David F. Wiley

Simplification of tetrahedral meshes

We present a method for the construction of multiple levels of tetrahedral meshes approximating a trivariate function at different levels of detail. Starting with an initial, high-resolution triangulation of a three-dimensional region, we construct coarser representation levels by collapsing tetrahedra. Each triangulation defines a linear spline function, where the function values associated with the vertices are the spline coefficients. Based on predicted errors, we collapse tetrahedron in the grid that do not cause the maximum error to exceed a use-specified threshold. Bounds are stored for individual tetrahedra and are updated as the mesh is simplified. We continue the simplification process until a certain error is reached. The result is a hierarchical data description suited for the efficient visualization of large data sets at varying levels of detail.

Adaptation of a support vector machine algorithm for segmentation and visualization of retinal structures in volumetric optical coherence tomography data sets

Recent developments in Fourier domain-optical coherence tomography (Fd-OCT) have increased the acquisition speed of current ophthalmic Fd-OCT instruments sufficiently to allow the acquisition of volumetric data sets of human retinas in a clinical setting. The large size and three-dimensional (3D) nature of these data sets require that intelligent data processing, visualization, and analysis tools are used to take full advantage of the available information. Therefore, we have combined methods from volume visualization, and data analysis in support of better visualization and diagnosis of Fd-OCT retinal volumes. Custom-designed 3D visualization and analysis software is used to view retinal volumes reconstructed from registered B-scans. We use a support vector machine (SVM) to perform semiautomatic segmentation of retinal layers and structures for subsequent analysis including a comparison of measured layer thicknesses. We have modified the SVM to gracefully handle OCT speckle noise by treating it as a characteristic of the volumetric data. Our software has been tested successfully in clinical settings for its efficacy in assessing 3D retinal structures in healthy as well as diseased cases. Our tool facilitates diagnosis and treatment monitoring of retinal diseases.

Correction of motion artifacts and scanning beam distortions in 3D ophthalmic optical coherence tomography imaging

The ability to obtain true three-dimensional (3D) morphology of the retinal structures is essential for future clinical and experimental studies. It becomes especially critical if the measurements acquired with different instruments need to be compared, or precise volumetric data are needed for monitoring and treatment of retinal disease. On the other hand, it is well understood that optical coherence tomography (OCT) images are distorted by several factors. Only limited work has been performed to eliminate these problems in ophthalmic retinal imaging, perhaps because they are less evident in the more common 2D representation mode of time-domain OCT. With recent progress in imaging speed of Fourier domain - OCT (Fd-OCT) techniques, however, 3D OCT imaging is more frequently being used, thereby exposing problems that have been ignored previously. In this paper we propose possible solutions to minimize and compensate for artifacts caused by subject eye and head motion, and distortions caused by the geometry of the scanning optics. The first is corrected by cross-correlation based B-scan registration techniques; the second is corrected by incorporating the geometry of the scanning beam into custom volume rendering software. Retinal volumes of optical nerve head (ONH) and foveal regions of healthy volunteer, with and without corrections, are presented. Finally, some common factors that may lead to increased distortions of the ophthalmic OCT image such as refractive error or position of the subjects head are discussed.

Individual differences in transcranial electrical stimulation current density

Transcranial electrical stimulation (TCES) is effective in treating many conditions, but it has not been possible to accurately forecast current density within the complex anatomy of a given subjects head. We sought to predict and verify TCES current densities and determine the variability of these current distributions in patient-specific models based on magnetic resonance imaging (MRI) data. Two experiments were performed. The first experiment estimated conductivity from MRIs and compared the current density results against actual measurements from the scalp surface of 3 subjects. In the second experiment, virtual electrodes were placed on the scalps of 18 subjects to model simulated current densities with 2 mA of virtually applied stimulation. This procedure was repeated for 4 electrode locations. Current densities were then calculated for 75 brain regions. Comparison of modeled and measured external current in experiment 1 yielded a correlation of r = .93. In experiment 2, modeled individual differences were greatest near the electrodes (ten-fold differences were common), but simulated current was found in all regions of the brain. Sites that were distant from the electrodes (e.g. hypothalamus) typically showed two-fold individual differences. MRI-based modeling can effectively predict current densities in individual brains. Significant variation occurs between subjects with the same applied electrode configuration. Individualized MRI-based modeling should be considered in place of the 10-20 system when accurate TCES is needed.

Ray casting curved-quadratic elements

We present a method for ray casting curved-quadratic elements in 3D. The advantages of this approach is that a curved element can be directly visualized. Conventionally, higher-order elements are tessellated with several linear elements so that standard visualization techniques can be applied to the linear elements. Our method primarily focuses on how to find an approximation to the intersection between a ray and a curved-quadratic element. Once this approximation is found, conventional accumulation and color mapping techniques can be applied to the approximation to produce a volumetric visualization of the element. A cutting plane implementation is also shown that leverages the ray casting technique.

On a construction of a hierarchy of best linear spline approximations using repeated bisection

We present a method for the construction of hierarchies of single-valued functions in one, two, and three variables. The input to our method is a coarse decomposition of the compact domain of a function in the form of an interval (univariate case), triangles (bivariate case), or tetrahedra (trivariate case). We compute best linear spline approximations, understood in an integral least squares sense, for functions defined over such triangulations and refine triangulations using repeated bisection. This requires the identification of the interval (triangle, tetrahedron) with largest error and splitting it into two intervals (triangles, tetrahedra). Each bisection step requires the recomputation of all spline coefficients due to the global nature of the best approximation problem. Nevertheless, this can be done efficiently by bisecting multiple intervals (triangles, tetrahedra) in one step and by reducing the bandwidths of the matrices resulting from the normal equations.

3D OCT imaging in clinical settings : toward quantitative measurements of retinal structures

The acquisition speed of current FD-OCT (Fourier Domain - Optical Coherence Tomography) instruments allows rapid screening of three-dimensional (3D) volumes of human retinas in clinical settings. To take advantage of this ability requires software used by physicians to be capable of displaying and accessing volumetric data as well as supporting post processing in order to access important quantitative information such as thickness maps and segmented volumes. We describe our clinical FD-OCT system used to acquire 3D data from the human retina over the macula and optic nerve head. B-scans are registered to remove motion artifacts and post-processed with customized 3D visualization and analysis software. Our analysis software includes standard 3D visualization techniques along with a machine learning support vector machine (SVM) algorithm that allows a user to semi-automatically segment different retinal structures and layers. Our program makes possible measurements of the retinal layer thickness as well as volumes of structures of interest, despite the presence of noise and structural deformations associated with retinal pathology. Our software has been tested successfully in clinical settings for its efficacy in assessing 3D retinal structures in healthy as well as diseased cases. Our tool facilitates diagnosis and treatment monitoring of retinal diseases.

Interactive processing and visualization of image data for biomedical and life science applications

BackgroundApplications in biomedical science and life science produce large data sets using increasingly powerful imaging devices and computer simulations. It is becoming increasingly difficult for scientists to explore and analyze these data using traditional tools. Interactive data processing and visualization tools can support scientists to overcome these limitations.ResultsWe show that new data processing tools and visualization systems can be used successfully in biomedical and life science applications. We present an adaptive high-resolution display system suitable for biomedical image data, algorithms for analyzing and visualization protein surfaces and retinal optical coherence tomography data, and visualization tools for 3D gene expression data.ConclusionWe demonstrated that interactive processing and visualization methods and systems can support scientists in a variety of biomedical and life science application areas concerned with massive data analysis.

Adaptive Contouring with Quadratic Tetrahedra

We present an algorithm for adaptively extracting and rendering isosurfaces of scalar-valued volume datasets represented by quadratic tetrahedra. Hierarchical tetrahedral meshes created by longest-edge bisection are used to construct a multiresolution C0-continuous representation using quadratic basis functions. A new algorithm allows us to contour higher-order volume elements efficiently.

Using quadratic simplicial elements for hierarchical approximation and visualization

Best quadratic simplicial spline approximations can be computed, using quadratic Bernstein-Bezier basis functions, by identifying and bisecting simplicial elements with largest errors. Our method begins with an initial triangulation of the domain; a best quadratic spline approximation is computed; errors are computed for all simplices; and simplices of maximal error are subdivided. This process is repeated until a user-specified global error tolerance is met. The initial approximations for the unit square and cube are given by two quadratic triangles and five quadratic tetrahedra, respectively. Our more complex triangulation and approximation method that respects field discontinuities and geometrical features allows us to better approximate data. Data is visualized by using the hierarchy of increasingly better quadratic approximations generated by this process. Many visualization problems arise for quadratic elements. First tessellating quadratic elements with smaller linear ones and then rendering the smaller linear elements is one way to visualize quadratic elements. Our results show a significant reduction in the number of simplices required to approximate data sets when using quadratic elements as compared to using linear elements.