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.

Manually labeled landmark sets are often required as inputs for landmark-based image registration. Identifying an optimal subset of landmarks from a training dataset may be useful in reducing the labor intensive task of manual labeling. In this paper, we present a new problem and a method to solve it: given a set of N landmarks, find the k(< N) best landmarks such that aligning these k landmarks that produce the best overall alignment of all N landmarks. The resulting procedure allows us to select a reduced number of landmarks to be labeled as a part of the registration procedure. We apply this methodology to the problem of registering cerebral cortical surfaces extracted from MRI data. We use manually traced sulcal curves as landmarks in performing inter-subject registration of these surfaces. To minimize the error metric, we analyze the correlation structure of the sulcal errors in the landmark points by modeling them as a multivariate Gaussian process. Selection of the optimal subset of sulcal curves is performed by computing the error variance for the subset of unconstrained landmarks conditioned on the constrained set. We show that the registration error predicted by our method closely matches the actual registration error. The method determines optimal curve subsets of any given size with minimal registration error.

Neuroimaging data, such as 3-D maps of cortical thickness or neural activation, can often be analyzed more informatively with respect to the cortical surface rather than the entire volume of the brain. Any cortical surface-based analysis should be carried out using computations in the intrinsic geometry of the surface rather than using the metric of the ambient 3-D space. We present parameterization-based numerical methods for performing isotropic and anisotropic filtering on triangulated surface geometries. In contrast to existing FEM-based methods for triangulated geometries, our approach accounts for the metric of the surface. In order to discretize and numerically compute the isotropic and anisotropic geometric operators, we first parameterize the surface using a p-harmonic mapping. We then use this parameterization as our computational domain and account for the surface metric while carrying out isotropic and anisotropic filtering. To validate our method, we compare our numerical results to the analytical expression for isotropic diffusion on a spherical surface. We apply these methods to smoothing of mean curvature maps on the cortical surface, a step commonly required for analysis of gyrification or for registering surface-based maps across subjects.

We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color images of the DTI dataset.

In order to compare anatomical and functional brain imaging data across subjects, the images must first be registered to a common coordinate system in which anatomical features are aligned. Intensity-based volume registration methods can align subcortical structures well, but the variability in sulcal folding patterns typically results in misalignment of the cortical surface. Conversely, surface-based registration using sulcal features can produce excellent cortical alignment but the mapping between brains is restricted to the cortical surface. Here we describe a method for volumetric registration that also produces an accurate one-to-one point correspondence between cortical surfaces. This is achieved by first parameterizing and aligning the cortical surfaces using sulcal landmarks. We then use a constrained harmonic mapping to extend this surface correspondence to the entire cortical volume. Finally, this mapping is refined using an intensity-based warp. We demonstrate the utility of the method by applying it to T1-weighted magnetic resonance images (MRIs). We evaluate the performance of our proposed method relative to existing methods that use only intensity information; for this comparison we compute the intersubject alignment of expert-labeled subcortical structures after registration.

Finite mixture models (FMMs) are an indispensable tool for unsupervised classification in brain imaging. Fitting an FMM to the data leads to a complex optimization problem. This optimization problem is difficult to solve by standard local optimization methods, such as the expectation-maximization (EM) algorithm, if a principled initialization is not available. In this paper, we propose a new global optimization algorithm for the FMM parameter estimation problem, which is based on real coded genetic algorithms. Our specific contributions are two-fold: 1) we propose to use blended crossover in order to reduce the premature convergence problem to its minimum and 2) we introduce a completely new permutation operator specifically meant for the FMM parameter estimation. In addition to improving the optimization results, the permutation operator allows for imposing biologically meaningful constraints to the FMM parameter values. We also introduce a hybrid of the genetic algorithm and the EM algorithm for efficient solution of multidimensional FMM fitting problems. We compare our algorithm to the self-annealing EM-algorithm and a standard real coded genetic algorithm with the voxel classification tasks within the brain imaging. The algorithms are tested on synthetic data as well as real three-dimensional image data from human magnetic resonance imaging, positron emission tomography, and mouse brain MRI. The tissue classification results by our method are shown to be consistently more reliable and accurate than with the competing parameter estimation methods.

The human cerebral cortex is topologically equivalent to a sheet and can be considered topologically spherical if it is closed at the brain stem. Low-level segmentation of magnetic resonance (MR) imagery typically produces cerebral volumes whose tessellations are not topologically spherical. We present a novel algorithm that analyzes and constrains the topology of a volumetric object. Graphs are formed that represent the connectivity of voxel segments in the foreground and background of the image. These graphs are analyzed and minimal corrections to the volume are made prior to tessellation. We apply the algorithm to a simple test object and to cerebral white matter masks generated by a low-level tissue identification sequence. We tessellate the resulting objects using the marching cubes algorithm and verify their topology by computing their Euler characteristics. A key benefit of the algorithm is that it localizes the change to a volume to the specific areas of its topological defects.