Abstract
This paper is devoted to an analytical approach to the magnetoacoustic tomography with magnetic induction (MAT-MI) problem for three-layer low-conductivity objects. For each layer, we determined closed-form analytical expressions for the eddy current density and Lorentz force vectors based on the separation of variables method. Next, the analytical formulas were validated with numerical solutions obtained with the help of the finite element method (FEM). Based on the acoustic dipole radiation theory, the influence of the transducer reception pattern on MAT-MI was investigated. To obtain acoustic wave patterns, as a system transfer function we proposed the Morlet wavelet. Finally, image reconstruction examples for objects of more complex shapes are presented, and the influence of the MAT-MI scanning resolution and the presence of the noise on the image reconstruction quality was studied in detail.
Highlights
The electrical properties of biological tissues, such as the electrical conductivity or permittivity, can provide important information regarding the physiological and pathological properties; the accurate quantification of these physical variables for use in early medical diagnosis is still valid and challenging [1]
Magnetoacoustic tomography with magnetic induction (MAT-MI) was recently established [2], which overcomes the unwanted shielding effect occurring in electrical impedance tomography (EIT), magnetoacoustic tomography with current injection (MAT-CI) [3], and magneto-acoustic tomography (MAT) [4,5,6] as well as defeats the problem of low spatial resolution of magnetic induction tomography (MIT) [7]
Lorentz force divergence distribution of the traditional magnetoacoustic tomography with magnetic induction (MAT-MI) image was reconstructed as illustrated in Figure 7a–d with the 360 calculated waveforms collected around the object
Summary
The electrical properties of biological tissues, such as the electrical conductivity or permittivity, can provide important information regarding the physiological and pathological properties; the accurate quantification of these physical variables for use in early medical diagnosis is still valid and challenging [1]. The MAT-MI technique—as a multiphysics imaging approach—is based on the coupling of electromagnetism and ultrasound into one hybrid method. The MAT-MI method can be divided in two main parts The former, the so-called forward problem, comes down to expressing the acoustic pressure generated in a biological tissue or any other low-conductivity object. The latter, called the inverse problem, is based on reconstructing the source of the ultrasonic waves according to the electrical signals collected by sensors. The impact of the MAT-MI scanning resolution on the image reconstruction quality was studied in detail This problem has never been fully considered in the past, as in this article. Similar problems were analyzed, either the authors did not quantify the details of eddy currents and Lorentz forces, or the objects’ shapes or number of layers were different [6,8,9,11,12,13,14,15,16,17,18,19,21,22,25]
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