Paul Thompson's Research Publications

Mathematical/Computational Challenges in Population-Based Brain Mapping

Invited Talk,
Joint Statistical Meetings, Indianapolis, IN, August 13-17 2000

Paul Thompson and Arthur W. Toga

Laboratory of Neuro Imaging, Dept. Neurology, Division of Brain Mapping,
UCLA School of Medicine, Los Angeles CA 90095, USA


Population-based brain maps reveal how the structural organization of the brain varies in large human populations. Both the quality and quantity of structural variability can be investigated, revealing general patterns in brain variability and asymmetry that can be used to detect and better understand abnormalities in disease.

We describe some exciting mathematical advances in our work as part of a collective effort to construct a probabilistic atlas of the human brain. Extreme variations in brain structure in human populations complicate the design of statistical approaches (1) to automatically identify structures in brain images; (2) to detect abnormal brain structure in an individual or a clinical group, (3) to relate these abnormalities to genetic or demographic factors; and (4) to compare the dynamics of 4-dimensional growth or degenerative processes in the human brain. Probabilistic brain atlases address these challenges by encoding variations in brain structure and function in large human populations. We describe our development of atlases that synthesize data across age, gender, time, and multiple brain imaging modalities, to represent normal populations and diseased subpopulations with Alzheimer's Disease and schizophrenia. To identify disease-specific patterns of brain structure and function, we combine mathematical approaches from Riemannian geometry, the theory of Gaussian random fields, and covariant partial differential equations, with supercomputing algorithms for image warping and analysis. Current challenges will be described that will be of interest to applied mathematicians and statisticians in general, as well as researchers in the image analysis and brain mapping fields.

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    Paul Thompson
    73-360 Brain Research Institute
    UCLA Medical Center
    10833 Le Conte Avenue
    Westwood, Los Angeles CA 90095-1761, USA.

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