Abstract
Magneto-Acousto-Electric Tomography with coil detection, known as Magneto-Acousto-Electric Tomography with Magnetic Induction (MAET-MI), is a non-contact resistivity-based imaging method that employs a coil to detect the induced current generated by the ultrasound in biological tissue, which lie under a static magnetic field. To reconstruct an image of the tissue's conductivity, we propose a reciprocal model to describe the relationship between the inducted voltage of a coil and its conductivity. Previous work on the reciprocal theorem demonstrates that reconstructing conductivity using this method is effective. The forward and inverse problem are usually not verified both numerically and experimentally. In this paper, different approaches are adopted to calculate the forward and the inverse problems for verification of the reciprocal model. This verifies that the reconstruction method based on electrode detection can be applied to MAET-MI. This means that the inverse problem of MAET-MI can be transformed into an inverse source reconstruction of a wave equation based on the coil detection. In the forward problem, the moment method is employed to calculate the Radon transform and generate the ultrasonic signals. For the inverse problem, the filtered back projection method is chosen to reconstruct the ultrasound sources, which are related to the curl of the current density in the reciprocal process. Based on the curl of the current density in the reciprocal process, four sets of correlation coefficients of the original and reconstructed images' model are all greater than 90%. The uniform error criterion is obtained via multiple reconstructions and comparison of multiple models. The reciprocal model exhibits a good uniformity and stability when describing the actual physical process. It also provides additional effective ideas for solving the inverse problem quickly to reconstruct the ultrasonic sources, which is corresponding to the actual distribution of the conductivity.
Highlights
Some surveys show that understanding the electrical properties of biological tissue is very important for the early diagnosis of cancer [1]
Many electrical impedance imaging methods have been proposed for detecting the electrical properties of biological tissues non-invasively, such as Electrical Impedance Tomography (EIT), Magnetoacousto Tomography (MAT), Magnetoacoustic Tomography with Magnetic Induction (MAT-MI) and Magneto-AcoustoElectrical Tomography (MAET) [2]–[8]
Guo et al [13] reported that electromagnetic signals can be detected via customized coils in MAET, which is known as MagnetoAcousto-Elect0rical Tomography with Magnetic Induction (MAET-MI)
Summary
Some surveys show that understanding the electrical properties of biological tissue is very important for the early diagnosis of cancer [1]. To improve the resolution of biological tissue conductivity images, researchers have studied methods that use a combination of electromagnetic fields and ultrasonic waves such as MAT-MI and MAET [10]–[12]. We reconstruct the curl of the current density by transforming the previous matrix via a compressed sensing method based inverse problem. In order to avoid these problems, we solve the forward and the inverse problem via a variety of methods, i.e., the filtered back projection method instead of directly calculating the compressed sensing problem Both the forward and inverse problems are verified by applying curl of the reciprocal current density, which will be described in future research. Circular coil is used to detect the magnetic field intensity generated This is more conducive to the rapid imaging of axisymmetric model. That the filtered back-projection method can be used to image the model quickly
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