High-Resolution Random Mesh Algorithms for Creating a Probabilistic 3D Surface Atlas of the Human Brain

Abstract

Striking variations exist, across individuals, in the internal and external geometry of the brain. Such normal variations in the size, orientation, topology, and geometric complexity of cortical and subcortical structures have complicated the problem of quantifying deviations from normal anatomy and of developing standardized neuroanatomical atlases. This paper describes the design, implementation, and results of a technique for creating a three-dimensional (3D) probabilistic surface atlas of the human brain. We have developed, implemented, and tested a new 3D statistical method for assessing structural variations in a database of anatomic images. The algorithm enables the internal surface anatomy of new subjects to be analyzed at an extremely local level. The goal was to quantify subtle and distributed patterns of deviation from normal anatomy by automatically generating detailed probability maps of the anatomy of new subjects. Connected systems of parametric meshes were used to model the internal course of the following structures in both hemispheres: the parieto-occipital sulcus, the anterior and posterior rami of the calcarine sulcus, the cingulate and marginal sulci, and the supracallosal sulcus. These sulci penetrate sufficiently deeply into the brain to introduce an obvious topological decomposition of its volume architecture. A family of surface maps was constructed, encoding statistical properties of local anatomical variation within individual sulci. A probability space of random transformations, based on the theory of Gaussian random fields, was developed to reflect the observed variability in stereotaxic space of the connected system of anatomic surfaces. A complete system of probability density functions was computed, yielding confidence limits on surface variation. The ultimate goal of brain mapping is to provide a framework for integrating functional and anatomical data across many subjects and modalities. This task requires precise quantitative knowledge of the variations in geometry and location of intracerebral structures and critical functional interfaces. The surface mapping and probabilistic techniques presented here provide a basis for the generation of anatomical templates and expert diagnostic systems which retain quantitative information on intersubject variations in brain architecture.