Exploration of the Brain’s White Matter Structure through Visual Abstraction and Multi-Scale Local Fiber Tract Contraction

A compound graph is a frequently encountered type of data set. Relations are given between items, and a hierarchy is defined on the items as well. We present a new method for visualizing such compound graphs. Our approach is based on visually bundling the adjacency edges, i.e., non-hierarchical edges, together. We realize this as follows. We assume that the hierarchy is shown via a standard tree visualization method. Next, we bend each adjacency edge, modeled as a B-spline curve, toward the polyline defined by the path via the inclusion edges from one node to another. This hierarchical bundling reduces visual clutter and also visualizes implicit adjacency edges between parent nodes that are the result of explicit adjacency edges between their respective child nodes. Furthermore, hierarchical edge bundling is a generic method which can be used in conjunction with existing tree visualization techniques. We illustrate our technique by providing example visualizations and discuss the results based on an informal evaluation provided by potential users of such visualizations.

This paper investigates the use of color to represent the directional information contained in the diffusion tensor. Ideally, one wants to take into account both the properties of human color vision and of the given display hardware to produce a representation in which differences in the orientation of anisotropic structures are proportional to the perceived differences in color. It is argued here that such a goal cannot be achieved in general and therefore, empirical or heuristic schemes, which avoid some of the common artifacts of previously proposed approaches, are implemented. Directionally encoded color (DEC) maps of the human brain obtained using these schemes clearly show the main association, projection, and commissural white matter pathways. In the brainstem, motor and sensory pathways are easily identified and can be differentiated from the transverse pontine fibers and the cerebellar peduncles. DEC maps obtained from diffusion tensor imaging data provide a simple and effective way to visualize fiber direction, useful for investigating the structural anatomy of different organs. Magn Reson Med 42:526-540, 1999. Copyright 1999 Wiley-Liss, Inc.

We present a novel, computerized method of examining cerebral cortical thickness. The normal cortex varies in thickness from 2 to 4 mm, reflecting the morphology of neuronal sublayers. Cortical pathologies often manifest abnormal variations in thickness, with examples of Alzheimer's disease and cortical dysplasia as thin and thick cortex, respectively. Radiologically, images are 2-D slices through a highly convoluted 3-D object. Depending on the relative orientation of the slices with respect to the object, it is impossible to deduce abnormal cortical thickness without additional information from neighboring slices. We approach the problem by applying Laplace's Equation (V2psi = 0) from mathematical physics. The volume of the cortex is represented as the domain for the solution of the differential equation, with separate boundary conditions at the gray-white junction and the gray-CSF junction. Normalized gradients of psi form a vector field, representing tangent vectors along field lines connecting both boundaries. We define the cortical thickness at any point in the cortex to be the pathlength along such lines. Key advantages of this method are that it is fully three-dimensional, and the thickness is uniquely defined for any point in the cortex. We present graphical results that map cortical thickness everywhere in a normal brain. Results show global variations in cortical thickness consistent with known neuroanatomy. The application of this technique to visualization of cortical thickness in brains with known pathology has broad clinical implications.