Detection, visualization and animation of abnormal anatomic structure with a deformable probabilistic brain atlas based on random vector field transformations

This paper describes the design, implementation and preliminary results of a technique for creating a comprehensive probabilistic atlas of the human brain based on high-dimensional vector field transformations. The goal of the atlas is to detect and quantify distributed patterns of deviation from normal anatomy, in a 3-D brain image from any given subject. The algorithm analyzes a reference population of normal scans and automatically generates color-coded probability maps of the anatomy of new subjects. Given a 3-D brain image of a new subject, the algorithm calculates a set of high-dimensional volumetric maps (with typically 384² × 256 × 3 ≡ 10⁸ degrees of freedom) elastically deforming this scan into structural correspondence with other scans, selected one by one from an anatomic image database. The family of volumetric warps thus constructed encodes statistical properties and directional biases of local anatomical variation throughout the architecture of the brain. A probability space of random transformations, based on the theory of anisotropic Gaussian random fields, is then developed to reflect the observed variability in stereotaxic space of the points whose correspondences are found by the warping algorithm. A complete system of 384² × 256 probability density functions is computed, yielding confidence limits in stereotaxic space for the location of every point represented in the 3-D image lattice of the new subject's brain. Color-coded probability maps are generated, densely defined throughout the anatomy of the new subject. These indicate locally the probability of each anatomic point being unusually situated, given the distributions of corresponding points in the scans of normal subjects. 3-D MRI and high-resolution cryosection volumes are analyzed from subjects with metastatic tumors and Alzheimer's disease. Gradual variations and continuous deformations of the underlying anatomy are simulated and their dynamic effects on regional probability maps are animated in video format (on the accompanying CD-ROM). Applications of the deformable probabilistic atlas include the transfer of multi-subject 3-D functional, vascular and histologic maps onto a single anatomic template, the mapping of 3-D atlases onto the scans of new subjects, and the rapid detection, quantification and mapping of local shape changes in 3-D medical images in disease and during normal or abnormal growth and development.