The Center for Computational Biology (CCB) is a multidisciplinary program where biomedical scientists, engineers, and clinicians work jointly to combine modern mathematical and computational techniques, to perform phenotypic and genotypic studies of biological structure, function, and physiology in health and disease. CCB has developed a computational framework built around the Manifold Atlas, an integrated biomedical computing environment that enables statistical inference on biological manifolds. These manifolds model biological structures, features, shapes, and flows, and support sophisticated morphometric and statistical analyses. The Manifold Atlas includes tools, workflows, and services for multimodal population-based modeling and analysis of biological manifolds. The broad spectrum of biomedical topics explored by CCB investigators include the study of normal and pathological brain development, maturation and aging, discovery of associations between neuroimaging and genetic biomarkers, and the modeling, analysis, and visualization of biological shape, form, and size. CCB supports a wide range of short-term and long-term collaborations with outside investigators, which drive the center's computational developments and focus the validation and dissemination of CCB resources to new areas and scientific domains.

We present a diffeomorphic approach for constructing intrinsic shape atlases of sulci on the human cortex. Sulci are represented as square-root velocity functions of continuous open curves in R³, and their shapes are studied as functional representations of an infinite-dimensional sphere. This spherical manifold has some advantageous properties--it is equipped with a Riemannian L² metric on the tangent space and facilitates computational analyses and correspondences between sulcal shapes. Sulcal shape mapping is achieved by computing geodesics in the quotient space of shapes modulo scales, translations, rigid rotations, and reparameterizations. The resulting sulcal shape atlas preserves important local geometry inherently present in the sample population. The sulcal shape atlas is integrated in a cortical registration framework and exhibits better geometric matching compared to the conventional euclidean method. We demonstrate experimental results for sulcal shape mapping, cortical surface registration, and sulcal classification for two different surface extraction protocols for separate subject populations.

We present an intrinsic framework for constructing sulcal shape atlases on the human cortex. We propose the analysis of sulcal and gyral patterns by representing them by continuous open curves in ℝ(3). The space of such curves, also termed as the shape manifold is equipped with a Riemannian L(2) metric on the tangent space, and shows desirable properties while matching shapes of sulci. On account of the spherical nature of the shape space, geodesics between shapes can be computed analytically. Additionally, we also present an optimization approach that computes geodesics in the quotient space of shapes modulo rigid rotations and reparameterizations. We also integrate the elastic shape model into a surface registration framework for a population of 176 subjects, and show a considerable improvement in the constructed surface atlases.

For various 3D shape analysis tasks, the Laplace-Beltrami(LB) embedding has become increasingly popular as it enables the efficient comparison of shapes based on intrinsic geometry. One fundamental difficulty in using the LB embedding, however, is the ambiguity in the eigen-system, and it is conventionally only handled in a heuristic way. In this work, we propose a novel and intrinsic metric, the spectral l2-distance, to overcome this difficulty. We prove mathematically that this new distance satisfies the conditions of a rigorous metric. Using the resulting optimal embedding determined by the spectral l2-distance, we can perform both local and global shape analysis intrinsically in the embedding space. We demonstrate this by developing a template matching approach in the optimal embedding space to solve the challenging problem of identifying major sulci on vervet cortical surfaces. In our experiments, we validate the robustness of our method by the successful identification of major sulcal lines on a large data set of 698 cortical surfaces and illustrate its potential in brain mapping studies.

In the field of template-based medical image analysis, image registration and normalization are frequently used to evaluate and interpret data in a standard template or reference atlas space. Despite the large number of image-registration (warping) techniques developed recently in the literature, only a few studies have been undertaken to numerically characterize and compare various alignment methods. In this paper, we introduce a new approach for analyzing image registration based on a selective-wavelet reconstruction technique using a frequency-adaptive wavelet shrinkage. We study four polynomial-based and two higher complexity nonaffine warping methods applied to groups of stereotaxic human brain structural (magnetic resonance imaging) and functional (positron emission tomography) data. Depending upon the aim of the image registration, we present several warp classification schemes. Our method uses a concise representation of the native and resliced (pre- and post-warp) data in compressed wavelet space to assess quality of registration. This technique is computationally inexpensive and utilizes the image compression, image enhancement, and denoising characteristics of the wavelet-based function representation, as well as the optimality properties of frequency-dependent wavelet shrinkage.

The authors describe the development of a four-dimensional atlas and reference system that includes both macroscopic and microscopic information on structure and function of the human brain in persons between the ages of 18 and 90 years. Given the presumed large but previously unquantified degree of structural and functional variance among normal persons in the human population, the basis for this atlas and reference system is probabilistic. Through the efforts of the International Consortium for Brain Mapping (ICBM), 7,000 subjects will be included in the initial phase of database and atlas development. For each subject, detailed demographic, clinical, behavioral, and imaging information is being collected. In addition, 5,800 subjects will contribute DNA for the purpose of determining genotype- phenotype-behavioral correlations. The process of developing the strategies, algorithms, data collection methods, validation approaches, database structures, and distribution of results is described in this report. Examples of applications of the approach are described for the normal brain in both adults and children as well as in patients with schizophrenia. This project should provide new insights into the relationship between microscopic and macroscopic structure and function in the human brain and should have important implications in basic neuroscience, clinical diagnostics, and cerebral disorders.