Figure 1: (a)Cluttered image showing the fibers in a healthy brain by seeding in the whole volume. The color coding shows main eigenvalue. (b)(c)(d) Clustering results. The color coding represents the clusters.(b) Hierarchical clustering with single-link and mean distance between fibers. (c) The same as (b) but with closest point distance between fibers. (d) Shared nearest neighbor with mean distance between fibers. Fiber tracking is a standard approach for the visualization of the results of Diffusion Tensor Imaging (DTI). If fibers are reconstructed and visualized individually through the complete white matter, the display gets easily cluttered making it difficult to get insight in the data. Various clustering techniques have been proposed to automatically obtain bundles that should represent anatomical structures, but it is unclear which clustering methods and parameter settings give the best results. We propose a framework to validate clustering methods for white-matter fibers. Clusters are compared with a manual classification which is used as a ground truth. For the quantitative evaluation of the methods, we developed a new measure to assess the difference between the ground truth and the clusterings. The measure was validated and calibrated by presenting different clusterings to physicians and asking them for their judgement. We found that the values of our new measure for different clusterings match well with the opinions of physicians. Using this framework, we have evaluated different clustering algorithms, including shared nearest neighbor clustering, which has not been used before for this purpose. We found that the use of hierarchical clustering using single-link and a fiber similarity measure based on the mean distance between fibers gave the best results.

We describe a virtual reality environment for visualizing tensorvalued volumetric datasets acquired with diffusion tensor magnetic resonance imaging (DT-MRI). We have prototyped a virtual environment that displays geometric representations of the volumetric second-order diffusion tensor data and are developing interaction and visualization techniques for two application areas: studying changes in white-matter structures after gamma-knife capsulotomy and pre-operative planning for brain tumor surgery. Our feedback shows that compared to desktop displays, our system helps the user better interpret the large and complex geometric models, and facilitates communication among a group of users. CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism---Virtual Reality

We present a threads and halos representation for interactive volume rendering of vector-field structure and describe a number of additional components that combine to create effective visualizations of multivalued 3D scientific data. After filtering linear structures, such as flow lines, into a volume representation, we use a multi-layer volume rendering approach to simultaneously display this derived volume along with other data values. We demonstrate the utility of threads and halos in clarifying depth relationships within dense renderings, and we present results from two scientific applications: visualization of second-order tensor valued magnetic resonance imaging (MRI) data and simulated 3D fluid flow data. In both application areas, the interactivity of the visualizations proved to be important to the domain scientists. Finally, we describe a PC-based implementation of our framework along with domain specific transfer functions, including an exploratory data culling tool, that enable fast data exploration. Keywords--- Scientific Visualization, Diffusion Tensor Imaging (DTI), Fluid Flow Visualization, Medical Imaging, Direct Volume Rendering, Volume Graphics, Volume Shading, Multi-textures, PC Graphics Hardware I.

Abstract not found

While tensors occur in many areas of science and engineering, little has been done to visualize tensors with order higher than two. Tensors of higher orders can be used for example to describe complex diffusion patterns in magnetic resonance imaging (MRI). Recently, we presented a method for tracking lines in higher order tensor fields that is a generalization of methods known from first order tensor fields (vector fields) and symmetric second order tensor fields. Here, this method is applied to magnetic resonance imaging where tensor fields are used to describe diffusion patterns for example of hydrogen in the human brain. These patterns align to the internal structure and can be used to analyze interconnections between different areas of the brain, the so called tractography problem. The advantage of using higher order tensor lines is the ability to detect crossings locally, which is not possible in second order tensor fields. In this paper, the theoretical details will be extended and tangible results will be given on MRI data sets.

Abstract — Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging method that can be used to measure local information about the structure of white matter within the human brain. Combining DTI data with the computational methods of MR tractography, neuroscientists can estimate the locations and sizes of nerve bundles (white matter pathways) that course through the human brain. Neuroscientists have used visualization techniques to better understand tractography data, but they often struggle with the abundance and complexity of the pathways. In this paper, we describe a novel set of interaction techniques that make it easier to explore and interpret such pathways. Specifically, our application allows neuroscientists to place and interactively manipulate box- or ellipsoid-shaped regions to selectively display pathways that pass through specific anatomical areas. These regions can be used in coordination with a simple and flexible query language which allows for arbitrary combinations of these queries using Boolean logic operators. A representation of the cortical surface is provided for specifying queries of pathways that may be relevant to gray matter structures, and for displaying activation information obtained from functional magnetic resonance imaging. By precomputing the pathways and their statistical properties, we obtain the speed necessary for interactive question-and-answer sessions with brain researchers. We survey some questions that researchers have been asking about tractography data and show

Figure 1: The corona radiata. Our system uses dynamic queries to find structure in neural pathways suggested by MR tractography. Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging method that can be used to measure local information about the structure of white matter within the human brain. Combining DTI data with the computational methods of MR tractography, neuroscientists can estimate the locations and sizes of nerve bundles (white matter pathways) that course through the human brain. Neuroscientists have used visualization techniques to better understand tractography data, but they often struggle with the abundance and complexity of the pathways. In this paper, we describe a novel set of interaction techniques that make it easier to explore and interpret such pathways. Specifically, our application allows neuroscientists to place and interactively manipulate box-shaped regions (or volumes of interest) to selectively display pathways that pass through specific anatomical areas. A simple and flexible query language allows for arbitrary combinations of these queries using Boolean logic operators. Queries can be further restricted by numerical path properties such as length, mean fractional anisotropy, and mean curvature. By precomputing the pathways and their statistical properties, we obtain the speed necessary for interactive question-andanswer sessions with brain researchers. We survey some questions that researchers have been asking about tractography data and show how our system can be used to answer these questions efficiently.

Diffusion tensor MRI tractography aims to reconstruct noninvasively the 3D trajectories of white matter fasciculi within the brain, providing neuroscientists and clinicians with a potentially useful tool for mapping brain architecture. While this technique is widely used to visualize white matter pathways, the associated uncertainty in fiber orientation and artifacts have, to date, not been visualized in conjunction with the trajectory data. In this work, the bootstrap method was used to determine the distributions of diffusion indices such as trace and anisotropy, together with the uncertainty in fiber orientation. A novel visualization scheme was developed to encode this information at each point along reconstructed trajectories. By integrating these schemes into a graphical user interface, a new tool which we call PASTA (Pointwise Assessment of Streamline Tractography Attributes) was created to facilitate identification of artifacts in tractography that would otherwise go undetected. Magn Reson Med

the apparent diffusion tensor of water (D) in the brain (1). Diagonalizing D produces eigenvalues and eigenvectors, the effective principal diffusivities along the orthotropic axes of the tissue, which can be used to measure the mean diffusivity (#D#) and diffusion anisotropy indices, such as the fractional anisotropy (FA) (2). Values of #D# indicate the magnitude of water molecule diffusion, while FA provides a scalar measure of diffusion anisotropy, which is the deviation from pure isotropic diffusion of water mobility in vivo. While measuring the #D# and FA values of different parenchymal structures is important in characterizing the imaging signatures of healthy and diseased brain, a more complete understanding of anatomical connectivity and how it is altered in various pathologies requires the underlying white matter structure to be accurately mapped. This 3D tracking of white matter fiber bundles can be achieved using the information contained within the eigenvectors of D if it

Figure 1: Top view of the streamline clusters on the whole brain. Streamlines within the same cluster share the same color. From the picture, the cingulum bundles can be easily identified in two clusters. Neural fibers along the corpus callosum are clustered into coherent bundles. Some of the U-fibers also form clusters.