Suk Hoon Oh

Conductivity and current density image reconstruction using harmonic Bz algorithm in magnetic resonance electrical impedance tomography

Magnetic resonance electrical impedance tomography (MREIT) is to provide cross-sectional images of the conductivity distribution sigma of a subject. While injecting current into the subject, we measure one component Bz of the induced magnetic flux density B = (Bx, By, Bz) using an MRI scanner. Based on the relation between (inverted delta)2 Bz and inverted delta sigma, the harmonic Bz algorithm reconstructs an image of sigma using the measured Bz data from multiple imaging slices. After we obtain sigma, we can reconstruct images of current density distributions for any given current injection method. Following the description of the harmonic Bz algorithm, this paper presents reconstructed conductivity and current density images from computer simulations and phantom experiments using four recessed electrodes injecting six different currents of 26 mA. For experimental results, we used a three-dimensional saline phantom with two polyacrylamide objects inside. We used our 0.3 T (tesla) experimental MRI scanner to measure the induced Bz. Using the harmonic Bz algorithm, we could reconstruct conductivity and current density images with 82 x 82 pixels. The pixel size was 0.6 x 0.6 mm2. The relative L2 errors of the reconstructed images were between 13.8 and 21.5% when the signal-to-noise ratio (SNR) of the corresponding MR magnitude images was about 30. The results suggest that in vitro and in vivo experimental studies with animal subjects are feasible. Further studies are requested to reduce the amount of injection current down to less than 1 mA for human subjects.

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

Recently, a new static resistivity image reconstruction algorithm is proposed utilizing internal current density data obtained by magnetic resonance current density imaging technique. This new imaging method is called magnetic resonance electrical impedance tomography (MREIT). The derivation and performance of J-substitution algorithm in MREIT have been reported as a new accurate and high-resolution static impedance imaging technique via computer simulation methods. In this paper, we present experimental procedures, denoising techniques and image reconstructions using a 0.3-tesla (T) experimental MREIT system and saline phantoms. MREIT using J-substitution algorithm effectively utilizes the internal current density information resolving the problem inherent in a conventional EIT, that is, the low sensitivity of boundary measurements to any changes of internal tissue resistivity values. Resistivity images of saline phantoms show an accuracy of 6.8%-47.2% and spatial resolution of 64 /spl times/ 64. Both of them can be significantly improved by using an MRI system with a better signal-to-noise ratio.

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.

Three-dimensional forward solver and its performance analysis for magnetic resonance electrical impedance tomography (MREIT) using recessed electrodes

In magnetic resonance electrical impedance tomography (MREIT), we try to reconstruct a cross-sectional resistivity (or conductivity) image of a subject. When we inject a current through surface electrodes, it generates a magnetic field. Using a magnetic resonance imaging (MRI) scanner, we can obtain the induced magnetic flux density from MR phase images of the subject. We use recessed electrodes to avoid undesirable artefacts near electrodes in measuring magnetic flux densities. An MREIT image reconstruction algorithm produces cross-sectional resistivity images utilizing the measured internal magnetic flux density in addition to boundary voltage data. In order to develop such an image reconstruction algorithm, we need a three-dimensional forward solver. Given injection currents as boundary conditions, the forward solver described in this paper computes voltage and current density distributions using the finite element method (FEM). Then, it calculates the magnetic flux density within the subject using the Biot-Savart law and FEM. The performance of the forward solver is analysed and found to be enough for use in MREIT for resistivity image reconstructions and also experimental designs and validations. The forward solver may find other applications where one needs to compute voltage, current density and magnetic flux density distributions all within a volume conductor.

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.

Magnetic resonance electrical impedance tomography at 3 tesla field strength

Magnetic resonance electrical impedance tomography (MREIT) is a recently developed imaging technique that combines MRI and electrical impedance tomography (EIT). In MREIT, cross‐sectional electrical conductivity images are reconstructed from the internal magnetic field density data produced inside an electrically conducting object when an electrical current is injected into the object. In this work we present the results of electrical conductivity imaging experiments, and performance evaluations of MREIT in terms of noise characteristics and spatial resolution. The MREIT experiment was performed with a 3.0 Tesla MRI system on a phantom with an inhomogeneous conductivity distribution. We reconstructed the conductivity images in a 128 × 128 matrix format by applying the harmonic Bz algorithm to the z‐component of the internal magnetic field density data. Since the harmonic Bz algorithm uses only a single component of the internal magnetic field data, it was not necessary to rotate the object in the MRI scan. The root mean squared (RMS) errors of the reconstructed images were between 11% and 35% when the injection current was 24 mA. Magn Reson Med 51:1292–1296, 2004.

Static resistivity image of a cubic saline phantom in magnetic resonance electrical impedance tomography (MREIT)

In magnetic resonance electrical impedance tomography (MREIT) we inject currents through electrodes placed on the surface of a subject and try to reconstruct cross-sectional resistivity (or conductivity) images using internal magnetic flux density as well as boundary voltage measurements. In this paper we present a static resistivity image of a cubic saline phantom (50 x 50 x 50 mm3) containing a cylindrical sausage object with an average resistivity value of 123.7 ohms cm. Our current MREIT system is based on an experimental 0.3 T MRI scanner and a current injection apparatus. We captured MR phase images of the phantom while injecting currents of 28 mA through two pairs of surface electrodes. We computed current density images from magnetic flux density images that are proportional to the MR phase images. From the current density images and boundary voltage data we reconstructed a cross-sectional resistivity image within a central region of 38.5 x 38.5 mm2 at the middle of the phantom using the J-substitution algorithm. The spatial resolution of the reconstructed image was 64 x 64 and the reconstructed average resistivity of the sausage was 117.7 ohms cm. Even though the error in the reconstructed average resistivity value was small, the relative L2-error of the reconstructed image was 25.5% due to the noise in measured MR phase images. We expect improvements in the accuracy by utilizing an MRI scanner with higher SNR and increasing the size of voxels scarifying the spatial resolution.

High field MREIT: setup and tissue phantom imaging at 11 T

Magnetic resonance electrical impedance tomography (MREIT) has the potential to provide conductivity and current density images with high spatial resolution and accuracy. Recent experimental studies at a field strength of 3 T showed that the spatial resolution of conductivity and current density images may be similar to that of conventional MR images as long as enough current is injected, at least 20 mA when the object being imaged has a size similar to the human head. To apply the MREIT technique to image small conductivity changes using less injection current, we performed MREIT studies at 11 T field strength, where noise levels in measured magnetic flux density data are significantly lower. In this paper we present the experimental results of imaging biological tissues with different conductivity values using MREIT at 11 T. We describe technical difficulties encountered in using high-field MREIT systems and possible solutions. High-field MREIT is suggested as a research tool for obtaining accurate conductivity data from tissue samples and animal subjects.

Electrical conductivity imaging by magnetic resonance electrical impedance tomography (MREIT).

Magnetic resonance electrical impedance tomography (MREIT) is a recently developed imaging technique that combines MRI and electrical impedance tomography (EIT). In MREIT, cross‐sectional electrical conductivity images are reconstructed from the internal magnetic field density data produced inside an electrically conducting subject when an electrical current is injected into the subject. In this work the results of an electrical conductivity imaging experiment are presented, along with some practical considerations regarding MREIT. The MREIT experiment was performed with a 0.3 Tesla MRI system on a phantom made of two compartments with different electrical conductivities. The current density inside the phantom was measured by the MR current density imaging (MRCDI) technique. The measured current density was then used for conductivity image reconstruction by the J‐substitution algorithm. The conductivity phantom images obtained with an injection current of 28mA showed conductivity errors of about 25.5%. Magn Reson Med 50:875–878, 2003.

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/spl middot/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.