Proc. American Mathematical Society (AMS) 2004, Phoenix, AZ, Jan. 2004.
Paul Thompson and Arthur W. Toga
UCLA School of Medicine, Los Angeles, CA
Abstract: Great progress has been made in developing mathematical algorithms to analyze 3D brain images. Drawing upon large image databases, powerful computer algorithms can now detect disease-specific patterns of brain structure and function. In one approach, we and others have created statistical atlases to measure how the brain varies across age and gender, across time, in health and disease, and in large human populations. We model brain structures as 3D curves and surfaces. Flows, metrics, and statistical fields are defined on these manifolds, and used to detect anatomical differences across subjects or groups. A mathematical framework based on covariant partial differential equations (PDEs), pull-backs of mappings under harmonic flows, and high-dimensional random fields is used encode anatomical variations in a brain image database (N>1000 scans). We use this reference information to detect brain abnormalities in Alzheimer's disease and schizophrenia, including how the brain changes over time, and responds to medication. This has revealed surprising patterns that were not apparent in individual brain images, visualizing in detail how disease and development impact the brain.
Paul Thompson, Ph.D.
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