Magnetic Resonance Electrical Impedance Tomography Research Articles

In vivo mapping of current density distribution in brain tissues during deep brain stimulation (DBS)

New methods for in vivo mapping of brain responses during deep brain stimulation (DBS) are indispensable to secure clinical applications. Assessment of current density distribution, induced by internally injected currents, may provide an alternative method for understanding the therapeutic effects of electrical stimulation. The current flow and pathway are affected by internal conductivity, and can be imaged using magnetic resonance-based conductivity imaging methods. Magnetic resonance electrical impedance tomography (MREIT) is an imaging method that can enable highly resolved mapping of electromagnetic tissue properties such as current density and conductivity of living tissues. In the current study, we experimentally imaged current density distribution of in vivo canine brains by applying MREIT to electrical stimulation. The current density maps of three canine brains were calculated from the measured magnetic flux density data. The absolute current density values of brain tissues, including gray matter, white matter, and cerebrospinal fluid were compared to assess the active regions during DBS. The resulting current density in different tissue types may provide useful information about current pathways and volume activation for adjusting surgical planning and understanding the therapeutic effects of DBS.

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.

Two alternatives for magnetic resonance electrical impedance tomography: injected or induced current

In this paper, the abilities of injected current magnetic resonance electrical impedance tomography (MREIT) and induced current magnetic resonance electrical impedance tomography (ICMREIT) systems to differentiate a conductivity perturbation from an otherwise uniform conductivity distribution are compared. The sensitivity of MREIT measurements changes as a function of distance to the electrodes used for current injection. The sensitivity of ICMREIT measurements is related to the radial location, being a minimum for concentrically located small conductivity perturbations. The very low sensitivity of ICMREIT to conductivity perturbations at central locations seems to be the major drawback of the method compared with MREIT. When the diameter of a concentric and/or an eccentric circular conductivity inhomogeneity inside an otherwise homogeneous circular conductor is close to half of the diameter of the conductor region, the distinguishability of the perturbation by MREIT increases. MREIT is more sensitive to perturbations with lower conductivity with respect to background conductivity (resistive perturbations) than to conductive perturbations. In the case of ICMREIT, concentric inhomogeneities are equally distinguishable for conductive and resistive conductivity perturbations. Eccentric resistive inhomogeneities are more distinguishable then conductive inhomogeneities. Distinguishability increases with the size and number of conductivity perturbations.

Current-induced alternating reversed dual-echo-steady-state for joint estimation of tissue relaxation and electrical properties.

To develop a current-induced, alternating reversed dual-echo-steady-state-based magnetic resonance electrical impedance tomography for joint estimation of tissue relaxation and electrical properties. The proposed method reverses the readout gradient configuration of conventional, in which steady-state-free-precession (SSFP)-ECHO is produced earlier than SSFP-free-induction-decay (FID) while alternating current pulses are applied in between the two SSFPs to secure high sensitivity of SSFP-FID to injection current. Additionally, alternating reversed dual-echo-steady-state signals are modulated by employing variable flip angles over two orthogonal injections of current pulses. Ratiometric signal models are analytically constructed, from which T1 , T2 , and current-induced Bz are jointly estimated by solving a nonlinear inverse problem for conductivity reconstruction. Numerical simulations and experimental studies are performed to investigate the feasibility of the proposed method in estimating relaxation parameters and conductivity. The proposed method, if compared with conventional magnetic resonance electrical impedance tomography, enables rapid data acquisition and simultaneous estimation of T1 , T2 , and current-induced Bz , yielding a comparable level of signal-to-noise ratio in the parameter estimates while retaining a relative conductivity contrast. We successfully demonstrated the feasibility of the proposed method in jointly estimating tissue relaxation parameters as well as conductivity distributions. It can be a promising, rapid imaging strategy for quantitative conductivity estimation. Magn Reson Med 78:107-120, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

A method for MREIT-based source imaging: simulation studies

This paper aims to provide a method for using magnetic resonance electrical impedance tomography (MREIT) to visualize local conductivity changes associated with evoked neuronal activities in the brain. MREIT is an MRI-based technique for conductivity mapping by probing the magnetic flux density induced by an externally injected current through surface electrodes. Since local conductivity changes resulting from evoked neural activities are very small (less than a few %), a major challenge is to acquire exogenous magnetic flux density data exceeding a certain noise level. Noting that the signal-to-noise ratio is proportional to the square root of the number of averages, it is important to reduce the data acquisition time to get more averages within a given total data collection time. The proposed method uses a sub-sampled k-space data set in the phase-encoding direction to significantly reduce the data acquisition time. Since the sub-sampled data violates the Nyquist criteria, we only get a nonlinearly wrapped version of the exogenous magnetic flux density data, which is insufficient for conductivity imaging. Taking advantage of the sparseness of the conductivity change, the proposed method detects local conductivity changes by estimating the time-change of the Laplacian of the nonlinearly wrapped data.

Validating dilute settling suspensions numerical data through MRI, UVP and EIT measurements

The measurement of fluid dynamic quantities are of great interest both for extending the range of validity of current correlations to be used in equipment design and for verification of fundamental hydrodynamic models. Studies where comparisons are made between imaging techniques serve to provide confidence on the validity of each technique for the study of multiphase flow systems. The advantage of cross-validation is that it can help establish the limitations of each technique and the necessary steps towards improvement. A small amount of comparative studies are found in the literature and none of them reports the study of settling particles suspension flow using simultaneously Ultrasonic Velocity Profiling (UVP), Magnetic Resonance Imaging (MRI) and Electrical Impedance Tomography (EIT), at least not to the best of the authors knowledge. In the present paper the authors report efforts made on the characterization of dilute suspensions of glass particles in turbulent flow, with increasing flow velocities and particles concentrations, in a pilot rig at a laboratorial scale, using both MRI, EIT and UVP: direct comparisons of EIT, MRI and UVP measurements acquired and mixture model numerical simulations are presented and the level of agreement explored.

Experimental evaluation of electrical conductivity imaging of anisotropic brain tissues using a combination of diffusion tensor imaging and magnetic resonance electrical impedance tomography

Anisotropy of biological tissues is a low-frequency phenomenon that is associated with the function and structure of cell membranes. Imaging of anisotropic conductivity has potential for the analysis of interactions between electromagnetic fields and biological systems, such as the prediction of current pathways in electrical stimulation therapy. To improve application to the clinical environment, precise approaches are required to understand the exact responses inside the human body subjected to the stimulated currents. In this study, we experimentally evaluate the anisotropic conductivity tensor distribution of canine brain tissues, using a recently developed diffusion tensor-magnetic resonance electrical impedance tomography method. At low frequency, electrical conductivity of the biological tissues can be expressed as a product of the mobility and concentration of ions in the extracellular space. From diffusion tensor images of the brain, we can obtain directional information on diffusive movements of water molecules, which correspond to the mobility of ions. The position dependent scale factor, which provides information on ion concentration, was successfully calculated from the magnetic flux density, to obtain the equivalent conductivity tensor. By combining the information from both techniques, we can finally reconstruct the anisotropic conductivity tensor images of brain tissues. The reconstructed conductivity images better demonstrate the enhanced signal intensity in strongly anisotropic brain regions, compared with those resulting from previous methods using a global scale factor.

Imaging of complex-valued tensors for two-dimensional Maxwell’s equations

Abstract This paper concerns the imaging of a complex-valued anisotropic tensor γ = σ + 𝜾 ⁢ ω ⁢ ε ${\gamma=\sigma+\boldsymbol{\iota}\omega\varepsilon}$ from knowledge of several inter magnetic fields H, where H satisfies the anisotropic Maxwell system on a bounded domain X ⊂ ℝ 2 ${X\subset\mathbb{R}^{2}}$ with prescribed boundary conditions on ∂ ⁡ X ${\partial X}$ . We show that γ can be uniquely reconstructed with a loss of two derivatives from errors in the acquisition H. A minimum number of five well-chosen functionals guaranties a local reconstruction of γ in dimension two. The explicit inversion procedure is presented in several numerical simulations, which demonstrate the influence of the choice of boundary conditions on the stability of the reconstruction. This problem finds applications in the medical imaging modalities Current Density Imaging and Magnetic Resonance Electrical Impedance Tomography.

Electric field distribution in relation to cell membrane electroporation in potato tuber tissue studied by magnetic resonance techniques

Abstract Magnetic resonance electrical impedance tomography (MREIT) enables determination of electric field distribution during electroporation in which cell membrane permeability is increased by application of an external high electric field. In this study, MREIT was performed for the first time to predict electroporated areas in a pulsed electric field (PEF) treated vegetable tissue. The study was performed on potato tubers using different amplitudes of electric pulses and results were evaluated also by means of multiparametric MRI. MREIT determined regions of electric field distribution corresponded to visible darkened areas of the treated potatoes, as well to the results of multiparametric MRI. Results of this study suggest that MREIT could be used as an efficient tool for improving the effectiveness of PEF treatment applications. Industrial relevance This study presents a method capable of determining electric field distribution during PEF treatment using magnetic resonance electrical impedance tomography. The method has a practical value as it can potentially enable monitoring of the outcome of PEF applications which strongly depends on local electric field. Measurement of electric field distribution would enable detection of insufficient electric field coverage before the end of the PEF treatment, thus increasing and assuring its effectiveness.

Enhanced magnetic flux density mapping using coherent steady state equilibrium signal in MREIT

Measuring the z-component of magnetic flux density B = (Bx, By, Bz) induced by transversally injected current, magnetic resonance electrical impedance tomography (MREIT) aims to visualize electrical property (current density and/or conductivity distribution) in a three-dimensional imaging object. For practical implementations of MREIT technique, it is critical to reduce injection of current pulse within safety requirements. With the goal of minimizing the noise level in measured Bz data, we propose a new method to enhance the measure Bz data using steady-state coherent gradient multi-echo (SSC-GME) MR pulse sequence combining with injection current nonlinear encoding (ICNE) method in MREIT, where the ICNE technique injects current during a readout gradient to maximize the signal intensity of phase signal including Bz. The total phase offset in SSC-GME includes additional magnetic flux density due to the injected current, which is different from the phase signal for the conventional spoiled MR pulse sequence. We decompose the magnetization precession phase from the total phase offset including Bz and optimize Bz data using the steady-state equilibrium signal. Results from a real phantom experiment including different kinds of anomalies demonstrated that the proposed method enhanced Bz comparing to a conventional spoiled pulse sequence.

Feasibility of Imaging Tissue Electrical Conductivity by Switching Field Gradients with MRI.

Tissue conductivity is a biophysical marker of tissue structure and physiology. Present methods of measuring tissue conductivity are limited. Electrical impedance tomography and magnetic resonance electrical impedance tomography rely on passing an external current through the object being imaged, which prevents its use in most human imaging. More recently, tissue conductivity has been determined noninvasively from measurements of the radiofrequency (RF) field used in magnetic resonance imaging (MRI). This technique is promising, but conductivity at higher frequencies is less sensitive to tissue structure. Measuring tissue conductivity noninvasively at low frequencies remains elusive. It has been proposed that eddy currents generated during the rise and decay of gradient pulses could act as a current source to map low-frequency conductivity. This work centers on a gradient echo pulse sequence that uses large gradients before excitation to create eddy currents. The electric and magnetic fields during a gradient pulse are simulated by a finite-difference time-domain simulation. The sequence is also tested with a phantom and animal MRI scanner equipped with gradients of high gradient strengths and slew rates. The simulation demonstrates that eddy currents in materials with a conductivity similar to biological tissue decay with a half-life on the order of nanoseconds, and any eddy currents generated before excitation decay completely before influencing the RF signal. Gradient-induced eddy currents can influence phase accumulation after excitation, but the effect is too small to image. The animal scanner images show no measurable phase accumulation. Measuring low-frequency conductivity by gradient-induced eddy currents is presently unfeasible.

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

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. 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. 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. 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. 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 flux density measurement through phase decomposition using non‐interleaved scan in MREIT

Magnetic resonance electrical impedance tomography (MREIT) measures the z-component of magnetic flux density B = (Bx, By, Bz) induced by externally injected current through a pair of electrodes. MREIT visualises in-vivo electrical current density and/or conductivity distribution in a three-dimensional imaging object from the measured magnetic flux density Bz. MREIT techniques typically use the phase difference approach in an interleaved encoding scheme by the injection of positive and negative currents to cancel systematic phase artefacts. Developed is a method to measure Bz data using only a single scan by the injection of one current, avoiding the interleaved encoding scheme. The method separates measured multiple k-space lines into acquired k-space lines with and without injection currents and develops an algorithm to measure the magnetic flux density Bz using acquired k-space lines by the injecting current. Results from phantom experiments demonstrate that the method has potential to measure magnetic flux density using only a single scan by the injection of one current.

Reconstruction of apparent orthotropic conductivity tensor image using magnetic resonance electrical impedance tomography

Magnetic resonance electrical impedance tomography visualizes current density and/or conductivity distributions inside an electrically conductive object. Injecting currents into the imaging object along at least two different directions, induced magnetic flux density data can be measured using a magnetic resonance imaging scanner. Without rotating the object inside the scanner, we can measure only one component of the magnetic flux density denoted as Bz. Since the biological tissues such as skeletal muscle and brain white matter show strong anisotropic properties, the reconstruction of anisotropic conductivity tensor is indispensable for the accurate observations in the biological systems. In this paper, we propose a direct method to reconstruct an axial apparent orthotropic conductivity tensor by using multiple Bz data subject to multiple injection currents. To investigate the anisotropic conductivity properties, we first recover the internal current density from the measured Bz data. From the recovered internal current density and the curl-free condition of the electric field, we derive an over-determined matrix system for determining the internal absolute orthotropic conductivity tensor. The over-determined matrix system is designed to use a combination of two loops around each pixel. Numerical simulations and phantom experimental results demonstrate that the proposed algorithm stably determines the orthotropic conductivity tensor.

The nonlinear variation regularization algorithm for the magnetic resonance electrical impedance tomography

ABSTRACTThe nonlinear variation regularization algorithm (NVRA) is an effective method to enhance the contrast and robustness of the reconstruction in medical imaging. In order to improve the reconstruction quality the variation regularization is introduced to the nonlinear algorithm based on one component of the magnetic flux density by injecting one current. Firstly, we propose a novel algorithm for magnetic resonance electrical impedance tomography (MREIT) using NVRA, and clarify the implementation of this algorithm. Secondly, we analyze the performance of the proposed nonlinear algorithm and the linear sensitivity method with noisy data in the phantom models. Finally, in the case of 0.36 T low field intensity magnetic resonance scanner, we present the method for reducing the electrode model error, and evaluate the performance of two reconstruction algorithms in the agar gel model. The results indicate that the NVRA is able to improve the reconstruction quality with sharp contrast and more robust to noise in comparison to the sensitivity method. In addition, this study shows that with just one current injection and one component of the magnetic flux density we can obtain a high quality imaging, which promotes the MREIT in clinical application. © 2015 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 25, 68–76, 2015

Fast conductivity imaging in magnetic resonance electrical impedance tomography (MREIT) for RF ablation monitoring

Purpose: This study shows the potential of magnetic resonance electrical impedance tomography (MREIT) as a non-invasive RF ablation monitoring technique.Materials and methods: We prepared bovine muscle tissue with a pair of needle electrodes for RF ablation, a temperature sensor, and two pairs of surface electrodes for conductivity image reconstructions. We used the injected current non-linear encoding with multi-echo gradient recalled echo (ICNE-MGRE) pulse sequence in a series of MREIT scans for conductivity imaging. We acquired magnetic flux density data induced by externally injected currents, while suppressing other phase artefacts. We used an 8-channel RF head coil and 8 echoes to improve the signal-to-noise ratio (SNR) in measured magnetic flux density data. Using the measured data, we reconstructed a time series of 180 conductivity images at every 10.24 s during and after RF ablation.Results: Tissue conductivity values in the lesion increased with temperature during RF ablation. After reaching 60 °C, a steep increase in tissue conductivity values occurred with relatively little temperature increase. After RF ablation, tissue conductivity values in the lesion decreased with temperature, but to values different from those before ablation due to permanent structural changes of tissue by RF ablation.Conclusion: We could monitor temperature and also structural changes in tissue during RF ablation by producing spatio-temporal maps of tissue conductivity values using a fast MREIT conductivity imaging method. We expect that the new monitoring method could be used to estimate lesions during RF ablation and improve the efficacy of the treatment.

Frequency-dependent conductivity contrast for tissue characterization using a dual-frequency range conductivity mapping magnetic resonance method.

Electrical conductivities of biological tissues show frequency-dependent behaviors, and these values at different frequencies may provide clinically useful diagnostic information. MR-based tissue property mapping techniques such as magnetic resonance electrical impedance tomography (MREIT) and magnetic resonance electrical property tomography (MREPT) are widely used and provide unique conductivity contrast information over different frequency ranges. Recently, a new method for data acquisition and reconstruction for low- and high-frequency conductivity images from a single MR scan was proposed. In this study, we applied this simultaneous dual-frequency range conductivity mapping MR method to evaluate its utility in a designed phantom and two in vivo animal disease models. Magnetic flux density and B(1)(+) phase map for dual-frequency conductivity images were acquired using a modified spin-echo pulse sequence. Low-frequency conductivity was reconstructed from MREIT data by the projected current density method, while high-frequency conductivity was reconstructed from MREPT data by B(1)(+) mapping. Two different conductivity phantoms comprising varying ion concentrations separated by insulating films with or without holes were used to study the contrast mechanism of the frequency-dependent conductivities related to ion concentration and mobility. Canine brain abscess and ischemia were used as in vivo models to evaluate the capability of the proposed method to identify new electrical properties-based contrast at two different frequencies. The simultaneous dual-frequency range conductivity mapping MR method provides unique contrast information related to the concentration and mobility of ions inside tissues. This method has potential to monitor dynamic changes of the state of disease.

Iterative Reconstruction Methods for Hybrid Inverse Problems in Impedance Tomography

For a general formulation of hybrid inverse problems in impedance tomography the Picard and Newton iterative schemes are adapted and four iterative reconstruction algorithms are developed. The general problem formulation includes several existing hybrid imaging modalities such as current density impedance imaging, magnetic resonance electrical impedance tomography, and ultrasound modulated electrical impedance tomography, and the unified approach to the reconstruction problem encompasses several algorithms suggested in the literature. The four proposed algorithms are implemented numerically in two dimensions and the properties of the algorithms and the implementations are investigated, both theoretically and on simulated data obtained from a numerical phantom. The numerical results show similarities and differences between the proposed algorithms, and they justify that the choice of algorithm should be based on a theoretical analysis of the underlying inverse problem.

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.

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 relaxation time. In due consideration of the ICNE-SPMGE pulse sequence, using a reference information of 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.