J-substitution algorithm in magnetic resonance electrical impedance tomography (MREIT): phantom experiments for static resistivity images

Research Trends and Hotspots of Medical Electrical Impedance Tomography Algorithms: A Bibliometric Analysis From 1987 to 2021

Electrical impedance tomography (EIT) is a gradually maturing medical imaging technique that relies on computational algorithms for reconstructing and visualizing internal conductivity distributions within the human body. To provide a comprehensive and objective understanding of the current state and trends in the EIT algorithm research, we conducted bibliometric analysis on a 25-year EIT algorithm research dataset sourced from Web of Science Core Collections. We visualized publication characteristics, collaboration patterns, keywords, and co-cited references. The results indicate a steady increase in annual publications over recent decades. The United States, United Kingdom, China, and South Korea contributed 60% of the articles collaboratively. Keyword analysis unveiled three distinct stages in the evolution of EIT algorithm research: the establishment of fundamental algorithm frameworks, optimization for improved imaging performance, and the development of algorithms for clinical applications. Additionally, there has been a shift in research focus from traditional theories to the incorporation of new methods, such as artificial intelligence. Co-cited references suggest that integrating EIT with other established imaging techniques may emerge as a new trend in EIT algorithm research. In summary, EIT algorithms have been a consistent research focus, with current efforts centered on optimizing algorithms to enhance imaging performance. The emerging research trend involves utilizing more diverse and intersecting algorithms.

Magnetic Resonance Electrical Impedance Tomography

Magnetic Resonance Electrical Impedance Tomography (MREIT) is a high-resolution bioimpedance imaging technique that has developed over a period beginning in the early 1990s to measure low-frequency (<1 kHz) tissue electrical properties. Low-frequency electrical properties are particularly important because they provide valuable information on cell structures and ionic composition of tissues, which may be very useful for diagnostic purposes. MREIT uses one component of the magnetic flux density data induced due to an exogenous-current administration, measured using an MRI machine, to reconstruct isotropic or anisotropic electrical property distributions. The MREIT technique typically requires two linearly independent current administrations to reconstruct conductivity uniquely. Since its invention, researchers have explored its potential for measuring electrical conductivity in regions such as the brain and muscle tissue. It has also been investigated in disease models, for example, cerebral ischemia and early tumor detection. In this chapter, we aim to provide a solid foundation of the different MREIT image reconstruction algorithms, including both isotropic and anisotropic conductivity reconstruction approaches. We will also explore the newly developed diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) method, a practical method for anisotropic tissue property imaging, at the end of the chapter.

Phantom Construction and Equipment Configurations for Characterizing Electrical Properties Using MRI

Phantom objects are commonly employed in MRI systems as stable substitutes for biological tissues to ensure systems for measuring images are operating correctly and safely. For magnetic resonance electrical impedance tomography (MREIT) and magnetic resonance electrical property tomography (MREPT), conductivity or permittivity phantoms play an important role in checking MRI pulse sequences, MREIT equipment performance, and algorithm validation. The construction of these phantoms is explained in this chapter. In the first part, materials used for phantom construction are introduced. Ingredients for modifying the electromagnetic properties and relaxation times are presented, and the advantages and disadvantages of aqueous, gel, and hybrid conductivity phantoms are explained. The devices and methods used to confirm phantom electromagnetic properties are explained. Next, different types of MREIT electrode materials and the constant current sources used for MREIT studies are discussed. In the last section, we present the results of previous MREIT and MREPT studies.

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 L₂norm 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.

Low frequency conductivity reconstruction based on a single current injection via MREIT

Conventional magnetic resonance electrical impedance tomography (MREIT) reconstruction methods require administration of two linearly independent currents via at least two electrode pairs. This requires long scanning times and inhibits coordination of MREIT measurements with electrical neuromodulation strategies. We sought to develop an isotropic conductivity reconstruction algorithm in MREIT based on a single current injection, both to decrease scanning time by a factor of two and enable MREIT measurements to be conveniently adapted to general transcranial- or implanted-electrode neurostimulation protocols. In this work, we propose and demonstrate an iterative algorithm that extends previously published MREIT work using two-current administration approaches. The proposed algorithm is a single-current adaptation of the harmonic B _z algorithm. Forward modeling of electric potentials is used to capture changes of conductivity along current directions that would normally be invisible using data from a single-current administration. Computational and experimental results show that the reconstruction algorithm is capable of reconstructing isotropic conductivity images that agree well in terms of L ² error and structural similarity with exact conductivity distributions or two-current-based MREIT reconstructions. We conclude that it is possible to reconstruct high quality electrical conductivity images using MREIT techniques and one current injection only.

Sparse reconstruction of log-conductivity in current density impedance tomography

A new non-linear optimization approach is proposed for the sparse reconstruction of log-conductivities in current density impedance imaging. This framework comprises of minimizing an objective functional involving a least squares fit of the interior electric field data corresponding to two boundary voltage measurements, where the conductivity and the electric potential are related through an elliptic PDE arising in electrical impedance tomography. Further, the objective functional consists of a L ¹ regularization term that promotes sparsity patterns in the conductivity and a Perona-Malik anisotropic diffusion term that enhances the edges to facilitate high contrast and resolution. This framework is motivated by a similar recent approach to solve an inverse problem in acousto-electric tomography. Several numerical experiments and comparison with an existing method demonstrate the effectiveness of the proposed method for superior image reconstructions of a wide-variety of log-conductivity patterns.

Predicting irreversible electroporation-induced tissue damage by means of magnetic resonance electrical impedance tomography

Irreversible electroporation (IRE) is gaining importance in routine clinical practice for nonthermal ablation of solid tumors. For its success, it is extremely important that the coverage and exposure time of the treated tumor to the electric field is within the specified range. Measurement of electric field distribution during the electroporation treatment can be achieved using magnetic resonance electrical impedance tomography (MREIT). Here, we show improved MREIT-enabled electroporation monitoring of IRE-treated tumors by predicting IRE-ablated tumor areas during IRE of mouse tumors in vivo. The in situ prediction is enabled by coupling MREIT with a corresponding Peleg-Fermi mathematical model to obtain more informative monitoring of IRE tissue ablation by providing cell death probability in the IRE-treated tumors. This technique can potentially be used in electroporation-based clinical applications, such as IRE tissue ablation and electrochemotherapy, to improve and assure the desired treatment outcome.

Magnetoacoustic tomography with magnetic induction (MAT-MI) for imaging electrical conductivity of biological tissue: a tutorial review

Magnetoacoustic tomography with magnetic induction (MAT-MI) is a noninvasive imaging method developed to map electrical conductivity of biological tissue with millimeter level spatial resolution. In MAT-MI, a time-varying magnetic stimulation is applied to induce eddy current inside the conductive tissue sample. In the presence of a static magnetic field, the Lorentz force acting on the induced eddy current drives mechanical vibrations producing detectable ultrasound signals. These ultrasound signals can then be acquired to reconstruct a map related to the sample's electrical conductivity contrast. This work reviews fundamental ideas of MAT-MI and major techniques developed in recent years. First, the physical mechanisms underlying MAT-MI imaging are described, including the magnetic induction and Lorentz force induced acoustic wave propagation. Second, experimental setups and various imaging strategies for MAT-MI are reviewed and compared, together with the corresponding experimental results. In addition, as a recently developed reverse mode of MAT-MI, magneto-acousto-electrical tomography with magnetic induction is briefly reviewed in terms of its theory and experimental studies. Finally, we give our opinions on existing challenges and future directions for MAT-MI research. With all the reported and future technical advancement, MAT-MI has the potential to become an important noninvasive modality for electrical conductivity imaging of biological tissue.

Current Density Imaging During Transcranial Direct Current Stimulation Using DT-MRI and MREIT: Algorithm Development and Numerical Simulations

OBJECTIVE

Transcranial direct current stimulation (tDCS) is a neuromodulatory technique for neuropsychiatric diseases and neurological disorders. In the tDCS treatment, dc current is injected into the head through a pair of electrodes attached on the scalp over a target region. A current density imaging method is needed to quantitatively visualize the internal current density distribution during the tDCS treatment.

METHODS

We developed a novel current density image reconstruction algorithm using 1) a subject specific segmented 3-D head model, 2) diffusion tensor data, and 3) magnetic flux density data induced by the tDCS current. We acquired T1 weighted and diffusion tensor images of the head using the MRI scanner before the treatment. During the treatment, we can measure the induced magnetic flux density data using a magnetic resonance electrical impedance tomography (MREIT) pulse sequence. In this paper, the magnetic flux density data were numerically generated.

RESULTS

Numerical simulation results show that the proposed method successfully recovers the current density distribution including the effects of the anisotropic, as well as isotropic conductivity values of different tissues in the head.

CONCLUSION

The proposed current density imaging method using DT-MRI and MREIT can reliably recover cross-sectional images of the current density distribution during the tDCS treatment.

SIGNIFICANCE

Success of the tDCS treatment depends on a precise determination of the induced current density distribution within different anatomical structures of the brain. Quantitative visualization of the current density distribution in the brain will play an important role in understanding the effects of the electrical stimulation.

Magnetic resonance electrical impedance tomography for measuring electrical conductivity during electroporation

The electroporation effect on tissue can be assessed by measurement of electrical properties of the tissue undergoing electroporation. The most prominent techniques for measuring electrical properties of electroporated tissues have been voltage-current measurement of applied pulses and electrical impedance tomography (EIT). However, the electrical conductivity of tissue assessed by means of voltage-current measurement was lacking in information on tissue heterogeneity, while EIT requires numerous additional electrodes and produces results with low spatial resolution and high noise. Magnetic resonance EIT (MREIT) is similar to EIT, as it is also used for reconstruction of conductivity images, though voltage and current measurements are not limited to the boundaries in MREIT, hence it yields conductivity images with better spatial resolution. The aim of this study was to investigate and demonstrate the feasibility of the MREIT technique for assessment of conductivity images of tissues undergoing electroporation. Two objects were investigated: agar phantoms and ex vivo liver tissue. As expected, no significant change of electrical conductivity was detected in agar phantoms exposed to pulses of all used amplitudes, while a considerable increase of conductivity was measured in liver tissue exposed to pulses of different amplitudes.

J-based Magnetic Resonance Conductivity Tensor Imaging (MRCTI) at 3 T

In this study, current density (J) - based Magnetic Resonance Conductivity Tensor Imaging (MRCTI) reconstruction algorithms namely, the Anisotropic Equipotential Projection (AEPP), the Anisotropic J-Substitution (AJS) and the Anisotropic Hybrid J-Substitution (AHJS) algorithms are implemented to reconstruct conductivity tensor images of a physical phantom using a 3T magnetic resonance imaging system. 10mA current pulses are injected in synchrony with a conventional spin-echo pulse sequence. Furthermore, a new J-based hybrid algorithm namely, the Anisotropic Hybrid Equipotential Projection (AHEPP) is proposed. In addition, reconstruction performances of the four algorithms are evaluated.

Noninvasive measurement of conductivity anisotropy at larmor frequency using MRI

Anisotropic electrical properties can be found in biological tissues such as muscles and nerves. Conductivity tensor is a simplified model to express the effective electrical anisotropic information and depends on the imaging resolution. The determination of the conductivity tensor should be based on Ohm's law. In other words, the measurement of partial information of current density and the electric fields should be made. Since the direct measurements of the electric field and the current density are difficult, we use MRI to measure their partial information such as B1 map; it measures circulating current density and circulating electric field. In this work, the ratio of the two circulating fields, termed circulating admittivity, is proposed as measures of the conductivity anisotropy at Larmor frequency. Given eigenvectors of the conductivity tensor, quantitative measurement of the eigenvalues can be achieved from circulating admittivity for special tissue models. Without eigenvectors, qualitative information of anisotropy still can be acquired from circulating admittivity. The limitation of the circulating admittivity is that at least two components of the magnetic fields should be measured to capture anisotropic information.

Practical realization of magnetic resonance conductivity tensor imaging (MRCTI)

Magnetic resonance conductivity tensor imaging (MRCTI) is an emerging modality which reconstructs images of anisotropic conductivity distribution within a volume conductor. Images are reconstructed based on magnetic flux density distribution induced by an externally applied probing current, together with a resultant surface potential value. The induced magnetic flux density distribution is measured using magnetic resonance current density imaging techniques. In this study, MRCTI data acquisition is experimentally implemented and anisotropic conductivity images of test phantoms are reconstructed using recently proposed MRCTI reconstruction algorithms.

Ex vivo and in silico feasibility study of monitoring electric field distribution in tissue during electroporation based treatments

Magnetic resonance electrical impedance tomography (MREIT) was recently proposed for determining electric field distribution during electroporation in which cell membrane permeability is temporary increased by application of an external high electric field. The method was already successfully applied for reconstruction of electric field distribution in agar phantoms. Before the next step towards in vivo experiments is taken, monitoring of electric field distribution during electroporation of ex vivo tissue ex vivo and feasibility for its use in electroporation based treatments needed to be evaluated. Sequences of high voltage pulses were applied to chicken liver tissue in order to expose it to electric field which was measured by means of MREIT. MREIT was also evaluated for its use in electroporation based treatments by calculating electric field distribution for two regions, the tumor and the tumor-liver region, in a numerical model based on data obtained from clinical study on electrochemotherapy treatment of deep-seated tumors. Electric field distribution inside tissue was successfully measured ex vivo using MREIT and significant changes of tissue electrical conductivity were observed in the region of the highest electric field. A good agreement was obtained between the electric field distribution obtained by MREIT and the actual electric field distribution in evaluated regions of a numerical model, suggesting that implementation of MREIT could thus enable efficient detection of areas with insufficient electric field coverage during electroporation based treatments, thus assuring the effectiveness of the treatment.

Complex B1 mapping and electrical properties imaging of the human brain using a 16-channel transceiver coil at 7T

The electric properties of biological tissue provide important diagnostic information within radio and microwave frequencies, and also play an important role in specific absorption rate calculation which is a major safety concern at ultrahigh field. The recently proposed electrical properties tomography (EPT) technique aims to reconstruct electric properties in biological tissues based on B1 measurement. However, for individual coil element in multichannel transceiver coil which is increasingly utilized at ultrahigh field, current B1-mapping techniques could not provide adequate information (magnitude and absolute phase) of complex transmit and receive B1 which are essential for electrical properties tomography, electric field, and quantitative specific absorption rate assessment. In this study, using a 16-channel transceiver coil at 7T, based on hybrid B1-mapping techniques within the human brain, a complex B1-mapping method has been developed, and in vivo electric properties imaging of the human brain has been demonstrated by applying a logarithm-based inverse algorithm. Computer simulation studies as well as phantom and human experiments have been conducted at 7T. The average bias and standard deviation for reconstructed conductivity in vivo were 28% and 67%, and 10% and 43% for relative permittivity, respectively. The present results suggest the feasibility and reliability of proposed complex B1-mapping technique and electric properties reconstruction method.

Magnetic resonance electrical impedance tomography for monitoring electric field distribution during tissue electroporation

Electroporation is a phenomenon caused by externally applied electric field of an adequate strength and duration to cells that results in the increase of cell membrane permeability to various molecules, which otherwise are deprived of transport mechanism. As accurate coverage of the tissue with a sufficiently large electric field presents one of the most important conditions for successful electroporation, applications based on electroporation would greatly benefit with a method of monitoring the electric field, especially if it could be done during the treatment. As the membrane electroporation is a consequence of an induced transmembrane potential which is directly proportional to the local electric field, we propose current density imaging (CDI) and magnetic resonance electrical impedance tomography (MREIT) techniques to measure the electric field distribution during electroporation. The experimental part of the study employs CDI with short high-voltage pulses, while the theoretical part of the study is based on numerical simulations of MREIT. A good agreement between experimental and numerical results was obtained, suggesting that CDI and MREIT can be used to determine the electric field during electric pulse delivery and that both of the methods can be of significant help in planning and monitoring of future electroporation based clinical applications.

Difference frequency magneto-acousto-electrical tomography (DF-MAET): application of ultrasound-induced radiation force to imaging electrical current density

Magneto-acousto-electrical tomography (MAET) is a potential imaging modality which can provide high-spatial-resolution images of the impedance of conductive media. In MAET, the impedance is reconstructed from the mapped current density distribution J(ab)(r) that would exist in a sample if a current/voltage source were to be applied through measurement electrodes a and b. To map J(ab)(r) without applying a current/voltage source, the sample is placed in a static magnetic field and a focused ultrasonic pulse is directed to a point r to generate a point-like dipole source via the Lorentz force mechanism. The MAET voltage U(ab), which is directly proportional to J(ab)(r), is measured through electrodes a and b for each scanning point. To reconstruct the electrical impedance, we need to map the current density distribution at every point inside the sample. However, with the MAET experimental setup reported in our previous paper on MAET, the MAET signal from a homogenous interior of the sample is undetectable because of the spatially-oscillating nature of the ultrasound field inside the sample. In this paper, we propose to use dual-frequency ultrasound to generate the MAET signal at the difference frequency through the ultrasound radiation force mechanism. The dynamic radiation force causes vibrations inside the sample (and consequently, generates the electric field) with a wavelength much larger than the dimension of the sample along the transducer's axis. Therefore, the MAET signal caused by the radiation force will not be canceled out. We create a dynamic radiation force by applying an amplitude-modulated signal with a modulation frequency fm of several kilohertz and a carrier frequency f(0) of 2.25 MHz to drive the transducer. The dependence of the DF-MAET signal in experiments on the modulation frequency and on the density of the sample agrees with the prediction based on the radiation force mechanism. The spatial resolution of DF-MAET is also studied to verify the radiation force mechanism. Finally, we will prove that the parametric effect in the coupling oil is not a significant source of the DF-MAET signal by imaging a sample at different distances from the transducer. Potential improvements to the present DF-MAET experimental configuration are also discussed.

Imaging electric properties of biological tissues by RF field mapping in MRI

The electric properties (EPs) of biological tissue, i.e., the electric conductivity and permittivity, can provide important information in the diagnosis of various diseases. The EPs also play an important role in specific absorption rate calculation, a major concern in high-field MRI, as well as in nonmedical areas such as wireless telecommunications. The high-field MRI system is accompanied by significant wave propagation effects, and the RF radiation is dependent on the EPs of biological tissue. On the basis of the measurement of the active transverse magnetic component of the applied RF field (known as B(1)-mapping technique), we propose a dual-excitation algorithm, which uses two sets of measured B(1) data to noninvasively reconstruct the EPs of biological tissues. The finite-element method was utilized in 3-D modeling and B(1) field calculation. A series of computer simulations were conducted to evaluate the feasibility and performance of the proposed method on a 3-D head model within a TEM coil and a birdcage coil. Using a TEM coil, when noise free, the reconstructed EP distribution of tissues in the brain has relative errors of 12%-28% and correlated coefficients of greater than 0.91. Compared with other B(1)-mapping-based reconstruction algorithms, our approach provides superior performance without the need for iterative computations. The present simulation results suggest that good reconstruction of EPs from B1 mapping can be achieved.

Magnetic resonance electric property imaging of brain tissues

The electric properties (EPs) of brain tissues, i.e., the electric conductivity and permittivity, can provide important information for diagnosis of various brain disorders. A high-field MRI system is accompanied by significant wave propagation effects, and the radio frequency (RF) radiation is dependent on EPs of the biological tissue. Based on the measurement of the active transverse magnetic component of the applied RF field (known as B1-mapping technique), we have developed a dual-excitation algorithm, which uses two sets of measured B1 data, to noninvasively reconstruct the biological tissue's electric properties. A series of computer simulations were conducted to evaluate the feasibility and performance of the proposed method on a 3-D head model within a birdcage coil and a transverse electromagnetic coil. Compared with other B1-mapping based reconstruction algorithms, our approach provides superior performance without the need for iterative computations. The present simulation results indicate good reconstruction of electric properties of brain tissues from noninvasive MRI B1 mapping.

Magnetic resonance electrical impedance tomography (MREIT) for high-resolution conductivity imaging

Cross-sectional imaging of an electrical conductivity distribution inside the human body has been an active research goal in impedance imaging. By injecting current into an electrically conducting object through surface electrodes, we induce current density and voltage distributions. Based on the fact that these are determined by the conductivity distribution as well as the geometry of the object and the adopted electrode configuration, electrical impedance tomography (EIT) reconstructs cross-sectional conductivity images using measured current-voltage data on the surface. Unfortunately, there exist inherent technical difficulties in EIT. First, the relationship between the boundary current-voltage data and the internal conductivity distribution bears a nonlinearity and low sensitivity, and hence the inverse problem of recovering the conductivity distribution is ill posed. Second, it is difficult to obtain accurate information on the boundary geometry and electrode positions in practice, and the inverse problem is sensitive to these modeling errors as well as measurement artifacts and noise. These result in EIT images with a poor spatial resolution. In order to produce high-resolution conductivity images, magnetic resonance electrical impedance tomography (MREIT) has been lately developed. Noting that injection current produces a magnetic as well as electric field inside the imaging object, we can measure the induced internal magnetic flux density data using an MRI scanner. Utilization of the internal magnetic flux density is the key idea of MREIT to overcome the technical difficulties in EIT. Following original ideas on MREIT in early 1990s, there has been a rapid progress in its theory, algorithm and experimental techniques. The technique has now advanced to the stage of human experiments. Though it is still a few steps away from routine clinical use, its potential is high as a new impedance imaging modality providing conductivity images with a spatial resolution of a few millimeters or less. This paper reviews MREIT from the basics to the most recent research outcomes. Focusing on measurement techniques and experimental methods rather than mathematical issues, we summarize what has been done and what needs to be done. Suggestions for future research directions, possible applications in biomedicine, biology, chemistry and material science are discussed.

MR current density and conductivity imaging: the state of the art

Current density imaging (CDI) is an imaging technique that measures electrical current density distributions in a volume of material or tissue, which can be imaged using magnetic resonance imaging (MRI). Measurements of current density are obtained by applying an external current to the material/tissue during an MRI acquisition. The magnetic fields produced by the applied current are mapped onto the phase image of the MRI acquisition. The phase images are processed to compute the current density distribution. Performing CDI requires an MRI system, additional hardware, a modified pulse sequence (PSD) and data processing software. Greig C. Scott, Michael L.G. Joy and R. Mark Henkelman developed CDI in 1988 at the University of Toronto (Canada). The CDI Research Group is presently based at the University of Toronto and is supervised by the author. This paper describes the CDI technique, its applications by this and other groups and recently proposed methods for electrical conductivity imaging based on the technique.

Analysis of recoverable current from one component of magnetic flux density in MREIT and MRCDI

Magnetic resonance current density imaging (MRCDI) provides a current density image by measuring the induced magnetic flux density within the subject with a magnetic resonance imaging (MRI) scanner. Magnetic resonance electrical impedance tomography (MREIT) has been focused on extracting some useful information of the current density and conductivity distribution in the subject Omega using measured B(z), one component of the magnetic flux density B. In this paper, we analyze the map Tau from current density vector field J to one component of magnetic flux density B(z) without any assumption on the conductivity. The map Tau provides an orthogonal decomposition J = J(P) + J(N) of the current J where J(N) belongs to the null space of the map Tau. We explicitly describe the projected current density J(P) from measured B(z). Based on the decomposition, we prove that B(z) data due to one injection current guarantee a unique determination of the isotropic conductivity under assumptions that the current is two-dimensional and the conductivity value on the surface is known. For a two-dimensional dominating current case, the projected current density J(P) provides a good approximation of the true current J without accumulating noise effects. Numerical simulations show that J(P) from measured B(z) is quite similar to the target J. Biological tissue phantom experiments compare J(P) with the reconstructed J via the reconstructed isotropic conductivity using the harmonic B(z) algorithm.

Noise Analysis of MREIT at 3T and 11T Field Strength

In Magnetic Resonance Electrical Impedance Tomography (MREIT), we measure the induced magnetic flux density inside an imaging object subject to an external injection current. The magnetic flux density is contaminated with noise and this ultimately limits the quality of reconstructed conductivity and current density images. By using two methods to analyze amounts of noise in 3T and 11T MREIT systems, we found that a carefully designed MREIT study will be able to reduce the noise level below 0.1 nT.

On the measurement of conductivity distribution of the human head using magnetic resonance electrical impedance tomography

We have applied the magnetic resonance electrical impedance imaging (MREIT) technique to image the three-dimensional (3D) conductivity distribution of the human head. Computer simulations were carried out on a tradition four-sphere head model to test the feasibility of imaging conductivity distribution of the human head. The present results show that the 3D head conductivity distribution could be well reconstructed using MREIT.

Conductivity images of biological tissue phantoms using a 3.0 tesla MREIT system

We present cross-sectional conductivity images of a biological tissue phantom obtained by using a 3.0 Tesla magnetic resonance electrical impedance tomography (MREIT) system. Inside the cylindrical phantom with 140 mm diameter and 140 mm height, biological tissues such as bovine tongue and liver, porcine muscle, and chicken breast were placed within an agar gelatin. Injecting current of 480 mA.ms into the tissue phantom, we measured the z-component B/sub z/ of the induced magnetic flux density B=(B/sub x/, B/sub y/, B/sub z/). Using the harmonic B/sub z/ algorithm, we reconstructed cross-sectional conductivity images from the measured B/sub z/ data. Reconstructed images clearly distinguish different tissues in terms of both their shapes and conductivity values.

Distinguishability for magnetic resonance-electrical impedance tomography (MR-EIT)

A distinguishability measure is defined for magnetic resonance-electrical impedance tomography (MR-EIT) based on magnetic flux density measurements. This general definition is valid for 2D and 3D structures of any shape. As a specific case, a 2D cylindrical body with concentric inhomogeneity is considered and a bound of the distinguishability is analytically formulated. Distinguishabilities obtained with potential and magnetic flux density measurements are compared.

Measurement of induced magnetic flux density using injection current nonlinear encoding (ICNE) in MREIT

Magnetic resonance electrical impedance tomography (MREIT) measures induced magnetic flux densities subject to externally injected currents in order to visualize conductivity distributions inside an electrically conducting object. Injection currents induce magnetic flux densities that appear in phase parts of acquired MR image data. In the conventional current injection method, we inject currents during the time segment between the end of the first RF pulse and the beginning of the reading gradient in order to ensure the gradient linearity. Noting that longer current injections can accumulate more phase changes, we propose a new pulse sequence called injection current nonlinear encoding (ICNE) where the duration of the injection current pulse is extended until the end of the reading gradient. Since the current injection during the reading gradient disturbs the gradient linearity, we first analyze the MR signal produced by the ICNE pulse sequence and suggest a novel algorithm to extract the induced magnetic flux density from the acquired MR signal. Numerical simulations and phantom experiments show that the new method is clearly advantageous in terms of the reduced noise level in measured magnetic flux density data. The amount of noise reduction depends on the choice of the data acquisition time and it was about 24% when we used a prolonged data acquisition time of 10.8 ms. The ICNE method will enhance the clinical applicability of the MREIT technique when it is combined with an appropriate phase artefact minimization method.

Contrast and spatial resolution in MREIT using low amplitude current

Magnetic resonance-electrical impedance tomography employs low amplitude currents injected or induced inside an object. The additional magnetic field due to these currents results in a phase in the MR images. In this study, a modified fast spin-echo sequence was used to measure this magnetic field, which is obtained by scaling the MR phase image. A finite element method with first order triangular elements was used for the solution of the forward problem. An iterated sensitivity matrix-based algorithm was developed for the inverse problem. The resulting ill-conditioned matrix equation was regularized using the Tikhonov method and solved using a conjugate gradient solver. The spatial and contrast resolution of the technique was tested using agarose gel phantoms. A circular phantom with 7 cm diameter and 1 cm thickness is used in the phantom experiments. The amplitude of the injected current was 1 mA. 3, 5 and 8 mm diameter insulators and high conductor objects are used for the spatial resolution study and an average full-width half-maximum value of 4.7 mm is achieved for the 3 mm insulator case. For the contrast analysis, the conductivity of a 15 mm object is varied between 44% and 500% with respect to the background and results are compared to the ideal reconstruction.

A new magnetic resonance electrical impedance tomography (MREIT) algorithm: the RSM-MREIT algorithm with applications to estimation of human head conductivity

We have developed a new magnetic resonance electrical impedance tomography (MREIT) algorithm, the RSM-MREIT algorithm, for noninvasive imaging of the electrical conductivity distribution using only one component of magnetic flux density. The proposed RSM-MREIT algorithm uses the response surface methodology (RSM) algorithm for optimizing the conductivity distribution through minimizing the errors between the measured and calculated magnetic flux densities. A series of computer simulations has been conducted to assess the performance of the proposed RSM-MREIT algorithm to estimate electrical conductivity values of the scalp, the skull and the brain tissue, in a three-shell piecewise homogeneous head model. Computer simulation studies were conducted in both a spherical and realistic-geometry head model with a single variable (the brain-to-skull conductivity ratio) and three variables (the conductivity of the brain, the skull, and the scalp). The relative error between the target and estimated head conductivity values was less than 12% for both the single-variable and three-variable simulations. These promising simulation results demonstrate the feasibility of the proposed RSM-MREIT algorithm in estimating electrical conductivity values in a piecewise homogeneous head model of the human head, and suggest that the RSM-MREIT algorithm merits further investigation.

Measurement of ion diffusion using magnetic resonance electrical impedance tomography

In magnetic resonance electrical impedance tomography (MREIT), currents are applied to an object, the resulting magnetic flux density measured using MRI and the conductivity distribution reconstructed using these MRI data. In this study, we assess the ability of MREIT to monitor changes in the conductivity distribution of an agarose gel phantom, using injected current pulses of 900 microA. The phantom initially contained a distinct region of high sodium chloride concentration which diffused into the background over time. MREIT data were collected over a 12 h span, and conductivity images were reconstructed using the iterative sensitivity matrix method with Tikhonov regularization. The results indicate that MREIT was able to monitor the changing conductivity and concentration distributions resulting from the diffusion of ions within the agarose gel phantom.

Conductivity image reconstruction from defective data in MREIT: numerical simulation and animal experiment

Magnetic resonance electrical impedance tomography (MREIT) is designed to produce high resolution conductivity images of an electrically conducting subject by injecting current and measuring the longitudinal component, Bz, of the induced magnetic flux density B = (Bx, By, Bz). In MREIT, accurate measurements of Bz are essential in producing correct conductivity images. However, the measured Bz data may contain fundamental defects in local regions where MR magnitude image data are small. These defective Bz data result in completely wrong conductivity values there and also affect the overall accuracy of reconstructed conductivity images. Hence, these defects should be appropriately recovered in order to carry out any MREIT image reconstruction algorithm. This paper proposes a new method of recovering Bz data in defective regions based on its physical properties and neighboring information of Bz. The technique will be indispensable for conductivity imaging in MREIT from animal or human subjects including defective regions such as lungs, bones, and any gas-filled internal organs.

Harmonic Decomposition in PDE-Based Denoising Technique for Magnetic Resonance Electrical Impedance Tomography

Recent progress in magnetic resonance electrical impedance tomography (MREIT) research via simulation and biological tissue phantom studies have shown that conductivity images with higher spatial resolution and accuracy are achievable. In order to apply MREIT to human subjects, one of the important remaining problems to be solved is to reduce the amount of the injection current such that it meets the electrical safety regulations. However, by limiting the amount of the injection current according to the safety regulations, the measured MR data such as the z-component of magnetic flux density Bz in MREIT tend to have low SNR and get usually degraded in their accuracy due to the nonideal data acquisition system of an MR scanner. Furthermore, numerical differentiations of the measured Bz required by the conductivity image reconstruction algorithms tend to further deteriorate the quality and accuracy of the reconstructed conductivity images. In this paper, we propose a denoising technique that incorporates a harmonic decomposition. The harmonic decomposition is especially suitable for MREIT due to the physical characteristics of Bz. It effectively removes systematic and random noises, while preserving important key features in the MR measurements, so that improved conductivity images can be obtained. The simulation and experimental results demonstrate that the proposed denoising technique is effective for MREIT, producing significantly improved quality of conductivity images. The denoising technique will be a valuable tool in MREIT to reduce the amount of the injection current when it is combined with an improved MREIT pulse sequence.

Noise analysis in magnetic resonance electrical impedance tomography at 3 and 11 T field strengths

In magnetic resonance electrical impedance tomography (MREIT), we measure the induced magnetic flux density inside an object subject to an externally injected current. This magnetic flux density is contaminated with noise, which ultimately limits the quality of reconstructed conductivity and current density images. By analysing and experimentally verifying the amount of noise in images gathered from two MREIT systems, we found that a carefully designed MREIT study will be able to reduce noise levels below 0.25 and 0.05 nT at main magnetic field strengths of 3 and 11 T, respectively, at a voxel size of 3 x 3 x 3 mm(3). Further noise level reductions can be achieved by optimizing MREIT pulse sequences and using signal averaging. We suggest two different methods to estimate magnetic flux noise levels, and the results are compared to validate the experimental setup of an MREIT system.

Use of 3-D magnetic resonance electrical impedance tomography in detecting human cerebral stroke: a simulation study

We have developed a new three dimensional (3-D) conductivity imaging approach and have used it to detect human brain conductivity changes corresponding to acute cerebral stroke. The proposed Magnetic Resonance Electrical Impedance Tomography (MREIT) approach is based on the J-Substitution algorithm and is expanded to imaging 3-D subject conductivity distribution changes. Computer simulation studies have been conducted to evaluate the present MREIT imaging approach. Simulations of both types of cerebral stroke, hemorrhagic stroke and ischemic stroke, were performed on a four-sphere head model. Simulation results showed that the correlation coefficient (CC) and relative error (RE) between target and estimated conductivity distributions were 0.9245+/-0.0068 and 8.9997%+/-0.0084%, for hemorrhagic stroke, and 0.6748+/-0.0197 and 8.8986%+/-0.0089%, for ischemic stroke, when the SNR (signal-to-noise radio) of added GWN (Gaussian White Noise) was 40. The convergence characteristic was also evaluated according to the changes of CC and RE with different iteration numbers. The CC increases and RE decreases monotonously with the increasing number of iterations. The present simulation results show the feasibility of the proposed 3-D MREIT approach in hemorrhagic and ischemic stroke detection and suggest that the method may become a useful alternative in clinical diagnosis of acute cerebral stroke in humans.

Electrical conductivity images of biological tissue phantoms in MREIT

We present cross-sectional conductivity images of two biological tissue phantoms. Each of the cylindrical phantoms with both diameter and height of 140 mm contained chunks of biological tissues such as bovine tongue and liver, porcine muscle and chicken breast within a conductive agar gelatin as the background medium. We attached four recessed electrodes on the sides of the phantom with equal spacing among them. Injecting current pulses of 480 or 120 mA ms into the phantom along two different directions, we measured the z-component Bz of the induced magnetic flux density B=(Bx, By, Bz) with a magnetic resonance electrical impedance tomography (MREIT) system based on a 3.0 T MRI scanner. Using the harmonic Bz algorithm, we reconstructed cross-sectional conductivity images from the measured Bz data. Reconstructed images clearly distinguish different tissues in terms of both their shapes and conductivity values. In this paper, we experimentally demonstrate the feasibility of the MREIT technique in producing conductivity images of different biological soft tissues with a high spatial resolution and accuracy when we use a sufficient amount of the injection current.

Induced current magnetic resonance–electrical impedance tomography

Magnetic resonance-electrical impedance tomography (MR-EIT) is a conductivity imaging method based on injecting currents into the object. In this study, a new MR-EIT method, whereby currents are induced inside the object by using external coils, is proposed. This new method is called induced current magnetic resonance-electrical impedance tomography. In induced current MR-EIT surface electrodes are not used and thereby artifacts due to electrodes are eliminated. The reconstruction algorithm is based on the measurement of only one component of the secondary magnetic flux density. The algorithm is an iterative one, is 3D and is based on the solution of a linear matrix equation at each iteration. For the measurement of secondary magnetic flux density, a pulse sequence to be used in the MRI system is proposed. Numerical simulations are performed to test the algorithm for both noise-free and noisy cases. The singular value behavior of the matrix is monitored and it is observed that at least two current induction profiles improve the images significantly. It is shown that induced current MR-EIT can be used to reconstruct absolute conductivity images without the need for any additional peripheral voltage measurement.

Resolution and contrast in magnetic resonance electrical impedance tomography (MREIT) and its application to cancer imaging

It has been reported that the electrical impedance of malignancies could be 20-40 times lower than healthy tissues and benign formations. Therefore, in vivo impedance imaging of suspicious lesions may prove to be helpful in improving the sensitivity and specificity of detecting malignant tumors. Several systems have been developed to map the conductivity distribution inside a volume of tissue, however they suffer from poor spatial resolution because the measurements are taken only from surface electrodes. MRI based impedance imaging (MREIT) is a novel method, in which weak electrical currents are injected into the tissue and the resulting perturbations in the magnetic field are measured using MRI. This method has been shown to provide better resolution compared to previous techniques of impedance imaging because the measurements are taken from inside the object on a uniform grid. Thus, it has the potential to be a useful modality that may detect malignancies earlier. Several phantom imaging experiments were performed to investigate the spatial resolution and dynamic range of contrast of this technique. The method was also applied to a live rat bearing a R3230 AC tumor. Tumor location was identified by contrast enhanced imaging.

Image reconstruction of anisotropic conductivity tensor distribution in MREIT: computer simulation study

We describe a novel method of reconstructing images of an anisotropic conductivity tensor distribution inside an electrically conducting subject in magnetic resonance electrical impedance tomography (MREIT). MREIT is a recent medical imaging technique combining electrical impedance tomography (EIT) and magnetic resonance imaging (MRI) to produce conductivity images with improved spatial resolution and accuracy. In MREIT, we inject electrical current into the subject through surface electrodes and measure the z-component Bz of the induced magnetic flux density using an MRI scanner. Here, we assume that z is the direction of the main magnetic field of the MRI scanner. Considering the fact that most biological tissues are known to have anisotropic conductivity values, the primary goal of MREIT should be the imaging of an anisotropic conductivity tensor distribution. However, up to now, all MREIT techniques have assumed an isotropic conductivity distribution in the image reconstruction problem to simplify the underlying mathematical theory. In this paper, we firstly formulate a new image reconstruction method of an anisotropic conductivity tensor distribution. We use the relationship between multiple injection currents and the corresponding induced Bz data. Simulation results show that the algorithm can successfully reconstruct images of anisotropic conductivity tensor distributions. While the results show the feasibility of the method, they also suggest a more careful design of data collection methods and data processing techniques compared with isotropic conductivity imaging.

Static conductivity imaging using variational gradient Bz algorithm in magnetic resonance electrical impedance tomography

A new image reconstruction algorithm is proposed to visualize static conductivity images of a subject in magnetic resonance electrical impedance tomography (MREIT). Injecting electrical current into the subject through surface electrodes, we can measure the induced internal magnetic flux density B = (Bx, By, Bz) using an MRI scanner. In this paper, we assume that only the z-component Bz is measurable due to a practical limitation of the measurement technique in MREIT. Under this circumstance, a constructive MREIT imaging technique called the harmonic Bz algorithm was recently developed to produce high-resolution conductivity images. The algorithm is based on the relation between inverted delta2Bz and the conductivity requiring the computation of inverted delta2Bz. Since twice differentiations of noisy Bz data tend to amplify the noise, the performance of the harmonic Bz algorithm is deteriorated when the signal-to-noise ratio in measured Bz data is not high enough. Therefore, it is highly desirable to develop a new algorithm reducing the number of differentiations. In this work, we propose the variational gradient Bz algorithm where Bz is differentiated only once. Numerical simulations with added random noise confirmed its ability to reconstruct static conductivity images in MREIT. We also found that it outperforms the harmonic Bz algorithm in terms of noise tolerance. From a careful analysis of the performance of the variational gradient Bz algorithm, we suggest several methods to further improve the image quality including a better choice of basis functions, regularization technique and multilevel approach. The proposed variational framework utilizing only Bz will lead to different versions of improved algorithms.