (F2), the partial G-causality statistic (F1) can take negative values. This statement is not explained any further and has recently been challenged by Barrett and coworkers, who deem it theoretically impossible to obtain negative F1 values. This was also confirmed by their simulations. The question thus arises why Guo et al. found negative F1 values. A second issue is the way in which the CI's of the F1 tests were constructed. The methods section mentions that 2000 realizations of the time series were generated and that CI's were calculated by taking 3 sd around the mean F1 estimate. This is referred to as the bootstrap approach, which is confusing. Bootstrapping would involve resampling with repetition from the same realization and calculating the CI from that distribution, which is not the case here. It is therefore not clear, from the methods section whether an actual bootstrap was performed and if so, how exactly the bootstrap was parameterized. A new simulation study was performed to clear these issues.

Method Data generation was identical to Guo et al. Multivariable autoregressive (AR) time series of length 2000 were generated from the toy model from Ding et al. (2006). The influence of exogenous and/or latent variables could either be absent, weak, or strong, but was always identical for every time series. This reflected the theoretical case where partial G-causality should have the maximum advantage over conditional G-causality. For every condition one hundred realizations were generated and conditional and partial G-causality tests were computed.

Data analysis Data were analyzed using Anil Seth's GCCA toolbox for Matlab. Conditional G-causality was estimated by using standard parametric tests. We chose a probability threshold for significance of 5% with Bonferroni correction. To compute the partial G-causality confidence intervals, the bootstrap function was used (with a window of 10 data points) and again a significance of 5% with Bonferroni correction was chosen as the significance threshold.

Results and Discussion In contrast to the original paper, we never found negative F1 values. Perhaps a small coding error could have caused this finding. We also found conditional G-causality to perform better than partial G-causality in the presence of exogenous variables. In the presence of latent variables, partial G-causality was better able to control for false positives than conditional G-causality, but it systematically failed to detect the feedback loop in the network. Conditional G-causality only failed to detect the feedback loop when strong latent variables were present in the network. We believe these results to be of high practical value. Although partial G-causality might in theory be better able to eliminate the negative influence of exogenous and latent variables, in practice it will not always be the case.

R. Seurinck, B. Moerkerke, S. Kühn, W. Fias and S. Van Aelst (Ghent University)

fMRI pattern recognition: the influence of feature selection on various classifiers

Abstract: Recently, it has been suggested that classification is a valuable alternative for the classic mass-univariate voxel-based analysis of fMRI data. However, the amount of voxels in fMRI vastly exceeds the number of observations, requiring feature selection. Data from a study originally published by Ishai et al. (2000), available from the fMRIDC (accession no. 2-2000-1113D), were reanalyzed to assess the influence of feature selection on the behavior of three popular classification algorithms, a Linear Discriminant Analysis (LDA), a linear Support Vector Machine (SVM) and a Gaussian non-linear SVM.

Two informed methods of feature selection were used: a singular value decomposition (SVD) and an ANOVA, respectively resulting in uncorrelated components and correlated voxels as features. In addition we also used random selection of voxels as an uninformed selection method to control for the amount of features. Both informed methods of feature selection resulted in a dramatic increase in classification accuracy compared to the random feature selection, irrespective of classification algorithm.

A further comparison of SVD and ANOVA revealed differential effects on classification accuracy. The LDA demonstrated a decrease in prediction accuracy as the amount of features approached the number of observations. Furthermore, this decrease had an earlier onset when voxels (ANOVA) instead of components (SVD) were used as input. For the Gaussian SVM, the penalty parameter of the algorithm needed to be higher when components were used, as opposed to voxels, to avoid that the performance of the classifier decreased with an increasing amount of features. The results demonstrate that the feature selection method has an important impact on classification accuracy and highlight the importance of tuning the hyperparameters of a classification algorithm for an optimal performance.