The emerging discipline of Computational Functional Anatomy

Area of Science:

• Anatomical imaging and computational modeling.
• Multimodal data integration in biomedical research.

Background:

• Functional and physiological data require precise anatomical localization.
• Current methods lack robust frameworks for transferring functional information into anatomical coordinates.

Purpose of the Study:

• To introduce and review Computational Functional Anatomy (CFA) as a framework.
• To detail methods for constructing bijections between anatomical manifolds.
• To explain the transfer of functional data into anatomical atlases.

Main Methods:

• Construction of diffeomorphic bijections between human anatomy manifolds.
• Application of group action and parallel transport for data transfer.
• Unification of bijective comparison for anatomical submanifolds (points, curves, surfaces, imagery).
• Transfer of functional response variables using group action on DTI scalars/matrices and parallel transport of metric information.

Main Results:

• Advances in unifying bijective comparisons of anatomical submanifolds.
• Demonstration of functional information transfer into anatomical coordinates.
• Preservation of inner product via parallel transport across multiple templates.

Conclusions:

• CFA provides a robust framework for integrating functional and anatomical data.
• The developed methods facilitate advanced physiological response variable analysis within anatomical atlases.
• This approach enhances comparative studies across different anatomical templates.