Detection and mapping of abnormal brain structure with a probabilistic atlas of cortical surfaces

Elastic registration of fMRI data using Bézier-spline transformations

A three-dimensional (3-D) elastic registration algorithm has been developed to find a veridical transformation that maps activation patterns from functional magnetic resonance imaging (fMRI) experiments onto a 3-D high-resolution anatomical dataset. The proposed algorithm uses trilinear Bézier-splines and a 3-D voxel-based optimization technique to determine the transformation that maps the functional data onto the coordinate system of the anatomical dataset. Simple conditions are presented which guarantee that the data are mapped one-to-one on each other. Two voxel-based similarity measures, the linear correlation coefficient and the entropy correlation coefficient, are used. Their performance with respect to the registration of fMRI data is compared. Tests on simulated and real data have been performed to evaluate the accuracy of the method. Our results demonstrate that subvoxel accuracy can be achieved even for noisy low-resolution multislice datasets with local distortions up to 10 mm. Although the method is optimized for the registration of functional and anatomical MR images, it can also be used for solving other elastic registration problems.

Three-dimensional mapping of gyral shape and cortical surface asymmetries in schizophrenia: gender effects

OBJECTIVE

People with schizophrenia exhibit abnormalities in brain structure, often in the left hemisphere. Disturbed structural lateralization is controversial, however, and effects appear mediated by gender. The authors mapped differences between schizophrenic and normal subjects in gyral asymmetries, complexity, and variability across the entire cortex.

METHOD

Asymmetry and shape profiles for 25 schizophrenic patients (15 men) and 28 demographically similar normal subjects (15 men) were obtained for 38 gyral regions, including the sylvian fissure and temporal and postcentral gyri, by using magnetic resonance data and a novel surface-based mesh-modeling approach. Cortical complexity was examined for sex and diagnosis effects in lobar regions. Intragroup variability was quantified and visualized to assess regional group abnormalities at the cortical surface.

RESULTS

The patients showed greater variability in frontal areas than the comparison subjects. They also had significant deviations in gyral complexity asymmetry in the superior frontal cortex. In temporoparietal regions, significant gyral asymmetries were present in both groups. Sex differences were apparent in superior temporal gyral measures, and cortical complexity in inferior frontal regions was significantly greater in men.

CONCLUSIONS

Cortical variability and complexity show regional abnormalities in the frontal cortex potentially specific to schizophrenia. The results indicate highly significant temporoparietal gyral asymmetries in both diagnostic groups, contrary to reports of less lateralization in schizophrenia. Substantially larger study groups are necessary to isolate smaller deviations in surface asymmetries, if present in schizophrenia, suggesting their diagnostic value is minimal.

Cortical change in Alzheimer's disease detected with a disease-specific population-based brain atlas

We report the first detailed population-based maps of cortical gray matter loss in Alzheimer's disease (AD), revealing prominent features of early structural change. New computational approaches were used to: (i) distinguish variations in gray matter distribution from variations in gyral patterns; (ii) encode these variations in a brain atlas (n = 46); (iii) create detailed maps localizing gray matter differences across groups. High resolution 3D magnetic resonance imaging (MRI) volumes were acquired from 26 subjects with mild to moderate AD (age 75.8+/-1.7 years, MMSE score 20.0+/-0.9) and 20 normal elderly controls (72.4+/-1.3 years) matched for age, sex, handedness and educational level. Image data were aligned into a standardized coordinate space specifically developed for an elderly population. Eighty-four anatomical models per brain, based on parametric surface meshes, were created for all 46 subjects. Structures modeled included: cortical surfaces, all major superficial and deep cortical sulci, callosal and hippocampal surfaces, 14 ventricular regions and 36 gyral boundaries. An elastic warping approach, driven by anatomical features, was then used to measure gyral pattern variations. Measures of gray matter distribution were made in corresponding regions of cortex across all 46 subjects. Statistical variations in cortical patterning, asymmetry, gray matter distribution and average gray matter loss were then encoded locally across the cortex. Maps of group differences were generated. Average maps revealed complex profiles of gray matter loss in disease. Greatest deficits (20-30% loss, P<0.001-0.0001) were mapped in the temporo-parietal cortices. The sensorimotor and occipital cortices were comparatively spared (0-5% loss, P>0.05). Gray matter loss was greater in the left hemisphere, with different patterns in the heteromodal and idiotypic cortex. Gyral pattern variability also differed in cortical regions appearing at different embryonic phases. 3D mapping revealed profiles of structural deficits consistent with the cognitive, metabolic and histological changes in early AD. These deficits can therefore be (i) charted in a living population and (ii) compared across individuals and groups, facilitating longitudinal, genetic and interventional studies of dementia.

The role of image registration in brain mapping

Image registration is a key step in a great variety of biomedical imaging applications. It provides the ability to geometrically align one dataset with another, and is a prerequisite for all imaging applications that compare datasets across subjects, imaging modalities, or across time. Registration algorithms also enable the pooling and comparison of experimental findings across laboratories, the construction of population-based brain atlases, and the creation of systems to detect group patterns in structural and functional imaging data. We review the major types of registration approaches used in brain imaging today. We focus on their conceptual basis, the underlying mathematics, and their strengths and weaknesses in different contexts. We describe the major goals of registration, including data fusion, quantification of change, automated image segmentation and labeling, shape measurement, and pathology detection. We indicate that registration algorithms have great potential when used in conjunction with a digital brain atlas, which acts as a reference system in which brain images can be compared for statistical analysis. The resulting armory of registration approaches is fundamental to medical image analysis, and in a brain mapping context provides a means to elucidate clinical, demographic, or functional trends in the anatomy or physiology of the brain.

Location-probability profiles for the mouth region of human primary motor-sensory cortex: model and validation

The mouth representation of the human, primary motor cortex (M1) is not reliably identified by surface anatomy but may be reliably localized by means of spatial coordinates. For this report, three quantitative metanalyses were performed which jointly described the mean location, location variability and location-probability profiles of the human M1-mouth representation. First, a literature metanalysis of intersubject functional-area variability was performed using eleven, per-subject studies, each of which reported a coordinate-referenced measure of intersubject variability for one or more brain areas. From these data, a weighted-mean value for intersubject variability was computed, which proved to be small (5.6 mm, standard deviation), consistent across coordinate axes (x, y, z), and consistent across brain areas. Second, a literature metanalysis of the location of M1-mouth was performed using seven, coordinate-referenced, group-mean studies (71 subjects in all), each of which reported a grand-average location for M1-mouth. From this, a weighted-mean location and weighted values for total variability (interlaboratory plus interindividual) were determined. Using these two literature metanalyses as input data, location-probability profiles were computed for the cardinal axes (x, y, and z) of the reference space, using the functional volumes modeling (FVM) statistical model. Third, an original-data metanalysis was performed on in-house PET data from 30 normal subjects performing overt-speech tasks. M1-mouth's mean location, location variability, and location-probability profiles were consistent with those conjointly modeled by FVM from the two literature metanalyses. Collectively, these observations provide a detailed, consensus probabilistic description of the location of the human M1-mouth representation in standardized coordinates.

Topology preserving deformable image matching using constrained hierarchical parametric models

In this paper, we address the issue of topology preservation in deformable image matching. A novel constrained hierarchical parametric approach is presented, that ensures that the mapping is globally one-to one and thus preserves topology in the deformed image. The transformation between the source and target images is parameterized at different scales, using a decomposition of the deformation vector field over a sequence of nested (multiresolution) subspaces. The Jacobian of the mapping is controlled over the continuous domain of the transformation, ensuring actual topology preservation on the whole image support. The resulting fast nonlinear constrained optimization algorithm enables to track large nonlinear deformations while preserving the topology. Experimental results are presented both on simulated data and on real medical images.

Automatic labelling of the human cortical surface using sulcal basins

Human brain mapping aims at establishing correspondences between brain function and brain anatomy. One of the most intriguing problems in this field is the high interpersonal variability of human neuroanatomy which makes studies across many subjects very difficult. The cortical folds ('sulci') often serve as landmarks that help to establish correspondences between subjects. In this paper, we will present a method that automatically detects and attributes neuroanatomical names to the cortical folds using image analysis methods applied to magnetic resonance data of human brains. We claim that the cortical folds can be subdivided into a number of substructures which we call sulcal basins. The concept of sulcal basins allows us to establish a complete parcellation of the cortical surface into separate regions. These regions are neuroanatomically meaningful and can be identified from MR data sets across many subjects. Sulcal basins are segmented using a region growing approach. The automatic labelling is achieved by a model matching technique.

Growth patterns in the developing brain detected by using continuum mechanical tensor maps

The dynamic nature of growth and degenerative disease processes requires the design of sensitive strategies to detect, track and quantify structural change in the brain in its full spatial and temporal complexity. Although volumes of brain substructures are known to change during development, detailed maps of these dynamic growth processes have been unavailable. Here we report the creation of spatially complex, four-dimensional quantitative maps of growth patterns in the developing human brain, detected using a tensor mapping strategy with greater spatial detail and sensitivity than previously obtainable. By repeatedly scanning children (aged 3-15 years) across time spans of up to four years, a rostro-caudal wave of growth was detected at the corpus callosum, a fibre system that relays information between brain hemispheres. Peak growth rates, in fibres innervating association and language cortices, were attenuated after puberty, and contrasted sharply with a severe, spatially localized loss of subcortical grey matter. Conversely, at ages 3-6 years, the fastest growth rates occurred in frontal networks that regulate the planning of new actions. Local rates, profiles, and principal directions of growth were visualized in each individual child.

Mathematical/computational challenges in creating deformable and probabilistic atlases of the human brain

Striking variations in brain structure, especially in the gyral patterns of the human cortex, present fundamental challenges in human brain mapping. Probabilistic brain atlases, which encode information on structural and functional variability in large human populations, are powerful research tools with broad applications. Knowledge-based imaging algorithms can also leverage atlased information on anatomic variation. Applications include automated image labeling, pathology detection in individuals or groups, and investigating how regional anatomy is altered in disease, and with age, gender, handedness and other clinical or genetic factors. In this report, we illustrate some of the mathematical challenges involved in constructing population-based brain atlases. A disease-specific atlas is constructed to represent the human brain in Alzheimer's disease (AD). Specialized strategies are developed for population-based averaging of anatomy. Sets of high-dimensional elastic mappings, based on the principles of continuum mechanics, reconfigure the anatomy of a large number of subjects in an anatomic image database. These mappings generate a local encoding of anatomic variability and are used to create a crisp anatomical image template with highly resolved structures in their mean spatial location. Specialized approaches are also developed to average cortical topography. Since cortical patterns are altered in a variety of diseases, gyral pattern matching is used to encode the magnitude and principal directions of local cortical variation. In the resulting cortical templates, subtle features emerge. Regional asymmetries appear that are not apparent in individual anatomies. Population-based maps of cortical variation reveal a mosaic of variability patterns that segregate sharply according to functional specialization and cytoarchitectonic boundaries.

Volume rendering quantification algorithm for reconstruction of CT volume-rendered structures: Part I. Cerebral arteriovenous malformations

Volume rendering is a visualization technique that has important applications in diagnostic radiology and in radiotherapy but has not achieved widespread use due, in part, to the lack of volumetric analysis tools for comparison of volume rendering to conventional visualization techniques. The volume rendering quantification algorithm (VRQA), a technique for three-dimensional (3-D) reconstruction of a structure identified on six principal volume-rendered views, is introduced and described. VRQA involves three major steps: 1) preprocessing of the partial surfaces constructed from each of six volume-rendered images; 2) merging these processed partial surfaces to define the boundaries of a volume; and 3) computation of the volume of the structure from this boundary information. After testing on phantoms, VRQA was applied to CT data of patients with cerebral arteriovenous malformations (AVM's). Because volumetric visualization of the cerebral AVM is relatively insensitive to operator dependencies, such as the choice of opacity transfer function, and because precise volumetric definition of the AVM is necessary for radiosurgical treatment planning, it is representative of a class of structures that is ideal for testing and calibration of VRQA. AVM volumes obtained using VRQA are intermediate to those obtained using axial contouring and those obtained using CT-correlated biplanar angiography (two routinely used visualization techniques for treatment planning for AVM's). Applications and potential expansions of VRQA are discussed.

Analyzing functional brain images in a probabilistic atlas: a validation of subvolume thresholding

PURPOSE

The development of structural probabilistic brain atlases provides the framework for new analytic methods capable of combining anatomic information with the statistical mapping of functional brain data. Approaches for statistical mapping that utilize information about the anatomic variability and registration errors of a population within the Talairach atlas space will enhance our understanding of the interplay between human brain structure and function.

METHOD

We present a subvolume thresholding (SVT) method for analyzing positron emission tomography (PET) and single photon emission CT data and determining separately the statistical significance of the effects of motor stimulation on brain perfusion. Incorporation of a priori anatomical information into the functional SVT model is achieved by selecting a proper anatomically partitioned probabilistic atlas for the data. We use a general Gaussian random field model to account for the intrinsic differences in intensity distribution across brain regions related to the physiology of brain activation, attenuation effects, dead time, and other corrections in PET imaging and data reconstruction.

RESULTS

H2(15)O PET scans were acquired from six normal subjects under two different activation paradigms: left-hand and right-hand finger-tracking task with visual stimulus. Regional region-of-interest and local (voxel) group differences between the left and right motor tasks were obtained using nonparametric stochastic variance estimates. As expected from our simple finger movement paradigm, significant activation (z = 6.7) was identified in the left motor cortex for the right movement task and significant activation (z = 6.3) for the left movement task in the right motor cortex.

CONCLUSION

We propose, test, and validate a probabilistic SVT method for mapping statistical variability between groups in subtraction paradigm studies of functional brain data. This method incorporates knowledge of, and controls for, anatomic variability contained in modern human brain probabilistic atlases in functional statistical mapping of the brain.

Fast, accurate, and reproducible automatic segmentation of the brain in T1-weighted volume MRI data

A new fast automated algorithm has been developed to segment the brain from T1-weighted volume MR images. The algorithm uses automated thresholding and morphological operations. It is fully three-dimensional and therefore independent of scan orientation. The validity and the performance of the algorithm were evaluated by comparing the automatically calculated brain volume with semi-automated measurements in 10 subjects, by calculating the brain volume from repeated scans in another 10 subjects, and by visual inspection. The mean and standard deviation of the difference between semi-automated and automated measurements were 0.56% and 2.8% of the mean brain volume, respectively, which is within inter-observer variability of the semi-automated method. The mean and standard deviation of the difference between the total volumes calculated from repeated scans were 0.40% and 1.2% of the mean brain volume, respectively. Good results were also obtained from a scan of abnormal brains.

Reconstruction of the human cerebral cortex from magnetic resonance images

Reconstructing the geometry of the human cerebral cortex from MR images is an important step in both brain mapping and surgical path planning applications. Difficulties with imaging noise, partial volume averaging, image intensity inhomogeneities, convoluted cortical structures, and the requirement to preserve anatomical topology make the development of accurate automated algorithms particularly challenging. In this paper we address each of these problems and describe a systematic method for obtaining a surface representation of the geometric central layer of the human cerebral cortex. Using fuzzy segmentation, an isosurface algorithm, and a deformable surface model, the method reconstructs the entire cortex with the correct topology, including deep convoluted sulci and gyri. The method is largely automated and its results are robust to imaging noise, partial volume averaging, and image intensity inhomogeneities. The performance of this method is demonstrated, both qualitatively and quantitatively, and the results of its application to six subjects and one simulated MR brain volume are presented.

Measurement of brain structures with artificial neural networks: two- and three-dimensional applications

PURPOSE

To evaluate the ability of an artificial neural network (ANN) to identify brain structures. This ANN was applied to postprocessed magnetic resonance (MR) images to segment various brain structures in both two- and three-dimensional applications.

MATERIALS AND METHODS

An ANN was designed that learned from experience to define the corpus callosum, whole brain, caudate, and putamen. Manual segmentation was used as a training set for the ANN. The ANN was trained on two-thirds of the manually segmented images and was tested on the remaining one-third. The reliability of the ANN was compared against manual segmentations by two technicians.

RESULTS

The ANN was able to identify the brain structures as readily and as well as did the two technicians. Reliability of the ANN compared with the technicians was 0.96 for the corpus callosum, 0.95 for the whole brain, 0.86 (right) and 0.93 (left) for the caudate, and 0.71 (right) and 0.88 (left) for the putamen.

CONCLUSION

The ANN was able to identify the structures used in this study as well as did the two technicians. The ANN could do this much more rapidly and without rater drift. Several other cortical and subcortical structures could also be readily identified with this method.

Enhancing the multivariate signal of [15O] water PET studies with a new nonlinear neuroanatomical registration algorithm

This paper addresses the problem of neuro-anatomical registration across individuals for functional [15O] water PET activation studies. A new algorithm for three-dimensional (3-D) nonlinear structural registration (warping) of MR scans is presented. The method performs a hierarchically scaled search for a displacement field, maximizing one of several voxel similarity measures derived from the two-dimensional (2-D) histogram of matched image intensities, subject to a regularizer that ensures smoothness of the displacement field. The effect of the nonlinear structural registration is studied when it is computed on anatomical MR scans and applied to coregistered [15O] water PET scans from the same subjects: in this experiment, a study of visually guided saccadic eye movements. The performance of the nonlinear warp is evaluated using multivariate functional signal and noise measures. These measures prove to be useful for comparing different intersubject registration approaches, e.g., affine versus nonlinear. A comparison of 12-parameter affine registration versus non-linear registration demonstrates that the proposed nonlinear method increases the number of voxels retained in the cross-subject mask. We demonstrate that improved structural registration may result in an improved multivariate functional signal-to-noise ratio (SNR). Furthermore, registration of PET scans using the 12-parameter affine transformations that align the coregistered MR images does not improve registration, compared to 12-parameter affine alignment of the PET images directly.

A method for assessing the accuracy of intersubject registration of the human brain using anatomic landmarks

Several groups have developed methods for registering an individual's 3D MRI by deforming a standard template. This achievement leads to many possibilities for segmentation and morphology that will impact nuclear medical research in areas such as activation and receptor studies. Accordingly, there is a need for methods that can assess the accuracy of intersubject registration. We have developed a method based on a set of 128 anatomic landmarks per hemisphere, both cortical and subcortical, that allows assessment of both global and local transformation accuracy. We applied our method to compare the accuracy of two standard methods of intersubject registration, AIR 3.0 with fifth-order polynomial warping and the Talairach stereotaxic transformation (Talairach and Tournoux, 1988). SPGR MRI's (256 x 256 x 160) of six normal subjects (age 18-24 years) were derformed to match a standard template volume. To assess registration accuracy the landmarks were located on both the template volume and the transformed volumes by an experienced neuroanatomist. The resulting list of coordinates was analyzed graphically and by ANOVA to compare the accuracy of the two methods and the results of the manual analysis. ANOVA performed over all 128 landmarks showed that the Woods method was more accurate than Talairach (left hemisphere F = 2.8, P < 0.001 and right hemisphere F =2.4, P < 0.006). The Woods method provided a better brain surface transformation than did Talairach (F = 18.0, P < 0.0001), but as expected there was a smaller difference for subcortical structures and both had an accuracy <1 mm for the majority of subcortical landmarks. Overall, both the Woods and Talairach method located about 70% of landmarks with an error of 3 mm or less. More striking differences were noted for landmark accuracy </=1 mm, where the Woods method located about 40% and Talairach about 23%. These results demonstrate that this anatomically based assessment method can help evaluate new methods of intersubject registration and should be a helpful tool in appreciating regional differences in accuracy. Consistent with expectation, we confirmed that the Woods nonlinear registration method was more accurate than Talairach. Landmark-based anatomic analyses of intersubject registration accuracy offer opportunities to explore the relationship among structure, function and architectonic boundaries in the human brain.

High-resolution intersubject averaging and a coordinate system for the cortical surface

The neurons of the human cerebral cortex are arranged in a highly folded sheet, with the majority of the cortical surface area buried in folds. Cortical maps are typically arranged with a topography oriented parallel to the cortical surface. Despite this unambiguous sheetlike geometry, the most commonly used coordinate systems for localizing cortical features are based on 3-D stereotaxic coordinates rather than on position relative to the 2-D cortical sheet. In order to address the need for a more natural surface-based coordinate system for the cortex, we have developed a means for generating an average folding pattern across a large number of individual subjects as a function on the unit sphere and of nonrigidly aligning each individual with the average. This establishes a spherical surface-based coordinate system that is adapted to the folding pattern of each individual subject, allowing for much higher localization accuracy of structural and functional features of the human brain.

Extracting line representations of sulcal and gyral patterns in MR images of the human brain

This paper describes automatic procedures for extracting sulcal and gyral patterns from magnetic resonance (MR) images of the human brain. Specifically, we present three algorithms for the extraction of gyri, sulci, and sulcal fundi. These algorithms yield highly condensed line representations which can be used to describe the individual properties of the neocortical surface. The algorithms consist of a sequence of image analysis steps applied directly to the volumetric image data without requiring intermediate data representations such as surfaces or three-dimensional renderings. Previous studies have mostly focused on the extraction of surface representations, rather than line representations of cortical structures. We believe that line representations provide a valuable alternative to surface representations.

A probabilistic ribbon model for shape analysis of the cerebral sulci: application to the central sulcus

PURPOSE

An approach for quantifying the shapes of the cerebral sulci is presented, utilizing a probabilistic geometric model, and it is applied to the central sulcus.

METHOD

The geometric structure of the central sulcus is determined from a set of outlines on cross-sectional images and is used by a procedure that automatically labels the major crest lines, i.e., curves of locally maximal curvature, along the sulcus. An automated procedure then determines a parametric representation of the central sulcus that is consistent across individuals, in that it assigns the same parametric coordinates to corresponding regions of the sulcus.

RESULTS

The method is applied to the central sulci from 20 subjects. The use of this shape representation in cortical morphometric analysis applications is demonstrated, in particular in obtaining local depth and curvature measurements of a sulcus as well as in determining average shapes and variability.

CONCLUSION

With this method, we were able to build parametric representations of the sulcal ribbons by preserving anatomical homologies.

An image-processing system for qualitative and quantitative volumetric analysis of brain images

In this work, we developed, implemented, and validated an image-processing system for qualitative and quantitative volumetric analysis of brain images. This system allows the visualization and quantitation of global and regional brain volumes. Global volumes were obtained via an automated adaptive Bayesian segmentation technique that labels the brain into white matter, gray matter, and cerebrospinal fluid. Absolute volumetric errors for these compartments ranged between 1 and 3% as indicated by phantom studies. Quantitation of regional brain volumes was performed through normalization and tessellation of segmented brain images into the Talairach space with a 3D elastic warping model. Retest reliability of regional volumes measured in Talairach space indicated errors of < 1.5% for the frontal, parietal, temporal, and occipital brain regions. Additional regional analysis was performed with an automated hybrid method combining a region-of-interest approach and voxel-based analysis, named Regional Analysis of Volumes Examined in Normalized Space (RAVENS). RAVENS analysis for several subcortical structures showed good agreement with operator-defined volumes. This system has sufficient accuracy for longitudinal imaging data and is currently being used in the analysis of neuroimaging data of the Baltimore Longitudinal Study of Aging.

Brain mapping in animals and humans

Studies using functional magnetic resonance imaging (fMRI) to map cortical areas in humans have revealed many similarities with recent cortical mapping studies from nonhuman primates as well as some striking differences. Improved methods for analyzing, displaying and averaging fMRI data on an unfolded cortical surface atlas are poised to improve the integration of information across burgeoning numbers of imaging studies. By combining fMRI with electrical and passive magnetic imaging modalities, the millisecond-to-millisecond sequence of activation of different cortical regions elicited by an event can be imaged, provided the regions are sufficiently far apart.

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 384(2) x 256 x 3 approximately 10(8) 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 384(2) x 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.