Magnetic Induction Tomography: Separation of the Ill-Posed and Non-Linear Inverse Problem into a Series of Isolated and Less Demanding Subproblems.

Magnetic induction tomography (MIT) is based on remotely excited eddy currents inside a measurement object. The conductivity distribution shapes the eddies, and their secondary fields are detected and used to reconstruct the conductivities. While the forward problem from given conductivities to detected signals can be unambiguously simulated, the inverse problem from received signals back to searched conductivities is a non-linear ill-posed problem that compromises MIT and results in rather blurry imaging. An MIT inversion is commonly applied over the entire process (i.e., localized conductivities are directly determined from specific signal features), but this involves considerable computation. The present more theoretical work treats the inverse problem as a non-retroactive series of four individual subproblems, each one less difficult by itself. The decoupled tasks yield better insights and control and promote more efficient computation. The overall problem is divided into an ill-posed but linear problem for reconstructing eddy currents from given signals and a nonlinear but benign problem for reconstructing conductivities from given eddies. The separated approach is unsuitable for common and circular MIT designs, as it merely fits the data structure of a recently presented and planar 3D MIT realization for large biomedical phantoms. For this MIT scanner, in discretization, the number of unknown and independent eddy current elements reflects the number of ultimately searched conductivities. For clarity and better representation, representative 2D bodies are used here and measured at the depth of the 3D scanner. The overall difficulty is not substantially smaller or different than for 3D bodies. In summary, the linear problem from signals to eddies dominates the overall MIT performance.

A Deep Residual Neural Network for Image Reconstruction in Biomedical 3D Magnetic Induction Tomography.

In recent years, it has become increasingly popular to solve inverse problems of various tomography methods with deep learning techniques. Here, a deep residual neural network (ResNet) is introduced to reconstruct the conductivity distribution of a biomedical, voluminous body in magnetic induction tomography (MIT). MIT is a relatively new, contactless and noninvasive tomography method. However, the ill-conditioned inverse problem of MIT is challenging to solve, especially for voluminous bodies with conductivities in the range of biological tissue. The proposed ResNet can reconstruct up to two cuboid perturbation objects with conductivities of 0.0 and 1.0 S/m in the whole voluminous body, even in the difficult-to-detect centre. The dataset used for training and testing contained simulated signals of cuboid perturbation objects with randomised lengths and positions. Furthermore, special care went into avoiding the inverse crime while creating the dataset. The calculated metrics showed good results over the test dataset, with an average correlation coefficient of 0.87 and mean squared error of 0.001. Robustness was tested on three special test cases containing unknown shapes, conductivities and a real measurement that showed error results well within the margin of the metrics of the test dataset. This indicates that a good approximation of the inverse function in MIT for up to two perturbation objects was achieved and the inverse crime was avoided.

Three-Dimensional Magnetic Induction Tomography: Practical Implementation for Imaging throughout the Depth of a Low Conductive and Voluminous Body.

Magnetic induction tomography (MIT) is a contactless, low-energy method used to visualize the conductivity distribution inside a body under examination. A particularly demanding task is the three-dimensional (3D) imaging of voluminous bodies in the biomedical impedance regime. While successful MIT simulations have been reported for this regime, practical demonstration over the entire depth of weakly conductive bodies is technically difficult and has not yet been reported, particularly in terms of more realistic requirements. Poor sensitivity in the central regions critically affects the measurements. However, a recently simulated MIT scanner with a sinusoidal excitation field topology promises improved sensitivity (>20 dB) from the interior. On this basis, a large and fast 3D MIT scanner was practically realized in this study. Close agreement between theoretical forward calculations and experimental measurements underline the technical performance of the sensor system, and the previously only simulated progress is hereby confirmed. This allows 3D reconstructions from practical measurements to be presented over the entire depth of a voluminous body phantom with tissue-like conductivity and dimensions similar to a human torso. This feasibility demonstration takes MIT a step further toward the quick 3D mapping of a low conductive and voluminous object, for example, for rapid, harmless and contactless thorax or lung diagnostics.

Examination of the Liquid Volume Inside Metal Tanks Using Noncontact EMATs From Outside.

This article discusses ultrasound echo examination of the liquid volume inside a metal enclosure using noncontact electromagnetic acoustic transducers (EMATs) from outside the tank. Because only longitudinal sound waves exist in liquids, a novel and powerful EMAT design (kA currents in small coils) with a specifically enhanced transduction of longitudinal ultrasound is presented. Different wall materials (aluminum, steel, and stainless steel) and working frequencies are considered. A particular challenge, in addition to the already weak EMAT signals across an air gap, is the highly reflective interface between the metal wall and liquid because the acoustic impedances of the two media differ considerably. With thicker metal walls (here, 3mm), only either low frequencies < 100 kHz or frequencies close to the corresponding thickness resonance of the wall (here, about 1 MHz) are more suitable. The higher frequencies are preferred, as they show advantages due to a directed beam profile, shorter wavelengths in the liquid, and an overall better pulse fidelity. The simultaneous operation of several and closely neighboring EMATs demonstrates the feasibility of more demanding detection tasks, ultimately leading toward a 3-D localization inside the liquid using a noncontact EMAT array with eight independent elements.

Three-dimensional Magnetic Induction Tomography: Improved Performance for the Center Regions inside a Low Conductive and Voluminous Body.

Magnetic induction tomography (MIT) is a contactless technique that is used to image the distribution of passive electromagnetic properties inside a voluminous body. However, the central area sensitivity (CAS) of this method is critically weak and blurred for a low conductive volume. This article analyzes this challenging issue, which inhibits even faint imaging of the central interior region of a body, and it suggests a remedy. The problem is expounded via two-dimensional (2D) and three-dimensional (3D) eddy current simulations with different transmitter geometries. On this basis, it is shown that a spatially undulating exciter coil can significantly improve the CAS by >20 dB. Consequently, the central region inside a low conductive voluminous object becomes clearly detectable above the noise floor, a fact which is also confirmed by practical measurements. The improved sensitivity map of the new arrangement is compared with maps of more typical circular MIT geometries. In conclusion, 3D MIT reconstructions are presented, and for the same incidence of noise, their performance is much better with the suggested improvement than that with a circular setup.

Experimental Demonstration and Circuitry for a Very Compact Coil-Only Pulse Echo EMAT.

This experimental study demonstrates for the first time a solid-state circuitry and design for a simple compact copper coil (without an additional bulky permanent magnet or bulky electromagnet) as a contactless electromagnetic acoustic transducer (EMAT) for pulse echo operation at MHz frequencies. A pulsed ultrasound emission into a metallic test object is electromagnetically excited by an intense MHz burst at up to 500 A through the 0.15 mm filaments of the transducer. Immediately thereafter, a smoother and quasi "DC-like" current of 100 A is applied for about 1 ms and allows an echo detection. The ultrasonic pulse echo operation for a simple, compact, non-contacting copper coil is new. Application scenarios for compact transducer techniques include very narrow and hostile environments, in which, e.g., quickly moving metal parts must be tested with only one, non-contacting ultrasound shot. The small transducer coil can be operated remotely with a cable connection, separate from the much bulkier supply circuitry. Several options for more technical and fundamental progress are discussed.

Induction coil as a non-contacting ultrasound transmitter and detector: Modeling of magnetic fields for improving the performance.

A simple copper coil without a voluminous stationary magnet can be utilized as a non-contacting transmitter and as a detector for ultrasonic vibrations in metals. Advantages of such compact EMATs without (electro-)magnet might be: applications in critical environments (hot, narrow, presence of iron filings…), potentially superior fields (then improved ultrasound transmission and more sensitive ultrasound detection). The induction field of an EMAT strongly influences ultrasound transduction in the nearby metal. Herein, a simplified analytical method for field description at high liftoff is presented. Within certain limitations this method reasonably describes magnetic fields (and resulting eddy currents, inductances, Lorentz forces, acoustic pressures) of even complex coil arrangements. The methods can be adapted to conventional EMATS with a separate stationary magnet. Increased distances (liftoff) are challenging and technically relevant, and this practical question is addressed: with limited electrical power and given free space between transducer and target metal, what would be the most efficient geometry of a circular coil? Furthermore, more complex coil geometries ("butterfly coil") with a concentrated field and relatively higher reach are briefly investigated.

Ultrasound generation with high power and coil only EMAT concepts.

Electro-magnetic acoustic transducers (EMATs) are intended as non-contact and non-destructive ultrasound transducers for metallic material. The transmitted intensities from EMATS are modest, particularly at notable lift off distances. Some time ago a concept for a "coil only EMAT" was presented, without static magnetic field. In this contribution, such compact "coil only EMATs" with effective areas of 1-5cm(2) were driven to excessive power levels at MHz frequencies, using pulsed power technologies. RF induction currents of 10kA and tens of Megawatts are applied. With increasing power the electroacoustic conversion efficiency also increases. The total effect is of second order or quadratic, therefore non-linear and progressive, and yields strong ultrasound signals up to kW/cm(2) at MHz frequencies in the metal. Even at considerable lift off distances (cm) the ultrasound can be readily detected. Test materials are aluminum, ferromagnetic steel and stainless steel (non-ferromagnetic). Thereby, most metal types are represented. The technique is compared experimentally with other non-contact methods: laser pulse induced ultrasound and spark induced ultrasound, both damaging to the test object's surface. At small lift off distances, the intensity from this EMAT concept clearly outperforms the laser pulses or heavy spark impacts.