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. @en

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.

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Electrical properties, the conductivity and permittivity of tissue, are quantities that describe the interaction of an object and electromagnetic fields. These properties influence electromagnetic fields and are influenced themselves by physiological phe- nomena such as lesions or a stroke. Therefore, they are important in identifying or diagnosing the severity of pathologies, and they are essential in magnetic resonance imaging (MRI) safety and efficiency by determining tissue heating or sensitivity to excitation pulses and antenna designs. In two-dimensional electromagnetic fields, which occur in specific measurement geometries, it is possible to simplify the relationship between electromagnetic fields and electrical properties, and reconstruct these properties using essentially a forward operation, foregoing a full inversion scheme. These insights also help to find, and ex- plain, the cause of specific artefacts, such as those caused by mismatches in incident field used in the computation of the full electromagnetic fields. The two-dimensional field assumption necessary for the simplified relationship described above is subsequently tested, and it is shown that this assumption does not hold when the object is sufficiently translation variant in the longitudinal direction. That is, even if the fields for a translation invariant object would be two-dimensional, they become three-dimensional through the interaction of the tissue parameters with the fields, which cause out of plane current and field contributions. Another interesting application of closed form expressions between currents and fields is the target field method, which solves the inverse source problem between electric currents and static magnetic fields in a regularised manner by constraining their relationship to a cylindrical geometry. This method is adapted for transverse oriented magnetic fields to be used with Halbach type magnet arrays, and an open source tool is developed to make the method easy to apply for various design con- siderations. Moving away from constraints on the field or current structure, we show the intri- cate relationship between electrical properties and the measured signal in an MRI scanner. This is done by deriving the electro- (and magneto-) motive force for a typ- ical MRI scenario without any assumptions on the object or electro-magnetic fields. This model can then even be used to reconstruct electrical properties from the sim- plest MRI signal, namely the free induced decay (FID) signal. To round off our investigation of tissue properties we take a small detour to the magnetic tissue property, the permeability or magnetic susceptibility. For reconstruct- ing this tissue property a dipole deconvolution is required, where the dipole convolu- tion loses information of the original object through the zeros of the dipole kernel. A new machine learning based approach to reconstruct the lost information is investi- gated in the final chapter of this thesis.@en

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.@en

We describe the application of the target field method for designing three-axes gradients for the transverse magnetic field produced by a Halbach array, as well as verify this method by constructing a set of 3 gradient coils and using it for 3D imaging. Additionally an open-source tool is described which allows for easy gradient design using this method.@en

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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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.@en

CSI-EPT is an Electrical Properties Tomography (EPT) reconstruction method that uses a Contrast Source Inversion (CSI) optimization approach to retrieve the conductivity and permittivity profiles of tissue based on -data. The method can handle variations in tissue profiles and was originally implemented for profile reconstructions in the midplane of a birdcage coil, where the RF field exhibits an E-polarized field structure [1]. Recently, CSI-EPT has been extended to a fully 3-D volumetric reconstruction method that is generally applicable (in- or outside the midplane) and no particular field structure or smoothness is assumed [2]. This is a major step towards turning CSI-EPT into a practical reconstruction method. Unfortunately, the computation times significantly increase (hours or even days, depending on the reconstruction domain of interest) and from this point of view a 2-D approach may be preferable. We show, however, that a 2-D approach is only warranted under very specific circumstances and having an E-polarized field structure is a necessary but not sufficient condition. In particular, we show that to obtain accurate tissue reconstructions based on 3-D -data, it is in general necessary to take all electromagnetic field components into account and a 2-D reconstruction approach will lead to reconstruction artefacts. @en

The derivation of the standard signal model in Magnetic Resonance Imaging (MRI) is based on a quasi-static electromagnetic field approximation and is essentially obtained through an application of the Biot-Savart law [1]. Such an approach works fine for relatively low MR background fields (up till 1.5 T, say), but the model may lose its validity at higher static background fields, since the oscillation frequency of the electromagnetic radio-frequency fields is linearly related to the magnitude of this background field via the well-known Larmor equation [1]. Consequently, an increase in the strength of the static background field leads to an increased Larmor frequency and the quasi-static field approximation may no longer be applicable.@en

In this paper, we present an efficient dedicated electrical properties tomography (EPT) 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 from B ^ + 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 the B ^ + 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 artifacts 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.@en

In this paper, we present an Electrical Properties Tomography (EPT) methodology based on integral (Green's tensor) representations for the electromagnetic field. Inhomogeneous tissue profiles can easily be incorporated in such an approach and the reconstruction method is less sensitive to noise compared with more standard differential based EPT methods since smoothing integral operators act on measured field data. To keep the computational bookkeeping to a minimum, we derive our basic EPT field representations for two-dimensional E-polarized radio frequency fields, which is a valid assumption in the midplane of a loaded birdcage coil. The extension to the fully three-dimensional case is briefly discussed and some initial 3D reconstructions are presented as well. Possible extensions and practical implementation issues are also discussed.@en

In this abstract we present a first-order Electrical Properties Tomography (foEPT) method to retrieve the Electrical Properties (EPs) of tissue and the radio-frequency electric field strength (Ez) within themid-plane of a birdcage coil from measured B1+ data. The EPs and Ez are essential to determine the Specific Absorption Rate (SAR) and are important in many other medical application areas as well(e.g. hyperthermia treatment planning). As opposed to standard EPT methods based on Helmholtz’s equation1, our approach does not assume homogeneous media and first-order instead of second-orderdifferentiation operators act on B1+ as in a Helmholtz-based approach. Our foEPT method can therefore handle inhomogeneous structures and is less sensitive to noise. @en