Mathematical Challenges and New Directions in Computational Neuroanatomy

Tutorial Talk, 3rd Annual fMRI Data Center (fMRIDC) Summer Workshop, Dartmouth College, Hanover, New Hampshire, July 79, 2003; Organizer: Jack D. van Horn, Ph.D.

Paul Thompson, Ph.D.
Assistant Professor of Neurology
UCLA School of Medicine and Laboratory of Neuro Imaging


The last ten years have seen revolutionary advances in our ability to analyze patterns of brain structure and function in healthy and diseased populations. Population-based brain atlases, in particular, store vast repositories of neuroimaging data from patients with Alzheimer’s disease, schizophrenia, and normal and abnormal development. We review the mathematical algorithms, developed by our group and others, that can be used to:

(1) encode patterns of anatomical and functional variation, using computational anatomy techniques; (2) uncover disease-specific patterns of brain structure and function in human populations, and relate these differences to cognitive and clinical parameters; (3) analyze dynamic patterns of brain change over time; and (4) reveal the effects of medication, and even genetics, in altering these patterns.

To illustrate these methods, we describe our construction of probabilistic atlases that store detailed information on how the brain varies with age, gender and disease, and across time, in large human populations. Specifically, we introduce a mathematical framework based on modeling anatomy as parameterized manifolds (i.e., geometric curves and surfaces). We describe how high-dimensional image warping techniques and random field methods can be applied to encode variations in cortical patterning, asymmetry and tissue distribution in a population-based brain image database (N=1000 scans). We use this reference information to detect disease-specific abnormalities in Alzheimer's disease and schizophrenia, including dynamic changes and response to medication over time. We will present examples to show how patterns of cortical organization, asymmetry, and disease-specific trends can be resolved that are not apparent in individual brain images. Finally, we create four-dimensional (4D) maps that store probabilistic information on the dynamics of brain change in development and disease. Digital atlases that generate these maps show considerable promise in identifying general patterns of structural and functional variation in diseased populations, and revealing how these features depend on demographic, genetic, clinical and therapeutic parameters. New research directions are highlighted, including methods that associate brain structure and function with genetic variation at the family or allelic level.

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Fig. 1. Creating Brain Maps and Anatomical Models. An image analysis pipeline (Thompson et al., 2001) is shown here, which can reveal how brain structure varies in large populations, differs in disease, and is modulated by risk genes or medications. This approach aligns new 3D MRI scans from patients and controls (1) with an average brain template based on a population (here the ICBM template is used, developed by the International Consortium for Brain Mapping). Tissue classification algorithms then generate maps of gray matter, white matter and CSF (2). To help compare cortical features from subjects with different anatomy, individual gyral patterns are flattened (3) and warped to match a group average gyral pattern (4). If a color code indexing 3D cortical locations is flowed along with the same deformation field (5), a crisp group average model of the cortex can be made (6), relative to which individual gyral pattern differences (7), group variability (8) and cortical asymmetry (9) are computed. Once individual gyral patterns are aligned to the mean template, differences in gray matter distribution or thickness (10) are mapped, pooling data from homologous regions of cortex. Correlations can be mapped between disease-related deficits and genetic risk factors (11). Maps may also be generated visualizing linkages between deficits and clinical symptoms, cognitive scores, and medication effects, or risk genes.

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