Intrinsic and extrinsic analysis in computational anatomy.

Area of Science:

• Neuroimaging
• Statistical Modeling
• Computational Anatomy

Background:

• Studying anatomical variations in physiological signals across clinical populations is crucial for understanding disease mechanisms.
• Current methods for statistical inference on anatomical coordinates can be limited in scope and statistical power.

Purpose of the Study:

• To develop and present novel intrinsic and extrinsic statistical methods for analyzing random physiological signals across anatomical coordinates.
• To apply these methods to a clinical study investigating cortical thickness in schizophrenia and compare their performance.

Main Methods:

• Introduction of generalized partition functions for constructing random fields on anatomical manifolds.
• Intrinsic method: building partition functions based on Courant's theorem and self-adjoint differential operators.
• Extrinsic method: utilizing a template coordinate system and diffeomorphic transformations.

Main Results:

• Both intrinsic and extrinsic methods successfully identified reduced cortical thickness in the left cingulate gyrus in schizophrenia patients compared to healthy controls.
• The intrinsic method demonstrated increased statistical power in detecting these variations.

Conclusions:

• The presented intrinsic and extrinsic methods provide robust frameworks for statistical inference on anatomical data.
• The intrinsic method offers advantages in statistical power for clinical neuroimaging studies, particularly in conditions like schizophrenia.