Paul M. Thompson and Arthur W. Toga
Laboratory of Neuro Imaging, Department of Neurology, Division of Brain Mapping, UCLA School of Medicine, Los Angeles, California 90095
Striking variations exist, across individuals, in the internal and external geometry of the brain. In the past, quantifying deviations from normal anatomy and comparing functional data from different subjects or patient subpopulations have been difficult because cortical topography and the internal geometry of the brain vary so greatly. 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 fluid transformations. High-dimensional warping algorithms locally deform one subject's anatomy into structural correspondence with another, and enable the transfer of 3D functional data between subjects or onto a single anatomic template, for subsequent comparison or integration. The goal of the probabilistic atlas is to detect and quantify subtle and distributed patterns of deviation from normal anatomy, in a 3D 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 3D brain image of a new subject, this algorithm calculates a set of high-dimensional volumetric maps (typically with 384x384x256x3 ~ 0.1 billion degrees of freedom) fluidly deforming this scan into structural correspondence with other scans, selected one by one from an anatomic image archive. The construction of extremely complex surface deformation maps on the internal cortex is made easier by building a generic structure to model it. Connected systems of parametric meshes model the ventricles and cortex, including a large number of deep, branching sulci whose trajectories represent critical functional, lobar and cytoarchitectonic boundaries in 3 dimensions. Integral distortion functions extend the deformation field required to elastically transform these surface systems into correspondence with their counterparts in a different brain. The family of volumetric warps so 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 384x384x256 probability density functions is computed, yielding confidence limits in stereotaxic space for the location of every point represented in the 3D 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 as unusually situated, given the distributions of corresponding points in the scans of normal subjects.
The algorithms are tested by analyzing 3D MRI and high-resolution cryosection volumes from subjects with metastatic tumors and Alzheimer's disease, using a probabilistic atlas based on age-matched normal subjects imaged in each modality. A variety of visualization methods are used.
These probabilistic atlasing and high-dimensional volume warping techniques provide a basis for the generation of anatomical templates and expert diagnostic systems which retain quantitative information on inter-subject variations in brain architecture. Applications of the random fluid-based probabilistic atlas include the transfer of multi-subject 3D functional, vascular and histologic maps onto a single anatomic template, the mapping of 3D atlases onto the scans of new subjects, and the rapid detection, quantification and mapping of local shape changes in 3D medical images in disease, and during normal or abnormal growth and development.
Key words: brain mapping, probabilistic atlas, sulcal anatomy, stereotaxic methods, digital image reconstruction
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