Motofumi Fushimi¹, Naohiro Eda¹, and Takaaki Nara^1
1The University of Tokyo, Tokyo, Japan

The present paper introduces novel reconstruction methods for electrical properties tomography (EPT), in which conductivity and permittivity are reconstructed from the complex B1 field, and phase-based EPT, in which only conductivity is reconstructed from the B1 phase. The proposed methods reconstruct electrical properties (EPs) by solving a linear integral equation derived from Helmholtz's identity, and does not require calculation of the second-order derivatives of the measured data nor iterative updating of the estimates. Numerical simulations and phantom experiments showed that the proposed method could retrieve EPs more stably than the conventional method that solves a linear partial differential equation.

Anita Karsa¹ and Karin Shmueli^1
1Department of Medical Physics and Biomedical Engineering, University College London, London, United Kingdom

Due to their extreme noise amplification, current Quantitative Conductivity Mapping (QCM) techniques require high SNR images. Simultaneous Quantitative Susceptibility Mapping and QCM uses low-SNR gradient-echo sequences, creating a need for QCM methods appropriate for noisy images. Here we proposed, optimised, and compared several new QCM methods (all shared on https://xip.uclb.com/i/software/MRI_conductivity.html) built on the widely-used phase-based formula and its equivalent, less popular integral form. We found that solving the integral equation provided lower errors and better edge preservation in both simulated and in-vivo images, and that edge preservation combining magnitude-based and image-segmentation-based techniques resulted in the best in-vivo conductivity map.

Anita Karsa¹, Patrick Fuchs¹, and Karin Shmueli^1
1Department of Medical Physics and Biomedical Engineering, University College London, London, United Kingdom

Quantitative conductivity mapping (QCM) techniques use the first spatial derivatives and/or the Laplacian of the B₁ phase. These are commonly estimated by fitting a 3D quadratic function within a kernel around each voxel. However, small kernels lead to severe noise amplification and large kernels induce inaccuracies. Here we determined the optimal kernel radii across a range of magnitude SNR using an anthropomorphic, numerical brain phantom. The optimal kernel size decreased with increasing SNR. Calculating the first derivatives required smaller kernels than calculating the Laplacian making QCM methods using first derivatives likely more accurate than Laplacian-based techniques.

Naohiro Eda¹, Motofumi Fushimi¹, and Takaaki Nara^1
1The University of Tokyo, Tokyo, Japan

This paper proposes a novel, integral-equation-based (IE-based) reconstruction method for magnetic resonance electrical properties tomography (MREPT). The proposed method can reconstruct the electric field and EPs simultaneously based on the Helmholtz decomposition of the electric field. In the proposed algorithm, we iteratively apply the projections onto the spaces in which the true electric field is contained. An advantage of the proposed method is that convergence is theoretically guaranteed in this iterative process. The efficacy of the proposed method is validated through numerical simulations.

Alessandro Arduino¹, Francesca Pennecchi¹, Ulrich Katscher², Luca Zilberti¹, and Maurice Cox^3
1Istituto Nazionale di Ricerca Metrologica (INRIM), Torino, Italy, ²Philips Research Laboratories, Hamburg, Germany, ³National Physical Laboratory (NPL), Teddington, United Kingdom

This work shows the uncertainty evaluation under repeatability conditions of the phase-based Helmholtz-electric properties tomography (EPT) technique. Repeated MRI scans of a homogeneous cylindrical phantom are analyzed with appropriate statistical techniques to evaluate the covariance matrix of the EPT input. This matrix is propagated through the EPT technique according to the law of propagation of uncertainty. The estimated electric conductivity is highly repeatable and exhibits a spatial dispersion, whose average value, within a central region, gives an accurate estimate of the phantom conductivity. The described approach will be applied in future to extend the characterization under reproducibility conditions.

Alessandro Arduino¹, Umberto Zanovello¹, Luca Zilberti¹, and Oriano Bottauscio^1
1Istituto Nazionale di Ricerca Metrologica (INRIM), Torino, Italy

This abstract introduces EPTlib, an open-source, extensible C++ library collecting electric properties tomography (EPT) methods. Currently, the library implements three methods (Helmholtz-EPT, convection reaction–EPT and gradient-EPT), but the list will be updated in the future. EPTlib comes along with a console application that allows to run all the implemented methods. After a brief description of the software architecture and of the EPT methods, an example of usage of each implemented method with simulated input data is provided.

Roy Kurtzbard¹, Anthony Price², Joseph V Hajnal^1,2, Jeffrey W Hand², and Shaihan J Malik^1,2
1Biomedical Engineering Department, School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom, ²Centre for the Developing Brain, School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom

Electromagnetic simulations for RF safety calculation require knowledge of tissue dielectric properties, but these are not well understood for neonates whose tissues have much higher water content than adults. This work retrospectively used MR-EPT on archived raw data obtained from a study on 800+ neonates, to measure tissue conductivity and permittivity at 128MHz. Presented are initial results from 50 subjects. The measured properties are rather noisy at the individual level, but across the whole cohort the median brain conductivity in neonates is approximately 1.8 times greater than in adults, in line with expectations from scaling arguments.

Safa Ozdemir¹, Efe Ilicak¹, Carmen Stutz¹, Mara Berger¹, Jascha Zapp¹, Lothar R. Schad¹, Yusuf Z. Ider², and Frank G. Zöllner^1,3
1Computer Assisted Clinical Medicine, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany, ²Electrical and Electronics Engineering, Bilkent University, Ankara, Turkey, ³Mannheim Institute for Intelligent Systems in Medicine, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany

Magnetic Resonance Electrical Properties Tomography (MREPT) technique utilizes complex B₁⁺ information to obtain conductivity (σ) and permittivity (ϵ). Since obtaining B₁⁺ magnitude is rather time consuming, several phase-based MREPT methods were previously suggested. However, these methods contain inaccuracies especially towards the periphery of the imaged object. In this paper, we utilize one of the fastest B₁⁺ magnitude mapping techniques in order to obtain fast and accurate B₁⁺ magnitude maps to be used in conductivity imaging. Phantom measurements show that accurate 3D B₁⁺ magnitude maps can be acquired in less than 30 seconds, therefore improving the practicality of conductivity imaging.

Alessandro Arduino¹ and Luca Zilberti^1
1Istituto Nazionale di Ricerca Metrologica (INRIM), Torino, Italy

A fast modelling of B1-mapping techniques is proposed for the in silico characterization of electric properties tomography method. The performances of three B1-mapping techniques are analyzed on a realistic model problem, obtaining information on the systematic errors and on the random errors through the application of a Monte Carlo method. An Helmholtz-based electric properties tomography technique is tested on input provided by the B1-mapping techniques.

Santhosh Iyyakkunnel^1,2, Carl Ganter³, Francesco Santini^1,2, and Oliver Bieri^1,2
1Department of Radiology, University Hospital Basel, Basel, Switzerland, ²Department of Biomedical Engineering, University of Basel, Basel, Switzerland, ³Department of Radiology, Technical University of Munich, Munich, Germany

Permittivity mapping strongly depends on the accuracy and the signal-to-noise ratio (SNR) of the underlying B₁⁺ magnitude estimation method. In this work, we assess the suitability of a transient phase SSFP method, termed B1-TRAP, for permittivity mapping and compare this B₁⁺ mapping method with the commonly-used Actual Flip Imaging (AFI) method.

Jose EC Serralles¹, Ilias I Giannakopoulos², Jacob K White¹, Luca Daniel¹, and Riccardo Lattanzi^2,3,4
1Electrical Engineering and Computer Science, Computational Prototyping Group (CPG), Research Laboratory of Electronics (RLE), Department of Electrical Engineering and Computer Science (EECS), Massachusetts Institute of Technology (MIT), Cambridge, MA, United States, ²Center for Advanced Imaging Innovation and Research (CAI2R), Department of Radiology, New York University Grossman School of Medicine, New York, NY, United States, ³The Bernard and Irene Schwartz Center for Biomedical Imaging (CBI), Department of Radiology, New York University Grossman School of Medicine, New York, NY, United States, ⁴Vilcek Institute of Graduate Biomedical Sciences, New York University Grossman School of Medicine, New York, NY, United States

Global Maxwell Tomography (GMT) is a recently introduced technique that estimates tissue electrical properties from magnetic resonance measurements by solving an inverse scattering problem. In this work, we propose a new implementation of GMT that uses a Projected Newton method to minimize the cost function, instead of the quasi-Newton method employed by the original GMT. We demonstrated the new approach with two numerical experiments, using a four--compartment phantom and a realistic head model. Compared to the results obtained with the original GMT, the number of iterations required for convergence was drastically reduced and the estimated EP were more accurate.

Patrick Fuchs¹ and Rob Remis^1
1Microelectronics, Delft University of Technology, Delft, Netherlands

By incorporating scattering of dielectric tissue into the measurement model of the MRI signal we show a direct relationship between conductivity and permittivity of the tissue and the measured signal. Simplifying this for a known geometry a reconstruction of the dielectric properties is demonstrated based on the most simple of MRI signals, the finite induction decay or FID. This relationship can of course be exploited for more complicated applications such as local SAR, antenna design and optimisation and SNR computations, especially for high field applications.

Xiangdong Sun¹, Chunyi Liu², Lijun Lu², Xiaoyun Liu¹, and Wufan Chen^1,2
1School of Automation Engineering,University of Electronic Science and Technology of China, Chengdu, China, ²School of Biomedical Engineering, Southern Medical University, Guangzhou, China

The conductivity of biological tissues can be potentially used for a cancer diagnostic. Thus, imaging conductivity is useful for clinical applications. Here, we developed a conductivity imaging method based on the gradient conductivity imaging method by incorporating information from anatomical MR images. The characteristic of the defined prior was extracting the structure information and guided the conductivity reconstruction. To evaluate the performance of the proposed method, the electromagnetic field and magnitude images were simulated for a cylindrical phantom and brain model. The results demonstrated that the proposed method preserves more details of the conductivity images and mitigates the noise affection.

Saurav Zaman Khan Sajib¹, Munish Chauhan¹, Sulagna Sahu¹, Enock Boakye¹, and Rosalind J Sadleir^1
1School of Biological and Health Systems Engineering, Arizona State University, Tempe, AZ, United States

Diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) and electrodeless conductivity tensor imaging (CTI) are two emerging modalities that can quantify low-frequency tissue anisotropic conductivity properties by considering the relationship between ion mobility and water diffusion. While both methods have potential applications to estimating neuro-modulation fields or formulating forward models used for electrical source imaging, a direct comparison of these two modalities has not yet been performed. Therefore, the aim of this study to test the equivalence of these two modalities.  

Guita Banan¹, Munish Chauhan², Manish Amin¹, Sudhir Ramanna³, Zahra Hosseini⁴, Essa Yacoub³, Michael Schär⁵, Thomas H Mareci¹, and Rosalind J Sadleir^2
1Department of Biochemistry and Molecular Biology, University of Florida, Gainesville, FL, United States, ²School of Biological and Health System Engineering, Arizona State University, Tempe, AZ, United States, ³University of Minnesota, Minneapolis, MN, United States, ⁴MR R&D Collaboration, Siemens Medical Solutions USA, Atlanta, GA, United States, ⁵Department of Radiology, Johns Hopkins University, Baltimore, MD, United States

Incorporating multiband excitation into phase-sensitive imaging introduces distortions in the phase measurements. We used simulations and phantom images to show that a previously unreported phase dispersion problem arises within multiband-slice phase maps. We show that this problem can be understood in terms of the steady-state signal behavior and propose imaging protocols to resolve it. Human scans using these protocols show minimal phase dispersion. We are adopting this protocol for our studies of phase-sensitive magnetic resonance electric impedance tomography (MREIT). 

Cihan Göksu^1,2, Klaus Scheffler^2,3, Fróði Gregersen^1,4,5, Hasan Hüseyin Eroğlu^1,4, Rahel Heule^2,3, Hartwig R. Siebner^1,6,7, Lars G. Hanson^1,4, and Axel Thielscher^1,4
1Danish Research Centre for Magnetic Resonance, Centre for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital, Amager and Hvidovre, Denmark, ²High-Field Magnetic Resonance Center, Max-Planck-Institute for Biological Cybernetics, Tübingen, Germany, ³Department of Biomedical Magnetic Resonance, University of Tübingen, Tübingen, Germany, ⁴Section for Magnetic Resonance, DTU Health Tech, Technical University of Denmark, Kgs Lyngby, Denmark, ⁵Sino-Danish Center for Education and Research, Aarhus, Denmark, ⁶Department of Neurology, Copenhagen University Hospital, Bispebjerg, Denmark, ⁷Institute for Clinical Medicine, Faculty of Medical and Health Sciences, University of Copenhagen, Copenhagen, Denmark

Effective use of transcranial electrical stimulation (TES) in clinical and neuroscience applications requires the exact knowledge of TES currents. MRCDI uses MRI to measure the TES-induced magnetic fields for estimating the underlying current flow distributions. Their accuracy highly depends on the sensitivity and spatial resolution of the MR measurements. Here, we propose an advanced gradient-echo-based MRCDI method utilizing an optimized spoiling, acquisition-weighting, and navigators to achieve a noise sensitivity of 84pT at 2×2×3mm³ resolution for a total scan time of less than five minutes. We test the method's performance by phantom and human in-vivo experiments for two TES injection profiles.

Mehdi Sadighi¹, Mert Şişman¹, and B. Murat Eyüboğlu^1
1Electrical and Electronics Eng., Middle East Technical University (METU), Ankara, Turkey

The clinical applicability of magnetic resonance current density imaging (MRCDI) is highly dependent on the sensitivity of the acquired current-induced magnetic flux density ($$$\widetilde{B}_z$$$) distribution. Here, the combined effect of relevant parameters of the ICNE-SPGE pulse sequence on the SNR level and the total acquisition time of the $$$\widetilde{B}_z$$$ images are analyzed. The optimized sequence parameters are estimated to acquire $$$\widetilde{B}_z$$$ images with the highest possible SNR for a given acquisition time or the desired SNR in the shortest scan time. Besides, alternative sequence parameters are estimated to acquire the same SNR level for a given acquisition time. 

Marco Marino^1,2, Dante Mantini^1,2, and Giulio Ferrazzi^2
1Research Center for Motor Control and Neuroplasticity, KU Leuven, Leuven, Belgium, ²IRCCS San Camillo Hospital, Venice, Italy

We propose a framework to achieve high-resolution whole-brain conductivity tensor imaging (CTI) with MRI at low frequencies. Our methodology overcomes the limitations of previous approaches based on B1 mapping techniques, both in terms of spatial resolution and brain coverage. This was attained by combining high-frequency conductivity estimates derived from a water-mapping technique with multi-b-value diffusion tensor imaging data. We obtained conductivity values for grey matter and white matter that are in line with previous studies. Overall, our findings highlight noteworthy within- and between- subject variability of the conductivity values.