Bias correction for phase-based cr-MREPT using low resolution B1+ magnitude.

ObjectiveFull-form Magnetic Resonance Electrical Properties Tomography (MREPT) requires bothB1+magnitude and phase information. SinceB1+phase can be obtained faster and with higher SNR compared toB1+magnitude, several phase-based methods have been developed for conductivity imaging. However, phase-based methods suffer from a concave bias due to the assumption that∇|B1+|is negligible in the ROI.ApproachIn this paper, we re-derive the central equation of phase-based cr-MREPT without assuming that∇|B1+|is negligible and thus propose a correction method directly integrated into the equation system.Main resultsProposed method successfully corrects the concave bias on both simulated and experimental data and significantly increases image quality.SignificanceThe proposed correction method depends on a very low-resolution|B1+|map, and therefore the imaging time does not increase significantly for obtainingB1+magnitude. Moreover, correction can be achieved using simulatedB1+magnitude, hence completely removing the additional imaging requirement.

SNR Weighting for Shear Wave Speed Reconstruction in Tomoelastography.

In tomoelastography, to achieve a final wave speed map by combining reconstructions obtained from all spatial directions and excitation frequencies, the use of weights is inevitable. Here, a new weighting scheme, which maximizes the signal-to-noise ratio (SNR) of the final wave speed map, has been proposed. To maximize the SNR of the final wave speed map, the use of squares of estimated SNR values of reconstructed individual maps has been proposed. Therefore, derivations of the SNR of the reconstructed wave speed maps have become necessary. Considering the noise on the complex MRI signal, the SNR of the reconstructed wave speed map was formulated by an analytical approach assuming a high SNR, and the results were verified using Monte Carlo simulations (MCSs). It has been assumed that the noise remains approximately Gaussian when the image SNR is high enough, despite the nonlinear operations in tomoelastography inversion. Hence, the SNR threshold was determined by comparing the SNR computed by MCSs and analytical approximations. The weighting scheme was evaluated for accuracy, spatial resolution and SNR performances on simulated phantoms. MR elastography (MRE) experiments on two different phantoms were conducted. Wave speed maps were generated for simulated 3D human abdomen MRE data and experimental human abdomen MRE data. The simulation results demonstrated that the SNR-weighted inversion improved the SNR performance of the wave speed map by a factor of two compared to the performance of the original (i.e., amplitude-weighted) reconstruction. In the case of a low SNR, no bias occurred in the wave speed map when SNR weighting was used, whereas 10% bias occurred when the original weighting (i.e., amplitude weighting) was used. Thus, while not altering the accuracy or spatial resolution of the wave speed map with the proposed weighting method, the SNR of the wave speed map has been significantly improved.

New approach for designing cVEP BCI stimuli based on superposition of edge responses.

The purpose of this study is to develop a new methodology for designing stimulus sequences for Brain Computer Interfaces that utilize code modulated Visually Evoked Potentials (cVEP BCIs), based on experimental results regarding the behavior and the properties of the actual EEG responses of the visual system to binary-coded visual stimuli, such that training time is reduced and possible number of targets is increased. EEG from 8 occipital sites is recorded with 2000 sps, in response to visual stimuli presented on a computer monitor with 60 Hz refresh rate. EEG responses of the visual system to black-to-white and white-to-black transitions of a target area on the monitor are recorded for 500 ms, for 160 trials, and signal-averaged to obtain the onset (positive edge) and offset (negative edge) responses, respectively. It is found that both edge responses are delayed by 50 ms and wane completely within 350 ms. These edge responses are then used to generate (predict) the EEG responses to arbitrary binary stimulus sequences using the superposition principle. It is found that the generated and the measured EEG responses to certain (16) simple short sequences (16.67-350 ms) are highly correlated. These 'optimal short patterns' are then randomly combined to design the long (120 bit, 2 sec) 'Superposition Optimized Pulse (SOP)' sequences, and their EEG response templates are obtained by superposition of the edge responses. A SOP sequence-based Visual Speller BCI application yielded higher accuracy (95.9%) and Information Transfer Rate (ITR) (57.2 bpm), compared to when superposition principle is applied to conventional m-sequences and randomly generated sequences. Training for the BCI application involves only the acquisition of the edge responses and takes less than 4 min. This is the first study in which the EEG templates for cVEP BCI sequences are obtained by the superposition of edge responses.

Use of dielectric padding to eliminate low convective field artifact in cr-MREPT conductivity images.

PURPOSE: Convection-reaction equation-based magnetic resonance electrical properties tomography (cr-MREPT) provides conductivity images that are boundary artifact-free and robust against noise. However, these images suffer from the low convective field (LCF) artifact. We propose to use dielectric pads to alter the transmit magnetic field (B1 + ), shift the LCF region, and eliminate the LCF artifact. METHODS: Computer simulations were conducted to analyze the effects of pad electrical properties, pad thickness, pad height, arc angle, and thickness of the pad-object gap. In 3T MR experiments, water pads and BaTiO3 pads were used with agar-saline phantoms. Two data sets (e.g., with the pad located on the left or on the right of the object [phantom]) were acquired, and the corresponding linear systems were simultaneously solved to get LCF artifact-free conductivity images. RESULTS: A pad needed to have 180° arc angle and the same height with the phantom for maximum benefit. Increasing the pad thickness and/or the relative permittivity of the pad increased the LCF shift, whereas excessive amounts of these parameters caused errors in conductivity reconstructions because the effect of neglected Bz terms became noticeable. Conductivity of the pad, on the other hand, had minimal effect on elimination of the LCF artifact. Combining 2 data sets (i.e., with 2 different dielectric pad positions) resulted in more accurate conductivity maps (low L2 -errors) as opposed to no pad or single pad cases in experiments and simulations. CONCLUSIONS: Using the proposed technique, LCF artifact is significantly removed, and the reconstructed conductivity values are improved.

bSSFP phase correction and its use in magnetic resonance electrical properties tomography.

PURPOSE: Balanced steady-state free precession (bSSFP) sequence is widely used because of its high SNR and high speed. However, bSSFP images suffer from "banding artifact" caused by B0 inhomogeneity. In this article, we propose a method to remove this artifact in bSSFP phase images and investigate the usage of the corrected phase images in phase-based magnetic resonance electrical properties tomography (MREPT). THEORY AND METHODS: Two bSSFP phase images, obtained with different excitation frequencies, are collaged to get rid of the regions containing banding artifacts. Phase of the collaged bSSFP image is the sum of the transceive phase of the RF system and an error term that depends on B0 and T2 . By using B0 and T2 maps, this error is eliminated from bSSFP phase images by using pixel-wise corrections. Conductivity maps are obtained from the uncorrected and the corrected phase images using the phase-based cr-MREPT method. RESULTS: Phantom and human experiment results of the proposed method are illustrated for both phase images and conductivity maps. It is shown that uncorrected phase images yield unacceptable conductivity images. When only B0 information is used for phase correction conductivity, reconstructions are substantially improved, and yet T2 information is still needed to fully recover accurate and undistorted conductivity images. CONCLUSIONS: With the proposed technique, B0 sensitivity of the bSSFP phase images can be removed by using B0 and T2 maps. It is also shown that corrected bSSFP phase images are of sufficient quality to be used in conductivity imaging.

[Formula: see text] phase retrieval for non-quadrature radio frequency excitation and its preliminary application in MR-EPT.

Non-quadrature radio frequency (RF) excitation has been widely studied in the fields of RF shimming, local SAR estimation, and MR-EPT with the use of multi-channel transceiver arrays. These studies generally require the retrieval of the complex transmit field ([Formula: see text]), which can be accomplished by acquiring its magnitude and phase in different steps. Magnitude of the transmit field is acquired with the conventional methods which give accurate results for both quadrature and non-quadrature excitations. On the other hand, there is no straightforward method to acquire the absolute phase of the transmit field and generally approximations in MRI experiments are made in order to get it. However, many of these approximations fail in non-quadrature excitation and/or in ultra high fields. In this study, we propose a simple method to acquire the absolute transmit phase in non-quadrature excitation with an eight channel transceiver TEM array for 3 T. The proposed method requires the application of a single additional quadrature drive in order to get the receive phases of the individual channels of the transceiver coil. These receive phases are then subtracted from the transceive phase of the non-quadrature drive experiment to acquire its transmit phase. The developed ideas are tested in the framework of simulations and MRI experiments with the use of four different non-quadrature drive configurations. It has been observed that the simulated and experimentally acquired transmit phase distributions tend to have a strong consensus which supports the validity of the proposed method. Finally, the estimated transmit phase distribution of non-quadrature drive is used in the standard MR-EPT study to get the conductivity reconstructions in order for the validation of its eligibility in MR-EPT studies.

Optimal multichannel transmission for improved cr-MREPT.

Magnetic resonance electrical properties tomography (MR-EPT), aiming at reconstructing the EP's at radio frequencies, uses the H + field (both magnitude and phase) distribution within the object. One of the MR-EPT algorithms, cr-MREPT, accurately reconstructs the internal tissue boundaries, however, it faces an artifact which occurs at the regions where the convective field, [Formula: see text], [Formula: see text], has a low magnitude (at the noise level). This study aims to develop an artifact-free conductivity reconstruction by modifying the H + field inside the region of interest (ROI), using multiple RF transmission techniques in MRI. An eight channel multi-transmit transverse electromagnetic array is used in two different drive configurations. The first drive is the standard volume excitation configuration where all ports are driven with the same magnitude and with 45° phase increment between adjacent channels. In the second drive, the drive voltage magnitude and phases for each of the eight drive ports are modified to generate a desired H + distribution such that the low convective field region moves to another non-overlapping position. Finally, data from both drive experiments are simultaneously used to reconstruct EP's. Computer simulations using cylindrical phantoms and a brain model are conducted and it is shown that the low convective field artifact can be eliminated. It is further shown that it is not necessary to re-calculate the port drive RF voltage magnitude and phases for each patient. The implementation issues of this method are briefly discussed.

Gradient-based electrical conductivity imaging using MR phase.

PURPOSE: To develop a fast, practically applicable, and boundary artifact free electrical conductivity imaging method that does not use transceive phase assumption, and that is more robust against the noise. THEORY: Starting from the Maxwell's equations, a new electrical conductivity imaging method that is based solely on the MR transceive phase has been proposed. Different from the previous phase based electrical properties tomography (EPT) method, a new formulation was derived by including the gradients of the conductivity into the equations. METHODS: The governing partial differential equation, which is in the form of a convection-reaction-diffusion equation, was solved using a three-dimensional finite-difference scheme. To evaluate the performance of the proposed method numerical simulations, phantom and in vivo human experiments have been conducted at 3T. RESULTS: Simulation and experimental results of the proposed method and the conventional phase-based EPT method were illustrated to show the superiority of the proposed method over the conventional method, especially in the transition regions and under noisy data. CONCLUSION: With the contributions of the proposed method to the phase-based EPT approach, a fast and reliable electrical conductivity imaging appears to be feasible, which is promising for clinical diagnoses and local SAR estimation. Magn Reson Med 77:137-150, 2017. © 2016 Wiley Periodicals, Inc.

Feasibility of conductivity imaging using subject eddy currents induced by switching of MRI gradients.

PURPOSE: To investigate the feasibility of low-frequency conductivity imaging based on measuring the magnetic field due to subject eddy currents induced by switching of MRI z-gradients. METHODS: We developed a simulation model for calculating subject eddy currents and the magnetic fields they generate (subject eddy fields). The inverse problem of obtaining conductivity distribution from subject eddy fields was formulated as a convection-reaction partial differential equation. For measuring subject eddy fields, a modified spin-echo pulse sequence was used to determine the contribution of subject eddy fields to MR phase images. RESULTS: In the simulations, successful conductivity reconstructions were obtained by solving the derived convection-reaction equation, suggesting that the proposed reconstruction algorithm performs well under ideal conditions. However, the level of the calculated phase due to the subject eddy field in a representative object indicates that this phase is below the noise level and cannot be measured with an uncertainty sufficiently low for accurate conductivity reconstruction. Furthermore, some artifacts other than random noise were observed in the measured phases, which are discussed in relation to the effects of system imperfections during readout. CONCLUSION: Low-frequency conductivity imaging does not seem feasible using basic pulse sequences such as spin-echo on a clinical MRI scanner. Magn Reson Med 77:1926-1937, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Approximate Fourier domain expression for Bloch-Siegert shift.

PURPOSE: In this study, a new simple Fourier domain-based analytical expression for the Bloch-Siegert (BS) shift-based B1 mapping method is proposed to obtain |B1+| more accurately while using short BS pulse durations and small off-resonance frequencies. THEORY AND METHODS: A new simple analytical expression for the BS shift is derived by simplifying the Bloch equations. In this expression, the phase is calculated in terms of the Fourier transform of the radiofrequency pulse envelope, and thus making the off- and on-resonance effects more easily understandable. To verify the accuracy of the proposed expression, Bloch simulations and MR experiments are performed for the hard, Fermi, and Shinner-Le Roux pulse shapes. RESULTS: Analyses of the BS phase shift-based B1 mapping method in terms of radiofrequency pulse shape, pulse duration, and off-resonance frequency show that |B1+| can be obtained more accurately with the aid of this new expression. CONCLUSIONS: In this study, a new simple frequency domain analytical expression is proposed for the BS shift. Using this expression, |B1+| values can be predicted from the phase data using the frequency spectrum of the radiofrequency pulse. This method works well even for short pulse durations and small offset frequencies.

Magnetic resonance electrical impedance tomography (MREIT) based on the solution of the convection equation using FEM with stabilization.

Most algorithms for magnetic resonance electrical impedance tomography (MREIT) concentrate on reconstructing the internal conductivity distribution of a conductive object from the Laplacian of only one component of the magnetic flux density (∇²B(z)) generated by the internal current distribution. In this study, a new algorithm is proposed to solve this ∇²B(z)-based MREIT problem which is mathematically formulated as the steady-state scalar pure convection equation. Numerical methods developed for the solution of the more general convection-diffusion equation are utilized. It is known that the solution of the pure convection equation is numerically unstable if sharp variations of the field variable (in this case conductivity) exist or if there are inconsistent boundary conditions. Various stabilization techniques, based on introducing artificial diffusion, are developed to handle such cases and in this study the streamline upwind Petrov-Galerkin (SUPG) stabilization method is incorporated into the Galerkin weighted residual finite element method (FEM) to numerically solve the MREIT problem. The proposed algorithm is tested with simulated and also experimental data from phantoms. Successful conductivity reconstructions are obtained by solving the related convection equation using the Galerkin weighted residual FEM when there are no sharp variations in the actual conductivity distribution. However, when there is noise in the magnetic flux density data or when there are sharp variations in conductivity, it is found that SUPG stabilization is beneficial.

Fourier transform magnetic resonance current density imaging (FT-MRCDI) from one component of magnetic flux density.

Fourier transform (FT)-based algorithms for magnetic resonance current density imaging (MRCDI) from one component of magnetic flux density have been developed for 2D and 3D problems. For 2D problems, where current is confined to the xy-plane and z-component of the magnetic flux density is measured also on the xy-plane inside the object, an iterative FT-MRCDI algorithm is developed by which both the current distribution inside the object and the z-component of the magnetic flux density on the xy-plane outside the object are reconstructed. The method is applied to simulated as well as actual data from phantoms. The effect of measurement error on the spatial resolution of the current density reconstruction is also investigated. For 3D objects an iterative FT-based algorithm is developed whereby the projected current is reconstructed on any slice using as data the Laplacian of the z-component of magnetic flux density measured for that slice. In an injected current MRCDI scenario, the current is not divergence free on the boundary of the object. The method developed in this study also handles this situation.