Medical and Neuroscience Applications of Computational Anatomy
Paul Thompson
UCLA
School of Medicine
Great progress has been made in developing mathematical algorithms for the analysis of three-dimensional brain images. Drawing upon large imaging databases, powerful computational methods can now detect disease-specific patterns of brain structure and function.
In one approach, we and others have constructed statistical atlases to characterize how the brain varies across age and gender, over time, in health and disease, and across large human populations. Brain structures are modeled as three-dimensional 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 to encode anatomical variation in a large brain image database (N > 1000 scans). This reference information is then applied to detect brain abnormalities in Alzheimer’s disease and schizophrenia, including longitudinal changes and treatment effects.
These analyses have revealed unexpected patterns not evident in individual brain images, providing detailed visualization of how disease and development affect brain structure.