Fig. 1. Pressure field on the ONERA M6 Wing (Section 5.1.2), rendered using ElVis and illustrating the application of color maps and contour lines on curved and planar surfaces.Abstract-This paper presents the Element Visualizer (ElVis), a new, open-source scientific visualization system for use with highorder finite element solutions to PDEs in three dimensions. This system is designed to minimize visualization errors of these types of fields by querying the underlying finite element basis functions (e.g., high-order polynomials) directly, leading to pixel-exact representations of solutions and geometry. The system interacts with simulation data through runtime plugins, which only require users to implement a handful of operations fundamental to finite element solvers. The data in turn can be visualized through the use of cut surfaces, contours, isosurfaces, and volume rendering. These visualization algorithms are implemented using NVIDIA's OptiX GPU-based ray-tracing engine, which provides accelerated ray traversal of the high-order geometry, and CUDA, which allows for effective parallel evaluation of the visualization algorithms. The direct interface between ElVis and the underlying data differentiates it from existing visualization tools. Current tools assume the underlying data is composed of linear primitives; high-order data must be interpolated with linear functions as a result. In this work, examples drawn from aerodynamic simulations-high-order discontinuous Galerkin finite element solutions of aerodynamic flows in particular-will demonstrate the superiority of ElVis' pixel-exact approach when compared with traditional linear-interpolation methods. Such methods can introduce a number of inaccuracies in the resulting visualization, making it unclear if visual artifacts are genuine to the solution data or if these artifacts are the result of interpolation errors. Linear methods additionally cannot properly visualize curved geometries (elements or boundaries) which can greatly inhibit developers' debugging efforts. As we will show, pixel-exact visualization exhibits none of these issues, removing the visualization scheme as a source of uncertainty for engineers using ElVis.
It is a challenging task to plan a radiofrequency (RF) ablation therapy to achieve the best outcome of the treatment and avoid recurrences at the same time. A patient specific simulation in advance that takes the cooling effect of blood vessels into account is a helpful tool for radiologists, but this needs a very high accuracy and thus high computational costs. In this work, we present various methods, which improve and extend the planning of an RF ablation procedure. First, we discuss two extensions of the simulation model to obtain a higher accuracy, including the vaporization of the water in the tissue and identifying the model parameters and to analyze their uncertainty. Furthermore, we discuss an extension of the planning procedure namely the optimization of the probe placement, which optimizes the overlap of the tumor area with the estimated coagulation in order to avoid recurrences. Since the optimization is constrained by the model, we have to take into account the uncertainties in the model parameters for the optimization as well. Finally, applications of our methods to a real RF ablation case are presented.
The prediction of the temperature profile for radio frequency ablation-a minimal form of tumor treatment-depends on a variety of material parameters (e.g. electric and thermal conductivities) as the coefficients of a system of partial differential equations. We discuss a basic model for the identification of such material parameters from measured temperature data, which bases on an objective function of tracking type which is constrained by the system of PDE. After the discretization of the PDE system with a standard finite element method we optimize the discrete system with an SQP solver. Numerical results are shown for a test scenario consisting of an artificial tumor and artificially generated target temperature profile. Simulation and Parameter IdentificationFor the treatment of tumor diseases there exists a wide variety of approaches ranging from transplantation or surgical resection over chemotherapy to non-invasive techniques. One of these minimally invasive treatments is the radio-frequency (RF) ablation, which is widely used for the destruction of hepatic tumors. In RF ablation a probe, which is connected to an electric generator, is inserted into the tumor. Due to the resistance of the tissue the electric current generates heat, which destroys the cells around the probe. If the temperature reaches a certain critical value the proteins of the tissue coagulate and the cells die. If all malignant tissue cells are destroyed, the therapy is considered to be successful. To a high extent the success of an RF ablation depends on the experience of the radiologist. This motivates the desire for a numerical support (cf. e.g. The main aspect of the model is the description of the temperature profile which induces a volume of destroyed tissue. This part consists of two coupled partial differential equations (PDEs), the electrostatic equation, which describes the electric potential of the tissue, and the heat equation, which takes a heat source due to the electric current into account [2]:and appropriate boundary conditions on ∂D.• Heat equation:with source and sinkand appropriate boundary and initial conditions.The sink term Q perf accounts for the cooling effect of the blood perfusion [2]. The source term Q rf describes the energy, which enters the domain through the electric field of the probe. Here, P eff is a nonlinear function, which models the characteristics of the electric generator. Moreover, these PDEs depend on material parameters like the electric conductivity σ, the density ρ, the heat capacity c, the thermal conductivity λ and the perfusion coefficient ν. Although there exist studies concerning these material parameters, they are in fact not known for a specific patient. Moreover, the existing studies have been performed
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