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

Doctor of Philosophy

dissertationDiffusion magnetic resonance imaging (dMRI) has become a popular technique to detect brain white matter structure. However, imaging noise, imaging artifacts, and modeling techniques, etc., create many uncertainties, which may generate misleading information for further analysis or applications, such as surgical planning. Therefore, how to analyze, effectively visualize, and reduce these uncertainties become very important research questions. In this dissertation, we present both rank-k decomposition and direct decomposition approaches based on spherical deconvolution to decompose the fiber directions more accurately for high angular resolution diffusion imaging (HARDI) data, which will reduce the uncertainties of the fiber directions. By applying volume rendering techniques to an ensemble of 3D orientation distribution function (ODF) glyphs, which we call SIP functions of diffusion shapes, one can elucidate the complex heteroscedastic structural variation in these local diffusion shapes. Furthermore, we quantify the extent of this variation by measuring the fraction of the volume of these shapes, which is consistent across all noise levels, the certain volume ratio. To better understand the uncertainties in white matter fiber tracks, we propose three metrics to quantify the differences between the results of diffusion tensor magnetic resonance imaging (DT-MRI) fiber tracking algorithms: the area between corresponding fibers of each bundle, the Earth Mover's Distance (EMD) between two fiber bundle volumes, and the current distance between two fiber bundle volumes. Based on these metrics, we discuss an interactive fiber track comparison visualization toolkit we have developed to visualize these uncertainties more efficiently. Physical phantoms, with high repeatability and reproducibility, are also designed with the hope of validating the dMRI techniques. In summary, this dissertation provides a better understanding about uncertainties in diffusion magnetic resonance imaging: where and how much are the uncertainties? How do we reduce these uncertainties? How can we possibly validate our algorithms