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The fact that the Talairach brain fails to match individual scans stems partly from two facts. First, Talairach registration is only based on linear transformations (rotation, scaling, translation). Second, the origin of the coordinate system was selected to solve mapping and localization problems deep in the brain where individual variability is relatively low.

Atlases can be greatly improved if they are elastically deformed to fit a new image set from an incoming subject. Local warping transformations (including local dilations, contractions, and shearing) can adapt the shape of a digital atlas to reflect the anatomy of an individual subject, producing an individualized brain atlas. Introduced by Bajcsy and colleagues at the University of Pennsylvania [4,10,42,43], this approach was adopted by the Karolinska Brain Atlas Program [53,93,116], where warping transformations are applied to a digital cryosection atlas to adapt it to individual CT or MR data and coregistered functional scans.

Image warping algorithms, specifically designed to handle 3D neuroanatomic data [2,11,14,15,17,19,23,81,104a, 108,134], can transfer all the information in a 3D digital brain atlas onto the scan of any given subject, while respecting the intricate patterns of structural variation in their anatomy. These transformations must allow any segment of the atlas anatomy to grow, shrink, twist, and rotate to produce a transformation that encodes local differences in topography from one individual to another. Deformable atlases [14,31,42,67,85,87,88,93] resulting from these transformations can carry 3D maps of functional and vascular territories into the coordinate system of different subjects. The transformations also can be used to equate information on different

Bfc 3D Asymmetry Ml Map

3D Asymmetry Map

3D rm.ii. Variability Map

Elderly Controls

Alzheimer's Disease

Elderly Controls

Alzheimer's Disease

FIGURE 4 Population-based maps of 3D structural variation and asymmetry. Statistics of 3D deformation maps can be computed to determine confidence limits on normal anatomic variation. 3D maps of anatomic variability and asymmetry are shown for 10 subjects with Alzheimer's disease (AD; age: 71.9 + 10.9 yrs), and 10 normal elderly subjects matched for age (72.9 + 5.6 yrs), gender, handedness, and educational level [112]. Normal Sylvian fissure asymmetries (right higher than left; p < 0.0005), mapped for the first time in three dimensions, were significantly greater in AD than in controls (p< 0.0002, top panels). In the 3D variability maps derived for each group (lowerpanels), the color encodes the root mean square magnitude of the displacement vectors required to map the surfaces from each of the 10 patients' brains onto the average. Confidence limits on 3D cortical variation (lower right panel) exhibited severe increases in AD from 2-4 mm at the corpus callosum to a peak standard deviation of 19.6mm at the posterior left Sylvian fissure. See also Plate 107.

tissue types, boundaries of cytoarchitectonic fields, and their neurochemical composition.

Warping algorithms calculate a 3D deformation field that can be used to nonlinearly register one brain with another (or with a neuroanatomic atlas). The resultant deformation fields can subsequently be used to transfer physiologic data from different individuals to a single anatomic template. This enables functional data from different subjects to be compared and integrated in a context where confounding effects of anatomical shape differences are factored out. Nonlinear registration algorithms therefore support the integration of multisubject brain data in a stereotaxic framework and are increasingly used in functional image analysis packages [40,93].

Any successful warping transform for cross-subject registration of brain data must be high-dimensional, in order to accommodate fine anatomic variations [16,112]. This warping is required to bring the atlas anatomy into structural correspondence with the target scan at a very local level. Another difficulty arises from the fact that the topology and connectivity of the deforming atlas have to be maintained under these complex transforms. This is difficult to achieve in traditional image warping manipulations [15]. Physical continuum models of the deformation address these difficulties by

Individual Subject

Cryosection Atlas

* Target Brain Target Braif

Individualized Atlas

Tensor Map

FIGURE 5 A deformable brain atlas measures patterns of anatomic differences. Structure boundaries from a patient with clinically determined Alzheimer's disease (top left) are overlaid on a cryosection atlas (top right), which has been registered to it using a simple linear transformation. A surface-based image warping algorithm is applied to drive the atlas into the configuration of the patient's anatomy (bottom left). Histologic and neurochemical maps accessible only postmortem can be transferred onto the living subject's scan [64]. The amount of deformation required can be displayed as a tensor map (here only two components of the fully three-dimensional transformation are shown). Tensor maps and derived vector or scalar fields can be analyzed in a statistical setting to examine anatomic variation, detect pathology, or track structural changes over time. See also Plate 108.

considering the deforming atlas image to be embedded in a three-dimensional deformable medium, which can be either an elastic material or a viscous fluid. The medium is subjected to certain distributed internal forces, which reconfigure the medium and eventually lead the image to match the target. These forces can be based mathematically on the local intensity patterns in the datasets, with local forces designed to match image regions of similar intensity.

7.1 Model-Driven Registration

To guide the mapping of an atlas onto an individual, higherlevel structural information can be invoked to guarantee the biological validity of the resulting transform [20,23,55,108]. In one approach [108], anatomic surfaces, curves, and points are extracted (with a combination of automatic and manual methods) and forced to match (Fig. 5). The procedure calculates the volumetric warp of one brain image into the shape of another, by calculating the deformation field required to elastically transform functionally important surfaces in one brain into precise structural correspondence with their counterparts in a target brain. The scheme involves the determination of several model surfaces, a warp between these surfaces, and the construction of a volumetric warp from the surface warp.

Model-driven warping algorithms perform well when warping neuroanatomic data not only between subjects but also between modalities. This presents new opportunities to transfer cytoarchitectural and neurochemical maps from highresolution 3D cryosection data onto in vivo functional scans, and digitally correlate the resulting maps within a stereotaxic atlas space. Recent studies have used a deformable cryosection atlas to correlate histologic markers of Alzheimer's disease with metabolic PET signals in vivo, while correcting for tissue deformation due to post mortem changes and histologic processing [64]. Deformable atlas approaches offer a powerful means to transfer multimodal 3D maps of functional and neurochemical territories between individuals and neuroana-tomic atlases, respecting complex differences in the topography of the cortex and deep anatomic systems. These algorithms can also be applied to high-resolution brain atlases based on 3D digital cryosection images, to produce flexible high-resolution templates of neuroanatomy that can be adapted to reflect individual subjects' anatomy [122].

Automated deformable atlases promise to have considerable impact on clinical and research imaging applications. Atlas deformations can carry presegmented digital anatomic models, defined in atlas space, into new patients' scans, automatically labeling their anatomy [19]. Nonlinear registration of 3D geometric atlases onto individual datasets has been used to support automated brain structure labeling for hippocampal morphometry [48], analysis of subcortical structure volumes in schizophrenia [52], estimation of structural variation in normal and diseased populations [17,111], and segmentation and classification of multiple sclerosis lesions [128]. Projection of digital anatomic models into PET data can also serve to define regions of interest for quantitative calculations of regional cerebral blood flow [53].

7.2 Measuring Structural Differences

Deformable atlas algorithms produce extremely detailed 3D maps of regional differences that can be used to investigate dynamic structure alterations in disease or during brain development. The complex profiles of dilation and contraction required to warp a digital atlas onto a new subject's brain provide an index of the anatomical shape differences between that subject's brain and the atlas [7,9,24,101,110]. Atlas deformation maps offer a framework for pathology detection [9,47,110,112], identification of gender-specific anatomic patterns [23], and mapping of dynamic patterns of structural change in neurodevelopmental and degenerative disease processes [113,120].

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