Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

Cortical Surface Reconstruction from High-Resolution MR Brain Images

Reconstruction of the cerebral cortex from magnetic resonance (MR) images is an important step in quantitative analysis of the human brain structure, for example, in sulcal morphometry and in studies of cortical thickness. Existing cortical reconstruction approaches are typically optimized for standard resolution (~1 mm) data and are not directly applicable to higher resolution images. A new PDE-based method is presented for the automated cortical reconstruction that is computationally efficient and scales well with grid resolution, and thus is particularly suitable for high-resolution MR images with submillimeter voxel size. The method uses a mathematical model of a field in an inhomogeneous dielectric. This field mapping, similarly to a Laplacian mapping, has nice laminar properties in the cortical layer, and helps to identify the unresolved boundaries between cortical banks in narrow sulci. The pial cortical surface is reconstructed by advection along the field gradient as a geometric deformable model constrained by topology-preserving level set approach. The method's performance is illustrated on exvivo images with 0.25–0.35 mm isotropic voxels. The method is further evaluated by cross-comparison with results of the FreeSurfer software on standard resolution data sets from the OASIS database featuring pairs of repeated scans for 20 healthy young subjects

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus

Pycortex: an interactive surface visualizer for fMRI.

Surface visualizations of fMRI provide a comprehensive view of cortical activity. However, surface visualizations are difficult to generate and most common visualization techniques rely on unnecessary interpolation which limits the fidelity of the resulting maps. Furthermore, it is difficult to understand the relationship between flattened cortical surfaces and the underlying 3D anatomy using tools available currently. To address these problems we have developed pycortex, a Python toolbox for interactive surface mapping and visualization. Pycortex exploits the power of modern graphics cards to sample volumetric data on a per-pixel basis, allowing dense and accurate mapping of the voxel grid across the surface. Anatomical and functional information can be projected onto the cortical surface. The surface can be inflated and flattened interactively, aiding interpretation of the correspondence between the anatomical surface and the flattened cortical sheet. The output of pycortex can be viewed using WebGL, a technology compatible with modern web browsers. This allows complex fMRI surface maps to be distributed broadly online without requiring installation of complex software

Imaging Informatics and the Human Brain Project: the Role of Structure, Review

(no abstract

Segmentation of medical images under topological constraints

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2006.Includes bibliographical references (p. 135-142).Major advances in the field of medical imaging over the past two decades have provided physicians with powerful, non-invasive techniques to probe the structure, function, and pathology of the human body. This increasingly vast and detailed amount of information constitutes a great challenge for the medical imaging community, and requires significant innovations in all aspect of image processing. To achieve accurate and topologically-correct delineations of anatomical structures from medical images is a critical step for many clinical and research applications. In this thesis, we extend the theoretical tools applicable to the segmentation of images under topological control, apply these new concepts to broaden the class of segmentation methodologies, and develop generally applicable and well-founded algorithms to achieve accurate segmentations of medical images under topological constraints. First, we introduce a digital concept that offers more flexibility in controlling the topology of digital segmentations. Second, we design a level set framework that offers a subtle control over the topology of the level set components. Our method constitutes a trade-off between traditional level sets and topology-preserving level sets.(cont.) Third, we develop an algorithm for the retrospective topology correction of 3D digital segmentations. Our method is nested in the theory of Bayesian parameter estimation, and integrates statistical information into the topology correction process. In addition, no assumption is made on the topology of the initial input images. Finally, we propose a genetic algorithm to accurately correct the spherical topology of cortical surfaces. Unlike existing approaches, our method is able to generate several potential topological corrections and to select the maximum-a-posteriori retessellation in a Bayesian framework. Our approach integrates statistical, geometrical, and shape information into the correction process, providing optimal solutions relatively to the MRI intensity profile and the expected curvature.by Florent Ségonne.Ph.D

The Wiring Economy Principle: Connectivity Determines Anatomy in the Human Brain

Minimization of the wiring cost of white matter fibers in the human brain appears to be an organizational principle. We investigate this aspect in the human brain using whole brain connectivity networks extracted from high resolution diffusion MRI data of 14 normal volunteers. We specifically address the question of whether brain anatomy determines its connectivity or vice versa. Unlike previous studies we use weighted networks, where connections between cortical nodes are real-valued rather than binary off-on connections. In one set of analyses we found that the connectivity structure of the brain has near optimal wiring cost compared to random networks with the same number of edges, degree distribution and edge weight distribution. A specifically designed minimization routine could not find cheaper wiring without significantly degrading network performance. In another set of analyses we kept the observed brain network topology and connectivity but allowed nodes to freely move on a 3D manifold topologically identical to the brain. An efficient minimization routine was written to find the lowest wiring cost configuration. We found that beginning from any random configuration, the nodes invariably arrange themselves in a configuration with a striking resemblance to the brain. This confirms the widely held but poorly tested claim that wiring economy is a driving principle of the brain. Intriguingly, our results also suggest that the brain mainly optimizes for the most desirable network connectivity, and the observed brain anatomy is merely a result of this optimization