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    NEUROSCIENCE | Contents | Next

    Algorithms and Codes for Refining and Linking Brain Data

    PARTICIPANTS
    Colin Holmes, Paul Thompson, Arthur W. Toga , UCLA
    Michael I. Miller, Tilak Ratnanather Johns Hopkins University
    Ulf Grenander, Brown University
    David C. Van Essen, Heather A. Drury, Marcus Raichle,
    Washington University

    B rains are all alike, in that they perform the same or similar functions, some of which are known precisely, such as senses and body control, and some of which are still unknown. And they are all different, from one species to the next and, certainly in mammals, from one individual to the next. So what does it mean to draw a representative map of, say, the human brain? Whose brain is most typical?

    "New answers to these deep questions, and to many others--What happens to the brain under normal aging? What happens in disease? What are the effects of disease on all scales, from the neuron to the substructure to the gross anatomy of the brain?--are coming from our brain mapping project in the Neuroscience thrust," said Arthur W. Toga, director of the Laboratory of Neuro Imaging (LONI) at UCLA. "We're working to develop the tools that can answer these questions, using brain imaging of many kinds. We're working to bring the answers closer in time and space, for real-time use by the clinician."

    ATLASES AND BRAIN WARPING

    PROBABILISTIC APPROACHES

    COMPUTATIONAL CHALLENGES

    Directional Biases in Anatomical Differences
    Figure 1 - Directional Biases in Anatomical Differences

    Directional Biases in Anatomical Differences
    Figure 1 - Directional Biases in Anatomical Differences
    Brain surface shown as color-coded spheres, created by Art Toga, Paul Thompson, and Colin Holmes at UCLA. Pink spheres represent areas of highest variability between the template and the target brain anatomy; blue spheres map lower variability. The probabilities of finding variability at any point are also encoded within the picture, giving the bubble-like appearance.

    ATLASES AND BRAIN WARPING

    "The overwhelming challenge facing the analyst of medical imaging data is understanding the randomness that represents biological variability," said Michael I. Miller of Johns Hopkins University, director of the multi-institutional Center for Imaging Studies (CIS), which includes Washington University in St. Louis, Harvard University, MIT's Lincoln Laboratory, and the Universities of Texas at Austin and El Paso. "Because sophisticated mathematical approaches are required to achieve such understandings, I call our field computational anatomy," he said.

    The proliferation of complex imaging methods--including positron emission tomography (PET), computed tomography of x-rays (CT), magnetic resonance (MR), high-resolution cryosectioning, and variants--has permitted brain imaging across the electromagnetic spectrum and has vastly increased the volume of brain data and the speed with which it can be accumulated. LONI, for example, has collected complete datasets by various methods for the brains of mice, rats, macaques, and human subjects--including, for the latter, functional MR imaging at high resolution.

    The inherent resolution of the various imaging modalities differs, so analyzing images of the same brain made by the different methods is not straightforward. To find normal or abnormal variability within a population of brains is still more difficult, to say nothing of the added complications of identifying brain substructures and relating neuroanatomic labels to a 3-D coordinate system.

    A collection of images for a single brain is usually termed an atlas. One of the first modern brain atlases was developed by French neuroscientist Jean Talairach and collaborators, who began their work in the 1950s, using a coordinate system based on two identifiable structures in the midplane of the brain, the anterior and posterior commissures. In the mid-1980s, Marc Raichle of Washington University in St. Louis helped pioneer the use of the Talairach coordinates to organize PET images. Today's digital brain atlases are compilations of views and sections of brains describable in precise mathematical terms with respect to an explicit coordinate system, generally derived from the Talairach system.

    With a brain atlas based on one subject as the template, brain-warping algorithms elastically deform the scan of a target brain until the brain or brain structures are in registration with the template. This procedure removes anatomic variability, permitting the study of functionally homologous regions from brain to brain. Both template and target data may come from post-mortem analyses of cryosectioned brains or from any of the new scanning modalities.

    "Warping algorithms can also be used to create three-dimensional maps of the differences in anatomy between individuals or groups," Toga said. "This is a field of investigation whose explosive development has been enabled by modern computational methods." Toga has recently edited a book, Brain Warping (Academic Press, 1999), in which nearly 30 transformation algorithms and methods are discussed in 20 articles by 36 contributors. A simple brain-warping transformation might consist of repositioning one image set or atlas relative to another by translation and rotation. In practice, Toga noted, warping algorithms can perform many kinds of geometric transformations, including global scaling, affine transformations, and linear, nonlinear, and local deformations.

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    Hippocampus in Health and Disease
    Hippocampus in Health and Disease
    Hippocampus in Health and Disease
    Hippocampus in Health and Disease
    Figure 2. Hippocampus in Health and Disease
    The three green images, by Lei Wang of Washington University and Tilak Ratnanather of Johns Hopkins, show how probabilistic methods can exhibit differences in anatomy that are difficult to extract from other kinds of image analysis. The right and left halves of a hippocampus from an atlas averaged over normal subjects (top) differ from those of a patient with epilepsy (middle) or Alzheimer's (bottom). In epilepsy, the right half is smaller than the left; in Alzheimer's, both halves are smaller than normal. The location of the hippocampus in the brain is shown in the last image.

    PROBABILISTIC APPROACHES

    In recent years, the sheer volume of available brain atlas data has permitted a more sophisticated statistical approach to the question of whose brain should be the template. To realize the potential of such atlases, data from single subjects are being extended to populations in various ways, at LONI, CIS, and other laboratories.

    An initial template is constructed, not as an absolute representation of any particular neuroanatomy, but rather as an average over a sample population of subjects. Transformations that warp the average brain template onto individual brains are used to compute a probability measure that stores information on patterns of anatomic variability. Differences between template and target may be described and visualized in terms of the magnitude and direction of displacement in the transformation of the atlas into the shape of another subject's brain (Figure 1). Toga and Thompson are pursuing the promise of these methods. "The population-based atlases can incorporate regional structural variability and show promise in identifying group trends and characteristics," Toga said.

    Working with applied mathematician Ulf Grenander, Miller and his group have developed computational anatomy as a formalization of the warping and morphing algorithms. "What we're looking for is a set of 'equations of motion' for growth and transformation that can serve neuroscientists in the same way that the Navier-Stokes equations serve students of fluid mechanics," Miller said. "Our primary tool is pattern theory, which applies probability measures to families of transformations observed in actual anatomies."

    Miller, John Csernansky of Washington University, and Richard Bucholz of St. Louis University have shown how pattern-theoretic methods can reveal normal and diseased brain structure. Clear anatomical differences may be seen between a normal and diseased hippocampus (Figure 2), a structure in the temporal lobe important in learning and memory.

    The cerebral cortex, the brain's outer layer, is a special case. The brain's convolutions and folds are extremely intricate, and David C. Van Essen and Heather A. Drury of Washington University and their students have worked with Miller, Raichle, and others on specialized algorithms to allow the "flattening" and comparison of cortical structure.

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    COMPUTATIONAL CHALLENGES

    In addition to the problem presented by such intricate structures as the cortical surface, computational anatomists are tackling an especially interesting problem, a comprehensive visual description of the development of the brain from embryo to adult. "Here we need four-dimensional atlases, so that comparisons over time can be made--again, between individuals and groups," Toga said.

    Most of the questions that can now be asked about the human brain are data-dependent. The data themselves consist of images, and the ability to visualize it before, during, and after warping is essential. While most warping algorithms have been developed on workstations and PCs to allow easy use in the lab, such machines can rarely take advantage of the full resolution of the data. The brain mapping project is working to parallelize algorithms in collaboration with Scott Baden of the UC San Diego Computer Science and Engineering department, using Baden's KeLP code libraries, under accelerated development in the Programming Tools and Environments thrust area.

    Work in this subarea of the thrust also includes development of computationally intensive parallel codes for tomographic reconstruction of cellular and subcellular structures from high-voltage electron microscopy and the linking of these reconstructions into multiscale brain maps. Production and distribution of such maps is one of the ultimate goals of the neuroscience thrust. Parallel codes for electron tomography have been developed by scientists at the National Center for Microscopy and Imaging Research and the National Biomedical Computation Resource in projects led by Mark Ellisman at UC San Diego. New versions of these now operate in a heterogeneous, distributed HPC environment. The latest version of the parallel tomography codes uses the Globus metacomputing environment, the AppLeS scheduler, and the Network Weather Service--representing a collaboration between Ellisman's group and NPACI computer scientists Carl Kesselman (University of Southern California), Fran Berman (UC San Diego), and Rich Wolski (University of Tennessee). "We are demonstrating the possibilities for using distributed computational resources to refine data of value in mapping, visualizing, and ultimately understanding brain structure and function," Ellisman said, "linked right across the Grid."

    "Our goal is to obtain a continuous picture of the brain, from embryo to adult, in health and disease, at every scale from the molecular to gross morphology," Toga said. "At every step--obtaining, processing, visualizing, and comparing all our data--we become more and more reliant upon a robust computational infrastructure." --MM *

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