In this article, we present full-wave signal models for magnetic and electric field measurements in magnetic resonance imaging (MRI). Our analysis is based on a scattering formalism in which the presence of an object or body is taken into account via an electric scattering source. We show that these signal models can be evaluated, provided that Green's tensors of the background field are known along with the dielectric parameters of the object and the magnetization within the excited part of the object. Furthermore, explicit signal expressions are derived in the case of a small homogeneous ball that is embedded in free space and for which the quasi-static Born approximation can be applied. The conductivity and permittivity of the ball appear as explicit parameters in the resulting signal models and allow us to study the sensitivity of the measured signals with respect to these dielectric parameters. Moreover, for free induction decay signals, we show through simulations that, under certain conditions, it is possible to retrieve the dielectric parameters of the ball from noise-contaminated induction decay signals that are based on electric or magnetic field measurements.

Purpose: To remove the necessity of the tranceive phase assumption for CSI-EPT and show electrical properties maps reconstructed from measured data obtained using a standard 3T birdcage body coil setup. Methods: The existing CSI-EPT algorithm is reformulated to use the transceive phase rather than relying on the transceive phase assumption. Furthermore, the radio frequency (RF)-shield is numerically implemented to accurately model the RF fields inside the MRI scanner. We verify that the reformulated two-dimensional (2D) CSI-EPT algorithm can reconstruct electrical properties maps given 2D electromagnetic simulations. Afterward, the algorithm is tested with three-dimensional (3D) FDTD simulations to investigate if the 2D CSI-EPT can retrieve the electrical properties for 3D RF fields. Finally, an MR experiment at 3T with a phantom is performed. Results: From the results of the 2D simulations, it is seen that CSI-EPT can reconstruct the electrical properties using MRI accessible quantities. For 3D simulations, it is observed that the electrical properties are underestimated, nonetheless, CSI-EPT has a lower standard deviation than the standard Helmholtz based methods. Finally, the first CSI-EPT reconstructions based on measured data are presented showing comparable accuracy and precision to reconstructions based on simulated data, and demonstrating the feasibility of CSI-EPT. Conclusions: The CSI-EPT algorithm was rewritten to use MRI accessible quantities. This allows for CSI-EPT to fully exploit the benefits of the higher static magnetic field strengths with a standard quadrature birdcage coil setup.

In this article, 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. 3-D images have been acquired using the constructed gradient coils with a 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.

The contrast source inversion (CSI) method is a well-known inversion technique that has been utilized in a wide range of application areas. Here we show that in the specific situation of electrical properties tomography (EPT) in magnetic resonance imaging (MRI), which is a so-called hybrid inverse problem, since data is collected inside the reconstruction domain, the CSI method can be simplified to what is essentially a single forward simulation provided the electromagnetic field has an E-polarized field structure. As a consequence, the computational costs are significantly reduced and our experiments show that reconstructions obtained with the simplified CSI method have essentially the same accuracy as reconstructions obtained with the full CSI inversion method.