Magnetic Resonance Current Density Imaging (MR-CDI).

Current density imaging (CDI) was developed with the aim of determining the three-dimensional distribution of externally applied electric current pathways inside a conductive medium, using measurements of magnetic flux density [Formula: see text] data. While the B field may be measurable using instruments such as a magnetometer, in magnetic resonance current density imaging (MR-CDI), an MRI scanner is used to measure the magnetic flux density data induced by current flow. In MR-CDI, the object must be rotated inside the MRI machine to find all three components of the B-field, as only the component of B parallel to the magnet main magnetic field can be measured. In principle, once the all three components of the B field have been obtained from an MR imaging experiment, the current density distribution [Formula: see text] can be reconstructed from Ampere's law [Formula: see text]. However, the need to rotate the object within the MRI scanner limits the usability of this technique. To overcome this problem, researchers have investigated the current density reconstruction problem using only one component of the magnetic flux density Bq, where q = x, y, z. In this chapter, we discuss numerical algorithms developed to reconstruct the distribution of J information from the measured B-field.

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.

Influence of Transcranial Electrical Stimulation (TES) waveforms on neural excitability of a realistic axon: a simulation study.

Neuromodulation caused by transcranial electrical stimulation (TES) has been used successfully to treat various neuro-degenerative diseases. Simulation models provide an essential tool to study brain and nerve stimulation. Simulation models of TES provide an opportunity to research personalization of therapy without extensive animal and human testing. A computer model of a realistic sensory axon was built by finding actual geometry of the trigeminal nerve through tractography. A finite element model of the head was solved to obtain electric potential distribution caused by TES. Different waveforms were defined to test transcranial direct current stimulation (tDCS) and transcranial alternating current stimulation (tACS) with varying amplitude and frequency. Neural activity patterns were observed. The strength-duration curve was plotted to verify the model.

Magnetic-resonance-based measurement of electromagnetic fields and conductivity in vivo using single current administration-A machine learning approach.

Diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) is a newly developed technique that combines MR-based measurements of magnetic flux density with diffusion tensor MRI (DT-MRI) data to reconstruct electrical conductivity tensor distributions. DT-MREIT techniques normally require injection of two independent current patterns for unique reconstruction of conductivity characteristics. In this paper, we demonstrate an algorithm that can be used to reconstruct the position dependent scale factor relating conductivity and diffusion tensors, using flux density data measured from only one current injection. We demonstrate how these images can also be used to reconstruct electric field and current density distributions. Reconstructions were performed using a mimetic algorithm and simulations of magnetic flux density from complementary electrode montages, combined with a small-scale machine learning approach. In a biological tissue phantom, we found that the method reduced relative errors between single-current and two-current DT-MREIT results to around 10%. For in vivo human experimental data the error was about 15%. These results suggest that incorporation of machine learning may make it easier to recover electrical conductivity tensors and electric field images during neuromodulation therapy without the need for multiple current administrations.

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.

Conductivity Tensor Imaging of In Vivo Human Brain and Experimental Validation Using Giant Vesicle Suspension.

Human brain mapping of low-frequency electrical conductivity tensors can realize patient-specific volume conductor models for neuroimaging and electrical stimulation. We report experimental validation and in vivo human experiments of a new electrodeless conductivity tensor imaging (CTI) method. From CTI imaging of a giant vesicle suspension using a 9.4-T MRI scanner, the relative error in the reconstructed conductivity tensor image was found to be less than 1.7% compared with the measured value using an impedance analyzer. In vivo human brain imaging experiments of five subjects were followed using a 3-T clinical MRI scanner. With the spatial resolution of 1.87 mm, the white matter conductivity showed considerably more position dependency compared with the gray matter and cerebrospinal fluid (CSF). The anisotropy ratio of the white matter was in the range of 1.96-3.25 with a mean value of 2.43, whereas that of the gray matter was in the range of 1.12-1.19 with a mean value of 1.16. The three diagonal components of the reconstructed conductivity tensors were from 0.08 to 0.27 S/m for the white matter, from 0.20 to 0.30 S/m for the gray matter, and from 1.55 to 1.82 S/m for the CSF. The reconstructed conductivity tensor images exhibited significant inter-subject variabilities in terms of frequency and position dependencies. The high-frequency and low-frequency conductivity values can quantify the total and extracellular water contents, respectively, at every pixel. Their difference can quantify the intracellular water content at every pixel. The CTI method can separately quantify the contributions of ion concentrations and mobility to the conductivity tensor.

Extracellular Total Electrolyte Concentration Imaging for Electrical Brain Stimulation (EBS).

Techniques for electrical brain stimulation (EBS), in which weak electrical stimulation is applied to the brain, have been extensively studied in various therapeutic brain functional applications. The extracellular fluid in the brain is a complex electrolyte that is composed of different types of ions, such as sodium (Na+), potassium (K+), and calcium (Ca+). Abnormal levels of electrolytes can cause a variety of pathological disorders. In this paper, we present a novel technique to visualize the total electrolyte concentration in the extracellular compartment of biological tissues. The electrical conductivity of biological tissues can be expressed as a product of the concentration and the mobility of the ions. Magnetic resonance electrical impedance tomography (MREIT) investigates the electrical properties in a region of interest (ROI) at low frequencies (below 1 kHz) by injecting currents into the brain region. Combining with diffusion tensor MRI (DT-MRI), we analyze the relation between the concentration of ions and the electrical properties extracted from the magnetic flux density measurements using the MREIT technique. By measuring the magnetic flux density induced by EBS, we propose a fast non-iterative technique to visualize the total extracellular electrolyte concentration (EEC), which is a fundamental component of the conductivity. The proposed technique directly recovers the total EEC distribution associated with the water transport mobility tensor.

Electrodeless conductivity tensor imaging (CTI) using MRI: basic theory and animal experiments.

The electrical conductivity is a passive material property primarily determined by concentrations of charge carriers and their mobility. The macroscopic conductivity of a biological tissue at low frequency may exhibit anisotropy related with its structural directionality. When expressed as a tensor and properly quantified, the conductivity tensor can provide diagnostic information of numerous diseases. Imaging conductivity distributions inside the human body requires probing it by externally injecting conduction currents or inducing eddy currents. At low frequency, the Faraday induction is negligible and it has been necessary in most practical cases to inject currents through surface electrodes. Here we report a novel method to reconstruct conductivity tensor images using an MRI scanner without current injection. This electrodeless method of conductivity tensor imaging (CTI) utilizes B1 mapping to recover a high-frequency isotropic conductivity image which is influenced by contents in both extracellular and intracellular spaces. Multi-b diffusion weighted imaging is then utilized to extract the effects of the extracellular space and incorporate its directional structural property. Implementing the novel CTI method in a clinical MRI scanner, we reconstructed in vivo conductivity tensor images of canine brains. Depending on the details of the implementation, it may produce conductivity contrast images for conductivity weighted imaging (CWI). Clinical applications of CTI and CWI may include imaging of tumor, ischemia, inflammation, cirrhosis, and other diseases. CTI can provide patient-specific models for source imaging, transcranial dc stimulation, deep brain stimulation, and electroporation.

Software Toolbox for Low-Frequency Conductivity and Current Density Imaging Using MRI.

OBJECTIVE: Low-frequency conductivity and current density imaging using MRI includes magnetic resonance electrical impedance tomography (MREIT), diffusion tensor MREIT (DT-MREIT), conductivity tensor imaging (CTI), and magnetic resonance current density imaging (MRCDI). MRCDI and MREIT provide current density and isotropic conductivity images, respectively, using current-injection phase MRI techniques. DT-MREIT produces anisotropic conductivity tensor images by incorporating diffusion weighted MRI into MREIT. These current-injection techniques are finding clinical applications in diagnostic imaging and also in transcranial direct current stimulation (tDCS), deep brain stimulation (DBS), and electroporation where treatment currents can function as imaging currents. To avoid adverse effects of nerve and muscle stimulations due to injected currents, conductivity tensor imaging (CTI) utilizes B1 mapping and multi-b diffusion weighted MRI to produce low-frequency anisotropic conductivity tensor images without injecting current. This paper describes numerical implementations of several key mathematical functions for conductivity and current density image reconstructions in MRCDI, MREIT, DT-MREIT, and CTI. METHODS: To facilitate experimental studies of clinical applications, we developed a software toolbox for these low-frequency conductivity and current density imaging methods. This MR-based conductivity imaging (MRCI) toolbox includes 11 toolbox functions which can be used in the MATLAB environment. RESULTS: The MRCI toolbox is available at http://iirc.khu.ac.kr/software.html . Its functions were tested by using several experimental datasets, which are provided together with the toolbox. CONCLUSION: Users of the toolbox can focus on experimental designs and interpretations of reconstructed images instead of developing their own image reconstruction softwares. We expect more toolbox functions to be added from future research outcomes. OBJECTIVE: Low-frequency conductivity and current density imaging using MRI includes magnetic resonance electrical impedance tomography (MREIT), diffusion tensor MREIT (DT-MREIT), conductivity tensor imaging (CTI), and magnetic resonance current density imaging (MRCDI). MRCDI and MREIT provide current density and isotropic conductivity images, respectively, using current-injection phase MRI techniques. DT-MREIT produces anisotropic conductivity tensor images by incorporating diffusion weighted MRI into MREIT. These current-injection techniques are finding clinical applications in diagnostic imaging and also in transcranial direct current stimulation (tDCS), deep brain stimulation (DBS), and electroporation where treatment currents can function as imaging currents. To avoid adverse effects of nerve and muscle stimulations due to injected currents, conductivity tensor imaging (CTI) utilizes B1 mapping and multi-b diffusion weighted MRI to produce low-frequency anisotropic conductivity tensor images without injecting current. This paper describes numerical implementations of several key mathematical functions for conductivity and current density image reconstructions in MRCDI, MREIT, DT-MREIT, and CTI. METHODS: To facilitate experimental studies of clinical applications, we developed a software toolbox for these low-frequency conductivity and current density imaging methods. This MR-based conductivity imaging (MRCI) toolbox includes 11 toolbox functions which can be used in the MATLAB environment. RESULTS: The MRCI toolbox is available at http://iirc.khu.ac.kr/software.html . Its functions were tested by using several experimental datasets, which are provided together with the toolbox. CONCLUSION: Users of the toolbox can focus on experimental designs and interpretations of reconstructed images instead of developing their own image reconstruction softwares. We expect more toolbox functions to be added from future research outcomes.

Anisotropic Conductivity Tensor Imaging of In Vivo Canine Brain Using DT-MREIT.

We present in vivo images of anisotropic electrical conductivity tensor distributions inside canine brains using diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT). The conductivity tensor is represented as a product of an ion mobility tensor and a scale factor of ion concentrations. Incorporating directional mobility information from water diffusion tensors, we developed a stable process to reconstruct anisotropic conductivity tensor images from measured magnetic flux density data using an MRI scanner. Devising a new image reconstruction algorithm, we reconstructed anisotropic conductivity tensor images of two canine brains with a pixel size of 1.25 mm. Though the reconstructed conductivity values matched well in general with those measured by using invasive probing methods, there were some discrepancies as well. The degree of white matter anisotropy was 2 to 4.5, which is smaller than previous findings of 5 to 10. The reconstructed conductivity value of the cerebrospinal fluid was about 1.3 S/m, which is smaller than previous measurements of about 1.8 S/m. Future studies of in vivo imaging experiments with disease models should follow this initial trial to validate clinical significance of DT-MREIT as a new diagnostic imaging modality. Applications in modeling and simulation studies of bioelectromagnetic phenomena including source imaging and electrical stimulation are also promising.

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.

Noise analysis in fast magnetic resonance electrical impedance tomography (MREIT) based on spoiled multi gradient echo (SPMGE) pulse sequence.

Magnetic resonance electrical impedance tomography (MREIT) is a promising non-invasive method to visualize a static cross-sectional conductivity and/or current density image by injecting low frequency currents. MREIT measures one component of the magnetic flux density caused by the injected current using a magnetic resonance (MR) scanner. For practical in vivo implementations of MREIT, especially for soft biological tissues where the MR signal rapidly decays, it is crucial to develop a technique for optimizing the magnetic flux density signal by the injected current while maintaining spatial-resolution and contrast. We design an MREIT pulse sequence by applying a spoiled multi-gradient-echo pulse sequence (SPMGE) to the injected current nonlinear encoding (ICNE), which fully injects the current at the end of the read-out gradient. The applied ICNE-SPMGE pulse sequence maximizes the duration of injected current almost up to a repetition time by measuring multiple magnetic flux density data. We analyze the noise level of measured magnetic flux density with respect to the pulse width of injection current and T*(2) relaxation time. In due consideration of the ICNE-SPMGE pulse sequence, using a reference information of T*(2) values in a local region of interest by a short pre-scan data, we predict the noise level of magnetic flux density to be measured for arbitrary repetition time TR. Results from phantom experiment demonstrate that the proposed method can predict the noise level of magnetic flux density for an appropriate TR = 40 ms using a reference scan for TR = 75 ms. The predicted noise level was compared with the noise level of directly measured magnetic flux density data.

Optimization of magnetic flux density measurement using multiple RF receiver coils and multi-echo in MREIT.

Magnetic Resonance Electrical Impedance Tomography (MREIT) is an MRI method that enables mapping of internal conductivity and/or current density via measurements of magnetic flux density signals. The MREIT measures only the z-component of the induced magnetic flux density B = (Bx, By, Bz) by external current injection. The measured noise of Bz complicates recovery of magnetic flux density maps, resulting in lower quality conductivity and current-density maps. We present a new method for more accurate measurement of the spatial gradient of the magnetic flux density gradient (∇ Bz). The method relies on the use of multiple radio-frequency receiver coils and an interleaved multi-echo pulse sequence that acquires multiple sampling points within each repetition time. The noise level of the measured magnetic flux density Bz depends on the decay rate of the signal magnitude, the injection current duration, and the coil sensitivity map. The proposed method uses three key steps. The first step is to determine a representative magnetic flux density gradient from multiple receiver coils by using a weighted combination and by denoising the measured noisy data. The second step is to optimize the magnetic flux density gradient by using multi-echo magnetic flux densities at each pixel in order to reduce the noise level of ∇ Bz and the third step is to remove a random noise component from the recovered ∇ Bz by solving an elliptic partial differential equation in a region of interest. Numerical simulation experiments using a cylindrical phantom model with included regions of low MRI signal to noise ('defects') verified the proposed method. Experimental results using a real phantom experiment, that included three different kinds of anomalies, demonstrated that the proposed method reduced the noise level of the measured magnetic flux density. The quality of the recovered conductivity maps using denoised ∇ Bz data showed that the proposed method reduced the conductivity noise level up to 3-4 times at each anomaly region in comparison to the conventional method.

Anisotropic conductivity tensor imaging in MREIT using directional diffusion rate of water molecules.

Magnetic resonance electrical impedance tomography (MREIT) is an emerging method to visualize electrical conductivity and/or current density images at low frequencies (below 1 KHz). Injecting currents into an imaging object, one component of the induced magnetic flux density is acquired using an MRI scanner for isotropic conductivity image reconstructions. Diffusion tensor MRI (DT-MRI) measures the intrinsic three-dimensional diffusion property of water molecules within a tissue. It characterizes the anisotropic water transport by the effective diffusion tensor. Combining the DT-MRI and MREIT techniques, we propose a novel direct method for absolute conductivity tensor image reconstructions based on a linear relationship between the water diffusion tensor and the electrical conductivity tensor. We first recover the projected current density, which is the best approximation of the internal current density one can obtain from the measured single component of the induced magnetic flux density. This enables us to estimate a scale factor between the diffusion tensor and the conductivity tensor. Combining these values at all pixels with the acquired diffusion tensor map, we can quantitatively recover the anisotropic conductivity tensor map. From numerical simulations and experimental verifications using a biological tissue phantom, we found that the new method overcomes the limitations of each method and successfully reconstructs both the direction and magnitude of the conductivity tensor for both the anisotropic and isotropic regions.

Reconstruction of dual-frequency conductivity by optimization of phase map in MREIT and MREPT.

BACKGROUND: The spectroscopic conductivity distribution of tissue can help to explain physiological and pathological status. Dual frequency conductivity imaging by combining Magnetic Resonance Electrical Property Tomography (MREPT) and Magnetic Resonance Electrical Impedance Tomography (MREIT) has been recently proposed. MREIT can provide internal conductivity distributions at low frequency (below 1 kHz) induced by an external injecting current. While MREPT can provide conductivity at the Larmor frequency related to the strength of the magnetic field. Despite this potential to describe the membrane properties using spectral information, MREPT and MREIT techniques currently suffer from weak signals and noise amplification as they both reply on differentiation of measured phase data. METHODS: We proposed a method to optimize the measured phase signal by finding weighting factors according to the echo signal for MREPT and MREIT using the ICNE (Injected current nonlinear encoding) multi-echo pulse sequence. Our target weights are chosen to minimize the measured noise. The noise standard deviations were precisely analyzed for the optimally weighted magnetic flux density and the phase term of the positive-rotating magnetic field. To enhance the quality of dual-frequency conductivity images, we applied the denoising method based on the reaction-diffusion equation with the estimated noise standard deviations. A real experiment was performed with a hollow cylindrical object made of thin insulating film with holes to control the apparent conductivity using ion mobility and an agarose gel cylinder wrapped in an insulating film without holes to show different spectroscopic conductivities. RESULTS: The ability to image different conductivity characteristics in MREPT and MREIT from a single MR scan was shown by including the two objects with different spectroscopic conductivities. Using the six echo signals, we computed the optimized weighting factors for each echo. The qualities of conductivity images for MREPT and MREIT were improved by optimization of the phase map. The proposed method effectively reduced the random noise artifacts for both MREIT and MREPT. CONCLUSION: We enhanced the dual conductivity images using the optimally weighted magnetic flux density and the phase term of positive-rotating magnetic field based on the analysis of the noise standard deviations and applying the optimization and denoising methods.

Simultaneous imaging of dual-frequency electrical conductivity using a combination of MREIT and MREPT.

PURPOSE: To propose a single magnetic resonance scan conductivity imaging technique providing dual-frequency characteristics of tissue conductivity. METHODS: Using a modified spin-echo pulse sequence, the magnetic flux density induced by externally injected currents and the B1+ phase map with injected current effects removed were acquired simultaneously. The low-frequency conductivity was reconstructed from the measured magnetic flux density by the projected current density method, while the high-frequency conductivity was reconstructed using the B1+ maps. Three different conductivity phantoms were used to demonstrate low- and high-frequency conductivity characteristics. RESULTS: A conductivity spectrum at two frequencies was successfully acquired with the proposed scheme. Magnetic resonance electrical impedance tomography is advantageous for seeing an anomaly itself wrapped with a thin insulating membrane. In addition, if the membrane is porous, the membrane property can be quantitatively visualized with magnetic resonance electrical impedance tomography. Magnetic resonance electrical properties tomography does not detect such membranes, which enable it to probe things inside an insulating membrane. CONCLUSION: Considering these pros and cons and also the fact that the conductivity of biological tissue changes with frequency, a dual-frequency conductivity imaging incorporating both magnetic resonance electrical impedance tomography and magnetic resonance electrical properties tomography in future animal and human experiments is suggested.

Numerical simulations of MREIT conductivity imaging for brain tumor detection.

Magnetic resonance electrical impedance tomography (MREIT) is a new modality capable of imaging the electrical properties of human body using MRI phase information in conjunction with external current injection. Recent in vivo animal and human MREIT studies have revealed unique conductivity contrasts related to different physiological and pathological conditions of tissues or organs. When performing in vivo brain imaging, small imaging currents must be injected so as not to stimulate peripheral nerves in the skin, while delivery of imaging currents to the brain is relatively small due to the skull's low conductivity. As a result, injected imaging currents may induce small phase signals and the overall low phase SNR in brain tissues. In this study, we present numerical simulation results of the use of head MREIT for brain tumor detection. We used a realistic three-dimensional head model to compute signal levels produced as a consequence of a predicted doubling of conductivity occurring within simulated tumorous brain tissues. We determined the feasibility of measuring these changes in a time acceptable to human subjects by adding realistic noise levels measured from a candidate 3 T system. We also reconstructed conductivity contrast images, showing that such conductivity differences can be both detected and imaged.

Simulations and phantom evaluations of magnetic resonance electrical impedance tomography (MREIT) for breast cancer detection.

MREIT is a new imaging modality that can be used to reconstruct high-resolution conductivity images of the human body. Since conductivity values of cancerous tissues in the breast are significantly higher than those of surrounding normal tissues, breast imaging using MREIT may provide a new noninvasive way of detecting early stage of cancer. In this paper, we present results of experimental and numerical simulation studies of breast MREIT. We built a realistic three-dimensional model of the human breast connected to a simplified model of the chest including the heart and evaluated the ability of MREIT to detect cancerous anomalies in a background material with similar electrical properties to breast tissue. We performed numerical simulations of various scenarios in breast MREIT including assessment of the effects of fat inclusions and effects related to noise levels, such as changing the amplitude of injected currents, effect of added noise and number of averages. Phantom results showed straightforward detection of cancerous anomalies in a background was possible with low currents and few averages. The simulation results showed it should be possible to detect a cancerous anomaly in the breast, while restricting the maximal current density in the heart below published levels for nerve excitation.

Regional absolute conductivity reconstruction using projected current density in MREIT.

Magnetic resonance electrical impedance tomography (MREIT) is a non-invasive technique for imaging the internal conductivity distribution in tissue within an MRI scanner, utilizing the magnetic flux density, which is introduced when a current is injected into the tissue from external electrodes. This magnetic flux alters the MRI signal, so that appropriate reconstruction can provide a map of the additional z-component of the magnetic field (B(z)) as well as the internal current density distribution that created it. To extract the internal electrical properties of the subject, including the conductivity and/or the current density distribution, MREIT techniques use the relationship between the external injection current and the z-component of the magnetic flux density B = (B(x), B(y), B(z)). The tissue studied typically contains defective regions, regions with a low MRI signal and/or low MRI signal-to-noise-ratio, due to the low density of nuclear magnetic resonance spins, short T(2) or T*(2) relaxation times, as well as regions with very low electrical conductivity, through which very little current traverses. These defective regions provide noisy B(z) data, which can severely degrade the overall reconstructed conductivity distribution. Injecting two independent currents through surface electrodes, this paper proposes a new direct method to reconstruct a regional absolute isotropic conductivity distribution in a region of interest (ROI) while avoiding the defective regions. First, the proposed method reconstructs the contrast of conductivity using the transversal J-substitution algorithm, which blocks the propagation of severe accumulated noise from the defective region to the ROI. Second, the proposed method reconstructs the regional projected current density using the relationships between the internal current density, which stems from a current injection on the surface, and the measured B(z) data. Combining the contrast conductivity distribution in the entire imaging slice and the reconstructed regional projected current density, we propose a direct non-iterative algorithm to reconstruct the absolute conductivity in the ROI. The numerical simulations in the presence of various degrees of noise, as well as a phantom MRI imaging experiment showed that the proposed method reconstructs the regional absolute conductivity in a ROI within a subject including the defective regions. In the simulation experiment, the relative L2-mode errors of the reconstructed regional and global conductivities were 0.79 and 0.43, respectively, using a noise level of 50 db in the defective region.

Potential of MREIT conductivity imaging to detect breast cancer: experimental and numerical simulation studies.

The conductivity values of cancerous tissues in the breast are significantly higher than those of surrounding normal tissues. Breast imaging using MREIT (Magnetic Resonance Electrical Impedance Tomography) may provide a new noninvasive way of detecting breast cancer in its early stage. In breast MREIT, the conductivity image quality highly depends on the amount of injected currents assuming a certain signal-to-noise ratio (SNR) of an MRI scanner. The injected current should not produce any significant adverse effect especially on the nerve conduction system of the heart and still distinguish a small cancerous anomaly inside the breast. In this paper, we present results of experimental and numerical simulation studies of breast MREIT. From breast phantom experiments, we evaluated practical amounts of noise in measured magnetic flux density data. We built a realistic three-dimensional model of the human breast connected to a simplified model of the chest including the heart. We performed numerical simulations of various scenarios in breast MREIT including different amplitudes of injected currents and predicted SNRs of MR images related with imaging parameters. Simulation results are promising to show that we may detect a cancerous anomaly in the breast while restricting the maximal current density inside the heart below a level of nerve excitation.