(Click here to Return to the Abstract of the Paper)

(Click here to Return to the List of Current Projects)

Probabilistic Brain Atlases:

(1) Strategy for Creating a Population-Based Brain Atlas. A family of high-dimensional volumetric warps relating a new subject's 3D MRI scan to each normal scan in a brain image database is calculated (I-II, above) and then used to quantify local structural variations. Differences in cortical, ventricular and deep sulcal topography are recorded in the form of vector field transformations in 3D stereotaxic space which drive both subcortical anatomy and the gyral/sulcal patterns of different subjects into register. The resulting family of warps encodes the distribution in stereotaxic space of anatomic points that correspond across a normal population (III), and their dispersion is used to determine the likelihood (IV) of local regions of the new subject's anatomy being in their actual configuration. Easily interpretable, color-coded topographic maps are generated to highlight regional patterns of deformity in the anatomy of the new subject. Abnormal structural patterns are quantified locally, and mapped in three dimensions.

(2) Scheme for Matching Cortical Regions with High-Dimensional Transformations and Color-Coded Spherical Maps.

High-resolution surface models of the cerebral cortex were extracted in parametric form, using the active surface algorithm of (MacDonald et al., 1993, 1994). This means that a continuous, invertible one-to-one mapping is always available between points on the cortical surface, (a), and their counterparts on the surface of a sphere. No 3D information is lost in this data representation scheme, as each point in the spherical map, (b), is color-coded with a color value which accurately and uniquely represents the location of its counterpart on the convoluted surface model (a) in 3D stereotaxic space. To preserve accuracy, floating point triplets, representing cortical surface point locations in stereotaxic space, are color-coded at 16 bits per channel to form an image of the parameter space in RGB color image format. To find good matches between cortical regions in different subjects [(a)/(d)], we first derive a colorized spherical map for each respective surface model (b and c) and perform the matching process in the angular parametric space. When spherical maps are made from two different cortical surfaces, the respective sulci will be in different positions in each spherical map (b and c), reflecting their different locations on the folded brain surface [shown here in pink, a and d]. Using a complex vector-valued flow field defined on the sphere (c), the system of sulcal curves in one spherical map can be driven into exact correspondence with their counterparts in the target spherical map, guiding the transformation of the adjacent regions. A spatially accurate, anatomically driven warping algorithm (Thompson and Toga, 1996), calculates the high-dimensional deformation field (typically with 65536x3 ~ 200,000 degrees of freedom) which reconfigures the starting spherical map, and the networks of curves embedded within it, into the shape of their counterparts in the target spherical map. This transformation is illustrated in (c) by its effect on a uniform grid, ruled over the starting spherical map and passively carried along in the resultant deformation. Notice the complex reconfiguration of sulcal landmarks, and how they drive the deformation of the surrounding cortex, allowing for complex profiles of dilation and contraction of the surface into the shape of the target surface. Note the complex non-linear flow in superior temporal regions, as the superior temporal sulcus (STS) extends further posteriorly in the target brain, and the posterior upswing of the Sylvian fissure (SYLV) is more pronounced in the reference brain (a) than in the target (d). Outlines are also shown for the superior frontal sulcus (SFS), and for the central sulcus (CENT) which is less convoluted in the reference brain than in the target. Because the color-coded spherical maps index cortical surface locations in 3-D, the transformation of one spherical map to another can be recovered in 3D stereotaxic space as a displacement of points in one subject's cortex onto their counterparts in the cortex of another subject. Matching can therefore be driven by a network of anatomically significant surface features. High spatial accuracy of the match is guaranteed in regions of particular functional significance or structural complexity, such as sulcal curves, lobar and cytoarchitectural boundaries, and critical functional landmarks.

(3) Distortions in Brain Architecture Induced by Tumor Tissue: Probability Maps for Major Sulci in Both Hemispheres. (Top) 3D r.m.s. variability maps are shown for major occipital and paralimbic sulci; (bottom) color-coded probability maps quantify the impact of two focal metastatic tumors (illustrated in red) on the supracallosal, parieto-occipital, and anterior and posterior calcarine sulci in both hemispheres.