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Duncan JS, Papademetris X, Yang J, Jackowski M, Zeng X, Staib LH.
Geometric strategies for neuroanatomic analysis from MRI.
Neuroimage. 2004:23 Suppl 1:S34-45.


In this paper, we describe ongoing work in the Image Processing and Analysis Group (IPAG) at Yale University specifically aimed at the analysis of structural information as represented within magnetic resonance images (MRI) of the human brain. Specifically, we will describe our applied mathematical approaches to the segmentation of cortical and subcortical structure, the analysis of white matter fiber tracks using diffusion tensor imaging (DTI), and the intersubject registration of neuroanatomical (aMRI) data sets. Many of our methods rally around the use of geometric constraints, statistical (MAP) estimation, and the use of level set evolution strategies. The analysis of gray matter structure and connecting white matter paths combined with the ability to bring all information into a common space via intersubject registration should provide us with a rich set of data to investigate structure and variation in the human brain in neuropsychiatric disorders, as well as provide a basis for current work in the development of integrated brain function-structure analysis.

M. Jackowski, C. Y. Kao, M. Qiu, R. T. Constable, and L. H. Staib.
White Matter Tractography by Anisotropic Wavefront Evolution and Diffusion Tensor Imaging
Medical Image Analysis, v. 9, no. 5, October 2005, pp. 427-440, 2005.


Determination of axonal pathways provides an invaluable means to study the connectivity of the human brain and its functional network. Diffusion Tensor Imaging (DTI) is unique in its ability to capture the restricted diffusion of water molecules which can be used to infer the directionality of tissue components. In this paper, we introduce a white matter tractography method based on anisotropic wavefront propagation in diffusion tensor images. A front propagates in the white matter with a speed profile governed by the isocontour of the diffusion tensor ellipsoid. By using the ellipsoid, we avoid possible misclassification of the principal eigenvector in oblate regions. The wavefront evolution is described by an anisotropic version of the static Hamilton-Jacobi equation, which is solved by a sweeping method in order to obtain correct arrival times. Pathways of connection are determined by tracing minimum-cost trajectories using the characteristic vector field of the resulting partial differential equation. A validity index is described to rate the goodness of the resulting pathways with respect to the directionality of the tensor field. Connectivity results using normal human DTI brain images are illustrated and discussed. We also compared our method with a similar level set-based tractography technique, and found that the anisotropic evolution increased the validity index of the obtained pathways by 18%.

Sinusas AJ, Papademetris X, Constable RT, Dione DP, Slade MD, Shi P, Duncan JS.
Quantification of 3-D regional myocardial deformation: shape-based analysis of magnetic resonance images.
Am J Physiol Heart Circ Physiol. 2001 Aug;281(2):H698-714.


A comprehensive three-dimensional (3-D) shape-based approach for quantification of regional myocardial deformations was evaluated in a canine model (n = 8 dogs) with the use of cine magnetic resonance imaging. The shape of the endocardial and epicardial surfaces was used to track the 3-D trajectories of a dense field of points over the cardiac cycle. The shape-based surface displacements are integrated with a continuum biomechanics model incorporating myofiber architecture to estimate both cardiac- and fiber-specific endocardial and epicardial strains and shears for 24 left ventricular regions. Whereas radial and circumferential end-systolic strains were fairly uniform, there was a significant apex-to-base gradient in longitudinal strain and radial-longitudinal shear. We also observed transmural epicardial-to-endocardial gradients in both cardiac- and fiber-specific strains. The increase in endocardial strain was accompanied by increases in radial-longitudinal shear and radial-fiber shears in the endocardium, supporting previous theories of regional myocardial deformation that predict considerable sliding between myocardial fibers.

Marcel Jackowski, Xenophon Papademetris, LawrenceW. Dobrucki, Albert J. Sinusas, and Lawrence H. Staib
Characterizing Vascular Connectivity from microCT Images
In the proceedings of MICCAI 2005, LNCS 3750 pp 701-708.


X-ray microCT (computed tomography) has become a valuable tool in the analysis of vascular architecture in small animals. Because of its high resolution, a detailed assessment of blood vessel physiology and pathology is possible. Vascular measurement from noninvasive imaging is important for the study and quantification of vessel disease and can aid in diagnosis, as well as measure disease progression and response to therapy. The analysis of tracked vessel trajectories enables the derivation of vessel connectivity information, lengths between vessel junctions as well as level of ramification, contributing to a quantitative analysis of vessel architecture. In this paper, we introduce a new vessel tracking methodology based on wave propagation in oriented domains. Vessel orientation and vessel likelihood are estimated based on an eigenanalysis of gray-level Hessian matrices computed at multiple scales. An anisotropic wavefront then propagates through this vector field with a speed modulated by the maximum vesselness response at each location. Putative vessel trajectories can be found by tracing the characteristics of the propagation solution between different points. We present preliminary results from both synthetic and mouse microCT image data.

Papademetris X, Shkarin P, Staib LH, Behar KL.
Regional Whole Body Fat Quantification in Mice.
G.E. Christensen and M. Sonka (Eds.): In the Proceedings of Information Processing in Medical Imaging 2005, LNCS 3565, pp. 369--380, 2005. Springer-Verlag Berlin Heidelberg 2005


Obesity has risen to epidemic levels in the United States and around the world. Global indices of obesity such as the body mass index (BMI) have been known to be inaccurate predictors of risk of diabetes, and it is commonly recognized that the distribution of fat in the body is a key measure. In this work, we describe the early development of image analysis methods to quantify regional body fat distribution in groups of both male and female wildtype mice using magnetic resonance images. In particular, we present a new formulation which extends the expectation- maximization formalism commonly applied in brain segmentation to multi-exponential data and applies it to the problem of regional whole body fat quantification. Previous segmentation approaches for multispectral data typically perform the classification on fitted parameters, such as the density and the relaxation times. In contrast, our method directly computes a likelihood term from the raw data and hence explicitly accounts for errors in the fitting process, while still using the fitted parameters to model the variation in the appearance of each tissue class. Early validation results, using magnetic resonance spectroscopic imaging as a gold standard, are encouraging. We also present results demonstrating differences in fat distribution between male and female mice.