Anatomical standardization of the human brain in euclidean 3-space and on the cortical 2-manifold

Abstract

Anatomical standardization (also called spatial normalization) is a key process in cross-sectional studies of brain structure and function using MRI, fMRI, PET and other imaging techniques. This process has two components: (i) specification of a 3D template brain, which defines a common coordinate space for analysis of any subsequent datasets; and (ii) a method to align the template with an individual 3D brain image, thereby associating each point of the standard template to a point on the individual. The association should be able to consistently match a particular template location to an anatomically corresponding location on each individual of a population. Standardization methods in widespread use employ a 3D affine spatial transformation to map from the individual to the template, which matches only overall size and gross shape of the input brain. A wide range of more flexible image deformation algorithms have been developed in order to better match fine detail. All such algorithms involve design choices that are subject to debate, and most have numerical parameters whose value must be specified by the user. In order to provide guidance for such choices, the first part of this thesis develops two measures of alignment consistency that are used to evaluate performance of a standardization method. The performance of different choices for algorithm design, numerical parameters, and template selection strategy for 3D normalization are compared. Since the processing of brain function occurs on a thin, highly convoluted sheet of cortex along the surface of the brain, there has been much recent interest in studying the structure and function along the brain cortex only, modelled as a 2D manifold. The second part of this thesis proposes an algorithm for highly-flexible deformation in 2D of a template cortex to an individual. The alignment consistency measures developed for 3D are reformulated for the 2D manifold and used to evaluate the algorithm design and numerical parameters. Finally, the question of whether it is better to standardize the 3D images or the 2D cortical manifold is addressed, identifying the problem classes which are best suited to each type of normalization.

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