Magneto-acousto-electrical Tomography Research Articles

Magneto-acousto-electrical tomography using nonlinearly frequency-modulated ultrasound.

Objective. In this study, nonlinearly frequency-modulated (NLFM) ultrasound was applied to magneto-acousto-electrical tomography (MAET) to increase the dynamic range of detection.Approach. Generation of NLFM signals using window function method-based on the principle of stationary phase-and piecewise linear frequency modulation method-based on the genetic algorithm-was discussed. The MAET experiment systems using spike, linearly frequency-modulated (LFM), or NLFM pulse stimulation were constructed, and three groups of MAET experiments on saline agar phantom samples were carried out to verify the performance-respectively the sensitivity, the dynamic range, and the longitudinal resolution of detection-of MAET using NLFM ultrasound in comparison to that using LFM ultrasound. Based on the above experiments, a pork sample was imaged by ultrasound imaging method, spike MAET method, LFM MAET method, and NLFM MAET method, to compare the imaging accuracy.Main results. The experiment results showed that, through sacrificing very little main-lobe width of pulse compression or equivalently the longitudinal resolution, the MAET using NLFM ultrasound achieved higher signal-to-interference ratio (and therefore higher detection sensitivity), lower side-lobe levels of pulse compression (and therefore larger dynamic range of detection), and large anti-interference capability, compared to the MAET using LFM ultrasound.Significance. The applicability of the MAET using NLFM ultrasound was proved in circumferences where sensitivity and dynamic range of detection were mostly important and slightly lower longitudinal resolution of detection was acceptable. The study furthered the scheme of using coded ultrasound excitation toward the clinical application of MAET.

Iterative Reconstruction Algorithms in Magneto-Acousto-Electrical Computed Tomography (MAE-CT) for Image Quality Improvement.

Magneto-acousto-electrical computed tomography (MAE-CT) is a recently developed rotational magneto-acousto-electrical tomography (MAET) method, which can map the conductivity parameter of tissues with high spatial resolution. Since the imaging mode of MAE-CT is similar to that of CT, the reconstruction algorithms for CT are possible to be adopted for MAE-CT. Previous studies have demonstrated that the filtered back-projection (FBP) algorithm, which is one of the most common CT reconstruction algorithms, can be used for MAE-CT reconstruction. However, FBP has some inherent shortcomings of being sensitive to noise and non-uniform distribution of views. In this study, we introduced iterative reconstruction (IR) method in MAE-CT reconstruction and compared its performance with that of the FBP. The numerical simulation, the phantom, and in vitro experiments were performed, and several IR algorithms (ART, SART, SIRT) were used for reconstruction. The results show that the images reconstructed by the FBP and IR are similar when the data is noise-free in the simulation. As the noise level increases, the images reconstructed by SART and SIRT are more robust to the noise than FBP. In the phantom experiment, noise and some stripe artifacts caused by the FBP are removed by SART and SIRT algorithms. In conclusion, the IR method used in CT is applicable in MAE-CT, and it performs better than FBP, which indicates that the state-of-the-art achievements in the CT algorithm can also be adopted for the MAE-CT reconstruction in the future.

Magneto-Acoustic Imaging in Biology

This review examines the use of magneto-acoustic methods to measure electrical conductivity. It focuses on two techniques developed in the last two decades: Magneto-Acoustic Tomography with Magnetic Induction (MAT-MI) and Magneto-Acousto-Electrical Tomography (MAET). These developments have the potential to change the way medical doctors image biological tissue.

Three-dimensional magneto-acousto-electrical tomography (3D MAET) with single-element ultrasound transducer and coded excitation: A phantom validation study

Magneto-acousto-electrical tomography (MAET) is a hybrid imaging modality combining the merits of high contrast and high resolution. Current studies in MAET mainly focus on two-dimensional (2D) imaging. In practice, an object's conductivity is usually three-dimensional inhomogeneous. Therefore, three-dimensional MAET (3D MAET) may provide a more comprehensive understanding of the conductivity distribution of an object. The basic idea of realizing 3D MAET is to move the ultrasound transducer mechanically to accomplish the 3D scanning. However, this mechanical scanning procedure is time-consuming. Moreover, due to the weak MAE signal, traditional MAET based on single-pulse excitation requires thousands of signal averaging operations to improve the signal-to-noise ratio (SNR) of imaging, which may further increase the time burden of 3D MAET. This study aims to investigate the feasibility of 3D MAET based on a 1D ultrasound transducer and coded-excitation technology. A 13-bit Barker code was used as the excitation code, and two 3D biological phantoms were used to validate the imaging accuracy. The experimental results show that the imaging results of this method can reflect the change of conductivity in 3D space. The average relative errors of the measured slope of the conductivity distribution in Phantom 1 and Phantom 2 are 6.72% and 2.02%, respectively. Moreover, compared with the short-pulse excitation method, the Barker-coded excitation method can obtain comparative imaging SNR with about a quarter average, thus demonstrating the feasibility of 3D MAET with a single-element ultrasound transducer and coded excitation.

General principle and optimization of magneto-acousto-electrical tomography based on image distortion evaluation.

As a novel non-invasive multi-physics imaging methodology, the magneto-acousto-electrical (MAE) technology is capable of detecting electric conductivity changes for biological tissues, exhibiting prosperous perspectives in medical applications. However, the acoustic beam was often simplified to a straight line or a focused one, being perpendicular to layered boundaries of tissues in previous studies. Linear-scanning measurements were carried out to reconstruct B-mode MAE images for layered models without considering the radiation pattern of transducers. Obvious image distortions in both shape and brightness were observed in experiments without any reasonable explanation. This study aims to establish a general physical model for MAE measurements and solve the problem of B-mode image distortion, and hence provide theoretical and technical supports for the improvement of MAE imaging in practical applications. By considering the radiation pattern of actual transducers and the inclined angle of electric conductivity boundaries, a general principal of MAE measurements applicable for objects of arbitrary shapes is proposed based on the theories of acoustic radiation, Hall Effect and electrical detection. The influences of inclined conductivity boundaries and transducer directivities are numerically analyzed with Matlab programming and also demonstrated by experimental measurements. To evaluate the degree of B-mode image distortion, the deformation length (3dB amplitude decrease) of approximate straight lines for a circular model is defined as L=dtan(βm /2), with d and βm being the measurement distance and the half radiation angle of the main-lobe, respectively. The rotary-scanning-based MAE tomography (MAET) is employed to reduce the image distortion, and the rotation angle step is further optimized based on the criterion of the boundary radius fluctuation coefficient <0.01mm. The experimental results of MAE signals and B-mode images as well as MAETs show good agreements with simulations. It is demonstrated that, as the increase of the inclined angle, the MAE decreases rapidly with an extended time interval and reaches the 20dB amplitude decrease when the angle exceeds 12°. Meanwhile, the deformation length of B-mode MAE imaging increases with the increase of the radiation angle for the transducer with a weaker radiation pattern, and hence results in a more serious image distortion. A smaller rotation angle step should be adopted to the MAET system with a longer deformation length, and the optimized maximum angle step of 12° is also achieved for the omnidirectional radiation of point sources with a long deformation length. The image distortion is originated from the amplitude decrease, the time shift and the time interval expansion of MAE signals introduced by the deformation length and the incident angle. The favorable results demonstrate that the fast high-resolution imaging can be accomplished by the minimum rotations of the rotary-scanning-based MAET using an actual transducer, and also provide an optimized scheme for the rotary-based MAET without scanning using a linear array of point sources.

Magneto-Acousto-Electrical Tomography With Nonuniform Static Magnetic Field

Magneto-acousto-electrical tomography (MAET) is a powerful tool for numerous applications, including medical imaging and process tomography. In these applications, and to enable precise reconstruction of images of a given process using MAET, high-quality measurements must be obtained from the target of interest. It is thus obvious that the magnetic field excitation used in these measurements plays an important role in this task. However, the existing reports in the literature to date have usually assumed that the static magnetic field is a uniform field, which is challenging to achieve in practice. In this article, we circumvent this challenge and present a comprehensive mathematical model for MAET in the presence of nonuniform magnetic fields. In the proposed model, a relationship is established between the measurement signal and the reciprocal current density. The conductivity distribution is obtained via a simulation model and compared with the second norm error of the images and the various uniformities of the nonuniform magnetic fields obtained from the imaging results. The model is then validated for different test cases, which range from a simple phantom with three layers to a phantom with a cylindrical geometry. It is concluded that the use of a nonuniform magnetic field can lead to significant changes and improvements in the reconstruction of the conductivity, thus making it possible to use this technique in bedside detection applications.

ARU-DGAN: A dual generative adversarial network based on attention residual U-Net for magneto-acousto-electrical image denoising.

Magneto-Acousto-Electrical Tomography (MAET) is a multi-physics coupling imaging modality that integrates the high resolution of ultrasound imaging with the high contrast of electrical impedance imaging. However, the quality of images obtained through this imaging technique can be easily compromised by environmental or experimental noise, thereby affecting the overall quality of the imaging results. Existing methods for magneto-acousto-electrical image denoising lack the capability to model local and global features of magneto-acousto-electrical images and are unable to extract the most relevant multi-scale contextual information to model the joint distribution of clean images and noise images. To address this issue, we propose a Dual Generative Adversarial Network based on Attention Residual U-Net (ARU-DGAN) for magneto-acousto-electrical image denoising. Specifically, our model approximates the joint distribution of magneto-acousto-electrical clean and noisy images from two perspectives: noise removal and noise generation. First, it transforms noisy images into clean ones through a denoiser; second, it converts clean images into noisy ones via a generator. Simultaneously, we design an Attention Residual U-Net (ARU) to serve as the backbone of the denoiser and generator in the Dual Generative Adversarial Network (DGAN). The ARU network adopts a residual mechanism and introduces a linear Self-Attention based on Cross-Normalization (CNorm-SA), which is proposed in this paper. This design allows the model to effectively extract the most relevant multi-scale contextual information while maintaining high resolution, thereby better modeling the local and global features of magneto-acousto-electrical images. Finally, extensive experiments on a real-world magneto-acousto-electrical image dataset constructed in this paper demonstrate significant improvements in preserving image details achieved by ARU-DGAN. Furthermore, compared to the state-of-the-art competitive methods, it exhibits a 0.3 dB increase in PSNR and an improvement of 0.47% in SSIM.

Influence of density change on the detection of breast liposarcoma by magneto-acousto-electrical tomography

Magneto-Acousto-Electrical Tomography (MAET) has the advantage of high spatial resolution and high image contrast and is expected to achieve early breast cancer diagnosis. At present, the density of biological tissue is usually assumed to be the density of water. The effect of density changes on the MAET signal has not been studied. Liposarcoma of the breast is a common malignant tumor. Unlike normal breast cancer which occurs in the gland, liposarcoma of the breast occurs in the fat of the breast. However, the fat density of the breast is widely distributed, which is different from that of liposarcoma. Therefore, it is very important to study the effect of density change on the MAET signals. In this paper, a finite element simulation model is established to consider the influence of density variation on the MAET signal. The simulation results show that an increase in density reduces the amplitude of the original MAET signal. The degree of reduction in signal amplitude is proportional to the increase in signal density. The simulation results are consistent with the theoretical analysis. Finally, the MAET experimental platform is built to validate the simulation results of MAET signals. The simulation and experiment results show that the change of density greatly influences the detection of breast liposarcoma based on MAET. It cannot be directly equivalent to the density of water. The results of this study indicate that MAET is expected to detect the early diagnosis of breast liposarcoma.

A Dual-Modal Imaging Method Combining Ultrasound and Electromagnetism for Simultaneous Measurement of Tissue Elasticity and Electrical Conductivity.

The mechanical and electrical properties of soft tissues are relative to soft tissues' pathological state. Modern medical imaging devices have shown a trend to multi-modal imaging, which will provide complementary functional information to improve the accuracy of disease diagnosis. However, no method or system can simultaneously measure the mechanical and electrical properties of the soft tissue. In this study, we proposed a novel dual-modal imaging method integrated by shear wave elasticity imaging (SWEI) and Magneto-acousto-electrical tomography (MAET) to measure soft tissue's elasticity and conductivity simultaneously. A dual-modal imaging system based on a linear array transducer is built, and the imaging performances of MAET and SWEI were respectively evaluated by phantoms experiment and in vitro experiment. Conductivity phantom experiments show that the MAET in this dual-modal system can image conductivity gradient as low as 0.4 S/m. The phantom experiments show that the reconstructed 2-D elasticity maps of the phantoms with inclusions with a diameter larger than 5 mm are relatively accurate. In vitro experiments show that the elasticity parameter can significantly distinguish the changes in tissue before and after heating. This study first proposes a method that can simultaneously obtain tissue elasticity and electrical conductivity to the best of our knowledge. Although this paper just carried out the proof of concept experiments of the new method, it demonstrates great potential for disease diagnosis in the future.

Image quality improvement of magneto-acousto-electrical tomography with Barker coded excitation

Magneto-acousto-electrical tomography (MAET) combines the advantages of the high resolution of ultrasound imaging and the high contrast of electrical impedance tomography for imaging the conductivity of tissues. The traditional MAET uses a short pulse as the excitation waveform, and the amplitude of the MAE signal for a single acquisition is very weak. Thus, the multiple-acquisition mode for averaging was adopted to reduce the system noise while significantly increasing the data acquisition time. In this study, a coded-based MAET method was proposed to improve the image quality of MAET. We theoretically derived the principle of the coded-based MAET and analyzed the performance of different pulse compression techniques. The 13-bit Barker code was selected, and phantoms of different shapes and conductivity were used to verify the proposed method experimentally. Finally, in vitro experiment was conducted to investigate the performance of the proposed method in tissue level application. The experimental results show that the proposed method can significantly improve image quality and speed up the imaging time.

Simulation method of magneto-acousto-electrical tomography for improving computational efficiency

In this paper, a frequency domain simulation method of magneto-acousto-electrical tomography (MAET) was proposed. This method is based on discrete Fourier transform. With this approach, the solving degrees of freedom of the simulation model can be significantly reduced. It can greatly reduce the requirements of computer hardware and improve efficiency. At the same time, the interaction between fluid and biological tissues was considered, which makes the simulation model closer to the real model. In this paper, an MAET simulation model of acoustic–solid–electromagnetic multi-physical field coupling corresponding to the actual physical world was established. It is more reasonable to adopt the fully coupled method. However, the fully coupled method needs more computational memory. To further study the memory and time required for calculation, the segregated method was used to calculate the simulation model without affecting the accuracy and tolerance in this paper. The results show that using the segregated method can significantly reduce the memory requirement of the MAET model, but the solution time will increase accordingly. Therefore, the appropriate solution method can be selected according to the simulation computer configuration and the desired solution time. We, finally, built an experimental platform to conduct MAET experiments and verified the theoretical and simulation analyses.

Rapid rotational magneto-acousto-electrical tomography with filtered back-projection algorithm based on plane waves

Magneto-acousto-electrical tomography (MAET) is designed to produce conductivity images with high spatial resolution for a conducting object. In a previous study, for an irregular conductor, transverse scanning and rotational methods with a focus transducer were combined to collect complete electrical information. This kind of method, however, is time-consuming because of the transverse scanning procedure. In this study, we proposed a novel imaging method based on plane ultrasound waves and a new aspect of projection in rotational MAET. In the proposed method, we achieved the projection in each rotation angle by using plane waves rather than mechanical scanning of the focus waves along the transverse direction. Thus, the imaging time was significantly saved. To verify the proposed method, we derived a measurement formula containing a lateral integration, which built the relationship between the measurement formula and the projection under each rotation angle. Next, we constructed two different numerical models to compute magneto-acousto-electrical signals by using a finite element method and reconstructed the corresponding conductivity parameter images based on a filtered back-projection algorithm. Then, simulated signals under different signal-to-ratios (6, 20, 40, and 60 dB) were generated to test the performance of the proposed algorithm. To improve the image quality, we further analysed the influence of the filters and the frequency scaling factors embedded in the filtered back-projection algorithm. Moreover, we computed the L2 norm of the error in case of different frequency scaling factors and measurement noises. Finally, we conducted a phantom experiment with a 64-element linear phased array transducer (center frequency of 2.7 MHz) and reconstructed the conductivity parameter images of the circular phantom with an elliptical hole. The experimental results demonstrated the feasibility and time-efficiency of the proposed rapid rotational MAET.

The experimental study of mouse liver in magneto-acousto-electrical tomography by scan mode

Magneto-acousto-electrical tomography (MAET) is an imaging method coupled with sound field and magnetic field. The aim of this study is to present some novel experimental results of the mouse liver for the magneto-acousto-electrical tomography measured by two electrodes. The magnetic field in the space of 60 mm3 is about 300 mT which generate by two permanent magnets. A plane transducer with 2.25 MHz center frequency is utilized to generate acoustic waves inside the object. The signal is detected by two similar 1 mm copper foil electrodes. An amplifier is designed to receive the MAET signal, and the gain of the amplifier is adjusted to be 54 dB. The phantom used in this paper is a mouse liver surrounded by a gel phantom with the conductivity of 0.7 S m−1. The gel phantom with the conductivity of 0.7 S m−1 is used to simulate the liver tumor, and the normal mouse liver is filled in the phantom. A series of the MAET signals are detected by the electrodes when the transducer is moved on a pre-set line route, then a B-scan image is realized. The experimental system can provide more information about the tumor and the results show that the MAET is sensitive enough for the potential clinical application of tumor in animal or human.

Three-dimensional model of conductivity imaging for magneto-acousto-electrical tomography

This article presents a series of three-dimensional results for Magneto-acousto-electrical Tomography (MAET), which is a hybrid imaging modality combining the merits of high contrast and high resolution. The ultrasound field and electromagnetic field are coupled to generate current density distribution inside the sample. However, three-dimensional images have not yet been realized for MAET through voltage signals detected by electrodes. In this paper, the mathematical model of MAET is analyzed, and a new image reconstruction scheme is proposed, which is verified by a numerical framework. One three-dimensional numerical model of normal and tumor tissues is formed to analyze the multiphysics problems. In the model, vibration velocity is obtained for pulse type ultrasound excitations with the duration of 0.5 μs. The static magnetic field produced by two permanent magnets is about 300 mT. In order to measure the voltage caused by the MAET effect, two electrodes are attached on the surface of the sample. A series of MAET signals are obtained when the transducer locates in different positions. The distribution of three-dimensional conductivity is recovered by the new image reconstruction scheme. The reconstructed conductivity images are consistent with the original distribution, thus verifying the effectiveness of the new image reconstruction scheme. In addition, the experiment has also validated the mathematical model and simulation results. The simulation and the experimental results indicate that the MAET has the potential to become a new tool to study the electrical properties of tumors in humans.

Research on Factors Affecting the Imaging Resolution of Magneto–Acousto–Electrical Tomography

As the conductivities of healthy tissue and cancerous tissue are different, methods for detecting conductivity variations of biological tissue are potential medical imaging modalities for early diagnosis of cancer in the future. Magneto-acousto-electrical tomography (MAET) is a noninvasive and hybrid conductivity imaging technology that integrates the advantage of high contrast. It has been demonstrated to have an excellent capability to distinguish conductivity variations along the direction of acoustic propagation and extremely promising as an alternative medical imaging technology for early detection of cancer. However, the existing MAET has a low resolution, and the factors affecting the imaging resolution of MAET are rarely studied systematically. Therefore, we firstly designed an MAET detection system and performed several verification experiments. A B-scan algorithm was then proposed for enhancing the system resolution. Subsequently, two uniform phantoms with different intermediate gaps in the middle and a B-mode imaging experiment on pork tissue were used for testing the performance of detection resolution. Finally, comparative analyses were performed to verify whether the frequency, the cycle number of the excitation signal, and the B-scan algorithm can influence the detection resolution. We obtained the following results: 1) The longitudinal resolution of the conductivity B-scan image increases as the number of cycle excitation decreases. 2) Vertical resolution using a 2.5 MHz probe excitation is significantly better than using a 500 kHz probe excitation. 3) The B-scan algorithm can improve conductivity resolution, and it reveals that our proposed detection system's longitudinal resolution can reach 1mm. 4) we obtained the conductivity profile of pork tissue. The results showed that our detection platform could accurately distinguish the target sample's interfaces of conductivity variations, increasing the excitation frequency, reducing the cycle number, and adopting the B-mode imaging algorithm could improve its conductivity detection resolution, which laid the foundation for the design of a high-resolution MAET detection system.

Data acquisition system for MAET with magnetic field measurements

Magneto-acousto-electrical tomography (MAET) is an imaging modality to image the electrical conductivity of biological tissues. It is based on electrical current induction by using ultrasound under a static magnetic field. The aim of this study is to develop a data acquisition system for MAET based on magnetic field measurements. The static magnetic field is generated by six permanent neodymium magnets. A 16-element linear phased array (LPA) transducer is utilized to generate acoustic pressure waves inside the phantom. To measure the magnetic field intensity generated by the induced currents, contactless receiver sensors are developed using two similar disk multiple layer coils, which are Helmholtz coil sensor. Physical properties and electrical characteristics of the sensors are assessed. A two-stage cascaded amplifier is designed and utilized in the receiving system. The gain of the cascaded amplifier at 1 MHz is adjusted to be 96 dB. Experimental studies are conducted with two different phantoms, having 3 S m−1 and 58 S m−1 electrical conductivity, respectively. A-scan and B-scan images of phantoms are obtained with the LPA transducer. Comparison of the ultrasound (A-scan) and MAET signals reveals that 3 S m−1 conductive inhomogeneity can be detected with this data acquisition system. Furthermore, the front and rear interfaces of an inhomogeneity () of 58 S m−1 conductivity are detectable.

Noninvasive Treatment-Efficacy Evaluation for HIFU Therapy Based on Magneto-Acousto-Electrical Tomography.

As a novel noninvasive modality of oncotherapy or stroke treatment, high-intensity focused ultrasound (HIFU) has drawn more and more attention in the past decades. Whereas, real-time temperature monitoring and treatment-efficacy evaluation are still the key issues for HIFU therapy. Based on the temperature-conductivity relation of tissues with a sharp conductivity variation of irreversible thermocoagulation at 69°C, a noninvasive method of treatment-efficacy evaluation for HIFU ablation using the magneto-acousto-electrical tomography (MAET) technology is theoretically studied. By applying the nonlinear Khokhlov-Zabolotskaya-Kuznetsov equation and Pennes equation, a cylindrical model is established to simulate the distributions of pressure, temperature, and conductivity with the consideration of harmonic components. The MAET signals are simulated to analyze the characteristics of the peak amplitude and the axial interval of the two clusters generated by the conductivity boundary of HIFU ablation. The axial interval can be used as the indictor to evaluate the size of HIFU ablation with the minimum axial width of one wavelength. The favorable results demonstrate the feasibility of real-time treatment-efficacy evaluation for HIFU therapy using the MAET technology and suggest potential applications in clinical practice.

Numerical Simulations and Experimental Study of Magneto-Acousto-Electrical Tomography With Plane Transducer

This paper presents new results on a novel coupled-physics modality called magneto-acousto-electrical tomography (MAET). With static magnetic field, a beam of ultrasound is applied to the sample to be imaged; the ultrasonic vibration can lead to the separation of the charges due to the Lorentz force and produces the current distributed in the object. In this paper, simulations were conducted on biological tissue model, and the electrical properties were reconstructed, which could reflect the state of physiological or pathological. We also conducted experiments to detect the voltage signal of microvolt level by the electrodes placed around the sample. The series of experiments were conducted on low-conductivity (0.2 S/m) animal gelatin phantom and real biological tissue, successively placed in a 260 mT magnetic field and sonicated with a plane ultrasonic transducer of central frequency 2.25 MHz. In this paper, we obtained axis resolution of 1 mm, much more significant improvement than the previous reports. More importantly, the experimental result does also demonstrate the feasibility of MAET to image the electrical properties of biological tissue.

Numerical implementation of magneto-acousto-electrical tomography (MAET) using a linear phased array transducer

In this study, the performance and implementation of magneto-acousto-electrical tomography (MAET) is investigated using a linear phased array (LPA) transducer. The goal of MAET is to image the conductivity distribution in biological bodies. It uses the interaction between ultrasound and a static magnetic field to generate velocity current density distribution inside the body. The resultant voltage due to velocity current density is sensed by surface electrodes attached on the body. In this study, the theory of MAET is reviewed. A 16-element LPA transducer with 1 MHz excitation frequency is used to provide beam directivity and steerability of acoustic waves. Different two-dimensional numerical models of breast and tumour are formed to analyze the multiphysics problem coupled with acoustics and electromagnetic fields. In these models, velocity current density distributions are obtained for pulse type ultrasound excitations. The static magnetic field is assumed as 1 T. To sense the resultant voltage caused by the velocity current density, it is assumed that two electrodes are attached on the surface of the body. The performance of MAET is shown through sensitivity matrix analysis. The sensitivity matrix is obtained for two transducer positions with 13 steering angles between to with angular intervals. For the reconstruction of the images, truncated singular value decomposition method is used with different signal-to-noise ratio (SNR) values (20 dB, 40 dB, 60 dB and 80 dB). The resultant images show that the perturbation (5 mm × 5 mm) placed 35 mm depth can be detected even if the SNR is 20 dB.

Theoretical limits to sensitivity and resolution in magneto-acousto-electrical tomography

In this study, the performance of magneto-acousto-electrical tomography (MAET) is investigated quantitatively by considering interrelations between its sensitivity, resolution and conductivity contrast. An analytical solution for the forward problem of MAET is derived for two-dimensional (2D) concentric bodies by the separation of variables method. The electric potential and the acoustic pressure are separated into their angular and radial components. The series coefficients for these solutions are obtained from their respective boundary conditions. The electric potential on the boundary is related to the acoustic boundary acceleration analytically. From this relation, a sensitivity expression is derived relating fractional change in conductivity contrast to fractional change in the measured electric potential. This expression is a function of the resolution and conductivity contrast of the imaging system. It also depends on the acoustic wave number and the dimensions of the body. The pair-wise relations between these parameters are presented. The sensitivity behavior of MAET is compared with applied current electrical impedance tomography and the improvements for small inhomogeneities are presented. For eccentric bodies, a modified expression for the sensitivity is obtained by conformal mapping. For arbitrary periodic boundary excitations, the sensitivity expressions for harmonic cases are combined to obtain a unified sensitivity expression.