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

Electric Current Detection Based on the MR Signal Magnitude Decay

Purpose

Conventional current density imaging method, which relies on the detection of the magnetic field induced by the current in an image phase, is demanding and difficult to perform. In this study, a much simpler signal‐magnitude‐decay (SMD)–based current detection method is proposed.

Methods

Conductive test and biological samples were imaged at various TE times using the gradient‐ or spin‐echo imaging sequences with superimposed constant or bipolar currents, respectively. The SMD curve was sampled for each image voxel, which enabled voxel‐vise current density calculation by fitting an appropriate SMD model curve to the measured SMD curve. Effect of the voxel size on the signal decay and precision of the current density calculation was studied as well.

Results

It was shown theoretically, as well as verified by experiments on test and biological samples, that the current flowing though the sample creates an inhomogeneous magnetic field, which, as a consequence has a faster signal decay. Estimated current density from the measured signal decay increase agreed reasonably well with the actual current density, especially with the larger voxel sizes and longer times to signal acquisition. The sensitivity of the SMD method is up to 1/6 the sensitivity of the current density imaging method.

Conclusion

SMD method of current detection is not limited to any particular sample orientation or geometry, and any pulse sequence capable of acquisition of the current‐induced signal evolution in a voxel can be used for it. This widens the scope of its application from tissues to in vivo studies on animals and humans.

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.

Conductivity Tensor Imaging of the Human Brain Using Water Mapping Techniques

Conductivity tensor imaging (CTI) has been recently proposed to map the conductivity tensor in 3D using magnetic resonance imaging (MRI) at the frequency range of the brain at rest, i.e., low-frequencies. Conventional CTI mapping methods process the trans-receiver phase of the MRI signal using the MR electric properties tomography (MR-EPT) technique, which in turn involves the application of the Laplace operator. This results in CTI maps with a low signal-to-noise ratio (SNR), artifacts at tissue boundaries and a limited spatial resolution. In order to improve on these aspects, a methodology independent from the MR-EPT method is proposed. This relies on the strong assumption for which electrical conductivity is univocally pre-determined by water concentration. In particular, CTI maps are calculated by combining high-frequency conductivity derived from water maps and multi b-value diffusion tensor imaging (DTI) data. Following the implementation of a pipeline to optimize the pre-processing of diffusion data and the fitting routine of a multi-compartment diffusivity model, reconstructed conductivity images were evaluated in terms of the achieved spatial resolution in five healthy subjects scanned at rest. We found that the pre-processing of diffusion data and the optimization of the fitting procedure improve the quality of conductivity maps. We achieve reproducible measurements across healthy participants and, in particular, we report conductivity values across subjects of 0.55 ± 0.01Sm, 0.3 ± 0.01Sm and 2.15 ± 0.02Sm for gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF), respectively. By attaining an actual spatial resolution of the conductivity tensor close to 1 mm in-plane isotropic, partial volume effects are reduced leading to good discrimination of tissues with similar conductivity values, such as GM and WM. The application of the proposed framework may contribute to a better definition of the head tissue compartments in electroencephalograpy/magnetoencephalography (EEG/MEG) source imaging and be used as biomarker for assessing conductivity changes in pathological conditions, such as stroke and brain tumors.

Statistical analysis of the accuracy of water content-based electrical properties tomography

Water content-based electrical properties tomography (wEPT) can retrieve electrical properties (EPs) from water content maps, thereby eliminating the need for B₁ field measurement in the traditional magnetic resonance electrical properties tomography method. The wEPT is performed by conventional MR scanning, such as T₁ -weighted spin-echo imaging, and thus can be directly applied to clinical settings. However, the random noise propagation involved in wEPT causes inaccuracy in EP mapping. To guarantee the EP estimates desired for clinical practice, this study statically investigates the noise-specific uncertainty of wEPT through probability density function models. We calculated the probability distribution of EP maps with different noise levels and examined the effects of scan parameters on reconstruction accuracy with various flip angles (FAs) and repetition time (TR) settings. The theoretical derivation was validated by Monte Carlo simulations and human imaging experiment at 3 T. Results showed that a serious deviation could occur in tissues with large conductivity value at a low signal-to-noise ratio and quantitatively demonstrate that such deviation could be mitigated by increased FAs or TRs. This study provided useful information for the setup of scan parameters, evaluation of accuracy of the wEPT under specific SNR levels, and promote its clinical applications.

Electrical Properties Tomography Based on $B_{{1}}$ Maps in MRI: Principles, Applications, and Challenges

OBJECTIVE

The purpose is to provide a comprehensive review of the electrical properties tomography (EPT) technique, which was introduced to image the electrical properties (EPs) of tissue noninvasively by exploiting the measured field data of MRI.

METHODS

We reviewed the principle of EPT, reconstruction methods, biomedical applications such as tumor imaging, and existing challenges. As a key application of EPT, the estimation of specific absorption rate (SAR) due to MRI was discussed in the background of elevated risk of tissue heating at high field.

RESULTS AND CONCLUSION

Since the originally proposed local, homogeneous Helmholtz equation-based reconstruction algorithm, advanced EPT algorithms have emerged to address the challenges of EPT, including reconstruction error near tissue boundaries, noise sensitivity, inaccurate phase estimation, and elimination of the unmeasurable component, along with demonstrations of in vivo experiments. EPT techniques have been applied to investigate EPs of both healthy and pathological tissues in vivo and factors contributing to various EP value, including sodium, water content, etc. More studies are anticipated to consolidate the current findings. EPT-based subject-specific SAR estimation has led to in vivo demonstration of its feasibility and prediction of temperature increase of phantom during MRI scans merely using measured data.

SIGNIFICANCE

EPT has the advantage of high resolution and practical feasibility in a clinical setup for imaging the biomedically interesting EPs of tissue in the radiofrequency range. EPT-based SAR estimation is another promising topic for predicting tissue heating of individual subjects during a specific MRI scan.

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 sequences with separation of mobile-ion current from immobile-ion current

Three sequences for electric current density imaging (CDI) are studied by testing their ability to selectively detect the electric current of different types of charge carriers. Two of the methods are standard DC-CDI and AC-CDI sequences, and a new AC-DC-CDI sequence is also introduced. The methods rely on the application of square voltage pulses in combination with refocusing RF pulses that can, depending on their position with respect to the voltage pulses, eliminate resistive, capacitive or neither of the current components from the detection pathway. It is demonstrated by experiments on a model system that the DC-CDI sequence detects only the resistive current of mobile ions, the AC-DC-CDI sequence detects only the capacitive current of fixed ions, while the AC-CDI sequence detects both current components. The three sequences introduce a new MRI contrast mechanism that depends on the ion mobility of the sample. As such, the methods may play an important role in the study of electric conductivity phenomena in biological systems.

Review on solving the forward problem in EEG source analysis

Background

The aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes.

Methods

While other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field.

Results

It starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poisson's differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poisson's equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poisson's equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method.

Conclusion

Solving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem.

Investigation on magnetoacoustic signal generation with magnetic induction and its application to electrical conductivity reconstruction

A theoretical study on the magnetoacoustic signal generation with magnetic induction and its applications to electrical conductivity reconstruction is conducted. An object with a concentric cylindrical geometry is located in a static magnetic field and a pulsed magnetic field. Driven by Lorentz force generated by the static magnetic field, the magnetically induced eddy current produces acoustic vibration and the propagated sound wave is received by a transducer around the object to reconstruct the corresponding electrical conductivity distribution of the object. A theory on the magnetoacoustic waveform generation for a circular symmetric model is provided as a forward problem. The explicit formulae and quantitative algorithm for the electrical conductivity reconstruction are then presented as an inverse problem. Computer simulations were conducted to test the proposed theory and assess the performance of the inverse algorithms for a multi-layer cylindrical model. The present simulation results confirm the validity of the proposed theory and suggest the feasibility of reconstructing electrical conductivity distribution based on the proposed theory on the magnetoacoustic signal generation with magnetic induction.

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.

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 x 128 matrix format by applying the harmonic B(z) algorithm to the z-component of the internal magnetic field density data. Since the harmonic B(z) 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.