Computational techniques for analysis of shape and kinematics of biological structures

This chapter presents state-of-the-art methods for statistical shape analysis of biological structures obtained from sets of medical images. In particular, emphasis is placed on the techniques necessary to parameterize and then decompose a given set of 3D surfaces extracted from medical images. Shape representation methods such as medial representation (i.e., skeletonization) and harmonic topological mapping are presented as tools for parameterizing a given set of surfaces so that they can be quantitatively compared. Then, methods for statistical decomposition including the proper orthogonal decomposition (also called principal component analysis) and independent component analysis are shown for the decomposition of the set of parameterized shapes into the set of fundamental shape features that can be applied to cluster the shapes and build classifiers with the potential for relating shape characteristics to pathology. An example analysis is presented which applies these techniques to parameterize and decompose the shape change of two human right ventricles from cardiac CT scans throughout the cardiac cycle. Advantages, disadvantages, and the relevance of the described methods in clinical medical image applications will be addressed throughout the chapter.