PSTD Method for Thermoacoustic Tomography (TAT) and Related Experimental Investigation

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2009

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Abstract

In this work, the simulation (forward problem) and reconstruction (inverse problem) in Thermoacoustic Tomography (TAT) are studied using a pseudospectral time-domain (PSTD) method with 4th-order time integration.

The objective of the TAT simulation is to solve for the thermoacoustic pressure field in an inhomogeneous medium. Using the PSTD method, the spatial derivatives of pressure field and particle velocity can be obtained using fast fourier transform (FFT). Since the Fourier transforms used to represent the spatial derivatives of smooth functions are exact, only 2 points per wavelength are needed in the spatial discretization. The time integration is achieved by a 4th-order method to effectively reduce the computational time. The results of the algorithm are validated by analytical solutions. Perfectly Matched Layers (PMLs) are applied to absorb the outgoing waves and avoid ``wraparound'' effect. The maximum attenuation coefficient of the PMLs has an optimum value to minimize the reflections due to discretization and wraparound effect for 2D and 3D problems. Different PML profiles are also compared, quadratic profile is chosen because it can minimize the overall reflection. Spatial smoothing is needed for PSTD to avoid Gibbs' phenomenon in the modeling of a point source, and the effect of the smoothing function is studied.

In the TAT reconstruction problem, the PSTD method is used to reconstruct the thermoacoustic sources by solving the thermoacoustic wave equations in a reversed temporal order within the framework of time reversal imaging. The back-propagated pressure waves then refocus at the spatial locations of the original sources. Most other TAT reconstruction algorithms are based on the assumption that the tissue medium is acoustically homogeneous. In practice, however, even the mild tissue inhomogeneity will cause large phase errors and cause spatial misplacement and distortion of the sources. The proposed PSTD method utilizes a two-step process to solve this problem. In the first step, a homogeneous time reversal reconstruction is performed. Since an inhomogeneity itself is usually a source because of spatially dependent electrical conductivity (thus microwave absorption), the spatial location and the shape of the inhomogeneity can be estimated. In the second step, the updated acoustic property map is loaded followed by an inhomogeneous reconstruction. Numerical results show that this method greatly improves the reconstruction results. Images with improved quality are reconstructed from experimental data.

A 3D PSTD algorithm is developed and validated. Numerical results show that the PSTD algorithm with the 4th-order time integration is capable of simulating large 3D acoustic problems accurately and efficiently. A 3D breast phantom model is used to study the inhomogeneous reconstruction in 3D. Improved results over the homogeneous method are observed.

A preliminary study of the Thermoacoustic Tomography (TAT) using continuous-wave (CW) modulated microwaves is summarized. The theoretical background, system configuration, experiment setup, and measurement results are presented.

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Ye, Gang (2009). PSTD Method for Thermoacoustic Tomography (TAT) and Related Experimental Investigation. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/3205.

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