A mathematical and numerical framework for ultrasonically-induced Lorentz force electrical impedance tomography

We provide a mathematical analysis and a numerical framework for Lorentz force electrical conductivity imaging. Ultrasonic vibration of a tissue in the presence of a static magnetic field induces an electrical current by the Lorentz force. This current can be detected by electrodes placed around the tissue; it is proportional to the velocity of the ultrasonic pulse, but depends nonlinearly on the conductivity distribution. The imaging problem is to reconstruct the conductivity distribution from measurements of the induced current. To solve this nonlinear inverse problem, we first make use of a virtual potential to relate explicitly the current measurements to the conductivity distribution and the velocity of the ultrasonic pulse. Then, by applying a Wiener filter to the measured data, we reduce the problem to imaging the conductivity from an internal electric current density. We first introduce an optimal control method for solving such a problem. A new direct reconstruction scheme involving a partial differential equation is then proposed based on viscosity-type regularization to a transport equation satisfied by the current density field. We prove that solving such an equation yields the true conductivity distribution as the regularization parameter approaches zero. We also test both schemes numerically in the presence of measurement noise, quantify their stability and resolution, and compare their performance

Lorentz Force Electrical Impedance Tomography

This article describes a method called Lorentz Force Electrical Impedance Tomography. The electrical conductivity of biological tissues can be measured through their sonication in a magnetic field: the vibration of the tissues inside the field induces an electrical current by Lorentz force. This current, detected by electrodes placed around the sample, is proportional to the ultrasonic pressure, to the strength of the magnetic field and to the electrical conductivity gradient along the acoustic axis. By focusing at different places inside the sample, a map of the electrical conductivity gradient can be established. In this study experiments were conducted on a gelatin phantom and on a beef sample, successively placed in a 300 mT magnetic field and sonicated with an ultrasonic transducer focused at 21 cm emitting 500 kHz bursts. Although all interfaces are not visible, in this exploratory study a good correlation is observed between the electrical conductivity image and the ultrasonic image. This method offers an alternative to detecting pathologies invisible to standard ultrasonography

Optical Magnetic Induction Tomography of the Heart

Atrial Fibrillation (AF) affects a significant fraction of the ageing population, causing a high level of morbidity and mortality. Despite its significance, the causes of AF are still not uniquely identified. This, combined with the lack of precise diagnostic and guiding tools, makes the clinical treatment of AF sub-optimal. We identify magnetic induction tomography as the most promising technique for the investigation of the causes of fibrillation and for its clinical practice. We therefore propose a novel optical instrument based on optical atomic magnetometers, fulfilling the requirements for diagnostic mapping of the heart’s conductivity. The feasibility of the device is here discussed in view of the final application. Thanks to the potential of atomic magnetometers for miniaturisation and extreme sensitivity at room temperature, a new generation of compact and non-invasive diagnostic instrumentation, with both bedside and intra-operative operation capability, is envisioned. Possible scenarios both in clinical practice and biomedical research are then discussed. The flexibility of the system makes it promising also for application in other fields, such as neurology and oncology

Acousto-electrical speckle pattern in Lorentz force electrical impedance tomography

Ultrasound speckle is a granular texture pattern appearing in ultrasound imaging. It can be used to distinguish tissues and identify pathologies. Lorentz force electrical impedance tomography is an ultrasound-based medical imaging technique of the tissue electrical conductivity. It is based on the application of an ultrasound wave in a medium placed in a magnetic field and on the measurement of the induced electric current due to Lorentz force. Similarly to ultrasound imaging, we hypothesized that a speckle could be observed with Lorentz force electrical impedance tomography imaging. In this study, we first assessed the theoretical similarity between the measured signals in Lorentz force electrical impedance tomography and in ultrasound imaging modalities. We then compared experimentally the signal measured in both methods using an acoustic and electrical impedance interface. Finally, a bovine muscle sample was imaged using the two methods. Similar speckle patterns were observed. This indicates the existence of an "acousto-electrical speckle" in the Lorentz force electrical impedance tomography with spatial characteristics driven by the acoustic parameters but due to electrical impedance inhomogeneities instead of acoustic ones as is the case of ultrasound imaging

The Research on Steel Plate Defects Inspection by Magneto-acoustic Testing with Induction

随着工业化的发展，钢材被应用在了各种各样的领域，比如：天然气管道、轮船、汽车等等。然而，随着时间的推移，钢材在使用过程中会出现腐蚀、裂纹等缺陷，这些缺陷严重影响了使用的安全，所以必须在事故发生之前对其进行检测以评估其安全性。本文在对比多种无损检测方法及研究感应式磁声成像的基础上提出了感应式磁声检测的新方法。该方法是在静态磁场下，通过脉冲电流激励被测钢板表面，进而在钢板内部发生电－磁－声的相互转化，最后提取钢板表面的磁声信号。该方法与被测材料无接触，无耦合，可在恶劣环境下进行工作，非常适合钢板的在线检测。 本文首先分析了基于磁致伸缩机理下的感应式磁声检测技术的基本原理，并且推导出了磁声信号的波...With the development of industrialization, steel is used in a variety of areas, such as: natural gas pipelines, ships, cars, etc. However, with the time gone, the steel will appear corrosion, cracks and other defects, which seriously affect the use. Before the accident ,we test the steel to assess it’s safety. This paper proposed a new detection method－Magneto-acoustic Testing with Induction which...学位：工学硕士院系专业：物理与机电工程学院_机械电子工程学号：1992012115271

A mathematical and numerical framework for magnetoacoustic tomography with magnetic induction

We provide a mathematical analysis and a numerical framework for magnetoacoustic tomography with magnetic induction. The imaging problem is to reconstruct the conductivity distribution of biological tissue from measurements of the Lorentz force induced tissue vibration. We begin with reconstructing from the acoustic measurements the divergence of the Lorentz force, which is acting as the source term in the acoustic wave equation. Then we recover the electric current density from the divergence of the Lorentz force. To solve the nonlinear inverse conductivity problem, we introduce an optimal control method for reconstructing the conductivity from the electric current density. We prove its convergence and stability. We also present a point fixed approach and prove its convergence to the true solution. A new direct reconstruction scheme involving a partial differential equation is then proposed based on viscosity-type regularization to a transport equation satisfied by the electric current density field. We prove that solving such an equation yields the true conductivity distribution as the regularization parameter approaches zero. Finally, we test the three schemes numerically in the presence of measurement noise, quantify their stability and resolution, and compare their performance. © 2015 Elsevier Inc