We will contribute open-source methods for large and small deformation, symmetric registration of diffusion tensor, T1 structural and functional magnetic resonance neuroimaging data. These methods permit a variety of similarity metrics, including landmarks and mutual information, to enable construction of optimal population- specific templates and to provide unprecedented guidance in population normalization. Furthermore, we develop the necessary theoretical and software extensions to allow an integrative, fundamentally multiple modality approach to normalization in which each modality factors into finding the best subject to subject correspondence. The methods will be wrapped for seamless use with popular software tools currently in use for neuroimaging research, SPM and VoxBo. We will apply these methods to identify and quantify long-term effects of prenatal cocaine exposure in adolescents. The basis of our normalization transformations are diffeomorphisms, the set of differentiable maps with differentiable inverse. This transformation space captures the notion that image objects should transform smoothly. That is, a curve drawn in a template domain should remain a curve after transformation into the subject domain. Also, two neighboring regions will remain neighbors. Our algorithms perform a direct optimization in this space which most methods are only able to coarsely approximate. Linear elastic methods, for example, cannot guarantee topology preservation as strains become large. The large deformations captured by diffeomorphisms also guarantee our ability to accurately measure differences in populations with high shape variability. While intersubject anatomy may not be completely transferable under a diffeomorphism, we are able to study the majority of shared structures that exist in each individual, including major subcortical structures, sulci and gyri. In other words, although individual brains will actually differ in their refined topology, it is the shared anatomy among the individuals on which normalization relies and thus the viability of group analysis of brain structure and function. Diffeomorphisms are exactly the family of transformations that are necessary and sufficient for capturing the common neuroanatomical structure or topology shared among individuals. Furthermore, removing topology preserving variability ideally situates one to study the residual differences in non-topology preserving anatomic variability, an open problem in biology and medicine. PUBLIC HEALTH RELEVANCE: the specific aims of this proposal will have an immediate impact on studies in general of the brain in health and disease, and in particular of the effects of prenatal cocaine exposure. Analysis leveraging the new approach proposed in this application promises to bring greater sensitivity to the study of effects of prenatal cocaine exposure. They will also advance knowledge regarding mechanisms by which these effects occur, by pinpointing the specific neurocognitive systems whose function is altered, and localizing these changes to specific regions and/or their connections.