Arthur W. Toga and Paul Thompson

Laboratory of Neuro Imaging, Dept. of Neurology, Division of Brain Mapping, UCLA School of Medicine, Los Angeles, CA 90095-1769



I. Atlases, Maps and Databases in Brain Imaging

II. Coordinate Systems and Registration

III. Deformable Brain Atlases

IV. Probabilistic Brain Atlases

V. Population Specificity

VI. Queries and Applications

I. Atlases, Maps and Databases in Brain Imaging

The explosive growth in brain imaging technologies has been matched by an extraordinary increase in the number of investigations focusing on the structural and functional organization of the brain. Human brain structure is so complex and variable across subjects that engineering approaches drawn from computer vision, image analysis, computer graphics and artificial intelligence research fields are required to manipulate, analyze and communicate brain data. Central to these tasks is the construction of comprehensive brain atlases and databases of 3-dimensional brain maps, templates and models to describe how the brain and its component parts are organized. Design of appropriate reference systems for human brain data presents considerable challenges, since these systems must capture how brain structure and function vary in large human populations, across age and gender, in different disease states, across imaging modalities, and even across species.

Diversity of Brain Maps. Comprehensive maps of brain structure have been derived, at a variety of spatial scales, from 3D tomographic images (Damasio, 1995), anatomic specimens (Talairach et al., 1967; Talairach and Tournoux, 1988; Ono et al., 1990; Duvernoy, 1991) and a variety of histologic preparations which reveal regional cytoarchitecture (Brodmann, 1909) and regional molecular content such as myelination patterns (Smith, 1907), protein densities and mRNA distributions. Other brain maps have concentrated on function, quantified by positron emission tomography (PET; Minoshima et al., 1994), functional MRI (Le Bihan, 1996) or electrophysiology (Avoli et al., 1991; Palovcik et al., 1992). Additional maps have been developed to represent neuronal connectivity and circuitry (Van Essen and Maunsell, 1983), based on compilations of empirical evidence (Brodmann, 1909; Berger, 1929; Penfield and Boldrey, 1937).

Each of these brain maps has a different spatial scale and resolution, emphasizes different functional or structural characteristics, and none is inherently compatible with any other. Each strategy clearly has its place within a collective effort to map the brain, but unless certain precautions are taken (enabling common registration; see Section 2), these brain maps will remain as individual and independent efforts, and the correlative potential of the many diverse mapping approaches will be underexploited.

Brain Atlases. To address these difficulties, brain atlases provide a structural framework in which individual brain maps can be integrated. Most brain atlases are based on a detailed representation of a single subject's anatomy in a standardized 3D coordinate system, or stereotaxic space. The chosen data set acts as a template on which other brain maps (such as functional images) can be overlaid. The anatomic data provides the additional detail necessary to accurately localize activation sites, as well as providing other structural perspectives such as chemoarchitecture. Digital mapping of structural and functional image data into a common 3D coordinate space is a prerequisite for many types of brain imaging research, as it supplies a quantitative spatial reference system in which brain data from multiple subjects and modalities can be compared and correlated.

Given the fact that there is neither a single representative brain nor a simple method to construct an 'average' anatomy or represent the complex variations around it, the construction of brain atlases to represent large human populations has become the focus of intense research (Mazziotta et al., 1995). Deformable atlases, which can be adapted to reflect the anatomy of new subjects, and probabilistic atlases, which retain information on population variability, are powerful new research tools with a range of clinical and research applications. These atlases can be used to guide knowledge-based image analysis algorithms, and can even support pathology detection in individual subjects or groups (Sections 3-5). Single modality atlases may also be insufficient, because of the need to establish the relationship between different measurements of anatomy and physiology. In response to these challenges, multi-modal atlases combine detailed structural maps from multiple imaging sensors in the same 3D coordinate space. Multi-modal atlases will provide the best of all worlds, offering a realistically complex representation of brain morphology and function in its full spatial and multi-dimensional complexity.

Early Brain Atlases. Brain atlasing research was originally based on the premise that accurate localization of brain structure and function in any modality is improved by correlation with higher resolution anatomic data placed in an appropriate spatial coordinate system. Three-dimensional neuroanatomic templates also have the potential to provide important reference information when planning stereotaxic surgical procedures, including radiosurgery and electrode implantations (Talairach et al., 1967; Kikinis et al., 1996). Most early atlases of the human brain, and other species (Paxinos and Watson, 1986), were derived from one, or at best a few, individual post mortem specimens (Brodmann, 1909; Schaltenbrand and Bailey, 1959; Schaltenbrand and Wahren, 1977; Talairach et al., 1967; Matsui and Hirano, 1978; Talairach and Tournoux, 1988; Ono et al., 1990). Such atlases take the form of anatomical references or represent a particular feature of the brain (Van Buren and Maccubin, 1962; Van Buren and Borke, 1972), such as a specific neurochemical distribution (Mansour et al., 1995) or the cellular architecture of the cerebral cortex (Brodmann, 1909). Due to individual variations in anatomy among normal subjects, proportional scaling systems are typically employed to reference a given brain to an atlas brain (Talairach and Tournoux, 1988). More sophisticated elastic or fluid transformations, involving local matching, are becoming commonplace (see Section 3), and these approaches locally deform a digital atlas to reflect the anatomy of new subjects. Commonly used human atlases include those of Talairach and Tournoux (1988) and the thalamic and brainstem anatomical maps of Schaltenbrand and Wahren (1977).

Digital Atlases. The digitization and labeling of the most widely used paper atlases (Talairach and Tournoux, 1988; Schaltenbrand and Wahren, 1977), together with cortical and sulcal atlases employed in neuroradiology (Brodmann, 1909; Ono et al., 1990), has recently been the focus of a collaborative effort between Johns Hopkins University and National University of Singapore (Nowinski et al., 1997). The resulting atlases are mutually registered, may be interactively registered with patient scan data, and are linked to an anatomical index of 1,000 structures and 400 sulcal patterns. The flexibility of a digital format makes atlas templates easier to manipulate, and, using image registration algorithms (Section 2), easier to overlay onto volumetric radiologic scans. A related system for planning neurosurgical interventions, known as the CASS system (Computer Assisted Stereotaxic Surgery, Midco Corporation, CA), supports the digital overlay of the Schaltenbrand, Talairach and Brodmann atlas data onto individual patient MR scans to create composite maps and simulation displays for surgical planning (Hardy, 1994). Deferring, for now, the complications introduced by anatomic variations across subjects, the transfer of labeled atlas data into the coordinate system of an individual patient's scan also helps in the analysis of metabolic or functional studies based on PET or functional MRI (Seitz et al., 1990; Evans et al., 1991; Lehmann et al., 1991; Tiede et al., 1993; Ingvar et al., 1994).

MRI-Based Atlases. Recent atlases based on magnetic resonance image (MRI) data have the advantage of intrinsic three-axis registration and spatial coordinates (Damasio, 1995), but have relatively low resolution and lack anatomic contrast in important subregions. The Harvard Brain Atlas, based on a 1x1x1.5 mm resolution 3D SPGR (spoiled gradient-recalled acquisition) scan of a 25 year old, normal subject, was enhanced by anisotropic diffusion filtering (Kikinis et al., 1996), before being segmented into 150 hand-labeled regions, which include white matter tracts as well as major neuroanatomic structures. Nevertheless, many high-resolution MR atlases, with up to 100-150 slices, a section thickness of 2 mm, and 256x256 pixel imaging planes (Evans et al., 1991; Lehmann et al., 1991) still result in resolutions lower than the complexity of many neuroanatomic structures.

Cryosection Imaging. Several digital atlases have been developed using photographic images of cryoplaned frozen specimens (Bohm et al., 1983; Greitz et al., 1991). Photographed material, while providing superior anatomic detail, has limitations. For accurate correlations, data must be placed in a plane equivalent to that of the image of interest. Digital imaging, however, overcomes many limitations of conventional film photography. Using 1024x1024, 24-bits/pixel digital color cameras, spatial resolution can be as high as 100 microns/voxel for whole human head cadaver preparations, or higher for isolated brain regions (Toga et al., 1994). Cryosectioning in micron increments permits data collection with high spatial resolution in the axis orthogonal to the sectioning plane. Acquisition of images in series directly from the consistently positioned cryoplaned blockface also avoids the need for serial image registration prior to reconstruction. Serial images can be reconstructed to a 3D anatomic volume that is amenable to various resampling and positioning schemes.

Multi-Modality Atlases. Characterizing a single subject with multiple imaging devices clearly combines the strengths of each imaging modality. In the Visible Human Project (Spritzer, 1996), two (male and female) cadavers were cryoplaned and imaged at 1.0 mm intervals, and the entire bodies were also reconstructed via 5,000 post mortem CT and MRI images. The resulting digital datasets, available via the Internet, represent over 15 gigabytes of image data which can be viewed using IDL navigation software (Research Systems Inc., CO). Users interact with the data by browsing through axial, coronal and sagittal views and can annotate and retrieve images in common graphical formats for subsequent segmentation and analysis (King, 1996). While not an atlas per se, the Visible Human imagery has sufficient quality and accessibility to make it a test platform for developing methods and standards (Spritzer, 1996). The data has served as the foundation for developing related atlases of regions of the cerebral cortex (Drury and Van Essen, 1997), and high-quality brain models and visualizations (Schiemann et al., 1996; Stewart et al., 1996). Using multi-modality data from a patient with a localized pathology, and more recently the Visible Human data, Hohne and co-workers developed a commercially available brain atlas designed for teaching neuroanatomy (VOXEL-MAN; Hohne et al., 1990, 1992; Tiede et al., 1993; Pommert et al., 1994).

3D Anatomical Models. The Digital Anatomist project in Seattle (Sundsten et al., 1991) and the Harvard Surgical Planning Laboratory (Kikinis et al., 1996) have each supplemented their own volumetric atlas data with a range of digital anatomical models for teaching anatomy. These annotated models can be rotated and visualized interactively to illustrate complex spatial relationships among anatomic structures. Modeling strategies currently used to represent brain data have been motivated by the need to extract and analyze the complex shape of anatomical structures, for high-resolution visualization and quantitative comparisons. Ray-tracing and surface rendering techniques can then be applied to parameterized or triangulated structure models (Payne and Toga, 1990; Toga, 1994) to visualize complex anatomic systems (Fig. 1). Because digital models reside in the same stereotaxic space as the atlas data, surface and volume models stored as lists of vector coordinates are amenable to digital transformation, as well as geometric and statistical measurement (Thompson et al., 1996). An underlying 3D coordinate system is therefore central to all atlas systems, since it supports the linkage of structure models and associated image data with spatially-indexed neuroanatomic labels, preserving spatial information and adding anatomical knowledge.

II.Coordinate Systems and Registration

Matching a Brain to an Atlas. In existing atlases, proportional scaling systems are typically employed to reference a given brain with an atlas brain (Talairach et al., 1967; Talairach and Tournoux, 1988). This requires individual data to be superimposed on the data in the atlas - in other words, to be transformed to match the space occupied by the atlas. In the Talairach stereotaxic system, piecewise affine transformations are applied to 12 rectangular regions of brain, defined by vectors from the anterior and posterior commissures to the extrema of the cortex. These transformations re-position the anterior commissure of the subject's scan at the origin of the 3D coordinate space, vertically align the interhemispheric plane, and horizontally orient the line connecting the two commissures. Each point in the incoming brain image, after it is 'warped' into the atlas space, is labeled by an (x,y,z) address referable to the atlas brain.

Although originally developed to help interpret brain stem and ventricular studies acquired using pneumoencephalography (Talairach et al., 1967), the Talairach stereotaxic system rapidly became an international standard for reporting functional activation sites in PET studies, allowing researchers to compare and contrast results from different laboratories (Fox et al., 1985, 1988; Friston et al., 1989, 1991). The quantitative precision, objectivity and wide use of Talairach coordinates greatly simplified the task of developing BrainMap (Fox et al., 1994), a rapidly growing database of spatially-indexed functional brain data, founded on the Talairach coordinate system. This database supplies a variety of links to citation tables, research papers and experimental protocols from the scientific literature, offering an environment for exploration and meta-analysis of functional brain image data.

The success of any brain atlas depends on how well the anatomy of individual subjects match the representation of anatomy in the atlas. While stereotaxic methods provide a common coordinate system for pooling activation data and multi-subject comparisons, concern has been voiced over the anatomical template itself used by Talairach (Roland and Zilles, 1994). Based on post mortem sections of the brain of a 60 year-old female subject, which clearly did not reflect the in vivo anatomy of subjects in activation studies, the atlas plates were also compromised by having a variable slice separation (3 to 4 mm), and data from orthogonal planes were inconsistent. To address these limitations, the Montreal Neurological Institute (Evans et al., 1994) created a composite MRI dataset from 305 young normal subjects (239 males, 66 females; age: 23.4 +/- 4.1 years) whose scans were individually mapped into the Talairach system; 305 MRI volumes (2-mm thick slices) were mapped by linear transformation into stereotaxic space, intensity normalized, and averaged on a voxel-by-voxel basis (Evans et al., 1992). Although the resulting average brain (Fig. 2) has regions where individual structures are blurred out due to spatial variability in the population (Evans et al., 1992; 1994), the effect of anatomical variability in different brain areas is illustrated qualitatively by this average-intensity MRI dataset. The average intensity template is part of the widely-used Statistical Parametric Mapping package (SPM; Friston et al., 1995). The availability of an average MRI dataset in the Talairach coordinate system spurred the development of automated methods to map new MRI and PET data into stereotaxic space. Automated image registration algorithms could be used to optimally align new MR data with the template by maximizing a measure of intensity similarity, such as 3D cross-correlation (Collins et al., 1994a,1995), ratio image uniformity (Woods et al., 1992), or mutual information (Viola et al., 1995; Wells et al., 1997). Any alignment transformation defined for one modality, such as MRI, can be identically applied to another modality, such as PET, if a previous cross-modality intrasubject registration has been performed (Woods et al., 1993). For the first time then, PET data could be mapped into stereotaxic space via a correlated MR dataset (Woods et al., 1993; Evans et al, 1994). Registration algorithms therefore made it feasible to automatically map data from a variety of modalities into an atlas coordinate space based directly on the Talairach reference system.

III. Deformable Brain Atlases

Cross-Subject Anatomic Variations. Drastic normal variations in sulcal geometry have been found in primary motor, somatosensory and auditory cortex (Missir et al., 1989; Rademacher et al., 1993), primary and association visual cortex (Stensaas et al., 1974), frontal and pre-frontal areas (Rajkowska and Goldman-Rakic, 1995), and lateral perisylvian cortex (Geschwind and Levitsky, 1968; Steinmetz et al., 1989,1990; Ono et al., 1990). More recent 3-dimensional analyses of anatomic variability, in post mortem, in vivo normal and diseased populations, have found a highly heterogeneous pattern of anatomic variation (Thompson et al., 1996, 1998).

In view of the complex structural variability between individuals, a fixed brain atlas may fail to serve as a faithful representation of every brain (Roland and Zilles, 1994; Mazziotta et al., 1995). Since no two people's brains are the same, this presents a challenge for attempts to create standardized atlases. Even in the absence of any pathology, brain structures vary between individuals not only in shape and size, but also in their orientations relative to each other. Such normal variations have also complicated the goals of comparing functional and anatomic data from many subjects (Rademacher et al., 1993; Roland and Zilles, 1994).

Numerous studies, in our laboratory and elsewhere, have determined how severe the inter-subject variations in anatomy are, even after transforming individual anatomic data into the Talairach stereotaxic system (Fig. 3). Clearly, direct averaging of digital brain maps, after transformation to a common 3D coordinate space, is only valid if homologous cortical regions in different subjects have been brought into register by the stereotaxic transformation. Extreme variations in cortical patterns, observed in normal subjects and exacerbated in disease states by additional pathologic change, suggest that caution is necessary in using the Talairach stereotaxic system to support cross-subject and cross-group comparisons of cortically-derived events or functional maps. Direct digital subtraction of stereotaxic functional maps in studies of disease states, such as dementia, may lead to spurious results: maps of apparent significance may reflect differences which are anatomic, rather than functional, in character (Meltzer and Frost, 1994; Woods, 1996). These difficulties have led some groups to suggest that direct reference to the sulci that frame architectonic fields may present a more reliable basis for functional mapping than reference to a single standard or idealized brain (Steinmetz et al., 1990; Watson et al., 1993; Rademacher et al., 1993; Thompson et al., 1996, 1998).

Warping of Brain Atlases. The fact that the Talairach brain fails to match individual scans stems partly from the fact that only linear transformations (rotation, scaling, translation) are applied when attempting to adapt the atlas template to match a new scan.

Atlases would be greatly improved if they could be elastically deformed to fit a new image set from an incoming subject. Local warping transformations (including local dilations, contractions and shearing) can be used to adapt the shape of a digital atlas to reflect the anatomy of an individual subject, producing an individualized brain atlas. Pioneered by Bajcsy and colleagues at the University of Pennsylvania (Broit, 1981; Bajcsy and Kovacic, 1989; Gee et al., 1993, 1995), this approach was adopted by the Karolinska Brain Atlas Program (Seitz et al., 1990; Thurfjell et al., 1993; Ingvar et al., 1994), where warping transformations are applied to a digital cryosection atlas to adapt it to individual CT or MR data and co-registered functional scans.

Atlas to Brain Transformations. Image warping algorithms, specifically designed to handle 3D neuroanatomic data (Christensen et al., 1993; 1996; Collins et al., 1994a, 1995; Thirion, 1995; Rabbitt et al., 1995; Davatzikos, 1996; Thompson and Toga, 1996; Bro-Nielsen and Gramkow, 1996) can be used to 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, however small, to grow, shrink, twist and even rotate, to produce a transformation which represents and encodes local differences in topography from one individual to another. Such deformable atlases (Seitz et al., 1990; Evans et al., 1991; Miller et al., 1993; Gee et al., 1993; Christensen et al., 1993; Sandor and Leahy, 1994; 1995; Rizzo et al., 1995) can be used to carry 3D maps of functional and vascular territories into the coordinate system of different subjects, as well as information on different tissue types and the boundaries of cytoarchitectonic fields and their neurochemical composition.

Brain to Atlas Transformations. Warping algorithms calculate a 3D deformation field which can be used to non-linearly register one brain with another (or with a neuroanatomic atlas). Instead of warping the atlas into the configuration of a new subject's anatomy, the new subject's anatomy can be warped into the configuration of the atlas anatomy, removing subject-specific shape differences. The resultant deformation fields can subsequently be used to transfer physiologic data from different individuals to a single anatomic template, enabling functional data from different subjects to be compared and integrated in a context where confounding effects of anatomical shape differences are factored out. Non-linear registration algorithms therefore support the integration of multi-subject brain data in a stereotaxic framework, and are increasingly used in functional image analysis packages (Seitz et al., 1990; Friston et al., 1995).

How can One Brain be Deformed to Match Another? Any successful warping transform for cross-subject registration of brain data must be high-dimensional, in order to accommodate fine anatomic variations. 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 hard or simply impossible to achieve in traditional image warping manipulations (Christensen et al., 1995). Physical continuum models of the deformation address these difficulties by 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.

Deformable Atlases based on Continuum Mechanics. Several deformable atlases have been designed to deform according to the laws of continuum mechanics, which describe the deformational behavior of real materials. Recently, Christensen et al. (1993, 1995, 1996) proposed a deformable MRI-based atlas driven by a viscous-fluid based warping transform. The fluid model was motivated by capturing non-linear topological behavior and large image deformations. The deformation velocity of the atlas is governed by the creeping flow momentum equation for a Newtonian fluid, and a series of three algorithms adjust successively finer features of the atlas anatomy until the transformed atlas matches the target scan in exquisite detail. The optimal deformation field maximizes a global intensity similarity function (defined on the deformed template and the target), while satisfying continuum-mechanical constraints that guarantee the topological integrity of the deformed template (Christensen et al., 1996).

Model-Driven Deformable Brain Atlases. Linkage of continuum-mechanical models with criteria for optimal intensity matching results in an extremely difficult pattern recognition problem. To guide the mapping of an atlas onto an individual scan, higher-level structural information can be invoked to guarantee the biological validity of the resulting transform (Thompson and Toga, 1996; Davatzikos, 1996a; Collins et al., 1996). In one approach (Thompson and Toga, 1996) anatomic surfaces, curves and points are extracted (with a combination of automatic and manual methods), and forced to match (Fig. 4). The procedure calculates the volumetric warp of one brain image into the shape of another, by interpolating 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. Extremely complex surface deformation maps on the internal cortex are constructed by building a generic surface structure to model it. Connected systems of parametric meshes model primary sulci with deep trajectories. In advance, a high-resolution model of the external cortex is automatically extracted from both scans with an active surface algorithm (MacDonald et al., 1993). These models are subsequently re-parameterized to allow gyrus-by-gyrus matching of specific lobar and cortical regions (Fig. 3). The ventricular system is also partitioned into a system of connected surface elements, whose junctions match the boundaries of numerous cytoarchitectonic fields at the ventricular surface.

The algorithm then calculates the high-dimensional volumetric warp (typically with millions of degrees of freedom) deforming one 3D scan into structural correspondence with the other. Radial basis functions (Thompson and Toga, 1996) or continuum-mechanical models (Davatzikos, 1996; Thompson and Toga, 1998) are used to extend the deformation field required to elastically transform nested surfaces to their counterparts in the target scan. This mathematical framework provides a compact representation of the resulting high-dimensional deformation field and allows rapid computation of the complex maps relating different brain architectures.

Advantages of Model-Driven and Automated Deformable Atlases. 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 high-resolution 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 (Mega et al., 1997). Deformable atlas approaches offer a powerful means to transfer multi-modal 3D maps of functional and neurochemical territories between individuals and neuroanatomic atlases, respecting complex differences in the topography of the cortex and deep anatomic systems. High-dimensional warping algorithms can also be applied to high-resolution brain atlases based on 3D digital cryosection images, to produce flexible high-resolution templates of neuroanatomy which can be adapted to reflect the anatomy of individual subjects (Toga and Thompson, 1997a).

Automated deformable atlases promise to have considerable impact on clinical and research imaging applications. Atlas deformations can carry pre-segmented digital anatomic models, defined in atlas space, into new patients' scans, automatically labeling their anatomy (Collins et al., 1995). Non-linear mapping of raster volumes or 3D geometric atlases onto individual datasets has been used to support automated brain structure labeling for hippocampal morphometry (Haller et al., 1997), analysis of subcortical structure volumes in schizophrenia (Iosifescu et al., 1997), estimation of structural variation in normal and diseased populations (Collins et al., 1994b; Thompson et al., 1997), and segmentation and classification of multiple sclerosis lesions (Warfield et al., 1995). Projection of digital anatomic models into PET data can also serve to define regions of interest for quantitative calculations of regional cerebral blood flow (Ingvar et al., 1994). These template-driven segmentations require extensive validation relative to more labor-intensive manual delineation of structures, but show considerable promise in medical imaging applications.

Deformable Atlases as a Virtual Sensor. As an interesting by-product, deformable atlas algorithms produce extremely detailed 3D maps of regional differences in anatomy between individuals or groups, which can be analyzed in a statistical framework to investigate brain 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 (Bookstein, 1989, 1997; Davatzikos et al., 1996b; Subsol et al., 1997; Thompson and Toga, 1997). Differences in regional shape can therefore be assessed by analyzing the deformation tensor field which encodes the local dilation or contraction required to deform one brain volume into another. As a result, deformable atlases not only compensate for the anatomic variations and idiosyncrasies of each individual subject, but they can be regarded as a virtual sensor (Gee et al., 1995) which produces signals and maps of these structural differences (Fig. 4). When analyzed in a setting where normal variations are encoded, atlas deformation maps offer a framework for pathology detection (Thompson et al., 1997; Bookstein, 1997), identification of gender-specific anatomic patterns (Davatzikos, 1997), and mapping of dynamic patterns of structural change in neurodevelopmental and degenerative disease processes (Toga, Thompson and Payne, 1996).

IV. Probabilistic Brain Atlases

As noted earlier, due to pronounced anatomic variability between individual human brains, any atlas or clinical diagnostic system based on a single subject's anatomy cannot succeed fully. A deformable brain atlas counteracts some of the limitations of a fixed atlas by using mathematically flexible transformations, but its success is still based on the premise that brains resemble a prototypical template of anatomy, and can be produced by continuously deforming it.

To realize the quantitative potential of digital atlases, data from single subjects must be extendable to populations (Mazziotta et al., 1995). Atlasing considerations suggest that a statistical confidence limit, rather than an absolute representation of neuroanatomy, may be more appropriate for representing particular subpopulations.

Probabilistic atlasing is a research strategy whose goal is to generate anatomical templates that retain quantitative information on inter-subject variations in brain architecture (Mazziotta et al., 1995). A digital probabilistic atlas of the human brain, incorporating precise statistical information on positional variability of important functional and anatomic interfaces, may rectify many current atlasing problems, since it specifically stores information on the population variability.

Probabilistic Atlasing Approaches. Methods to create probabilistic brain representations currently fall into three major categories, each differing slightly in its conceptual foundations. The three methods are: the density-based, label-based, and deformation-based approaches. Benefits of each approach are outlined below.

1. Density-Based Approaches. Initial approaches to population-based atlasing concentrated on generating 'average' representations of anatomy by intensity averaging of multiple MRI scans (Evans et al., 1992; Andreasen et al., 1994). A large number of MRI scans are each linearly transformed into stereotaxic space, intensity-normalized and averaged on a voxel-by-voxel basis, producing an average intensity MRI dataset. The average brains that result have large areas, especially at the cortex, where individual structures are blurred out due to spatial variability in the population. While this blurring limits their usefulness as a quantitative tool, the templates can be used as targets for the automated registration and mapping of MR and co-registered functional data into stereotaxic space (Evans et al., 1994).

2. Label-Based Approaches. In label-based approaches (Evans et al., 1994; also known as SPAM approaches, short for 'statistical/probabilistic anatomy maps'), large ensembles of brain data are manually labeled, or 'segmented', into sub-volumes, after mapping individual datasets into stereotaxic space. A probability map is then constructed for each segmented structure, by determining the proportion of subjects assigned a given anatomic label at each voxel position in stereotaxic space (Evans et al., 1994; Otaky et al., 1995; Paus et al., 1996). The prior information which these probability maps provide on the location of various tissue classes in stereotaxic space has been useful in designing automated tissue classifiers and approaches to correct radio-frequency and intensity inhomogeneities in MR scans (Zijdenbos and Dawant, 1994). In our laboratory, we have also used SPAM probabilistic maps to constrain the search space for significant activations in PET and SPECT imaging experiments (Dinov et al., 1998; Mega et al., 1998). Statistical data on anatomic labels and tissue types normally found at given positions in stereotaxic space provide a vital independent source of information to guide and inform mathematical algorithms which analyze neuroanatomic data in stereotaxic space.

3. Deformation-Based Approaches. As noted earlier, when applied to two different 3D brain scans, a non-linear registration or warping algorithm calculates a deformation map (Fig. 4) which matches up brain structures in one scan with their counterparts in the other. The deformation map indicates 3-dimensional patterns of anatomic differences between the two subjects. In probabilistic atlases based on deformation maps (Thompson and Toga, 1997; Thompson et al., 1997), statistical properties of these deformation maps are encoded locally to determine the magnitude and directional biases of anatomic variation. Encoding of local variation can then be used to assess the severity of structural variants outside of the normal range, which may be a sign of disease (Thompson et al., 1997). A major goal in designing this type of pathology detection system is to recognize that both the magnitude and local directional biases of structural variability in the brain may be different at every single anatomic point (Thompson et al., 1996). In contrast to the intensity averaging of other current approaches (Evans et al., 1992; Andreasen et al., 1994), an anisotropic random vector field framework is introduced to encode directional biases in anatomic variability and map out abnormalities in new subjects (Thompson et al.,1997b).

The three major approaches for probabilistic atlas construction differ only in the attribute whose statistical distribution is modeled and analyzed. Random vector fields (i.e. vector distributions of deformation vectors at each point in space) are analyzed in approaches based on deformation maps, while random scalar fields are used to model MR intensity statistics in the density-based approach, and to model the incidence of binary labels in space in the label-based approach.

Encoding Brain Variation. Realistically complex mathematical strategies are needed to encode comprehensive information on structural variability in human populations. Particularly relevant is 3-dimensional statistical information on group-specific patterns of variation, and how these patterns are altered in disease (Fig. 6). This information can be encoded so that it can be exploited by expert diagnostic systems, whose goal is to detect subtle or diffuse structural alterations in disease. Strategies for detecting structural anomalies can leverage information in databased anatomic data by invoking encoded knowledge on the variations in geometry and location of neuroanatomic regions and critical functional interfaces, especially at the cortex.

Probabilistic Atlases of Cortical Patterns. The random vector field approach is a general strategy to construct population-based atlases of the brain (Thompson and Toga, 1997). Briefly, given a 3D MR image of a new subject, a high-resolution parametric surface representation of the cerebral cortex is automatically extracted (Fig. 3). The algorithm then calculates a set of high-dimensional volumetric maps, elastically deforming this surface into structural correspondence with other cortical surfaces, selected one by one from an anatomic image database. The family of volumetric warps so constructed encodes statistical properties of local anatomical variation across the cortical surface. Specialized strategies elastically deform the sulcal patterns of different subjects into structural correspondence, in a way which matches large networks of gyral and sulcal landmarks with their counterparts in the target brain (Fig. 3). Differences in the serial organization of cortical gyri prevent exact gyrus-by-gyrus matching of one cortex with another, but an important intermediate goal has been to match a comprehensive network of sulcal and gyral elements which have consistent topology across subjects (Drury et al., 1996; Thompson et al., 1997). A probability space of random transformations, based on the theory of anisotropic Gaussian random fields, is then used to encode information on complex variations in gyral and sulcal topography from one individual to another (Fig. 5). Confidence limits in stereotaxic space are determined, for cortical surface points in the new subject's brain, enabling the creation of color-coded probability maps to highlight and quantify regional patterns of deformity in the anatomy of new subjects.

Pathology Detection In view of the clear clinical and research applications, mathematical methods have been developed to create probabilistic measures of anatomic variation which are capable of detecting pathology. We (Thompson et al., 1996b) proposed a simple type of anomaly detection framework. Deformation fields are calculated which match elements of the deep surface anatomy in a range of N normal subjects. After affine components of the deformation fields are factored out, deviations from the mean deformation field are modeled, for small N, as a Hotelling's T-squared distributed random field, or for very large N, as a chi-squared distributed random field with 3 degrees of freedom, defined at nodes (u,v) in parametric mesh models of the anatomy of new subjects. Thompson et al. (1997) and Cao and Worsley (1998) proposed the use of a Hotelling's T-squared random field to detect abnormal deformations between groups, modeling the 3D deformation field, at each location, by a trivariate normal distribution with an arbitrary covariance tensor that allows for correlation between the coordinates. A T-squared or F statistic which indicates evidence of significant difference in deformations between the groups is calculated at each lattice location in a 3D image or parameterized 3D surface, to form a statistic image. Under the null hypothesis of no abnormal deformations, the statistic image is approximated by a T-squared random field. The global maximum of the random field can be used to test the hypothesis of no change (Worsley, 1994a,b; Cao and Worsley, 1998). Random field approaches, some of which are now widely used in packages for analyzing functional brain images (Friston et al., 1995), use the Euler characteristic (EC) of the excursion sets of a random field as an estimator of the number of local non-zero signal components, above a given threshold in a statistic image. They also use the expected value of the EC as an approximate p-value for the local maximum (Worsley, 1994a,b). Probabilistic atlases based on random deformation fields have been used to assess gender-specific differences in the brain (Cao and Worsley, 1998), and to detect structural abnormalities in neurodegenerative disorders such as Alzheimer's disease (Fig. 6, 7; Thompson et al., 1997).

Shape Theory Approaches. Deformation fields expressing neuroanatomic differences have also been analyzed using Procrustes methods, developed for the statistical analysis of biological shape (Bookstein, 1989; 1997). In Procrustes methods, affine components of neuroanatomic difference are factored out not by stereotaxic alignment, but by rotating and scaling configurations of point landmarks in each subject into least-squares correspondence with a Procrustes mean shape. Residual deformations which reflect individual change or anatomic difference are then expressed in terms of an orthogonal system of principal deformations derived from the bending energy matrix of the operator which governs the deformation (Bookstein, 1997). Of particular relevance are methods used to define a mean shape in such a way that departures from this mean shape can be treated as a linear process. Linearization of the pathology detection problem, by constructing Riemannian shape manifolds and their associated tangent spaces, allows the use of conventional statistical procedures and linear decomposition of departures from the mean to characterize shape change. These approaches have been applied to detect structural anomalies in schizophrenia (DeQuardo et al., 1996; Bookstein, 1997).

Pattern-Theoretic Approaches. In a related approach based on pattern theory (Grenander and Miller, 1994), a spectral approach to representing anatomic variation is developed. This approach, like the approaches described above, builds on the framework of deformable atlases by representing variation in terms of probabilistic transformations applied to deformable neuroanatomic templates. Deformation maps expressing variations in normal anatomies are calculated, with a non-linear registration procedure based on continuum-mechanics. In this formulation, the deformational behavior of each subject's anatomy, driven into correspondence with other anatomies, is expressed as a system of partial differential equations. The equations are governed by a differential operator controlling the way in which one anatomy is deformed into the other, and its properties can be used to make the deformation reflect the mechanical properties of deformable elastic or fluid media. Common choices of the differential operator are the Laplacian (Joshi et al., 1995), biharmonic (Bookstein, 1989) and Cauchy-Navier operator (Bajcsy and Kovacic, 1989; Gee et al., 1993, 1995; Miller et al., 1993; Christensen et al., 1996; Davatzikos, 1996; Thompson and Toga, 1998). Each deformation map is then expanded in terms of the eigenfunctions of the governing operator, and Gaussian probability measures are defined on the resulting sequences of expansion coefficients. Currently being tested as a framework for representing anatomic variation, this pattern-theoretic approach builds on the framework of deformable atlases and shows great promise in the automated detection of pathology.

V. Population Specificity

Genotype vs. Phenotype. Structural image databases from twin monozygotic versus dizygotic populations provide tremendous opportunities to investigate the relationship between genotype and phenotype. Striking similarities in brain structure for both mono- and dizygotic twins have been reported in studies of corpus callosum morphology (Oppenheim et al., 1989) and gyral patterning (Noga et al., 1996). These structural affinities can be exploited in clinical studies, since twins discordant for a specific disease-linked gene may be examined for regional structural differences in a context where effects of their shared genes are factored out (Goldberg et al., 1994; Noga et al., 1996). An on-going twin study (Gatz et al., 1997) focuses on 200 MR scans acquired from elderly Swedish twin pairs, where one member of each twin pair has Alzheimer's Disease (AD) or vascular dementia. Among 12 pairs of twins discordant for AD, the affected twin had greater temporal horn dilation, temporal lobe atrophy and 3rd ventricle enlargement, while significant within-pair correlations were found for measures of intracranial area, cerebellar area, temporal lobe volume, and white matter lesions (Gatz et al., 1997).

Pediatric and Embryonic Development. In 1992, the Visible Embryo Project (Doyle et al., 1996) was initiated as a collaboration between the Armed Forces Institute of Pathology and the National Institute of Child Health and Human Development, with the goal of digitizing, reconstructing, and archiving embryonic data from 660 fully serially sectioned embryos. Creation of a core database of fetal anatomic data is likely to create considerable opportunities for analyzing the complex characteristics of human brain development.

Coordinate Systems. Atlasing of developmental brain data presents unique challenges. The imposition of standardized coordinate systems is difficult, and their relationship to anatomic nomenclature is hard to define, when potentially drastic morphological differences exist among data sets. In Yoon et al. (1997), a photographic atlas of the human embryo was created, based on detailed observations in utero from the 4th to the 7th week after ovulation (Carnegie Stages 10-18). In Chong et al. (1997), 26 normal formalin-fixed fetal specimens with a gestational age of 9 to 24 weeks were examined with high-resolution MRI using a conventional clinical magnet and pulse sequences, and MR findings were correlated with histologic atlas data. Although templates of normal development helped to identify expected developmental features, it was noted that direct correlation of fetal MR images with anatomic atlases might result in a mistaken diagnosis of delayed development, because of a time lag in the detection of structures on MR images.

Current atlases of fetal development (O'Rahilly and Mueller, 1987; England, 1990) use collections of labeled data from multiple imaging modalities to characterize specific developmental stages. The first comprehensive MRI atlas of pediatric cranial anatomy (Salamon et al., 1990) incorporates 180 MRI scans acquired parallel to the orbito-meatal anatomical plane, and 360 explanatory diagrams depicting functional neuroanatomy from birth through 16 years of age. In this collection, 3D horizontal and sagittal images facilitate identification of sulci and gyri. However, stereotaxic coordinate systems were not applied to the atlas data due to difficulties in using them to reference embryonic and pediatric data. In the spirit of the deformable atlas methods described earlier, extreme deformations could be imposed to fit all stages of development into a standardized atlas, but this would hardly meet the primary requirement of atlasing, which is to provide a natural coordinate framework in which to localize and classify structures present in developing brains. Alternatively, different atlases and coordinate systems for several discrete stages of development might be used. Numerous anatomic features, due to their emergence and disappearance during development, could be used to place individual brains into an appropriate atlas in the set. Warping approaches could then be applied to the atlas coordinate systems as a basis to compare and quantitate development (Toga et al., 1996). Temporal interpolation between atlases in the set could be used to generate additional anatomic templates, representing brains at any stage of maturity in between those stages represented in the initial inventory.

VI. Queries and Applications

Human brain atlases based on populations invoke archived information in large databases. Rapid increases in the size, content and heterogeneity of these databases have resulted in several technical challenges. Interaction with population-based brain atlases clearly requires modern database technology to support complex queries and rapid searches over images and associated text and meta-data.

Brain Mapping Databases. BrainMap (Fox et al., 1994) is a searchable, relational database of functional brain maps, experimental protocols, and meta-analyses of data reported in the brain imaging research literature. Linked information on experimental parameters consists of descriptions of stimuli and modes of stimulation, as well as itemized textual information such as behavioral parameters and neuropsychiatric test data.. Meta-data includes means and statistical distributions for activation foci, and statistical probability maps of anatomy (SPAMs) developed by the International Consortium for Brain Mapping (ICBM; Mazziotta et al., 1995; see Section IV).

Users query the BrainMap system via a forms-based user interface, and can specify brain regions to query by clicking on coordinate locations in a built-in digital anatomic atlas. Findings published in the literature which refer to activations at specific stereotaxic locations can be requested by clicking on an atlas location. This automatically enters a coordinate location for the search. Search results are visualized by plotting the coordinates of activated locations onto a digitized atlas template based on that of Talairach et al. (1967). Five anatomical query schemes are available: users may request information by (1) specifying coordinate locations in stereotaxic space, by (2) referring to a specific region in a built-in parcellation of the cortex, by referring to (3) a particular Brodmann area in the cortex (Brodmann, 1909) or (4) a letter designation of a functional area (such as S1, V1 for primary somatosensory or visual cortex), or, finally, (5) by entering the anatomical name applied by the author to the activated area. Queries for behavioral data, citations and protocols related to each experiment are also supported. The resulting system shows considerable promise in becoming an international, electronic registry for human brain mapping data.

Neuronal Connectivity Atlases. A related graphical neuroanatomic database, Xanat (Olshausen and Press, 1994), stores results of numerous anatomical connectivity studies in a standardized format, providing tools to create summaries and comparisons of the archived data. Accumulated data from multiple connectivity studies are queried graphically according to injection or label site. By clicking on known anatomic landmarks or stereotaxic locations, results summarizing the total evidence for connectivity between regions are displayed as a color-coded heatmap, superimposed on an atlas template.

Content-Based Queries. Brain image archives, and image archives in general, differ from databases of purely numeric or textual information, in that they are not naturally suited to a textual (i.e., key-word based) description. Content-based querying systems (Wong and Huang, 1996, 1997) allow clinicians and researchers to search through image databases using knowledge of what the desired image actually contains, rather than by referring to a list of keywords or descriptions associated with the visual data. To enable content-based query, algorithms extract specific features in each image, and these features are retained as the basis for subsequent indexing and analysis. Encoding of image content as weighted sum of basis functions, such as Daubechies' wavelets (Daubechies et al., 1998, 1992; Wang et al., 1997) results in a compact set of parameters which computer algorithms can use to organize, search, and locate necessary visual information in given images or large sets of images (Gupta and Jain, 1997).

VII. Conclusion

Atlasing strategies to represent neuroanatomic and functional data, as well as increasingly powerful techniques to manipulate, query and detect patterns in the resulting image databases, will accelerate our understanding of brain function. The demand for comprehensive neuroanatomic templates and stereotaxic methods to integrate brain maps is continuing to increase in pace with the vast amount of high-resolution data being produced by 3-dimensional medical imaging devices. Access to the resulting digital image archives, as well as archive-based computational tools, will be fundamental to many future brain imaging investigations.

The complexity and density of brain image data obligates the design of a framework which allows scientific and clinical data collected at numerous research centers to be compared and integrated. In this chapter, we have described mathematical and computational strategies for constructing a variety of atlases of the human brain. The atlas systems compile multi-modality brain maps in a stereotaxic reference space making it easier to measure, correlate, and interpret multi-subject, multi-modality brain data. Because of their digital format, and the diversity of the image datasets they contain, population-based brain atlases offer significant advantages for detecting abnormality in the brain. They also provide a powerful reference framework for biomedical research and clinical imaging investigations, and a basis to integrate brain data from geographically disparate research centers, across imaging modalities and in large human populations.


This work was generously supported by research grants from the National Library of Medicine (LM/MH05639), the National Science Foundation (BIR 93-22434), by the NCRR (RR05956), and by a Human Brain Project grant to the International Consortium for Brain Mapping, which is funded jointly by NIMH and NIDA (P20 MH/DA52176). Paul Thompson was also supported by the United States Information Agency, under Grant G-1-00001, by a Fellowship of the Howard Hughes Medical Institute, and by a research grant from the U.S.-U.K. Fulbright Commission, London.

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    73-360 Brain Research Institute
    UCLA Medical Center
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