Numerical analysis and its applications in photoacoustic imaging
Date Issued
2010
Date
2010
Author(s)
Sheu, Yae-Lin
Abstract
Several photoacoustic (PA) techniques, such as photoacoustic imaging, spectroscopy, and parameter sensing, measure quantities that are closely related to optical absorption, position detection, and laser irradiation parameters. The photoacoustic waves in biomedical applications are usually generated by elastic thermal expansion, which has advantages of nondestructiveness and relatively high conversion efficiency from optical to acoustic energy. Most investigations describe this process using a heuristic approximation, which is invalid when the underlying assumptions are not met. This thesis developed a numerical solution of the general photoacoustic generation equations involving the heat conduction theory and the state, continuity, and Navier-Stokes equations in 2.5D axisymmetric cylindrical coordinates using a finite-difference time-domain (FDTD) and a pseudospectral time-domain (PSTD) scheme.
Simulation using the FDTD method included staggered grids and Berenger’s perfectly matched layers (PMLs). The spatial derivatives in the system of equations were approximated by the second-order-accurate central difference, and the time evolution was advanced by the method of lines. The numerical results were validated using the linear-perturbation analytical solutions and a heuristic model for generation and propagation of photoacoustic waves. In addition, as a free-space boundary, the 10-layer PML produced the lowest reflection error for commonly used boundary conditions.
Computation efficiency and accuracy can be further improved by the PSTD method. Derivatives in spatial domain were calculated using the differentiation theorem for Fourier transforms. Infinite order of accuracy is achieved with at least two sampling grids per minimum wavelength, as compared with the FDTD method, in which 15 or more sampling grids are necessary to reduce numerical dispersion. We developed an extended computation domain to avoid Gibbs phenomenon and wraparound effect associated with the periodicity inherent in the FFT operation by applying the concepts of PMLs and symmetry properties of boundary conditions in our simulation model. The accuracy of using four sampling grids was shown superior to those using 15 grids in FDTD method in the photoacoustic wave simulation. Furthermore, a nonlinear propagation of photoacoustic wave was demonstrated.
In the second part of the thesis, we explored feasibility and efficacy of applying limited-view reconstruction methods to intravascular photoacoustic (IVPA) imaging as a new type of scanning geometry in photoacoustic tomography. A very limited view angle can attribute to an enclosed scanning trajectory within the phantom. According to the data sufficiency condition, only a small portion of object interfaces can be reconstructed stably in such imaging configuration. To the present, intravascular images are obtained using only scan conversion, resulting in image distortion if a point-like detector is used. Analytical formulas such as the filtered backprojection (FBP) and the lambda-tomography method were employed to suggest object geometries. The reconstruction quality was further improved by the expectation maximization (EM) method which could minimize the error between the measured signals and those generated by a reconstructed image. Computer simulations and experiments were carried out to validate the methods.
Subjects
photoacoustic imaging
finite difference and time-domain method
pseudospectral and time-domain method
filtered backprojection method
local tomography method
expectation maximization method
Type
thesis
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