Mathematical/computational challenges in creating deformable and probabilistic atlases of the human brain

Striking variations in brain structure, especially in the gyral patterns of the human cortex, present fundamental challenges in human brain mapping. P robabilistic brain atlases, which encode information on structural and func tional variability in large human populations, are powerful research tools with broad applications. Knowledge-based imaging algorithms can also levera ge atlases information on anatomic variation. Applications include automate d image labeling, pathology detection in individuals or groups, and investi gating how regional anatomy is altered in disease, and with age, gender, ha ndedness and other clinical or genetic factors. In this report, we illustra te some of the mathematical challenges involved in constructing population- based brain atlases. A disease-specific atlas is constructed to represent t he human brain in Alzheimer's disease (AD). Specialized strategies are deve loped for population-based averaging of anatomy. Sets of high-dimensional e lastic mappings, based on the principles of continuum mechanics, reconfigur e the anatomy of a large number of subjects in an anatomic image database. These mappings generate a local encoding of anatomic variability and are us ed to create a crisp anatomical image template with highly resolved structu res in their mean spatial location. Specialized approaches are also develop ed to average cortical topography. Since cortical patterns are altered in a variety of diseases, gyral pattern matching is used to encode the magnitud e and principal directions of local cortical variation. In the resulting co rtical templates, subtle features emerge. Regional asymmetries appear that are not apparent in individual anatomies. Population-based maps of cortical variation reveal a mosaic of variability patterns that segregate sharply a ccording to functional specialization and cytoarchitectonic boundaries. Hum . Brain Mapping 9:81-92, 2000. (C) 2000 Wiley-Liss, Inc.