In this paper, we present an efficient dedicated electrical properties tomography algorithm (called first-order current density EPT) that exploits the particular radio frequency field structure, which is present in the midplane of a birdcage coil, to reconstruct conductivity and permittivity maps in this plane fromB + 1 data. The algorithm consists of a current density and an electrical properties step. In the current density reconstruction step, the induced currents in the midplane are determined by acting with a specific first-order differentiation operator on theB + 1 data. In the electrical properties step, we first determine the electric field strength by solving a particular integral equation, and subsequently determine conductivity and permittivity maps from the constitutive relations. The performance of the algorithm is illustrated by presenting reconstructions of a human brain model based on simulated (noise corrupted) data and of a known phantom model based on experimental data. The method manages to reconstruct conductivity profiles without model related boundary artefacts and is also more robust to noise because only first-order differencing of the data is required as opposed to second-order data differencing in Helmholtz-based approaches. Moreover, reconstructions can be performed in less than a second, allowing for essentially real-time electrical properties mapping.

In this paper we design and construct gradient coils for a Halbach permanent magnet array magnetic resonance (MR) scanner. The target field method, which is widely applied for the case of axial static magnetic fields, has been developed for a transverse static magnetic field as produced by a Halbach permanent magnet array. Using this method, current densities for three gradient directions are obtained and subsequently verified using a commercial magneto-static solver. Stream functions are used to turn the surface current densities into wire patterns for constructing the gradient coils. The measured fields are in good agreement with simulations and their prescribed target fields. Three dimensional images have been acquired using the constructed gradient coils with very low degree of geometric distortion.

The main objective of electrical-property tomography (EPT) is to retrieve dielectric tissue parameters from B ^ 1 + data as measured by a magnetic-resonance (MR) scanner. This is a so-called hybrid inverse problem in which data are defined inside the reconstruction domain of interest. In this paper, we discuss recent and new developments in EPT based on the contrast-source inversion (CSI) method. After a short review of the basics of this method, two- and three-dimensional implementations of CSI–EPT are presented along with a very efficient variant of 2D CSI–EPT called first-order induced current EPT (foIC-EPT). Practical implementation issues that arise when applying the method to measured data are addressed as well, and the limitations of a two-dimensional approach are extensively discussed. Tissue-parameter reconstructions of an anatomically correct male head model illustrate the performance of two- and three-dimensional CSI–EPT. We show that 2D implementation only produces reliable reconstructions under very special circumstances, while accurate reconstructions can be obtained with 3D CSI–EPT.

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Magnetic resonance imaging (MRI) based electrical properties tomography (EPT) is the quantification of the conductivity and permittivity of different tissues. These electrical properties can be obtained through different reconstruction methods and can be used as a contrast mechanism. The work presented here continues from the two-dimensional CSI-EPT algorithm which was shown to work with two-dimensional Matlab based simulations. The existing CSI-EPT algorithm is reformulated to use the transceive phase rather than relying on the transceive phase assumption. This is achieved by implementing a forward problem, computing the receive phase, into the inverse minimization problem, i.e. retrieving the electrical properties. Furthermore, the radio frequency (RF) shield is numerically implemented to model the RF fields inside the MRI more accurately. Afterwards, the algorithm is tested with three-dimensional FDTD simulations to investigate if the two-dimensional CSI-EPT can retrieve the electrical properties for three-dimensional RF fields. Finally, an MR experiment with a phantom is performed to show the potential for this method. From the results of the two-dimensional Matlab simulations it is seen that CSI-EPT can reconstruct the electrical properties using MRI accessible quantities. In the three-dimensional simulations it is observed that the electrical properties are underestimated, nonetheless, CSI-EPT is more precise than the standard Helmholtz based methods. Finally, the first CSI-EPT results using measured data are shown. The results for the reconstruction using measured data were of the same quality as the results from the FDTD simulation.