Convection-reaction equation based magnetic resonance electrical properties tomography (cr-MREPT)

Cataloged from PDF version of article.Images of electrical conductivity and permittivity of tissues may be used for diagnostic purposes as well as for estimating local specific absorption rate distributions. Magnetic resonance electrical properties tomography (MREPT) aims at noninvasively obtaining conductivity and permittivity images at radio-frequency frequencies of magnetic resonance imaging systems. MREPT algorithms are based on measuring the B1 field which is perturbed by the electrical properties of the imaged object. In this study, the relation between the electrical properties and the measured B1 field is formulated for the first time as a well-known convection-reaction equation. The suggested novel algorithm, called “cr-MREPT,” is based on the solution of this equation on a triangular mesh, and in contrast to previously proposed algorithms, it is applicable in practice not only for regions where electrical properties are relatively constant but also for regions where they vary. The convective field of the convection-reaction equation depends on the spatial derivatives of the B1 field, and in the regions where its magnitude is low, a spot-like artifact is observed in the reconstructed electrical properties images. For eliminating this artifact, two different methods are developed, namely “constrained cr-MREPT” and “double-excitation cr-MREPT.” Successful reconstructions are obtained using noisy and noise-free simulated data, and experimental data from phantoms

Convection-reaction equation based magnetic resonance electrical properties tomography (cr-MREPT)

Ankara : The Department of Electrical and Electronics Engineering and the Graduate School of Engineering and Science of Bilkent Univ., 2013.Thesis (Master's) -- Bilkent University, 2013.Includes bibliographical references leaves 54-59.Tomographic imaging of electrical conductivity and permittivity of tissues may be used for diagnostic purposes as well as for estimating local specific absorption rate (SAR) distributions. Magnetic Resonance Electrical Properties Tomography (MREPT) aims at noninvasively obtaining conductivity and permittivity images at RF frequencies of MRI systems. MREPT algorithms are based on measuring the B1 field which is perturbed by the electrical properties of the imaged object. In this study, the relation between the electrical properties and the measured B + 1 field is formulated, for the first time as, the well-known convection-reaction equation. The suggested novel algorithm, called “cr-MREPT”, is based on the solution of this equation, and in contrast to previously proposed algorithms, it is applicable in practice not only for regions where electrical properties are relatively constant but also for regions where they vary. The convection-reaction equation is solved using a triangular mesh based finite difference method and also finite element method (FEM). The convective field of the convection-reaction equation depends on the spatial derivatives of the B + 1 field. In the regions where the magnitude of convective field is low, a spot-like artifact is observed in the reconstructed conductivity and dielectric permittivity images. For eliminating this artifact, two different methods are developed, namely “constrained cr-MREPT” and “double-excitation cr-MREPT”. In the constrained cr-MREPT method, in the region where the magnitude of convective field is low, the electrical properties are reconstructed by neglecting the convective term in the equation. The obtained solution is used as a constraint for solving electrical properties in the whole domain. In the double-excitation cr-MREPT method, two B1 excitations, which create two convective field distributions having low magnitude of convective field in different locations, are applied separately. The electrical properties are then reconstructed simultaneously using data from these two applied B + 1 field. These methods are tested with both simulation and experimental data from phantoms. As seen from results, successful electrical property reconstructions are obtained in all regions including electrical property transition region. The performance of cr-MREPT method against noise is also investigated.Hafalır, Fatih SüleymanM.S

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. © 2016 Wiley Periodicals, Inc

Mathematical methods for magnetic resonance based electric properties tomography

Magnetic resonance-based electric properties tomography (MREPT) is a recent quantitative imaging technique that could provide useful additional information to the results of magnetic resonance imaging (MRI) examinations. Precisely, MREPT is a collective name that gathers all the techniques that elaborate the radiofrequency (RF) magnetic field B1 generated and measured by a MRI scanner in order to map the electric properties inside a human body. The range of uses of MREPT in clinical oncology, patient-specific treatment planning and MRI safety motivates the increasing scientific interest in its development. The main advantage of MREPT with respect to other techniques for electric properties imaging is the knowledge of the input field inside the examined body, which guarantees the possibility of achieving high-resolution. On the other hand, MREPT techniques rely on just the incomplete information that MRI scanners can measure of the RF magnetic field, typically limited to the transmit sensitivity B1+. In this thesis, the state of art is described in detail by analysing the whole bibliography of MREPT, started few years ago but already rich of contents. With reference to the advantages and drawbacks of each technique proposed for MREPT, the particular implementation based on the contrast source inversion method is selected as the most promising approach for MRI safety applications and is denoted by the symbol csiEPT. Motivated by this observation, a substantial part of the thesis is devoted to a thoroughly study of csiEPT. Precisely, a generalised framework based on a functional point of view is proposed for its implementation. In this way, it is possible to adapt csiEPT to various physical situations. In particular, an original formulation, specifically developed to take into account the effects of the conductive shield always employed in RF coils, shows how an accurate modelling of the measurement system leads to more precise estimations of the electric properties. In addition, a preliminary study for the uncertainty assessment of csiEPT, an imperative requirement in order to make the method reliable for in vivo applications, is performed. The uncertainty propagation through csiEPT is studied using the Monte Carlo method as prescribed by the Supplement 1 to GUM (Guide to the expression of Uncertainty in Measurement). The robustness of the method when measurements are performed by multi-channel TEM coils for parallel transmission confirms the eligibility of csiEPT for MRI safety applications

EPTlib: An Open-Source Extensible Collection of Electric Properties Tomography Techniques

open1noElectric properties tomography (EPT) is a novel magnetic resonance imaging–based method to estimate non-invasively the distribution of the electric properties in the human body. In this paper, EPTlib, an open-source extensible C++ library collecting ready-to-use algorithms for electric properties tomography, is presented. Currently, EPTlib implements three techniques, named Helmholtz-EPT, convection-reaction-EPT and gradient-EPT, whose derivation and implementation is deeply discussed. Moreover, the configuration files needed by the terminal application included in EPTlib to apply the implemented techniques are outlined. The three techniques are applied to a couple of model problems in order to highlight their main features and the effects of the tunable parameters.openArduino, AlessandroArduino, Alessandr

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. © 2016 International Society for Magnetic Resonance in Medicin

Electrical properties tomography: a methodological review

Electrical properties tomography (EPT) is an imaging method that uses a magnetic resonance (MR) system to non-invasively determine the spatial distribution of the conductivity and permittivity of the imaged object. This manuscript starts by providing clear definitions about the data required for, and acquired in, EPT, followed by comprehensively formulating the physical equations underlying a large number of analytical EPT techniques. This thorough mathematical overview of EPT harmonizes several EPT techniques in a single type of formulation and gives insight into how they act on the data and what their data requirements are. Furthermore, the review describes machine learning-based algorithms. Matlab code of several differential and iterative integral methods is available upon request.Imaging- and therapeutic targets in neoplastic and musculoskeletal inflammatory diseas

Configuration-based electrical properties tomography

Purpose: To introduce phase-based conductivity mapping from a configuration space analysis.Methods: The frequency response function of balanced SSFP (bSSFP) is used to perform a configuration space analysis. It is shown that the transceive phase for conductivity mapping can be directly obtained by a simple fast Fourier transform of a series of phase-cycled bSSFP scans. For validation, transceive phase and off-resonance mapping with fast Fourier transform is compared with phase estimation using a recently proposed method, termed PLANET. Experiments were performed in phantoms and for in vivo brain imaging at 3 T using a quadrature head coil.Results: For fast Fourier transform, aliasing can lead to systematic phase errors. This bias, however, decreases rapidly with increasing sampling points. Interestingly, Monte Carlo simulations revealed a lower uncertainty for the transceive phase and the off-resonance using fast Fourier transform as compared with PLANET. Both methods, however, essentially retrieve the same phase information from a set of phase-cycled bSSFP scans. As a result, configuration-based conductivity mapping was successfully performed using eight phase-cycled bSSFP scans in the phantoms and for brain tissues. Overall, the retrieved values were in good agreement with ex-pectations. Conductivity estimation and mapping of the field inhomogeneities can therefore be performed in conjunction with the estimation of other quantitative pa-rameters, such as relaxation, using configuration theory.Conclusions: Phase-based conductivity mapping can be estimated directly from a simple Fourier analysis, such as in conjunction with relaxometry, using a series of phase-cycled bSSFP scans