Publications by Year: 2007

One aim of this work is to investigate the feasibility of using a hierarchy of models to describe diffusion tensor magnetic resonance (MR) data in fixed tissue. Parsimonious model selection criteria are used to choose among different models of diffusion within tissue. Using this information, we assess whether we can perform simultaneous tissue segmentation and classification. Both numerical phantoms and diffusion weighted imaging (DWI) data obtained from excised pig spinal cord are used to test and validate this model selection framework. Three hierarchical approaches are used for parsimonious model selection: the Schwarz criterion (SC), the F-test t-test (F- t), proposed by Hext, and the F-test F-test (F-F), adapted from Snedecor. The F - t approach is more robust than the others for selecting between isotropic and general anisotropic (full tensor) models. However, due to its high sensitivity to the variance estimate and bias in sorting eigenvalues, the F-F and SC are preferred for segmenting models with transverse isotropy (cylindrical symmetry). Additionally, the SC method is easier to implement than the F - t and F - F methods and has better performance. As such, this approach can be efficiently used for evaluating large MRI data sets. In addition, the proposed voxel-by-voxel segmentation framework is not susceptible to artifacts caused by the inhomogeneity of the variance in neighboring voxels with different degrees of anisotropy, which might contaminate segmentation results obtained with the techniques based on voxel averaging.

This work presents a basic framework for constructing a 3D analytical MRI phantom in the Fourier domain. In the image domain the phantom is modeled after the work of Kak and Roberts on a 3D version of the famous Shepp-Logan head phantom. This phantom consists of several ellipsoids of different sizes, orientations, locations, and signal intensities (or gray levels). It will be shown that the k-space signal derived from the phantom can be analytically expressed. As a consequence, it enables one to bypass the need for interpolation in the Fourier domain when testing image-reconstruction algorithms. More importantly, the proposed framework can serve as a benchmark for contrasting and comparing different image-reconstruction techniques in 3D MRI with a non-Cartesian k-space trajectory. The proposed framework can also be adapted for 3D MRI simulation studies in which the MRI parameters of interest may be introduced to the signal intensity from the ellipsoid.

A minimalist numerical model of white matter is presented, the objective of which is to help provide a biological basis for improved diffusion tensor imaging (DTI) analysis. Water diffuses, relaxes, and exchanges in three compartments-intracellular, extracellular, and myelin sheath. Exchange between compartments is defined so as to depend on the diffusion coefficients and the compartment sizes. Based on the model, it is proposed that an additive "baseline tensor" that correlates with intraaxonal water volume be included in the computation. Anisotropy and tortuosity calculated from such analysis may correspond better to tract ultrastructure than if calculated without the baseline. According to the model, reduced extracellular volume causes increased baseline and reduced apparent diffusion. Depending on the pulse sequence, reduced permeability can cause an increase in both the baseline and apparent diffusion.

Diffusion MRI is a non-invasive imaging technique that allows the measurement of water molecular diffusion through tissue in vivo. In this paper, we present a novel statistical model which describes the diffusion-attenuated MR signal by the Laplace transform of a probability distribution over symmetric positive definite matrices. Using this new model, we analytically derive a Rigaut-type asymptotic fractal law for the MR signal decay which has been phenomenologically used before. We also develop an efficient scheme for reconstructing the multiple fiber bundles from the DW-MRI measurements. Experimental results on both synthetic and real data sets are presented to show the robustness and accuracy of the proposed algorithms.

Using pulsed-field-gradient (PFG) experiments, the sizes of the pores in ordered porous media can be estimated from the "diffraction" pattern that the signal attenuation curves exhibit. A different diffraction pattern is observed when the experiment is extended to a larger number (N) of diffusion gradient pulse pairs. Simulations to calculate signal values from arbitrary gradient waveforms are performed for diffusion in restricted geometries using a matrix operator formalism. The simulations suggest that the differences in the characteristics of the attenuation curves are expected to make it possible to measure smaller pore sizes, to improve the accuracy of pore size measurements and potentially to distinguish different pore shapes using the N-PFG technique. Moreover, when an even number of PFG pairs is used, it is possible to observe the diffraction pattern at shorter diffusion times and measure an approximation to the average pore size even when the sample contains pores with a broad distribution of sizes.

Diffusion MRI is a non-invasive imaging technique that allows the measurement of water molecule diffusion through tissue in vivo. The directional features of water diffusion allow one to infer the connectivity patterns prevalent in tissue and possibly track changes in this connectivity over time for various clinical applications. In this paper, we present a novel statistical model for diffusion-weighted MR signal attenuation which postulates that the water molecule diffusion can be characterized by a continuous mixture of diffusion tensors. An interesting observation is that this continuous mixture and the MR signal attenuation are related through the Laplace transform of a probability distribution over symmetric positive definite matrices. We then show that when the mixing distribution is a Wishart distribution, the resulting closed form of the Laplace transform leads to a Rigaut-type asymptotic fractal expression, which has been phenomenologically used in the past to explain the MR signal decay but never with a rigorous mathematical justification until now. Our model not only includes the traditional diffusion tensor model as a special instance in the limiting case, but also can be adjusted to describe complex tissue structure involving multiple fiber populations. Using this new model in conjunction with a spherical deconvolution approach, we present an efficient scheme for estimating the water molecule displacement probability functions on a voxel-by-voxel basis. Experimental results on both simulations and real data are presented to demonstrate the robustness and accuracy of the proposed algorithms.

Tracking deforming objects involves estimating the global motion of the object and its local deformations as a function of time. Tracking algorithms using Kalman filters or particle filters have been proposed for finite dimensional representations of shape, but these are dependent on the chosen parametrization and cannot handle changes in curve topology. Geometric active contours provide a framework which is parametrization independent and allow for changes in topology. In the present work, we formulate a particle filtering algorithm in the geometric active contour framework that can be used for tracking moving and deforming objects. To the best of our knowledge, this is the first attempt to implement an approximate particle filtering algorithm for tracking on a (theoretically) infinite dimensional state space.

The purpose of this paper is to describe certain alternative metrics for quantifying distances between distributions, and to explain their use and relevance in visual tracking. Besides the theoretical interest, such metrics may be used to design filters for image segmentation, that is for solving the key visual task of separating an object from the background in an image. The segmenting curve is represented as the zero level set of a signed distance function. Most existing methods in the geometric active contour framework perform segmentation by maximizing the separation of intensity moments between the interior and the exterior of an evolving contour. Here one can use the given distributional metric to determine a flow which minimizes changes in the distribution inside and outside the curve.

PURPOSE: To investigate the capabilities of a neurovascular navigation prototype in phantom experiments. MATERIALS AND METHODS: The proposed navigation system integrates three-dimensional (3D) visualization of the anatomy and real-time electromagnetic localization of the endovascular tools. A 3D model of an endovascular phantom was reconstructed from thresholded preprocedural computed tomographic (CT) data. The vascular model was aligned with the reference frame of an electromagnetic tracker by using paired-point matching based on eight external fiducials. The robustness and accuracy of the registration were evaluated in 29 experiments. A magnetically tracked catheter was inserted into the carotid artery of the phantom, and the navigation system was used to reach five predefined vascular landmarks. The spatial accuracy of the prototype was evaluated during 50 endovascular targeting attempts. RESULTS: The navigation system achieved accurate co-registration of the location of a catheter inside a 3D reconstruction of a phantom vasculature. The experiments demonstrated the robustness of the registration, with a standard deviation for the translation and rotation components of 0.7 mm and 0.3 degrees , respectively. The maximal average error on the fiducials was 3.2 mm. Endovascular navigation by using the 3D real-time display was successfully performed with a mean overall accuracy of 2.7 mm +/- 0.7 and no projection limitation. CONCLUSION: The authors developed a navigation system that provides real-time 3D visualization of the position of endovascular components in a neurovascular phantom. The preliminary in vitro experiments showed clinically acceptable accuracy.

Since the introduction of diffusion weighted imaging (DWI) as a method for examining neural connectivity, its accuracy has not been formally evaluated. In this study, we directly compared connections that were visualized using injected neural tract tracers (WGA-HRP) with those obtained using in-vivo diffusion tensor imaging (DTI) tractography. First, we injected the tracer at multiple sites in the brain of a macaque monkey; second, we reconstructed the histological sections of the labeled fiber tracts in 3D; third, we segmented and registered the fibers (somatosensory and motor tracts) with the anatomical in-vivo MRI from the same animal; and last, we conducted fiber tracing along the same pathways on the DTI data using a classical diffusion tracing technique with the injection sites as seeds. To evaluate the performance of DTI fiber tracing, we compared the fibers derived from the DTI tractography with those segmented from the histology. We also studied the influence of the parameters controlling the tractography by comparing Dice superimposition coefficients between histology and DTI segmentations. While there was generally good visual agreement between the two methods, our quantitative comparisons reveal certain limitations of DTI tractography, particularly for regions at remote locations from seeds. We have thus demonstrated the importance of appropriate settings for realistic tractography results.