A stable tensor-based deflection model for controlled fluid simulations

The association between fluids and tensors can be observed in some practical situations, such as diffusion tensor imaging and permeable flow. For simulation purposes, tensors may be used to constrain the fluid flow along specific directions. This work seeks to explore this tensor-fluid relationship and to propose a method to control fluid flow with an orientation tensor field. To achieve our purposes, we expand the mathematical formulation governing fluid dynamics to locally change momentum, deflecting the fluid along intended paths. Building upon classical computer graphics approaches for fluid simulation, the numerical method is altered to accomodate the new formulation. Gaining control over fluid diffusion can also aid on visualization of tensor fields, where the detection and highlighting of paths of interest is often desired. Experiments show that the fluid adequately follows meaningful paths induced by the underlying tensor field, resulting in a method that is numerically stable and suitable for visualization and animation purposes.A associação entre fluidos e tensores pode ser observada em algumas situações práticas, como em ressonância magnética por tensores de difusão ou em escoamento permeável. Para fins de simulação, tensores podem ser usados para restringir o escoamento do fluido ao longo de direções específicas. Este trabalho visa explorar esta relação tensor-fluido e propor um método para controlar o escoamento usando um campo de tensores de orientação. Para atingir nossos objetivos, nós expandimos a formulação matemática que governa a dinâmica de fluidos para alterar localmente o momento, defletindo o fluido para trajetórias desejadas. Tomando como base abordagens clássicas para simulação de fluidos em computação gráfica, o método numérico é alterado para acomodar a nova formulação. Controlar o processo de difusão pode também ajudar na visualização de campos tensoriais, onde frequentemente busca-se detectar e realçar caminhos de interesse. Os experimentos realizados mostram que o fluido, induzido pelo campo tensorial subjacente, percorre trajetórias significativas, resultando em um método que é numericamente estável e adequado para fins de visualização e animação

Segmentation of diffusion weighted MRI using the level set framework

Medical imaging is a rapidly growing field in which diffusion imaging is a recently developed modality. This novel imaging contrast permits in-vivo measurement of the diffusion of water molecules. This is particularly interesting in brain imaging where the diffusion reveals an amazing insight into the neuronal organization and cerebral cytoarchitecture. Diffusion images contain from six up to hundreds of values in each voxel and are represented as tensor fields (Diffusion Tensor Imaging (DTI)) or as fields of functions (High Angular Resolution Diffusion (HARD) imaging). To fully extract the large amount of data contained within these images new processing and analysis tools are needed. The aim of this thesis is the development of such tools. The method we have been mainly focusing on for this purpose is the level set method. The level set method is a numerical and theoretical tool for propagating interfaces. In image processing it is used for propagating curves in 2D or surfaces in 3D for delineation of objects or for regularization purposes. In this thesis we have explored some of the numerous aspects of the level set frame work to see how the diffusion properties can be used for segmentation. For segmentation of tensor fields we have considered similarity measures for comparison of tensors. From these similarity measures several applications of the level set method have been developed for the segmentation of different structures. Different measures of similarity have been used dependent on the application. When segmenting white matter regions in DTI, the similarity measure emphasizes anisotropic regions. The segmentation algorithm itself has a very local dependence since white matter, in general fiber tracts, experiences different diffusion in different parts of the structure. The presented results show segmentations of the major fiber tracts in the brain. Other structures, such as the deep cerebral nuclei, that are mainly composed of gray matter, have more homogenous diffusion properties than white matter structures. Therefore, in these structures we maximize the internal coherence within the entire structure by using a region based approach to the segmentation problem. Segmentations of the thalamus and its nuclei as well as on tensor fields from fluid mechanics are presented. For High Angular Resolution Diffusion (HARD) images, two methods for fiber tract segmentation are presented based on different types of coherence. The coherence is either measured as the similarity between fibers obtained from a tractography algorithm, or the similarity of scalar values in a five-dimensional non-Euclidean space. The similarity between two fibers is determined by a counting strategy and is equal to the number of voxels they have in common. A spectral clustering algorithm is then used for grouping fibers with a high inter-resemblance. When segmenting white matter with the level set method, we propose to expand the space we are working in from a three-dimensional space of Orientation Distribution Functions (ODF) to a five-dimensional space of position and orientation. By a careful definition of this space and an adaptation of the level set to five dimensions the fibers tracts can be segmented as separated structures. We show some preliminary results from segmentations in this 5D space. The approaches proposed in this thesis permit a consideration of the fiber tracts and gray matter structures as an entity, allowing quantitative measures of the diffusion without losing information by simplifying the images to scalar representations

Fiber consistency measures on brain tracts from digital streamline, stochastic and global tractography

La tractografía es el proceso que se emplea para estimar la estructura de las fibras nerviosas del interior del cerebro in vivo a partir de datos de Resonancia Magnética (MR). Existen varios métodos de tractografía, que generalmente se dividen en locales y globales. Los primeros intentan reconstruir cada fibra por separado, mientras que los segundos intentan reconstruir todas las estructuras neuronales a la vez, buscando una configuración que mejor se ajusta a los datos proporcionados. Dichos métodos globales han demostrado ser más precisos y fiables que los métodos de tractografía local, para datos sintéticos. Sin embargo hasta la fecha no hay estudios que definan la relación entre los parámetros de adquisición de la MR y los resultados de tractografía estocástica o global con datos reales. Esta tésis de Master pretende mostrar la influencia de ciertos parámetros de adquisición como el factor de difusión de las secuencias de adquisición, el espaciado entre voxels o el número de gradientes en la variabilidad de las tractografías obtenidas.Teoría de la Señal, Comunicaciones e Ingeniería TelemáticaMáster en Investigación en Tecnologías de la Información y las Comunicacione

Curve boxplot: Generalization of boxplot for ensembles of curves

pre-printIn simulation science, computational scientists often study the behavior of their simulations by repeated solutions with variations in parameters and/or boundary values or initial conditions. Through such simulation ensembles, one can try to understand or quantify the variability or uncertainty in a solution as a function of the various inputs or model assumptions. In response to a growing interest in simulation ensembles, the visualization community has developed a suite of methods for allowing users to observe and understand the properties of these ensembles in an efficient and effective manner. An important aspect of visualizing simulations is the analysis of derived features, often represented as points, surfaces, or curves. In this paper, we present a novel, nonparametric method for summarizing ensembles of 2D and 3D curves. We propose an extension of a method from descriptive statistics, data depth, to curves. We also demonstrate a set of rendering and visualization strategies for showing rank statistics of an ensemble of curves, which is a generalization of traditional whisker plots or boxplots to multidimensional curves. Results are presented for applications in neuroimaging, hurricane forecasting and fluid dynamics

High rank tensor and spherical harmonic models for diffusion MRI processing

Diffusion tensor imaging (DTI) is a non-invasive quantitative method of characterizing tissue micro-structure. Diffusion imaging attempts to characterize the manner by which the water molecules within a particular location move within a given amount of time. Measurement of the diffusion tensor (D) within a voxel allows a macroscopic voxel-averaged description of fiber structure, orientation and fully quantitative evaluation of the microstructural features of healthy and diseased tissue.;The rank two tensor model is incapable of resolving multiple fiber orientations within an individual voxel. This shortcoming of single tensor model stems from the fact that the tensor possesses only a single orientational maximum. Several authors reported this non-mono-exponential behavior for the diffusion-induced attenuation in brain tissue in water and N-Acetyl Aspartate (NAA) signals, that is why the Multi-Tensor, Higher Rank Tensor and Orientation Distribution Function (ODF) were introduced.;Using the higher rank tensor, we will propose a scheme for tensor field interpolation which is inspired by subdivision surfaces in computer graphics. The method applies to Cartesian tensors of all ranks and imposes smoothness on the interpolated field by constraining the divergence and curl of the tensor field. Results demonstrate that the subdivision scheme can better preserve anisotropicity and interpolate rotations than some other interpolation methods. As one of the most important applications of DTI, fiber tractography was implemented to study the shape geometry changes. Based on the divergence and curl measurement, we will introduce new scalar measures that are sensitive to behaviors such as fiber bending and fanning.;Based on the ODF analysis, a new anisotropy measure that has the ability to describe multi-fiber heterogeneity while remaining rotationally invariant, will be introduced, which is a problem with many other anisotropy measures defined using the ODF. The performance of this novel measure is demonstrated for data with varying Signal to Noise Ratio (SNR), and different material characteristics

Controlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation

We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our approach enables to control the error in the computation of the displacement and stress fields around the needle tip and needle shaft by suitably refining the mesh, whilst maintaining a coarser mesh in other parts of the domain. We demonstrate through academic and practical examples that our approach increases the accuracy of the displacement and stress fields around the needle without increasing the computational expense. This enables real-time simulations. The proposed methodology has direct implications to increase the accuracy and control the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anesthesia, or cryotherapy and can be essential to the development of robotic guidance.Comment: 21 pages, 14 figure

Reducing Occlusion in Cinema Databases through Feature-Centric Visualizations

In modern supercomputer architectures, the I/O capabilities do not keep up with the computational speed. Image-based techniques are one very promising approach to a scalable output format for visual analysis, in which a reduced output that corresponds to the visible state of the simulation is rendered in-situ and stored to disk. These techniques can support interactive exploration of the data through image compositing and other methods, but automatic methods of highlighting data and reducing clutter can make these methods more effective. In this paper, we suggest a method of assisted exploration through the combination of feature-centric analysis with image space techniques and show how the reduction of the data to features of interest reduces occlusion in the output for a set of example applications