Modelling and simulation of nonlinear wave propagation in ultrasound imaging
| Autor: | Rauscher, Teresa |
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| Jazyk: | angličtina |
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| Popis: | Nonlinear ultrasound imaging has become increasingly important in medical but also industrial areas. This project is in cooperation with GE Healthcare at a site specialized in diagnostic ultrasound. The aim of this thesis is to develop a model that takes nonlinear effects into account to make the ultrasound beam analysis more accurate and enhance the quality of images. The outcome is a three dimensional model for nonlinear ultrasound imaging and a numerical algorithm to simulate pressure waveforms. The main challenge is the computation time since ultrasound imaging works in real-time. To demonstrate the accuracy of the developed model, simulated results are compared to acoustic output measurements. The most widely used nonlinear wave equation to model the propagation of three dimensional sound beams is the KZK equation. Based on this equation a model for a rectangular source and wave propagation in water is developed. With an eigensystem approach for the Laplacian operator on a rectangular domain the KZK equation can be reduced to much simpler differential equations. An operator splitting method is used to efficiently take the effects of nonlinearity and diffraction sequentially into account. Due to further assumptions like for example Neumann boundary conditions this eigenvalue approach yields a discrete cosine transformation in the numerical algorithm. For stability reasons implicit finite difference schemes are chosen to take the effects of nonlinearity and diffraction into account.The algorithm is implemented and simulated in MATLAB. The initial data and also acoustic output measurements are provided by GE Healthcare. The simulations based on the developed algorithm show a high accuracy to acoustic output measurements performed by a hydrophone in a water tank. Some alternative approaches that can be interesting for future work are also presented. This includes a transformed form of the KZK equation, an approach based on a Fourier transform and a finite difference scheme on a graded mesh. Teresa Rauscher Masterarbeit Universität Klagenfurt 2021 |
| Databáze: | OpenAIRE |
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