A Study On Magnetoacoustic Tomography With Magnetic Induction (MAT-MI) For Imaging Electrical Impedance Of Biological Tissue

Magnetoacoustic Tomography with Magnetic Induction (MAT-MI) is a recently proposed imaging modality to image the electrical impedance of a biological tissue. It combines the good contrast of electrical impedance tomography with the high spatial resolution of sonography. In this thesis, we first derive MAT-MI linear wave equation, acoustic source formulas for both inside a homogeneous medium and on the interface between two medium with different conductivities. Then we investigate three-dimensional MAT-MI forward problem using the finite element method (FEM), image the conductivity distribution of biological tissues with time reversal method (TRM), and study the effect of conductivity anisotropy.We first derive MAT-MI linear wave equation for biological tissues from Navier-Stokes equation. Based on the relationship between electrical conductivity, magnetic stimulation, static magnetic field, induced electric field and MAT-MI acoustic source, the formulas for MAT-MI acoustic source both inside a homogeneous medium and on the interface between two medium with different conductivities are derived. The implementation methods for the numerical simulation of MAT-MI acoustic source are proposed, which can be used to calculate and compare the acoustic sources.A pilot MAT-MI forward solution method based on finite element analysis (FEA) for arbitrary geometry and real shape coil is proposed. Three-dimensional MAT-MI forward solution on two-layer concentric and eccentric spherical models is investigated using FEM. The method validation for finite element analysis and model calibration for acoustic field calculation is conducted to verify the MAT-MI forward solution method. The MAT-MI acoustic source inside inner sphere or outer sphere and the acoustic source on the boundary of two-layer spheres are displayed and compared. The acoustic pressure distributions for concentric and five eccentric models are displayed to show the effect of conductivity change on MAT-MI acoustic field. The effect of conductivity change on the acoustic time series on detecting points is studied.Time reversal method is applied to MAT-MI acoustic source reconstruction, and MAT-MI electrical conductivity reconstruction on a breast model with tumor, fatty and mammary tissues is conducted for the detection of the tumor. The derivation of TRM and its application on MAT-MI are described, and the validation method of TRM is conducted. MAT-MI forward problem on the breast tumor model is solved, the acoustic sources are back-projected using TRM, and the electrical conductivity distribution is reconstructed based on the relationship between the MAT-MI acoustic source and the electrical conductivity of biological tissues.The effect of electrical conductivity anisotropy during MAT-MI is examined. We derive MAT-MI acoustic source formulas for the medium of anisotropic conductivity. The numerical simulation is conducted on a two-layer concentric model of anisotropic electrical conductivity, and the MAT-MI acoustic sources inside the inner sphere or outer sphere and on the boundary of two-layer spheres are compared. MAT-MI forward problem on four models of anisotropic electrical conductivity is solved, and the effect of anisotropic electrical conductivity on MAT-MI acoustic field is studied.