Synopsis: The switching of magnetic field gradient coils in MRI inevitably induces transient eddy currents in conducting system components such as the cryostat vessel [1]. These eddy currents generate secondary magnetic fields that degrade the spatial and temporal performance of the gradient coil. This theoretical study shows that by incorporating the eddy current effects into the coil optimisation process, it is possible to modify a gradient coil design so that the fields created by the coil and the eddy currents combine together to generate a spatially homogeneous gradient, which follows the desired temporal variation. Shielded and unshielded longitudinal gradient coils are used to exemplify this novel approach.

Synopsis: Magnetic resonance technology employs a wide range of electromagnetic fields for rapid generation of high-resolution anatomical images. These electromagnetic fields are known to interact with living tissue in different ways and mechanisms causing potentially detrimental physiological effects. This study presents numerical investigations into the magnitudes and spatial distributions of induced in situ electric fields and associated current densities in tissue-equivalent, whole-body, male and female models of occupational workers when standing close to the ends of three cylindrical gradient coils. The results have been compared to the most recent IEEE, ICNIRP and EU-Directive 2004/40/EC standards for magnetic and electric field exposure in controlled environments.

With the latest developments in magnetic resonance imaging (MRI) technology, particularly in the areas of high-field superconducting magnets, high-performance ultra-short gradient coils and high radio-frequency (RF) excitation devices; the interaction of electromagnetic fields generated by the new generation of imagers and patients, healthcare workers as well as system components has recently attracted substantial attention. Due to the complexity of the electromagnetic field - tissue and field - metal interactions, computational modelling plays an essential role in the analysis, design and development of modern MRI systems. Recent progress in the development of MRI superconducting magnets has resulted in a considerable increase in human exposure to very large static magnetic fields of up to several Tesla. Body movement through these fields can cause the induction of currents that are potentially above the regulatory limits. In addition to that, novel imaging sequences demand very large magnitudes and high switching rates in magnetic field gradients, which are known to be the prime source of frequently reported peripheral nerve stimulation (PNS) sites in the patients. When highfrequency fields are employed to excite a spin ensemble during MRI imaging, electromagnetic energy is coupled with the tissue and deposited within, which causes regional temperature elevations within the patient, thus leading to possible tissue/cell injury. Overall, electromagnetic field – tissue interaction is a hot topic of research and requires further analysis and consideration. Apart from interacting with the patient, electromagnetic fields produced by the imager also couple to the conducting materials in the MRI system to induce eddy currents that degrade image quality. The eddy current manifestations are a significant concern in MRI and require accurate prediction models, analysis schemes and control methods. Overall this thesis is concerned with computational bioelectromagnetics and associated effects such as concomitant thermal changes. The developed methods are also used in novel design scenarios. In part, this research engages the numerical computational modelling of patient and healthcare worker exposures to strong static and low-frequency pulsed magnetic fields produced by different main superconducting magnets and gradient coils respectively. The main focus herein is on the computation of electric field and current density distributions and levels within tissue-equivalent models of males and females. Various exposure scenarios and setups are considered in the work to evaluate, analyze, compare, comprehend and predict the worst-case field induction in the tissue. This information is particularly useful in terms of compliant activity around and within the clinical MRI imagers. The thesis also details the development and utilization of modified finite-difference time-domain (FDTD) methods in cylindrical space for numerical modelling of lowfrequency transient eddy currents induced within realistic cryostat vessels during both longitudinal and transverse magnetic field gradient switching. In addition, transient eddy currents are numerically evaluated using the method and incorporated into a longitudinal gradient coil design process. In the optimization procedure the gradient coil is modified so that the fields created by the coil and the eddy currents combine together to generate spatially homogeneous gradients that follows the desired temporal variation. In that way the eddy currents are neither prevented nor minimized but rather constructively used in shaping uniform space-time magnetic field gradients. Furthermore, the research presents linear and non-linear heat transfer computational models on the basis of the conventional Penne’s bio-heat transfer equation. The nonlinear model is verified against experimental temperature results from a hyperthermia study on a mouse using a 150 kHz induction coil, while the linear model is used directly in a study on rats under the exposure of high-frequency volume resonators (0.5 - 1 GHz). The thermal models find applications in modelling the deposition of electromagnetic field energy within tissue and computation of associated thermal effects in high-field MRI.

Most magnetic resonance imaging (MRI) spatial encoding techniques employ low-frequency pulsed magnetic field gradients that undesirably induce multiexponentially decaying eddy currents in nearby conducting structures of the MRI system. The eddy currents degrade the switching performance of the gradient system, distort the MRI image, and introduce thermal loads in the cryostat vessel and superconducting MRI components. Heating of superconducting magnets due to induced eddy currents is particularly problematic as it offsets the superconducting operating point, which can cause a system quench. A numerical characterization of transient eddy current effects is vital for their compensation/control and further advancement of the MRI technology as a whole. However, transient eddy current calculations are particularly computationally intensive. In large-scale problems, such as gradient switching in MRI, conventional finite-element method (FEM)-based routines impose very large computational loads during generation/solving of the system equations. Therefore, other computational alternatives need to be explored. This paper outlines a three-dimensional finite-difference time-domain (FDTD) method in cylindrical coordinates for the modeling of low-frequency transient eddy currents in MRI, as an extension to the recently proposed time-harmonic scheme. The weakly coupled Maxwell's equations are adapted to the low-frequency regime by downscaling the speed of light constant, which permits the use of larger FDTD time steps while maintaining the validity of the Courant-Friedrich-Levy stability condition. The principal hypothesis of this work is that the modified FDTD routine can be employed to analyze pulsed-gradient-induced, transient eddy currents in superconducting MRI system models. The hypothesis is supported through a verification of the numerical scheme on a canonical problem and by analyzing undesired temporal eddy current effects such as the B0-shift caused by actively shielded symmetric/asymmetric transverse x-gradient head and unshielded z-gradient whole-body coils operating in proximity to a superconducting MRI magnet

A refined nonlinear heat transfer model of a mouse has been developed to simulate the transient temperature rise in a neoplastic tumour and neighbouring tissue during regional hyperthermia using a 150 kHz inductive coil. In this study, we incorporate various bio-energetic enhancements to the heat transfer equation and numerical validations based on experimental findings for the mouse, in terms of nonlinear metabolic heat production, homeothermy, blood perfusion parameters, thermoregulation, psychological and physiological effects. The discretized bio-heat transfer equation has been validated with the commercial software FEMLAB on a canonical multi-sphere object before applying the scheme to the inhomogeneous mouse voxel phantom. The time-dependent numerical results of regional hyperthermia of mouse thigh have been compared with the available experimental temperature results with only a few small disparities. During the first 20 min of local unfocused heating, the temperature in the tumour and the surrounding tissue increased by around 7.5 °C. The objective of this preliminary study was to develop a validated electrothermal numerical scheme for inductive hyperthermia of a small mammal with the intention of expanding the model into a complete numerical solution involving ferromagnetic nanoparticles for targeted heating of tumours at low frequencies. In addition, the numerical scheme herein could assist in optimizing and tailoring of focused electromagnetic fields for hyperthermia.

This paper presents a parallel-computing FDTD simulator for electromagnetic analysis and design applications in Magnetic Resonance Imaging system. It is intended to be a complete, high-performance FDTD model of an MRI system including all temporal RF and low-frequency field generating units and electrical models of the patient. The developed MRI-dedicated FDTD algorithm is adapted to a parallel computing architecture with the MPI library. Its capabilities are illustrated in two distinct, large-scale field problems. One concerns the interaction of RF-fields with human tissue at high magnitude fields. The other includes the characterization of the temporal eddy currents induced in the cryostat vessel during gradient switching. The presented examples demonstrate the computational efficiency and extended analyses available due to the parallel FDTD framework

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H. Sanchez Lopez, F. Liu, A. Trakic, S. Crozier School of Information Technology and Electrical Engineering, University of Queensland, Brisbane, Queensland, Australia Introduction: This study details the design trade-offs available for asymmetric gradients and particularly investigates both scaling laws and appropriate relaxation factors useful in the design process. Recently a linear function interrelating coil diameter and DSV with the shortest length high performance symmetric gradient coils has been presented [1]. It is well-known that relaxing the magnetic field quality is one of the ways to obtain gradient coils with high figure of merit M=(ηρ1)/L. It is not clear, however, how this relaxation factor is related with DSV size, coil length and radius to produce maximal M. In this work, we have studied the influence of DSV, coil length and radius, relative axial offset position of DSV and target gradient field uniformity over the figure of merit in multi-layer asymmetric transverse gradient coils. A simple linear function that defines the optimal coil length to produce a maximum figure of merit given a DSV size, coil radius, axial offset position and introduced uniformity error is obtained.

Eddy currents induced within a magnetic resonance imaging (MRI) cryostat bore during pulsing of gradient coils can be applied constructively together with the gradient currents that generate them, to obtain good quality gradient uniformities within a specified imaging volume over time. This can be achieved by simultaneously optimizing the spatial distribution and temporal pre-emphasis of the gradient coil current, to account for the spatial and temporal variation of the secondary magnetic fields due to the induced eddy currents. This method allows the tailored design of gradient coil/magnet configurations and consequent engineering trade-offs. To compute the transient eddy currents within a realistic cryostat vessel, a low-frequency finite-difference time-domain (FDTD) method using total-field scattered-field (TFSF) scheme has been performed and validated

H. Sanchez Lopez, F. Liu, A. Trakic, S. Crozier School of Information Technology and Electrical Engineering, University of Queensland, Brisbane, Queensland, Australia Introduction: The work describes design methods for target torque minimization for multi-layer, asymmetric, transverse gradient coils taking in account the magnetic field profiles of long and short bore symmetric and asymmetric magnets. It is well-know that an undesired net torque is produced due to the asymmetric nature of Lorentz force generated by the interaction between the static main magnetic field and an asymmetric head gradient coil. Different strategies to minimize the net torque have been presented [1, for example]. These methods, however, can not control the expected minimum torque/force value and hence its influence over figure of merit M=(ηρ1)/L (η: efficiency [T/m], ρ1: coil radius [m] layer 1, L: inductance [μH]). In some design methods the torque/force analysis is achieved without taking into account the real static magnetic field profile generated by the magnet. In this work, we present two ways to minimize the net torque/force in asymmetric gradient coils. A target torque minimization strategy is introduced which can control the expected M value given target torque/force constraints. For example, we demonstrate that a reduction of up to 80% in net torque decreases the figure of merit by 5% from its maximum value. Simple current patterns for minimum torque, high performance head asymmetric gradient coils are obtained combining the external magnetic field effects over the gradient coil with a specific axial position of the gradient coil’s linear region. Method: The method assumes N layers of the current density J(ρ,φ,z) flowing in concentric cylindrical surfaces of radii ρn. The J(ρ,φ,z) is confined in the interval (0≤z≤Ln). J(ρ,φ,z) in each layer is expressed as a sum of Q orthonormal functions multiplied by the amplitudes λnq. The target toque minimization strategy for asymmetric, multi-layer, transverse gradient coils is stated as quadratic programming under relaxed linear field conditions and linearly constrained torque/force generation [2]. Instead of balancing the constraints through weighting factors, we have introduced a non-uniformity error e in order to control the M-gradient uniformity trade-off. In order to assure practical gradient coil solutions with high M-gradient uniformity-minimum torque trade-off, the torque/force is not constrained to a null value. The torque/force value is constrained between mechanical permissible fixed target values in each elemental area of the current density J(ρn,φ,z). In our approach the torque/force produced in each elemental area J(ρn,φ,z) is calculated taking into account the real magnetic field profile and the mutual magnetic field influence generated by all the axial harmonic modes of J in each elemental area of current density. To achieve our analysis we have taken in account a simple linear relationship that determines the axial coil length as function of DSV, coil diameter and target non-uniformity error to produce maximum M [2]. Results and Discussions: An asymmetric 2-layer transverse gradient coil for whole-body imaging was calculated using the method described in [2]. The coil radii were set to ρ1=34 cm, ρ2=1.3·ρ1, respectively. The DSV and the non-uniformity error e were set to 0.5·ρ1 and 7.5%, respectively. The corresponding optimal coil length to produce maximum M was L1=1 m and L2=1.2 m, respectively [2].The torque/force minimization was not included at this stage. The torque/force was calculated assuming the same coil configuration placed in three different 1.5 T magnet bores [3] while matching the magnet’s DSV with the gradient coil’s DSV: long [F=7.3⋅10 N,T=6.3⋅10 Nm], short [F=8.5⋅10 N,T=7.3⋅10 Nm] and asymmetric [F=2.7⋅10 N,T=2.5⋅10 Nm]. For a perfectly homogeneous magnetic field: F=0 N, T=4.3⋅10 Nm. Note that a large error is introduced in the torque calculation when the main magnetic field is assumed to be perfectly homogenous. Actually the most common asymmetric gradient coils are designed for head imaging in long and short symmetric magnet bores where a relatively small yet undesirable torque persists. For a 2-layer asymmetric transverse gradient coil obtained in [2], the M value is 2.92⋅10 TmHA and the resulting torque was calculated assuming a 1.5 T short bore magnet [F=37.27 N, T=37.09 Nm]. In order to study the torque effect over the figure of merit M we have constrained the absolute torque from different values in the range between 0 to 37.09 Nm. Applying our target torque minimization technique we find that if the torque is reduced up to 80% (see Fig 1a), the M value decreases only 5%, however for torque reduction larger than 81% the winding complexity increases incrementing the coil inductance and hence small M values are obtained. Varying the axial offset position of the gradient coil’s DSV (z0) we note that there is an axial z0 value where the gradient coil is balanced producing zero net torque. Fig. (1b). This equilibrium condition is unique for a given external magnetic field profile.

This paper presents a parallel-computing FDTD simulator for electromagnetic analysis and design applications in Magnetic Resonance Imaging system. It is intended to be a complete, high-performance FDTD model of an MRI system including all temporal RF and low-frequency field generating units and electrical models of the patient. The developed MRI-dedicated FDTD algorithm is adapted to a parallel computing architecture with the MPI library. Its capabilities are illustrated in two distinct, large-scale field problems. One concerns the interaction of RF-fields with human tissue at high magnitude fields. The other includes the characterization of the temporal eddy currents induced in the cryostat vessel during gradient switching. The presented examples demonstrate the computational efficiency and extended analyses available due to the parallel FDTD framework. MPI library herein, field problems in MRI that require considerable memory resources can be solved much faster than using a single processor approach. Subsequently, in this work we implement MRI-dedicated cylindrical and Cartesian parallel FDTD schemes, which can be applied to different system geometries under a wide range of frequencies. The cylindrical FDTD method is demonstrated for the analysis of a low frequency (LF) problem, i.e., transient eddy currents in the cryostat induced during switching of a transverse gradient coil. The Cartesian FDTD method is parallelized for the comparative study of the interactions of RF-fields with male/female human models. The problems are treated with high spatial resolution, which is beyond the capability of the conventional non-parallelized FDTD algorithms. The simulation results indicate the enhanced performance of the developed FDTD simulator.

Results and Discussion: We demonstrate the use of the proposed parallel FDTD scheme in the analysis of low frequency transient eddy currents in nearby conducting structures when pulsing magnetic field gradients. We assess the Specific Absorption Rate (SAR) during the interaction of RF fields with inhomogeneous human tissues (both female and male models) within a linearly polarized birdcage resonator model at 340 MHz. Fig. 3 shows a comparison of normalized SAR between the female (NAOMI) and male (NORMAN) voxel phantom in a birdcage resonator. Fig. 4 illustrates spatial normalized axial magnetic and azimuthal electric fields in the symmetric gradient coil system and radiation shields for a single gradient pulse of 10 T/m/s. The devised parallel routine on the cluster of processors was approximately 10 times faster than when a single processor was used. Conclusion: An optimised and robust parallel FDTD scheme, which can be easily implemented using the MPI library, has been presented for MRI applications. Computational benefits of the proposed parallel FDTD structure has been demonstrated on two typical low and high frequency field problems. It has been shown that parallel computing can increase the computational efficiency and power. This is of considerable advantage to the advancement of MRI technology. Fig. 3 – Normalized SAR profiles inside a female model (NAOMI, left) and comparisons of SAR between female and male model (NORMAN, right). Fig.4 – System set-up and normalized fields (left: axial magnetic field; right: azimuthal electric field in the middle layer of each radiation shield).

A new passive shim design method is presented which is based on a magnetization mapping approach. Well defined regions with similar magnetization values define the optimal number of passive shims, their shape and position. The new design method is applied in a shimming process without prior-axial shim localization; this reduces the possibility of introducing new errors. The new shim design methodology reduces the number of iterations and the quantity of material required to shim a magnet. Only a few iterations (1-5) are required to shim a whole body horizontal bore magnet with a manufacturing error tolerance larger than 0.1 mm and smaller than 0.5 mm. One numerical example is presented

A. Trakic, H. Wang, F. Liu, H. S. Lopez, S. Crozier School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane, QLD, Australia Synopsis: Most Magnetic Resonance Imaging (MRI) spatial encoding techniques employ low-frequency pulsed magnetic field gradients that undesirably induce multi-exponentially decaying eddy currents in nearby conducting structures of the MRI scanner. This is particularly problematic in superconducting system components. The eddy currents degrade the switching performance of the gradient system, distort the MRI image and introduce thermal loads in the cryostat. A recently proposed three-dimensional (3D), low-frequency Finite-Difference Time-Domain (FDTD) method in cylindrical coordinates (Trakic et al., Cylindrical 3D FDTD algorithm for the computation of low frequency transient eddy currents in MRI, ISMRM 2006, submitted) is employed to analyse temporal eddy currents and manifest effects (e.g. B0-shift) induced by pulsed actively shielded symmetric/asymmetric transverse x-gradient head and whole body z-coils.