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Numerical field calculations considering the human subject for engineering and safety assurance in MRI
Abstract
Numerical calculations of static, switched, and radiofrequency (RF) electromagnetic (EM) fields considering the geometry and EM properties of the human body are used increasingly in MRI to explain observed phenomena, explore the limitations of various approaches, engineer improved techniques and technology, and assure safety. As the static field strengths and RF field frequencies in MRI have increased in recent years, the value of these methods has become more pronounced and their use has become more widespread. With the recent growth in parallel reception techniques and the advent of transmit RF arrays, the utility of these calculations will become only more critical to continued progress of MRI. Proper relation of field calculation results to the MRI experiment can require significant understanding of MRI physics, EM field principles, MRI coil hardware, and EM field safety. Here some fundamental principles are reviewed and current approaches and applications are catalogued to aid the reader in finding resources valuable in beginning field calculations for their own applications in MR, with an eye to the current needs and future utility of numerical field calculations in MRI.
... Meanwhile, coil optimization has remained a largely empirical process, in which prospective new designs are tested against highly variable benchmark designs, with no common standard or guarantee of theoretical optimality. The advent of accurate electrodynamic simulation tools (3,4) has greatly facilitated the testing of design hypotheses; however, the complexity of Maxwell's equations generally prevents all but the most seasoned experts from gaining clear intuition about what might constitute a truly task-optimal, as opposed to a merely "good," coil performance. ...
... 3. Multiply the resulting volumetric electric field by the conductivity distribution, yielding a conduction current density in the body. 4. Compute (with a solver of interest) the conjugate of the electric field resulting from the distribution of conduction currents in the body. ...
Purpose: Despite decades of collective experience, radiofrequency coil optimization for MR has remained a largely empirical process, with clear insight into what might constitute truly task-optimal, as opposed to merely 'good,' coil performance being difficult to come by. Here, a new principle, the Optimality Principle, is introduced, which allows one to predict, rapidly and intuitively, the form of optimal current patterns on any surface surrounding any arbitrary body. Theory: The Optimality Principle, in its simplest form, states that the surface current pattern associated with optimal transmit field or receive sensitivity at a point of interest (per unit current integrated over the surface) is a precise scaled replica of the tangential electric field pattern that would be generated on the surface by a precessing spin placed at that point. A more general perturbative formulation enables efficient calculation of the pattern modifications required to optimize signal-to-noise ratio in body-noise-dominated situations. Methods and Results: The unperturbed principle is validated numerically, and convergence of the perturbative formulation is explored in simple geometries. Current patterns and corresponding field patterns in a variety of concrete cases are then used to separate signal and noise effects in coil optimization, to understand the emergence of electric dipoles as strong performers at high frequency, and to highlight the importance of surface geometry in coil design. Conclusion: Like the Principle of Reciprocity from which it is derived, the Optimality Principle offers both a conceptual and a computational shortcut. In addition to providing quantitative targets for coil design, the Optimality Principle affords direct physical insight into the fundamental determinants of coil performance.
... Previous reviews have discussed the EM modeling of human body exposure to electromagnetic fields (EMF) 21 and applications in MRI. [22][23][24] The main goal of this study is to provide medical physicists a review of the application of EM modeling in MRI, with the focus being hardware development, installation, operation, and safety assurance. ...
... The small differences in susceptibility between different tissues or between tissue and air can cause perturbations of the B 0 field (on the order of ppm), which may lead to strong artifacts in certain types of MR images. 23 Electric fields induced by fast-switching gradient fields can cause nerve stimulation which is carefully restricted to just noticeable stimulation. The RF field interacts strongly with biological tissues and results in shortened B 1 wavelength and induced eddy currents, causing potentially severe image inhomogeneity and tissue heating. ...
Electromagnetic (EM) computational modeling is used extensively during the development of a Magnetic Resonance Imaging (MRI) scanner, its installation, and use. MRI, which relies on interactions between nuclear magnetic moments and the applied magnetic fields, uses a range of EM tools to optimize all of the magnetic fields required to produce the image. The main field magnet is designed to exacting specifications but challenges in manufacturing, installation, and use require additional tools to maintain target operational performance. The gradient magnetic fields, which provide the primary signal localization mechanism, are designed under another set of complex design trade-offs which include conflicting imaging performance specifications and patient physiology. Gradients are largely impervious to external influences, but are also used to enhance main field operational performance. The radiofrequency (RF) magnetic fields, which are used to elicit the signals fundamental to the MR image, are a challenge to optimize for a host of reasons that include patient safety, image quality, cost optimization, and secondary signal localization capabilities. This review outlines these issues and the EM modeling used to optimize MRI system performance. This article is protected by copyright. All rights reserved.
... In fact, at UHF, the energy deposition due to the radiofrequency (RF) field increases and its distribution inside the subject becomes extremely inhomogeneous. [1][2][3][4] The increase of RF energy deposition and of its spatial variability at UHF is due to the higher operating frequency of the UHF MR system. MR systems provide an estimation of the global SAR in the subject under test during the exam. ...
... This practice introduces a mismatch between real and simulated data, which can be compensated by simulating and comparing different human models. 2,11 The purpose of this work is to predict local and global subject SAR exposure in two 7.0 Tesla (T) imaging sequences in both adults and children by combining electromagnetic simulations on two generic anatomic human head models (one adult and one child) with subject-specific B 1 1 maps measured in vivo. ...
Purpose:
To predict local and global specific absorption rate (SAR) in individual subjects.
Materials and methods:
SAR was simulated for a head volume coil for two imaging sequences: axial T1-weighted "zero" time-of-echo (ZTE) sequence, sagittal T2-weighted fluid attenuated inversion recovery (FLAIR). Two head models (one adult, one child) were simulated inside the coil. For 19 adults and 27 children, measured B1 (+) maps were acquired, and global (head) SAR estimated by the system was recorded. We performed t-test between the B1 (+) in models and human subjects. The B1 (+) maps of individual subjects were used to scale the SAR simulated on the models, to predict local and global (head) SAR. A phantom experiment was performed to validate SAR prediction, using a fiberoptic temperature probe to measure the temperature rise due to ZTE scanning.
Results:
The normalized B1 (+) standard deviation in subjects was not significantly different from that of the models (P > 0.68 and P > 0.54). The rise in temperature generated in the phantom by ZTE was 0.3°C; from the heat equation it followed that the temperature-based measured SAR was 2.74 W/kg, while the predicted value was 3.1 W/kg.
Conclusion:
For ZTE and FLAIR, limits on maximum local and global SAR were met in all subjects, both adults and children. To enhance safety in adults and children with 7.0 Tesla MR systems, we suggest the possibility of using SAR prediction. J. Magn. Reson. Imaging 2016.
... Though the SNR profile can be rectified using proper filtering techniques, there is no known way to recover the correct contrast [4]. Numerical simulation of pTx coil arrays is a valuable tool to estimate the propagation of electromagnetic waves through tissue and to verify that SAR requirements are being met [14]. ...
... Simple geometrical shapes, despite allowing for analytical results, have limited application as anatomical models. SAR levels vary depending on the individual anatomy of the patient, and using numerical simulations is the more practical route towards testing the broad range of anatomical variation between subjects required to ensure safety [14]. The precessing spins create a dynamic magnetic flux in the transverse plane that can be detected as an electromotive force (EMF) by one or more conductive loops, called receive coils, according to Faraday's Law. ...
Parallel transmission (pTx) is a promising improvement to coil design that has been demonstrated to mitigate B1* inhomogeneity, manifest as center brightening, for high-field magnetic resonance imaging (MRI). Parallel transmission achieves spatially-tailored pulses through multiple radiofrequency (RF) excitation coils that can be activated independently. In this work, simulations of magnetic fields in numerical phantoms using an FDTD solver are used to estimate the excitation profiles for an 8-channel RF head coil. Each channel is driven individually in the presence of a dielectric load, and the excitation profiles for all channels are combined post-processing into a B1+ profile of the birdcage (BC) mode. The B1 profile is calculated for a dielectric sphere phantom with material properties of white matter at main magnetic field strengths of 3T and 7T to demonstrate center brightening associated with head imaging at high magnetic field strengths. Measurements of a circular ROI centered in the image show more B1+ inhomogeneity at 7T than at 3T. The B1* profile is then simulated for a numerical head phantom with spatially segmented tissue compartments at 7T. Comparison of the simulated and in vivo B1* profiles at 7T shows agreement in the B1 inhomogeneity. The results provide confidence in numerical simulation as a means to estimate magnetic fields for human imaging. This work will allow further numerical simulations to model the propagation of electric fields within the body, ultimately to provide an estimate of heat deposition in tissue, quantified by the specific absorption rate (SAR), which is a limiting factor of the use of high-field MRI in the clinical setting.
... Recent years have seen a dramatic increase in the use of numerical calculations considering heterogeneous human anatomies to predict SAR distributions during MRI (2). With the emergence of transmit array technologies, where it is possible to have a very wide range of maximum local SAR for a given patient, array configuration, and average SAR (3), it seems likely that methods to rapidly and accurately predict SAR distributions will become more critical (4,5). ...
... In the proton resonance frequency method, phase maps are acquired before and after a period of sample heating. The temperature change (ΔT) can then be calculated from the phase change (Δφ) as [2] where α is the temperature-dependent chemical shift co-efficient (−0.01 ppm/K for water), γ is the gyromagnetic ratio of hydrogen, B 0 is the strength of the main magnetic field (3 T in our case), and TE is the echo time. The phantom was once again inserted into the birdcage coil and placed inside of the bore overnight to achieve thermal equilibrium before beginning the experiment. ...
It is important to accurately characterize the heating of tissues due to the radiofrequency energy applied during MRI. This has led to an increase in the use of numerical methods to predict specific energy absorption rate distributions for safety assurance in MRI. To ensure these methods are accurate for actual MRI coils, however, it is necessary to compare to experimental results. Here, we report results of some recent efforts to experimentally map temperature change and specific energy absorption rate in a phantom and in vivo where the only source of heat is the radiofrequency fields produced by the imaging coil. Results in a phantom match numerical simulation well, and preliminary results in vivo show measurable temperature increase. With further development, similar methods may be useful for verifying numerical methods for predicting specific energy absorption rate distributions and in some cases for directly measuring temperature changes and specific energy absorption rate induced by the radiofrequency fields in MRI experiments.
... Many studies were conducted to solve problems pertaining to EM interactions between the RF coil and the target object by solving Maxwell's equation using the EM toolbox based on various solvers, such as finite element method (FEM), finite difference time domain method (FDTD), method of moments (MOM), hybrid approaches, and others [19][20][21][22][23][24]. Through these EM simulations, EM parameters such as EM fields (e.g., B1-and E-fields) and the specific absorption rate (SAR) related to safety could be calculated to evaluate the RF coil performance [25][26][27]. However, these EM simulation studies did not account for the RF circuitry, such as tuning, matching, and decoupling conditions at the excitation port of the RF coil, which can alter the total power balance of the RF coil as well as B1-field and SAR distribution [28]. ...
The feasibility and the development of a four-port elliptical birdcage radio frequency (RF) coil for generating a homogenous RF magnetic (B1) field is presented for a space-constrained narrow-bore magnetic resonance imaging (MRI) system. Optimization was performed for the elliptical birdcage RF coil by adjusting the position and the structure of the legs to maximize the B1+-field uniformity. Electromagnetic (EM) simulations based on RF coil circuit co-simulations were performed on a cylindrical uniform phantom and a three-dimensional human model to evaluate the B1+-field uniformity, the transmission efficiency, and the specific absorption rate (SAR) deposition. An elliptical birdcage RF coil was constructed, and its performance was evaluated through network analysis measurements such as S-parameters and Q-factor. Quadrature transmit and receive MRI experiments were conducted using both phantom and in vivo human for validation. The EM simulation results indicate reasonable B1+-field uniformity and transmission efficiency for the proposed elliptical birdcage RF coil. The signal-to-noise ratio and the flip angle maps of the uniform phantom and the in vivo human MR images acquired using an elliptical birdcage (62 cm × 58 cm) were similar to those of a commercial circular birdcage (diameter, 58 cm), thereby indicating acceptable performance. In conclusion, the proposed split-type asymmetric elliptical birdcage RF coil is useful for whole-body MRI applications and can be used for imaging larger human subjects comfortably in a spacious imaging space.
... Various methods have been proposed to evaluate device safety [16]. Numerical simulations of electromagnetic fields, induced currents and resulting temperature evolution (using the bio-heat transfer equation) [17][18][19] require precise knowledge of the device's 3D geometrical arrangements, its composition, size and its position relative to the MRI scanner's excitation coil, together with electrical and thermal tissue properties, making personalized simulation for each patient unpractical. To overcome this limitation, in vivo assessments are preferred. ...
Purpose
To propose a MR-thermometry method and associated data processing technique to predict the maximal RF-induced temperature increase near an implanted wire for any other MRI sequence.
Methods
A dynamic single shot echo planar imaging sequence was implemented that interleaves acquisition of several slices every second and an energy deposition module with adjustable parameters. Temperature images were processed in real time and compared to invasive fiber-optic measurements to assess accuracy of the method. The standard deviation of temperature was measured in gel and in vivo in the human brain of a volunteer. Temperature increases were measured for different RF exposure levels in a phantom containing an inserted wire and then a MR-conditional pacemaker lead. These calibration data set were fitted to a semi-empirical model allowing estimation of temperature increase of other acquisition sequences.
Results
The precision of the measurement obtained after filtering with a 1.6x1.6 mm ² in plane resolution was 0.2°C in gel, as well as in the human brain. A high correspondence was observed with invasive temperature measurements during RF-induced heating (0.5°C RMSE for a 11.5°C temperature increase). Temperature rises of 32.4°C and 6.5°C were reached at the tip of a wire and of a pacemaker lead, respectively. After successful fitting of temperature curves of the calibration data set, temperature rise predicted by the model was in good agreement (around 5% difference) with measured temperature by a fiber optic probe, for three other MRI sequences.
Conclusion
This method proposes a rapid and reliable quantification of the temperature rise near an implanted wire. Calibration data set and resulting fitting coefficients can be used to estimate temperature increase for any MRI sequence as function of its power and duration.
... Such magnetic fields interact in a complex way with biological tissue and might affect image quality and patient safety unless carefully designed. Specifically, the susceptibility contrast between different tissues or between tissue and air can perturb the B 0 field (on the order of ppm), leading to strong artifacts for certain imaging applications [100]. Furthermore, the fast on and off switching of gradient fields can induce electric fields that might cause peripheral nerve stimulation which should be restricted to a stimulation that is barely perceived by a patient [101]. ...
The promise of improved signal-to-noise ratio (SNR), higher spatial/spectral resolution, and shorter imaging time continues to motivate the pursuit of high and ultra-high field magnetic resonance imaging. However, as field strength increases, the associated radiofrequency (RF) magnetic fields become inhomogeneous resulting in regions with SNR drops and loss of image quality, while local hot-spots, due to specific absorption rate (SAR) peaks, may occur. These challenges present the opportunity to design the next-generation, sophisticated RF coils which will yield higher SNR and faster image acquisition without compromising patient safety and image quality. Such design, however, requires long computational cycles, in order to explore the high-order parametric space and monitor the trade-offs between array degrees of freedom and various metrics, such as SNR, SAR, and transmit efficiency (TXE). During this process, electromagnetic (EM) modeling constitutes an essential tool.
This thesis employs analytical methods and develops novel numerical methods for modeling the interactions between EM waves and biological tissue and for computing theoretical RF coils performance bounds consistent with electrodynamic principles along with their corresponding optimal RF excitation patterns, which we term ideal current patterns (ICP). We employ analytical methods and introduce a new performance metric, the ultimate intrinsic TXE (UITXE), which is the theoretically largest TXE that can be achieved by any RF coil in uniform spherical objects and calculate its associated ICP on spherical surfaces. We further develop a novel volume integral equation solver for the accurate computation of EM fields distributions within highly inhomogeneous realistic human body models (RHBM). Our solver presents remarkably stable convergence properties and yields reliable EM fields for challenging modeling scenarios and coarse resolutions without necessarily refining the computational grid. Finally, we describe robust algorithms for generating a consistent numerical EM fields basis able to represent all EM fields distributions inside inhomogeneous, arbitrary objects and demonstrate how such basis can be used to derive UITXE inside RHBM and ICP on arbitrary excitation surfaces that yield optimal SNR within RHBM. UITXE can provide an absolute reference for coil benchmarking while ICP can inform the non-convex RF coil optimization problem by providing an intuitive initial guess. We believe that these tools can offer the framework for a truly robust optimization of next-generation RF coils.
... Therefore, using EM simulation is an important part of RF coil engineering. Computational electromagnetics (CEM) includes an array of techniques used to efficiently compute approximations to Maxwell's equations (23)(24)(25). In doing so, CEM enables modeling of these complex electrodynamic systems. ...
... For the reason mentioned above, the implanted medical wires are considered as the major risk of RF heating in the MRI and most of the studies of MRI-induced RF heating are extensively carried out on this issue. To analyze the effect and develop a mitigation method of RF heating around the lead, a numerical simulation based on some electromagnetic solvers is an alternative and widely used technique to cover the infeasibility of clinical trials due to the safety issues (30)(31)(32)(33)(34). In the following chapter, procedures of the EM and thermal simulations are briefly explained. ...
... Für möglichst realitätsnahe Simulationsergebnisse beinhaltet die Simulation u. a. die Geometrie und die dielektrischen Eigenschaften der zu untersuchenden Objekte. Die Simulationen elektromagnetischer Felder haben zunehmend eine große Bedeutung in der MR-Tomographie, besonders mit steigenden statischen Magnetfeldern B 0 und folglich hohen HF-Anregungsfrequenzen ν 0 und geringen Wellenlängen [Collins, 2009;Fiedler et al., 2017b]. ...
Das Ziel dieser Arbeit war es, die In-vivo-23Na-Magnetresonanz(MR)-Bildgebung des Körperstamms bei B0 = 7 Tesla zu ermöglichen. Zur Anregung der 23Na-Kernspins sowie zur Detektion der 23Na-Magnetisierung wurde eine 23Na-HF-Körperspule entwickelt, aufgebaut und optimiert. Drei Spulenkonfigurationen der ovalen, eng anliegenden Birdcage-Spule wurden untersucht: Zur Erhöhung der Homogenität des Sende- und Empfangsfeldes wurde im ersten Optimierungsschritt die herkömmliche Zweikanal-Einspeisung zu einer Vierkanal-Einspeisung erweitert. Im zweiten Optimierungsschritt wurde durch eine Anpassung der Sendephasen der relative Flipwinkelfehler in einem Bereich der Größe (23×13×10) cm³ von 8,6 % auf 4,9 % reduziert. Die 23Na-HF-Körperspule mit vier Empfangskanälen stellt ein relativ homogenes Sendefeld ((11,97 ± 0,59) μT, HF-Sendeleistung 2,4 kW) sowie Empfangsfeld zur Verfügung, welche einen großen Bereich des Körperstamms abdecken. Daher ermöglicht die HF-Körperspule erstmalig die Aufnahme von In-vivo-23Na-MR-Bildern der gesamten Breite des Körperstamms eines Erwachsenen mit einer großen Abdeckung in Längsrichtung bei B0 = 7 Tesla (Sichtfeld FOV = (40 cm)³). In den rekonstruierten 23Na-MR-Bildern treten Verschmierungen aufgrund der Atembewegung auf. Daher wurde das intrinsische Atemsignal retrospektiv aus den 23Na-MR-Daten bestimmt. Basierend auf diesem Atemsignal wurden die aufgenommenen MR-Daten in zwei Atemzustände (eingeatmet, ausgeatmet) aufgeteilt, was zu einer Reduktion der Verschmierungen führt. Die Zuordnung basierend auf dem intrinsischen und dem extrinsischen Atemsignal (Atemgurt) zeigte für drei Probanden eine gute Übereinstimmung von (90,6 ± 2,8) % bei der 23Na-Lungen-MR-Bildgebung und von (82,3 ± 3,8) % bei der 23Na-MR-Bildgebung des Abdomens.
... 43 A good general discussion of the use of numerical field calculations for MRI safety applications can be found in Refs. [44][45][46] and with respect to the RF field specifically in Ref. 47. ...
The main risks associated with magnetic resonance imaging (MRI) have been extensively reported and studied; for example, everyday objects may turn into projectiles, energy deposition can cause burns, varying fields can induce nerve stimulation, and loud noises can lead to auditory loss. The present review article is geared toward providing intuition about the physical mechanisms that give rise to these risks. On the one hand, excellent literature already exists on the practical aspect of risk management, with clinical workflow and recommendations. On the other hand, excellent technical articles also exist that explain these risks from basic principles of electromagnetism. We felt that an underserved niche might be found between the two, ie, somewhere between basic science and practical advice, to help develop intuition about electromagnetism that might prove of practical value when working around MR scanners. Following a wide‐ranging introduction, risks originating from the main magnetic field, the excitation RF electromagnetic field, and switching of the imaging gradients will be presented in turn.
Level of Evidence: 5
Technical Efficacy: 1
J. Magn. Reson. Imaging 2018;47:28–43.
... The radiofrequency (RF) field B 1 that is in the order of μT [74,30] and is produced by RF-coils. It can potentially cause tissue heating, especially when implants are present [19,[75][76][77][78][79][80][81][82][83][84][85][86][87][88][89]16,[90][91][92][93][94][95][96][97][98][99][100]4,[101][102][103]10,[104][105][106][107][108][109][110][111][112][113][114][115][116]69,117]. ...
Magnetic resonance imaging (MRI) has a superior soft-tissue contrast compared to other radiological imaging modalities and its physiological and functional applications have led to a significant increase in MRI scans worldwide. A comprehensive MRI safety training to protect patients and other healthcare workers from potential bio-effects and risks of the magnetic fields in an MRI suite is therefore essential. The knowledge of the purpose of safety zones in an MRI suite as well as MRI appropriateness criteria is important for all healthcare professionals who will work in the MRI environment or refer patients for MRI scans. The purpose of this article is to give an overview of current magnetic resonance safety guidelines and discuss the safety risks of magnetic fields in an MRI suite including forces and torque of ferromagnetic objects, tissue heating, peripheral nerve stimulation, and hearing damages. MRI safety and compatibility of implanted devices, MRI scans during pregnancy, and the potential risks of MRI contrast agents will also be discussed, and a comprehensive MRI safety training to avoid fatal accidents in an MRI suite will be presented.
... Wellenleitermodell in verkleinertem Maÿstab durchgeführt. Die numerische Simulation der auftretenden elektromagnetischen Felder ist eine etablierte Methode in der Nachrichtentechnik und hat auch zur Entwicklung von HF-Komponenten für die MRT in den letzten Jahren wesentlich beigetragen[56]. Die Simulationen beschreiben immer einen optimalen und vereinfachten, jedoch auch klar denierten Fall, und erlauben dadurch eine schnelle und risikofreie Analyse verschiedener nicht das Verhaltens eines Wellenleiters in Körperspulengröÿe bei der verwendeten, sondern bei der halbierten Frequenz (bzw. ...
In der Hochfeld-MRT (B >= 7 Tesla) können aufgrund der höheren Larmorfrequenzen keine klassischen Volumenspulen zur Erzeugung eines homogenen hochfrequenten elektromagnetischen Feldes zur Spinanregung im Körperstamm verwendet werden. Als Alternative wird in dieser Arbeit eine koaxiale Wellenleiteranordnung vorgeschlagen, um laufende Wellen in einen definierten Messbereich zu senden und das induzierte MR-Signal daraus zu empfangen. Das Messobjekt wird im hohlen Innenleiter platziert, der in Längsrichtung unterbrochen ist um den Messbereich zu bilden. Die MR-relevanten Eigenschaften der koaxialen Wellenleiteranordnung wie Sendeeffizienz, Homogenität des Sendefeldes und die Belastung des Messobjektes durch die hochfrequente Strahlung wurden zunächst mit numerischen Simulationen (FDTD-Verfahren) charakterisiert. Außerdem wurde ein verkleinertes Modell des Wellenleiters konstruiert und Messungen mit Testobjekten und anatomischen Proben durchgeführt. Neben der koaxialen Grundmode TEM wurde auch die Verwendung höherer (TE-)Moden untersucht. Durch die Frequenzunabhänigkeit der TEM-Mode konnten MR-Messungen bei fünf verschiedenen Larmor-Frequenzen zwischen 29 und 297 MHz mit den Nukliden 1H, 23Na und 35Cl durchgeführt werden. Die Verwendung eines Frequenzdiplexers ermöglichte dabei die gleichzeitige MRT von 1H und 23Na bei B = 7 T. Die Ergebnisse zeigten, dass ein koaxialer Wellenleiter als HF-Antenne in der Hochfeld-MRT verwendet werden kann und sich aufgrund seiner Frequenzunabhängigkeit für multinukleare Studien eignet. Die erreichte Sendeeffizienz von 0,5-6 µT/sqrt(kW) und die Schwankungen in der Feldhomogenität um etwa eine Größenordnung entsprechen denen anderer Laufwellenverfahren, sind jedoch für die klinische MRT nur bedingt ausreichend.
... The results are directly applicable to safety assessments of metallic implants and wires involving homogenous phantoms specified in some standards (eg ASTM F2182 Standard 2011, ISO/TS 10974, 2012). Previous studies have shown that both FDTD and FIT are good at modelling complex heterogeneous geometries such anatomically realistic phantoms (Collins 2009, Kozlov and Turner 2010, Collins and Wang 2011. In these cases the evaluation of their reliability is more complex. ...
This paper presents an extended comparison between numerical simulations using the different computational tools employed nowadays in electromagnetic dosimetry and measurements of radiofrequency (RF) electromagnetic field distributions in phantoms with tissue-simulating liquids at 64 MHz, 128 MHz and 300 MHz, adopting a customized experimental setup. The aim is to quantify the overall reliability and accuracy of RF dosimetry approaches at frequencies in use in magnetic resonance imaging transmit coils.
Measurements are compared against four common techniques used for electromagnetic simulations, i.e. the finite difference time domain (FDTD), the finite integration technique (FIT), the boundary element method (BEM) and the hybrid finite element method–boundary element method (FEM–BEM) approaches. It is shown that FDTD and FIT produce similar results, which generally are also in good agreement with those of FEM-BEM. On the contrary, BEM seems to perform less well than the other methods and shows numerical convergence problems in presence of metallic objects.
Maximum uncertainties of about 30% (coverage factor k = 2) can be attributed to measurements regarding electric and magnetic field amplitudes. Discrepancies between simulations and experiments are found to be in the range from 10% to 30%. These values confirm other previously published results of experimental validations performed on a limited set of data and define the accuracy of our measurement setup.
... In addition to being used for more accurate coil designs, electromagnetic field calculations are also used to understand and interpret the interactions between the RF field and the subject inside the coil, which are more complex at high frequencies and affect image quality (23)(24)(25). For instance electromagnetic field calculations are very important for "B 1 shimming" techniques which aim at obtaining a relatively homogenous RF field distribution in the region of interest (ROI) (26)(27)(28)(29). ...
Design of magnetic resonance imaging (MRI) radiofrequency (RF) coils using lumped circuit modeling based techniques begins to fail at high frequencies, and therefore more accurate models based on the electromagnetic field calculations must be used. Field calculations are also necessary to understand the interactions between the RF field and the subject inside the coil. Furthermore, observing the resonance behavior of the coil and the fields at the resonance frequencies have importance for design and analysis. In this study, finite element method (FEM) based methods have been proposed for accurate time-harmonic electromagnetic simulations, estimation of the tuning capacitors on the rungs or end rings, and the resonant mode analysis of the birdcage coils. Capacitance estimation was achieved by maximizing the magnitude of the port impedance at the desired frequency while simultaneously minimizing the variance of RF magnetic field in the region of interest. In order for the proposed methods to be conveniently applicable, two software tools, resonant mode and frequency domain analyzer (RM-FDA) and Optimum Capacitance Finder (OptiCF), were developed. Simulation results for the validation and verification of the software tools are provided for different cases including human head simulations. Additionally, two handmade birdcage coils (low-pass and high-pass) were built and resonance mode measurements were made. Results of the software tools are compared with the measurement results as well as with the results of the lumped circuit modeling based method. It has been shown that the proposed software tools can be used for accurate simulation and design of birdcage coils. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering), 2015
... Since time, cost and complexity limit the practical number of receive channels and prototype arrays that can be built, simulations are a feasible alternative approach to investigate the effect of increasing the number of coil elements on imaging performance. Numerical techniques, such as the finite difference time domain technique, are widely used to simulate RF coil performance based on accurate electromagnetic (EM) field calculations (6)(7)(8)(9)(10). While the results show good agreement with experiments, the numerical complexity of the computations increases with the number of coil elements. ...
We investigated to what degree and at what rate the ultimate intrinsic (UI) signal-to-noise ratio (SNR) may be approached using finite radiofrequency detector arrays. We used full-wave electromagnetic field simulations based on dyadic Green's functions to compare the SNR of arrays of loops surrounding a uniform sphere with the ultimate intrinsic SNR (UISNR), for increasing numbers of elements over a range of magnetic field strengths, voxel positions, sphere sizes, and acceleration factors. We evaluated the effect of coil conductor losses and the performance of a variety of distinct geometrical arrangements such as “helmet” and “open-pole” configurations in multiple imaging planes. Our results indicate that UISNR at the center is rapidly approached with encircling arrays and performance is substantially lower near the surface, where a quadrature detection configuration tailored to voxel position is optimal. Coil noise is negligible at high field, where sample noise dominates. Central SNR for practical array configurations such as the helmet is similar to that of close-packed arrangements. The observed trends can provide physical insights to improve coil design. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering), 2015
... In the last decade, commercial high-frequency MRI systems with a higher field were developed so this crossover frequency is easily reached and exceeded. Recent studies have concentrated on numerical methods to quantify the interactions between RF fields and the electrically inhomogeneous human body in terms of spatial distribution of internal electric fields, currents and SAR [49][50][51]. ...
Magnetic Resonance Imaging (MRI) is considered a safe technology since it does not use ionizing radiation with high energy to detach electrons from atoms or molecules. However, as in any healthcare intervention, even in an MRI diagnostic procedure there are intrinsic hazards that must be understood and taken into consideration. Moreover, given the increasing number of clinical MRI exams and the widespread availability of MR scanners with high static magnetic fields (>3T), the consideration of possible risks and health effects associated with MRI procedures is gaining in importance and the term "dosimetry" has begun to be used also for non ionizing techniques as MRI. Engineering techniques are increasingly used in MRI to explain the interactions between electromagnetic fields and the human body, analyze aspects relative to signal and image generation, and assure patient and staff safety and comfort. In this review some engineering methods to quantify the interactions between MR fields and biological tissues will be reviewed and catalogued to aid the readers in finding resources for their own applications in MRI safety assurance. This paper should not be intended as another review of the biological effects of MRI but, for the reader's convenience, the possible hazards for each kind of MR magnetic field, will be anyway briefly described.
Copyright © 2015. Published by Elsevier Inc.
... Design and safety evaluation of local transmit coils require full wave three-dimensional (3D) electromagnetic (EM) field simulation (32), as well as experimental validation for establishing functionality and safety. The most commonly employed simulation method is the finite difference time domain technique (33), previously used for analysis and optimization of RF coils (34)(35)(36). ...
PurposeTo enhance sensitivity and coverage for calf muscle studies, a novel, form-fitted, three-channel phosphorus-31 (31P), two-channel proton (1H) transceiver coil array for 7 T MR imaging and spectroscopy is presented.Methods
Electromagnetic simulations employing individually generated voxel models were performed to design a coil array for studying nonpathological muscle metabolism. Static phase combinations of the coil elements' transmit fields were optimized based on homogeneity and efficiency for several voxel models. The best-performing design was built and tested both on phantoms and in vivo.ResultsSimulations revealed that a shared conductor array for 31P provides more robust interelement decoupling and better homogeneity than an overlap array in this configuration. A static B1+ shim setting that suited various calf anatomies was identified and implemented.Simulations showed that the 31P array provides signal-to-noise ratio (SNR) benefits over a single loop and a birdcage coil of equal radius by factors of 3.2 and 2.6 in the gastrocnemius and by 2.5 and 2.0 in the soleus muscle.Conclusion
The performance of the coil in terms of B1+ and achievable SNR allows for spatially localized dynamic 31P spectroscopy studies in the human calf. The associated higher specificity with respect to nonlocalized measurements permits distinguishing the functional responses of different muscles. Magn Reson Med 73:2376-2389, 2015. © 2014 Wiley Periodicals, Inc.
... We assume the main magnetic field of the MR scanner is oriented in the Z-direction, and consider the magnetic permeability inside biological tissues to be equal to that in vacuum. The RF fields excited in MRI coils at the Larmor frequency of protons can be treated as time-harmonic EM fields [65], [66]. It is also assumed, as in most existing EPT researches, that the EPs of the object of interest are isotropic; there have been a few studies investigating EPs anisotropy at Larmor frequency [67], [68], which are beyond the scope of this review. ...
Frequency-dependent electrical properties (EPs; conductivity and permittivity) of biological tissues provide important diagnostic information (e.g., tumor characterization), and also play an important role in quantifying radiofrequency (RF) coil induced specific absorption rate (SAR), which is a major safety concern in high- and ultrahigh-field magnetic resonance imaging (MRI) applications. Cross-sectional imaging of EPs has been pursued for decades. Recently introduced electrical properties tomography (EPT) approaches utilize the measurable RF magnetic field induced by the RF coil in an MRI system to quantitatively reconstruct the EP distribution in vivo and noninvasively with a spatial resolution of a few millimeters or less. This paper reviews the EPT approach from its basic theory in electromagnetism to the state-of-the-art research outcomes. Emphasizing on the imaging reconstruction methods rather than experimentation techniques, we review the developed imaging algorithms, validation results in physical phantoms and biological tissues, as well as their applications in in vivo tumor detection and subject-specific SAR prediction. Challenges for future research are also discussed.
... RF losses in the tissue loading are another area of concern at higher frequencies. Losses due to the magnetic field induced eddy current density and electrical field displacement current density both increase with increasing field strength [9][10][11][12]. ...
Multi-element volume radio-frequency (RF) coils are an integral aspect of the growing field of high field magnetic resonance imaging (MRI). In these systems, a popular volume coil of choice has become the transverse electromagnetic (TEM) multi-element transceiver coil consisting of microstrip resonators. In this paper, to further advance this design approach, a new microstrip resonator strategy in which the transmission line is segmented into alternating impedance sections referred to as stepped impedance resonators (SIRs) is investigated. Single element simulation results in free space and in a phantom at 7 tesla (298 MHz) demonstrate the rationale and feasibility of the SIR design strategy. Simulation and image results at 7 tesla in a phantom and human head illustrate the improvements in transmit magnetic field, as well as, RF efficiency (transmit magnetic field versus SAR) when two different SIR designs are incorporated in 8-element volume coil configurations and compared to a volume coil consisting of microstrip elements.
... As a result, excessively restrictive power limits are commonly used, preventing the flexible usage of parallel transmit technology. Efforts to evaluate local SAR have often relied upon electromagnetic field calculations in numerical simulations or experimental findings in "average" subjects (10). Commonly used techniques such as the finite difference time domain (FDTD) method or the finite element method (FEM) have been used as a development platform for evaluating the safety and performance of array coils and/or RF pulse designs. ...
In ultra-high-field magnetic resonance imaging, parallel radiofrequency (RF) transmission presents both opportunities and challenges for specific absorption rate management. On one hand, parallel transmission provides flexibility in tailoring electric fields in the body while facilitating magnetization profile control. On the other hand, it increases the complexity of energy deposition as well as possibly exacerbating local specific absorption rate by improper design or delivery of RF pulses. This study shows that the information needed to characterize RF heating in parallel transmission is contained within a local power correlation matrix. Building upon a calibration scheme involving a finite number of magnetic resonance thermometry measurements, this work establishes a way of estimating the local power correlation matrix. Determination of this matrix allows prediction of temperature change for an arbitrary parallel transmit RF pulse. In the case of a three transmit coil MR experiment in a phantom, determination and validation of the power correlation matrix were conducted in less than 200 min with induced temperature changes of <4°C. Further optimization and adaptation are possible, and simulations evaluating potential feasibility for in vivo use are presented. The method allows general characteristics indicative of RF coil/pulse safety determined in situ. Magn Reson Med, 2012. © 2012 Wiley Periodicals, Inc.
... Numerical calculation of RF electromagnetic fields in human models with realistic geometry and tissue properties using finite-difference time-domain (FDTD) algorithm is an efficient means in evaluating and optimizing coil configuration for better transmit/receive performance in MR imaging (26,27). The numerical calculation results lead to prospective insight into the coil performance for fetal MRI such as SNR, specific absorption rate (SAR) and parallel imaging feasibility, which provides important guideline for fetal array design and fabricating prototype coil arrays (28)(29)(30)(31)(32). ...
Fetal MRI on 1.5T clinical scanner has been increasingly becoming a powerful imaging tool for studying fetal brain abnormalities in vivo. Due to limited availability of dedicated fetal phased arrays, commercial torso or cardiac phased arrays are routinely used for fetal scans, which are unable to provide optimized SNR and parallel imaging performance with a small number coil elements, and insufficient coverage and filling factor. This poses a demand for the investigation and development of dedicated and efficient radiofrequency (RF) hardware to improve fetal imaging. In this work, an investigational approach to simulate the performance of multichannel flexible phased arrays is proposed to find a better solution to fetal MR imaging. A 32 channel fetal array is presented to increase coil sensitivity, coverage and parallel imaging performance. The electromagnetic field distribution of each element of the fetal array is numerically simulated by using finite-difference time-domain (FDTD) method. The array performance, including B(1) coverage, parallel reconstructed images and artifact power, is then theoretically calculated and compared with the torso array. Study results show that the proposed array is capable of increasing B(1) field strength as well as sensitivity homogeneity in the entire area of uterus. This would ensure high quality imaging regardless of the location of the fetus in the uterus. In addition, the paralleling imaging performance of the proposed fetal array is validated by using artifact power comparison with torso array. These results demonstrate the feasibility of the 32 channel flexible array for fetal MR imaging at 1.5T.
... The study evaluated the electric field induced by a 1 kHz homogeneous magnetic field at the distal tip of a lead in a saline tank, simulating a unipolar pacemaker lead in cardiac tissue ( Figure 1). Computational modeling of the experimental measurement system -properly validated with measured data -is highly desirable since it allows extrapolating the results to many configurations that would otherwise be tedious or too complex to test experimentally (5,6). The objective of this study was to implement a numerical model similar to the experimental system, compute electric field and currents induced along the lead by the low-frequency magnetic field using two commercially available software packages, and compare the results with the measured values. ...
Exposure of patients with active implants (e.g. cardiac pacemakers and neurostimulators) to magnetic gradient fields (kHz range) during magnetic resonance imaging presents safety issues, such as unintended stimulation. Magnetically induced electric fields generate currents along the implant's lead, especially high at the distal tip. Experimental evaluation of the induced electric field was previously conducted. This study aimed to perform the same evaluation by means of computational methods, using two commercially available software packages (SemcadX and COMSOL Multiphysics). Electric field values were analyzed 1-3 mm from the distal tip. The effect of the two-electrode experimental probe was evaluated. The results were compared with previously published experimental data with reasonable agreement at locations more than 2-3 mm from the distal tip of the lead. The results were affected by the computational mesh size, with up to one order of magnitude difference for SEMCAD (resolution of 0.1 mm) compared to COMSOL (resolution of 0.5 mm). The results were also affected by the dimensions of the two-electrode probe, suggesting careful selection of the probe dimensions during experimental studies.
... Models that describe vessels discretely (Baish et al 1986, Huang et al 1996, Kotte et al 1996 offer a more accurate means of estimating heat transport within tissues. However, Collins (2009) commented that these more complex thermal models may result in a less conservative estimate of temperature increase for the purposes of ensuring safety. In the case of maternal/foetal heat transfer, the umbilical vessels present a highly significant parallel pathway for heat transfer in addition to that occurring across the foetal skin/amniotic fluid and amniotic fluid/uterine wall boundaries. ...
Numerical simulations of specific absorption rate (SAR) and temperature changes in a 26-week pregnant woman model within typical birdcage body coils as used in 1.5 T and 3 T MRI scanners are described. Spatial distributions of SAR and the resulting spatial and temporal changes in temperature are determined using a finite difference time domain method and a finite difference bio-heat transfer solver that accounts for discrete vessels. Heat transfer from foetus to placenta via the umbilical vein and arteries as well as that across the foetal skin/amniotic fluid/uterine wall boundaries is modelled. Results suggest that for procedures compliant with IEC normal mode conditions (maternal whole-body averaged SAR(MWB) < or = 2 W kg(-1) (continuous or time-averaged over 6 min)), whole foetal SAR, local foetal SAR(10 g) and average foetal temperature are within international safety limits. For continuous RF exposure at SAR(MWB) = 2 W kg(-1) over periods of 7.5 min or longer, a maximum local foetal temperature >38 degrees C may occur. However, assessment of the risk posed by such maximum temperatures predicted in a static model is difficult because of frequent foetal movement. Results also confirm that when SAR(MWB) = 2 W kg(-1), some local SAR(10g) values in the mother's trunk and extremities exceed recommended limits.
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In this article, we examine the correlation between temperature increments induced in the human body by RF exposure from magnetic resonance imaging (MRI) scanners and the corresponding power absorption. In particular, we consider the influences of absorption metrics-namely, the specific absorption rate (SAR) or volumetric absorption rate (VAR), averaging scheme, and exposure time-on the correlation.
The specific absorption rate produced in a rat’s brain phantom inside of quadrature birdcage coil as a function of the rung number was studied at 300 MHz. Electromagnetic field simulations and specific absorption rate and loss return responses were performed using a rat’s brain phantom weighing 100 mg. To assure optimal simulations and to evaluate coil performance, S-parameters were simulated and compared with experimentally data. Simulations showed that magnetic field uniformity improves and that electric field is increased with the number of rungs. Specific absorption rate and temperature values obtained from axial bi-dimensional maps increase as the number of rungs grows. These results corroborated very well with published data. A quadrature 16-rung birdcage coil was developed for comparison and phantom images were acquired to show its feasibility. The presented approach yields information on specific absorption rate allowing to previously develop RF coils and their possible effects on the biological sample.
Over the past two decades, magnetic resonance imaging (MRI) has become familiar as being synonymous with medical examination. The chapter provides a brief overview of the fundamental notions leading to the basic principle behind MRI. It describes the conditions in which the signal is collected, progressively discussing the organization of an MRI installation in a hospital. The chapter presents an analysis of the acquisition parameters which give rise to the contrast whilst attempting to form associations between those elements and situations corresponding to clinical practice. It draws the connection between the procedures for reconstruction and the execution of the acquisition sequences by taking a number of examples from the numerous families and filiations of sequences. The chapter covers biomedical applications of MRI, and focuses on the functional and metabolic aspect of MRI, such as spectroscopy and its links with imaging.
Local specific absorption rate (SAR) evaluation in ultra high field (UHF) magnetic resonance (MR) systems is a major concern. In fact, at UHF, radiofrequency (RF) field inhomogeneity generates hot-spots that could cause localized tissue heating. Unfortunately, local SAR measurements are not available in present MR systems; thus, electromagnetic simulations must be performed for RF fields and SAR analysis. In this study, we used three-dimensional full-wave numerical electromagnetic simulations to investigate the dependence of local SAR at 7.0 T with respect to subject size in two different scenarios: surface coil loaded by adult and child calves and quadrature volume coil loaded by adult and child heads. In the surface coil scenario, maximum local SAR decreased with decreasing load size, provided that the RF magnetic fields for the different load sizes were scaled to achieve the same slice average value. On the contrary, in the volume coil scenario, maximum local SAR was up to 15% higher in children than in adults. Bioelectromagnetics © 2015 Wiley Periodicals, Inc.
© 2015 Wiley Periodicals, Inc.
The goal of this study is to increase patient safety in parallel transmission (pTx) MRI systems. A major concern in these systems is radiofrequency-induced tissue heating, which can be avoided by specific absorption rate (SAR) prediction and SAR monitoring before and during the scan.Methods
In this novel comprehensive safety concept, the SAR is predicted prior to the scan based on precalculated fields obtained from electromagnetic simulations on different body models. The radiofrequency fields and the global and local SAR are supervised in real time during the scan. This concept is integrated into a 3 T pTx MR scanner and validated experimentally.ResultsPhantom and in vivo experiments successfully validated the basic feasibility of the real-time SAR supervision concept. Supervising the SAR minimizes SAR overestimation. Monitoring the radiofrequency fields allows the detection of unsafe radiofrequency situations for the patient, which a SAR supervision system alone cannot detect.Conclusion
This study demonstrates safe scanning in a pTx system. This new safety concept is also applicable for field strengths above 3 T and represents an important step toward safe operation of pTx systems. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.
Numerical methods based on solutions of Maxwell's equations are usually adopted for the electromagnetic characterization of Magnetic Resonance (MR) Radiofrequency (RF) coils. In this context, many different numerical methods can be employed, including time domain methods, e.g., the Finite-Difference Time-Domain (FDTD), and frequency domain methods, e.g., the Finite Element Methods (FEM) and the Method of Moments (MoM). We provide a quantitative comparison of performances and a detailed evaluation of advantages and limitations of the aforementioned methods in the context of RF coil design for MR applications. Specifically, we analyzed three RF coils which are representative of current geometries for clinical applications: a 1.5 T proton surface coil; a 7T dual tuned surface coil; a 7T proton volume coil. The numerical simulation results have been compared with measurements, with excellent agreement in almost every case. However, the three methods differ in terms of required computing resources (memory and simulation time) as well as their ability to handle a realistic phantom model. For this reason, this work could provide "a guide to select the most suitable method for each specific research and clinical applications at low and high field".
A multi-turn transmit surface coil design was presented to improve B1 efficiency when used with current source amplification.
Three different coil designs driven by an on-coil current-mode class-D amplifier with current envelope feedback were tested on the benchtop and through imaging in a 1.5 T scanner. Case temperature of the power field-effect transistor at the amplifier output stage was measured to evaluate heat dissipation for the different current levels and coil configurations. In addition, a lower power rated device was tested to exploit the potential gain in B1 obtained with the multi-turn coil.
As shown both on the benchtop and in a 1.5 T scanner, B1 was increased by almost 3-fold without increasing heat dissipation on the power device at the amplifier's output using a multi-turn surface coil. Similar gain was obtained when connecting a lower power rated field-effect transistor to the multi-turn coil.
In addition to reduce heat dissipation per B1 in the device, higher B1 per current efficiency allows the use of field-effect transistors with lower current ratings and lower port capacitances, which could improve the overall performance of the on-coil current source transmit system. Magn Reson Med 69:1180–1185, 2013.
Accurate prediction of specific absorption rate (SAR) for high field MRI is necessary to best exploit its potential and guarantee safe operation. To reduce the effort (time, complexity) of SAR simulations while maintaining robust results, the minimum requirements for the creation (segmentation, labeling) of human models and methods to reduce the time for SAR calculations for 7 Tesla MR-imaging are evaluated. The geometric extent of the model required for realistic head-simulations and the number of tissue types sufficient to form a reliable but simplified model of the human body are studied. Two models (male and female) of the virtual family are analyzed. Additionally, their position within the head-coil is taken into account. Furthermore, the effects of retuning the coils to different load conditions and the influence of a large bore radiofrequency-shield have been examined. The calculation time for SAR simulations in the head can be reduced by 50% without significant error for smaller model extent and simplified tissue structure outside the coil. Likewise, the model generation can be accelerated by reducing the number of tissue types. Local SAR can vary up to 14% due to position alone. This must be considered and sets a limit for SAR prediction accuracy. All these results are comparable between the two body models tested. Magn Reson Med, 2012. © 2012 Wiley Periodicals, Inc.
A Bi-2223 surface RF coil was developed for a 0.3T permanent MRI system to achieve better signal-to-noise ratio (SNR) of images. Based on the finite element method (FEM), the SNR of a copper-made surface coil is analyzed, and the emphasis is put on the coil self-resistance that accounts for much higher percentage of the equivalent noise resistance in low field MRI than that in high field MRI. In order to improve SNR, a surface coil that is made of a Bi-2223 tape is fabricated for a 0.3T permanent MRI system. Phantom images are acquired, and the image SNR by the Bi-2223 coil in liquid nitrogen is improved by up to 35% compared with that by a copper coil at room temperature.
Radiofrequency magnetic fields are critical to nuclear excitation and signal reception in magnetic resonance imaging. The interactions between these fields and human tissues in anatomical geometries results in a variety of effects regarding image integrity and safety of the human subject. In recent decades, numerical methods of calculation have been used increasingly to understand the effects of these interactions and aid in engineering better, faster, and safer equipment and methods. As magnetic resonance imaging techniques and technology have evolved through the years, so to have the requirements for meaningful interpretation of calculation results. Here, we review the basic physics of radiofrequency electromagnetics in magnetic resonance imaging and discuss a variety of ways radiofrequency field calculations are used in magnetic resonance imaging in engineering and safety assurance from simple systems and sequences through advanced methods of development for the future.
In vivo radiofrequency (RF) field B(1) mapping represents an essential prerequisite for parallel transmit applications. However, the large dynamic range of the transmit fields of the individual coil elements challenges the accuracy of MR-based B(1) mapping techniques. In the present work, the B(1) mapping error and its impact on the RF performance are studied based on a coil eigenmode analysis. Furthermore, the linear properties of the transmit chain are exploited to virtually adjust the weighting of the different coil eigenmodes in the B(1) mapping procedure, resulting in considerably reduced mapping errors. In addition, the weighting of the eigenmodes is tailored to potential target applications, e.g., specific absorption rate (SAR) reduced RF shimming or multidimensional RF pulses, resulting in improved RF performance. The basic theoretic principles of the concept are elaborated and validated by corresponding simulations. Furthermore, results on B(1) mapping and RF shimming experiments, performed on phantoms and in vivo using a 3-T scanner equipped with an eight-channel transmit/receive body coil, are presented to prove the feasibility of the approach.
Introduction Some recent numerical calculations have indicated a region of relatively high SAR near the center of the brain (1, 2). This can seem counter-intuitive from analytical theory, which predicts a low-SAR region near the center of a symmetric sample in a symmetric magnetic field (3). Here we compare SAR distributions in a homogeneous, symmetric sample (sphere) placed in the center of a volume coil with those for a heterogeneous human head with the majority of brain above the coil center. It is seen that in this case the overall pattern in the brain has some similarities to that in the upper half of the sphere, helping to explain the region of high SAR near the center of the brain. Method Cylindrical TEM coils were simulated at frequencies from 200 to 400 MHz and loaded with either a spherical sample of brain-equivalent material or an anatomically-accurate human head model. The coil had 16 copper elements, a 30-cm inner diameter, and a 16-cm length. Each rung was 1-cm wide. The diameter and length of the shield were 38 cm and 24 cm, respectively. Current sources were placed in each of four break points of each rung of the MRI coil and a 22.5-degree phase-shift was set between currents in adjacent rungs. All models had a resolution of 3mm in each direction. For the sphere model, the dielectric constant of 56.1, 51.9, 50.9, and 49.7, and conductivity of 0.51, 0.55, 0.57, and 0.59 S/m were used at 200 MHz (4.7T), 300 MHz (7T), 340 MHz (8T), and 400 MHz (9.4T), respectively. A Four-Cole-Cole extrapolation technique was used to determine values for the dielectric properties of the human head tissues at different frequencies. The tissue parameters and model geometry used in the computer simulation are available from the Brooks Air Force Laboratory database. Home-built 3D FDTD code was used in all simulations. All field values were normalized so that B 1 + at the coil center had a magnitude of 1µT. Results and Discussion Figure 1 shows the SAR distributions on axial, sagittal, and coronal planes through the sphere and head models at 200 through 400 MHz. The SAR distributions are nearly symmetric in any one direction about the center of the spheres. For the spheres, the SAR decreases to a value of zero at the center and maxima are located above and below the center of the sphere, where eddy currents concentrated due to the geometry. These maxima exist throughout each cycle during quadrature excitation. At the lower frequencies, the maximum SAR is located at the edge of the sphere and SAR decreases with distance from the center. However, due to decreasing wavelengths the maximum SAR migrates toward the center of the spheres with increasing frequency, though SAR at the very center remains at a minimum. As the frequency increases, a standing-wave type SAR pattern rather complementary to the standing wave pattern in the magnetic fields exists inside the sphere. On the axial plane this standing-wave pattern gives the appearance of a circular band of enhanced SAR distribution inside the spheres. The diameter of the circular bands decreases with increasing frequency (i.e., is roughly proportional to the wavelength in the brain tissue). These results alone cannot be used to reconcile calculations showing a region of high SAR at the center of a spherical sample placed at the center of a volume coil (4). Due to its highly heterogeneous and asymmetric nature, the maximum local SAR values in the head are much higher than those in the sphere model (5). As in the sphere, the maximum SAR in the head occurs at different locations with different frequencies. At lower frequency, SAR is nearly zero in the center of the head. With increasing RF frequency, the change in field pattern is not as simple as in the homogeneous and symmetric sphere, but some similarities can be seen. As in the spheres, a high-SAR region above the center migrates toward the center (visible most plainly on the coronal slice). Due to the asymmetric and heterogeneous nature of the head this also appears to drift in the anterior direction at high frequency. A high-SAR region below the coil center is not as evident in the head model because the electrical currents are not as constrained in the neck and shoulders as they are in the upper portion of the head and the spherical geometry. Acknowledgements Thanks to Graeme McKinnon and James C. Lin for guidance and support in developing the FDTD code. Thanks to the NIH for funding through R01 EB000454.
INTRODUCTION: A critical concern with multi-channel transmission is high specific absorption rate (SAR) due to the potential superposition of electric fields when using many simultaneous TX channels, and the possible inefficiency of producing excitation patterns via regional cancellation. To fully realize the clinical benefits of these systems, it is crucial to design RF pulses that not only achieve high-fidelity excitations, but ensure SAR falls within mandated limits. To explore this issue, we develop a method for calculating the SAR of an arbitrary RF pulse sequence on a parallel excitation system. Then we compare peak and average SAR due to three different RF pulse design methods: traditional singular value decomposition (SVD)-based inversion [1], Least Squares QR (LSQR) [2] and Conjugate Gradient Least Squares (CGLS) [3]. Calculating the SAR of each requires only an RF pulse set, knowledge of the steady state electric fields generated per unit of power sent to each TX coil, and knowledge of the tissue's electrical properties.
INTRODUCTION With transmit RF arrays it is possible to vary the RF magnetic (B 1) field distribution within a given subject to achieve any number of goals with methods such as RF shimming (1) and transmit SENSE (2). With some methods, such as transmit SENSE, the magnetic field distribution is varied during the RF pulse. This makes determination of local SAR levels very difficult because the SAR pattern will change through time. Although the safety of a single RF coil can be determined based on the expected B 1 field distribution of that coil, with a transmit array the field distributions that will be used in an experiment may not be known before the beginning of an experiment. This makes it difficult to accurately assess local SAR levels for specific experiments in a timely manner. Here we propose a method for ensuring the safety of the transmit array based on finding the worst-case ratio of local SAR to average SAR and using that ratio along with the real-time measured input power to the array to ensure limits on maximum local SAR are not exceeded.
A fast calculation method for the magnetic field distribution due to (dynamic) changes in susceptibility may allow real-time interventional applications. Here it is shown that a direct relationship can be obtained between the magnetic field perturbation and the susceptibility distribution inside the MR magnet using a first order perturbation approach to Maxwell's magneto-static equations, combined with the Fourier transformation technique to solve partial derivative equations. The mathematical formalism does not involve any limitation with respect to shape or homogeneity of the susceptibility field. A first order approximation is sufficient if the susceptibility range does not exceed 10−4 (or 100 ppm). The formalism allows fast numerical calculations using 3D matrices. A few seconds computation time on a PC is sufficient for a 128 × 128 × 128 matrix size. Predicted phase maps fitted both analytical and experimental data within 1% precision. © 2003 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 19B: 26–34, 2003.
Confusion exists over the application of the Principle of Reciprocity to NMR signal strength calculations when wavelength in a sample is comparable to the latter's size. A simple and easily reproduced bench experiment that validates the principle is therefore described. Building on the experimental results, elementary mathematics are employed to derive simple equations for the B 1 fields in both the negatively and the positively rotating frames. Using these equations, the reader is then guided through the steps needed to deduce correctly the signal received in an NMR experiment. The article should serve as a resource for those attempting signal strength calculations. © 2000 John Wiley & Sons, Inc. Concepts Magn Reson 12: 173–187, 2000
New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementary to Fourier preparation by linear field gradients. Thus, by using multiple receiver coils in parallel scan time in Fourier imaging can be considerably reduced. The problem of image reconstruction from sensitivity encoded data is formulated in a general fashion and solved for arbitrary coil configurations and k-space sampling patterns. Special attention is given to the currently most practical case, namely, sampling a common Cartesian grid with reduced density. For this case the feasibility of the proposed methods was verified both in vitro and in vivo. Scan time was reduced to one-half using a two-coil array in brain imaging. With an array of five coils double-oblique heart images were obtained in one-third of conventional scan time. Magn Reson Med 42:952-962, 1999.
Introduction The need to avoid peripheral nerve stimulation due to rapidly switched magnetic fields sets an upper limit on the magnetic field gradient strengths that can be employed in fast MRI and diffusion measurements. It is generally recognised that in whole-body imaging the y-gradient coil, which produces a linear variation of the z-component of the magnetic field (B z) in the anterior-posterior direction, causes nerve stimulation at the lowest rates of gradient change with time (1). This is thought to mainly result from the effect of the concomitant, B y -field, which as a consequence of Maxwell's equations must show a linear variation with z in the region of the coil where B z varies linearly with y, and therefore causes a high flux linkage in the large body cross section of the x-z plane. Although the linearly varying B y cannot be eliminated , it is possible to vary the z-position where this field goes to zero by the addition of a homogeneous B y field of variable strength (2). Adding such a field varying synchronously in time with the field produced by the transverse gradient coil should allow larger rates of change of gradient to be achieved before nerve stimulation occurs by reducing the rate of change of magnetic field in regions prone to stimulation. Here we describe the design of a coil system consisting of a standard transverse gradient coil, paired with a tailored coil designed to produce a uniform concomitant field over the gradient coil's region of linearity. The performance of the coil system was evaluated using electromagnetic field simulation software. Method An unscreened, cylindrical y-gradient coil of 62 cm inner diameter and length, L = 1.55 m was designed using a variant of the target field approach (3) in which the azimuthal component of the current distribution was represented as a linear superposition of axial harmonics of the form) sin cos (sin z (n n N 1 n nkz nkz J γ + λ φ =) φ, ∑ = φ where k=2π/L. λ n and γ n are constants which are found by minimising a functional made up of a weighted sum of the coil inductance, the sum of the values of (B z – Gy) 2 calculated over a set of points defining the gradient coil's region of linearity and the sum of the values of B y 2 calculated over a second set of points defining the region where B y minimisation was desired. B z and B y were calculated using the appropriate Fourier-Bessel expressions. The region of gradient homogeneity (less than 5 % deviation from linearity), was chosen to be a central sphere of 40 cm diameter. The conventional transverse gradient coil was produced by finding wirepaths to represent the symmetric part of J φ (i.e. relating to the coefficients λ n) while the coil to produce uniform B y was calculated in a similar manner from the anti-symmetric part of J φ (relating to the coefficients, γ n). The magnetic and electric fields produced by the actual coil designs were calculated using the commercial electromagnetic field simulation package, MAFIA (CST Darmstadt), which is based on the finite integration method. For calculating the electric field in the human body, analysis was applied to the HUGO body model (Medical VR Studio GmbH, Lorrach) with 6.5 mm isotropic resolution, located at various positions within the coil cylinder. Results and Discussion In designing the coil, it was found that varying the position of B y minimisation within the gradient coil's homogeneous volume, or the weighting of this term in the functional, changed the amplitude of the field produced by the concomitant field coil, but did not significantly vary its spatial form. The concomitant field coil used in further simulations was designed to null B y at a distance of 17 cm from the gradient coil isocentre, when both coils carry the same current. Wire patterns with 20 turns per quadrant (transverse gradient coil) and 9 turns per half (concomitant field coil) were used in further numerical simulations. The wire arrangement of the concomitant field coil is shown in Fig. 1. The gradient coil was calculated to have an efficiency of 0.093 mTm -1 A -1 and an inductance of 585 µH, while the concomitant field coil generates a field of 0.016 mTA -1 and has an inductance of 162 µH. Figure 2 shows the calculated on-axis variation of the y-component of the magnetic field for: (a) 1 A current in the gradient coil; (b) 1A current in the concomitant field coil; (c) 1 A in the gradient coil and 0.5 A in the concomitant field coil; (d) 1 A in both coils. Combination of the two fields is seen to reduce the concomitant field at negative z-values, whilst increasing it at positive z-values. Calculation of the z-component of the magnetic field indicates that gradient homogeneity is maintained in the central 40 cm diameter spherical volume for ratios of the current in the concomitant and gradient coils in the range 0 to 5.
The electromotive force due to thermal agitation in conductors is calculated by means of principles in thermodynamics and statistical mechanics. The results obtained agree with results obtained experimentally.
An attempt is made to remove some of the uncertainty surrounding the sensitivity of an NMR experiment involving human samples. It is shown that noise may be associated not only with the receiving coil resistance, but also with dielectric and inductive losses in the sample. Although steps may be taken to minimize the dielectric losses, this is not the case for the magnetic losses, and an estimate is made of their effects upon the signal-to-noise ratio. Approximate values of the latter are calculated for the head and torso and some experimental constraints briefly discussed.
To measure and correct nonuniformity in magnetic resonance images, large cylindrical water phantoms have traditionally been used. Above about 0.5 T, the large dielectric constant of water causes standing wave effects in water phantoms, giving a nonuniform RF field inside the phantom, even when the external field is uniform. The held and signal inside a nonconducting long cylinder are calculated for coils with circular and linear polarization, as a function of phantom diameter and field strength. At 1.5 T, the signal drops by 10% at the edge of a 9.5 cm diameter water cylinder. Oil phantoms are preferred, since the dielectric constant is lower (80 for water, about 5 for oil). At 1.5 T, the signal drops 10% at the edge of a 38 cm oil cylinder. A previous expression (G. H. Glover et al., J. Magn. Reson.64, 255, 1985) for the internal field and signal for a coil with circular polarization is in error.
A numerical model of a female body is developed to study the effects of different body types with different coil drive methods on radio-frequency magnetic (B
1) field distribution, specific energy absorption rate (SAR), and intrinsic signal-to-noise ratio (ISNR) for a body-size birdcage coil at 64 and 128 MHz. The coil is loaded with either a larger, more muscular male body model (subject 1) or a newly developed female body model (subject 2), and driven with-two-port (quadrature), four-port, or many (ideal) sources. Loading the coil with subject 1 results in significantly less homogeneousB
1 field, higher SAR, and lower ISNR than those for subject 2 at both frequencies. This dependence of MR performance and safety measures on body type indicates a need for a variety of numerical models representative of a diverse population for future calculations. The different drive methods result in similarB
1 field patterns, SAR, and ISNR in all cases.
The finite difference time domain method is used to calculate the specific absorption rate (SAR) due to a butterfly surface coil in a realistic tissue model of the leg. The resulting temperature distribution and temperature changes are found using a finite difference solution to the bioheat transfer equation. Reasonable agreement is found between predicted temperature changes and those measured in vivo provided that the resulting hyperthermia does not induce noticeable changes in perfusion. The method is applicable to radiofrequency dosimetry problems associated with high Bo field magnetic resonance systems and where knowledge of spatial variation in SAR is important in assessing the safety of new magnetic resonance procedures. Magn Reson Med 42:183–192, 1999. © 1999 Wiley-Liss, Inc.
Calculations of radiofrequency magnetic (B1) field and specific energy absorption rate (SAR) distributions in a sphere of tissue and a multi-tissue human head model in a 12-element birdcage coil are presented. The coil model is driven in linear and quadrature modes at 63, 175, 200, and 300 MHz. Plots of B, field magnitude and SAR distributions, average SAR, maximum local SAR, and measures of B1 field homogeneity and signal-to-noise ratio are given. SAR levels for arbitrary pulse sequences can be estimated from the calculated data. Maximum local SAR levels are lower at lower frequencies, in quadrature rather than in linear coils, and in linear fields oriented posterior-to-anterior rather than left-to-right in the head. It should be possible to perform many experiments in the head at frequencies up to 300 MHz without exceeding standard limits for local or average SAR levels.
A tuned transmission line resonator has been developed in theory and in practical design for the clinical NMR volume coil application at 4.1 tesla. The distributed circuit transmission line resonator was designed for high frequency, large conductive volume applications where conventional lumped element coil designs perform less efficiently. The resonator design has made use of a resonant coaxial cavity, which could be variably tuned to the Larmor frequency of interest by tunable transmission line elements. Large head- and body-sized volumes, high efficiencies, and broad tuning ranges have been shown to be characteristic of the transmission line resonator to frequencies of 500 MHz. The B1 homogeneity of the resonator has been demonstrated to be a function of the electromagnetic properties of the load itself. By numerically solving Maxwell's: equations for the fully time-dependent B1 field, coil homogeneity was predicted with finite-element models of anatomic structure, and inhomogeneities corrected for. A how-to exposition of coil design and construction has been included. Simple methods of quadrature driving and double tuning the transmission line resonator have also been presented. Human head images obtained with a tuned transmission line resonator at 175 MHz have clearly demonstrated uncompromised high field advantages of signal-to-noise and spatial resolution.
Birdcage coils are widely used as a radiofrequency (RF) resonator in magnetic resonance imaging (MRI) because of their capability to Produce a highly homogeneous B1 field Over a large volume within the coil. When they are employed for high-frequency MRI, the interaction between the electromagnetic field and the object to be imaged deteriorates the B1-field homogeneity and increases the specific absorption rate (SAR) in the object. To investigate this problem, a finite-element method (FEM) is developed to analyze the SAR and the B1 field in a two-dimensional (2D) model of a birdcage coil loaded with a 2D model of a human head. The electric field, magnetic field, and SAR distributions are shown, and a comprehensive study is carried out for both linear and quadrature birdcage coils at 64, 128, 171, and 256 MHz. It is that to generate the same value of the B1 field, the SAR is increased significantly with the frequency, and for the same imaging method the SAR produced by a quadrature coil is significantly lower than that of a linear coil. It is also shown that the B1-field inhomogeneity is increased significantly with the frequency.
Confusion exists over the application of the Principle of Reciprocity to NMR signal strength calculations when wavelength in a sample is comparable to the latter's size. A simple and easily reproduced bench experiment that validates the principle is therefore described. Building on the experimental results, elementary mathematics are employed to derive simple equations for the B1 fields in both the negatively and the positively rotating frames. Using these equations, the reader is then guided through the steps needed to deduce correctly the signal received in an NMR experiment. The article should serve as a resource for those attempting signal strength calculations. © 2000 John Wiley & Sons, Inc. Concepts Magn Reson 12: 173–187, 2000
Calculations of the RF magnetic (B1) field as a function of frequency between 64 and 345 MHz were performed for a head model in an idealized birdcage coil. Absorbed power (Pabs) and SNR were calculated at each frequency with three different methods of defining excitation pulse amplitude: maintaining 90° flip angle at the coil center (center = π/2), maximizing FID amplitude (Max. AFID), and maximizing total signal amplitude in a reconstructed image (Max. Aimage). For center = π/2 and Max. Aimage, SNR increases linearly with increasing field strength until 260 MHz, where it begins to increase at a greater rate. For these two methods, Pabs increases continually, but at a lower rate at higher field strengths. Above 215 MHz in MRI of the human head, the use of FID amplitude to set B1 excitation pulses may result in apparent decreases in SNR and power requirements with increasing static field strength. Magn Reson Med 45:684–691, 2001. © 2001 Wiley-Liss, Inc.
Calculations of the radiofrequency magnetic (B1) field, SAR, and SNR as functions of frequency between 64 and 345 MHz for a surface coil against an anatomically-accurate human chest are presented. Calculated B1 field distributions are in good agreement with previously-published experimental results up to 175 MHz, especially considering the dependence of field behavior on subject anatomy. Calculated SNR in the heart agrees well with theory for low frequencies (nearly linear increase with B0 field strength). Above 175 MHz, the trend in SNR with frequency begins to depend largely on location in the heart. At all frequencies, present limits on local (1 g) SAR levels are exceeded before limits on whole-body average limits. At frequencies above 175 MHz, limits on SAR begin to be an issue in some common imaging sequences. These results are relevant for coils and subjects similar to those modeled here. Magn Reson Med 45:692–699, 2001. © 2001 Wiley-Liss, Inc.
Calculations and experiments were used to examine the B1 field behavior and signal intensity distribution in a 16-cm diameter spherical phantom excited by a 10-cm diameter surface coil at 300 MHz. In this simple system at this high frequency very complex RF field behavior exists, resulting in different excitation and reception distributions. Included in this work is a straightforward demonstration that coil receptivity is proportional to the magnitude of the circularly polarized component of the B1 field that rotates in the direction opposite to that of nuclear precession. It is clearly apparent that even in very simple systems in head-sized samples at this frequency it is important to consider the separate excitation and reception distributions in order to understand the signal intensity distribution. Magn Reson Med 47:1026–1028, 2002. © 2002 Wiley-Liss, Inc.
A method to calculate the ultimate intrinsic signal-to-noise ratio (SNR) in a magnetic resonance experiment for a point inside an arbitrarily shaped object is presented. The ultimate intrinsic SNR is determined by body noise. A solution is obtained by optimizing the electromagnetic field to minimize total power deposition while maintaining a constant right-hand circularly polarized component of the magnetic field at the point of interest. A numerical approximation for the optimal field is found by assuming a superposition of a large number of plane waves. This simulation allowed estimation of the ultimate intrinsic SNR attainable in a human torso model. The performance of six coil configurations was evaluated by comparing the SNR of images obtained by the coils with the ultimate values. In addition, the behavior of ultimate intrinsic SNR was investigated as a function of main field strength. It was found that the ultimate intrinsic SNR increases better than linearly with the main magnetic field up to 10 T for our model. It was observed that for field strengths of 4 T or higher, focusing is required to reach the ultimate intrinsic SNR.
Inhomogeneous B0-magnetic fields generate distortion in magnetic resonance images, particularly those produced using echo planar imaging, and are responsible for signal reduction due to intravoxel dephasing in gradient echo experiments. Such effects increase in magnitude in proportionality with the static field strength, and with the growing use of high-field (3 T and above) systems in medical imaging, it is increasingly important to be able to quantify field inhomogeneities. Here, we describe the implementation and use of a method for rapidly calculating frequency shifts due to spatially varying magnetic susceptibility that is based on an approach previously used to calculate long-range dipolar field effects. The method relies on a simple expression that relates the three-dimensional Fourier transforms of the magnetization distribution and the field, and can naturally include the effect of the sphere of Lorentz. It has been used to evaluate field inhomogeneity in the head due to the variation of magnetic susceptibility with tissue type and to calculate the change in field inhomogeneity that occurs due to small rotations of the head. In addition, this approach has been used to simulate the effect of lung volume changes in generating respiration induced resonant offsets in the brain. © Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 25B: 65–78, 2005
PurposeTo examine peripheral nerve stimulation (PNS) thresholds for normal human subjects in magnetic resonance imaging (MRI) gradient coils, and determine if observed thresholds could be predicted based on gross physiologic measurements.Materials and MethodsPNS thresholds for 21 healthy normal subjects were measured using a whole-body gradient coil. Subjects were exposed to a trapezoidal echo-planar imaging (EPI) gradient waveform and the total change in gradient strength (ΔG) required to cause PNS as a function of the duration of the gradient switching time (τ) were measured. Correlation coefficients and corresponding P values were calculated for the PNS threshold measurements against simple physiologic measurements taken of the subjects, including weight, height, girth, and average body fat percentage, in order to determine if there were any easily observable dependencies.ResultsNo convincing correlations between threshold parameters and gross physiologic measurements were observed.Conclusion
These results suggest it is unlikely that a simple physiologic measurement of subject anatomy can be used to guide the operation of MRI scanners in a subject-specific manner in order to increase gradient system performance while avoiding PNS. J. Magn. Reson. Imaging 2003;17:716–721. © 2003 Wiley-Liss, Inc.
In this study a novel partially parallel acquisition method is presented, which can be used to accelerate image acquisition using an RF coil array for spatial encoding. In this technique, Parallel Imaging with Localized Sensitivities (PILS), it is assumed that the individual coils in the array have localized sensitivity patterns, in that their sensitivity is restricted to a finite region of space. Within the PILS model, a detailed, highly accurate RF field map is not needed prior to reconstruction. In PILS, each coil in the array is fully characterized by only two parameters: the center of coil's sensitive region in the FOV and the width of the sensitive region around this center. In this study, it is demonstrated that the incorporation of these coil parameters into a localized Fourier transform allows reconstruction of full FOV images in each of the component coils from data sets acquired with a reduced number of phase encoding steps compared to conventional imaging techniques. After the introduction of the PILS technique, primary focus is given to issues related to the practical implementation of PILS, including coil parameter determination and the SNR and artifact power in the resulting images. Finally, in vivo PILS images are shown which demonstrate the utility of the technique. Magn Reson Med 44:602–609, 2000. © 2000 Wiley-Liss, Inc.
In MRI, increasing radiofrequency magnetic (B
1) field frequency is a consequence of employing higher static magnetic (B
0) field strengths in the drive to improve signal-to-noise ratio (SNR). Due to the direct proportionality between B
0 field strength and B
1 field frequency in MRI, B
1 field distributions become more complex at higher B
0 fields due in part to shorter wavelengths and penetration depths. Consequently, it becomes both more difficult to calculate RF field behavior and more important to do so accurately for high-field MRI. In this chapter the basics of electromagnetic properties of tissue, the method of radiofrequency field calculation currently most prevalent in high-field MRI (the FDTD method), and methods for relating calculation results to MRI are covered briefly before results from calculations are used to discuss current challenges in high-field MRI including central brightening, SNR, power absorption by tissue, and image homogeneity.
Transmit coil arrays allowing independent control of individual coil drives facilitate adjustment of the B(1) field distribution, but when the B(1) field distribution is changed the electric field and SAR distributions are also altered. This makes safety evaluation of the transmit array a challenging problem because there are potentially an infinite number of possible field distributions in the sample. Local SAR levels can be estimated with numerical calculations, but it is not practical to perform separate full numerical calculations for every current distribution of interest. Here we evaluate superposition of separate electric field calculations-one for each coil-for predicting SAR in a full numerical calculation where all coils are driven simultaneously. It is important to perform such an evaluation because the effects of coil coupling may alter the result. It is shown that while there is good agreement between the superimposed and simultaneous drive results when using current sources in the simulations, the agreement is not as good when voltage sources are used. Finally, we compare maximum local SAR levels for B(1) field distributions that are either unshimmed or shimmed over one of three regions of interest. When B(1) field homogeneity is improved in a small region of interest without regard for SAR, the maximum local SAR can become very high.
Modern open MRI systems have far more electromagnetic (EM) interaction with the environment than conventional cylindrical-bore systems. An EM simulation of an open MRI system has to include the entire examination room as well as detailed objects like internal body organs. This paper will discuss simulations involving an open MRI system and a heterogeneous human-body model. Validations with measurements will be presented.
A comparison of experimental imaging results obtained with linearly polarized and circularly polarized radiofrequency excitation and reception is presented. Simulation images in good agreement with the experimental scans are described. The simulations are calculated with a model in which a homogeneous, isotropic cylinder of lossy dielectric material and infinite axial extent is immersed in a uniform rf magnetic field perpendicular to the axis. It is found that with the usual linear polarization, reconstructions of uniform objects have regions of decreased intensity. These artifacts are shown to arise from dielectric standing wave effects and eddy currents. The effects become more severe as the frequency or object size is increased, and depend upon the complex conductivity of the object. Results indicate that a significant reduction in the artifact intensity is achieved when circular polarization is employed for both transmission and reception. The expected benefits of circular polarization over linear polarization in reduction of excitation power (up to 50% reduction) and signal-to-noise advantage (√2) have been realized in practice with cylindrical objects and human subjects.
In modern MRI, occupational workers are exposed to strong, non-uniform static magnetic fields generated by the main superconducting magnet. Previous studies have indicated that movement of the body through these fields can stimulate in situ electric fields/ current densities approaching physiological significance. The relationship between the magnetic field pattern/strength and the current distribution/level induced in the body is not well understood. This paper presents numerical evaluations of electric fields/currents in tissue-equivalent, whole-body male and female human models (occupational workers) at various positions and a variety of normalized body motions around three superconducting magnets with central field strengths of 1.5T, 4T and 7T. Possible correlations between the magnetic field characteristics and the induced current density distribution are described and simulations show that it is possible to induce electric fields/current densities above the ICNIRP and IEEE safety standards when the worker is moving very close to the magnets.
A new method for ameliorating high-field image distortion caused by radio frequency/tissue interaction is presented and modeled, The proposed method uses, but is not restricted to, a shielded four-element transceive phased array coil and involves performing two separate scans of the same slice with each scan using different excitations during transmission. By optimizing the amplitudes and phases for each scan, antipodal signal profiles can be obtained, and by combining both images together, the image distortion can be reduced several-fold. A hybrid finite-difference time-domain/method-of-moments method is used to theoretically demonstrate the method and also to predict the radio frequency behavior inside the human head. in addition, the proposed method is used in conjunction with the GRAPPA reconstruction technique to enable rapid imaging. Simulation results reported herein for IIT (470 MHz) brain imaging applications demonstrate the feasibility of the concept where multiple acquisitions using parallel imaging elements with GRAPPA reconstruction results in improved image quality. (c) 2006 Wiley Periodicals, Inc.
The magnetic field penetration, phase shift and power deposition in planar and cylindrical models of biological tissue exposed to a sinusoidal time-dependent magnetic field have been investigated theoretically over the frequency range 1 to 100 MHz. The results are based on measurements of the relative permittivity and resistivity dispersions of a variety of freshly excised rat tissue at 37 and 25 degrees C, and are analysed in terms of their implications for human body nuclear magnetic resonance (NMR) imaging. The results indicate that at NMR operating frequencies much greater than about 30 MHz, magnetic field amplitude and phase variations experienced by the nuclei may cause serious distortions in an image of a human torso. The maximum power deposition envisaged during an NMR imaging experiment on a human torso is likely to be comparable to existing long-term safe exposure levels, and will depend ultimately on the imaging technique and NMR frequency employed.
We describe a numerical technique for calculating the 2D magnetic field in arbitrary magnetic susceptibility distribution. The technique we used is the explicit finite difference method with an addition of the Du Fort-Frankle algorithm. The proposed algorithm is unconditionally stable and has excellent convergence properties. For simple geometries, numerical results were compared against analytical solutions and appeared to be in excellent agreement.
A high frequency solution of the electromagnetic field produced by a circular surface coil adjacent to a homogeneous conducting, dielectric sphere is used to predict the attainable signal to noise ratio (S/N) and specific absorption rate (SAR) for in vivo 1H NMR spectroscopy experiments from 200 to 430 MHz (4.7-10 T). Above 200 MHz the S/N increases more rapidly with frequency and the SAR increases less rapidly compared with the respective S/N and SAR frequency dependence below 200 MHz. The difference in frequency dependence is due to dielectric resonances of the magnetic field inside the sphere at frequencies above 200 MHz. It is predicted that surface coil 1H NMR experiments may be performed on a head-sized sphere, having conductivity and relative dielectric constant of brain, at frequencies up to 430 MHz without exceeding 8 W/kg local SAR and 3.2 W/kg SAR. The calculations of the S/N and SAR are used to determine optimum surface coil geometries for NMR experiments. The power radiated by the surface coil in the absence of shielding and asymmetries in the received signal with respect to the plane defined by the surface coil axis and the direction of the static magnetic field are significant at high frequency. Experimental measurements of the magnetic field inside a head-sized sphere verify the presence of dielectric resonances at frequencies above 200 MHz.
The three-dimensional impedance method was used to estimate specific absorption rate (SAR) in a human-torso model during exposure to the time-varying and static magnetic fields used in magnetic resonance imaging (MRI). Analytical data for discrete tissues as well as the entire torso are presented. Generalized equations were derived that enable calculation of whole-torso SAR over a broad range of conditions. In addition, the impedance method can generate data about internal distributions of SAR, which are needed to predict critical organs that might undergo excessive elevations of temperature. Fair to good agreement was found between impedance-method SAR and those predicted by simple phenomenological models.
We describe methods for simultaneously acquiring and subsequently combining data from a multitude of closely positioned NMR receiving coils. The approach is conceptually similar to phased array radar and ultrasound and hence we call our techniques the "NMR phased array." The NMR phased array offers the signal-to-noise ratio (SNR) and resolution of a small surface coil over fields-of-view (FOV) normally associated with body imaging with no increase in imaging time. The NMR phased array can be applied to both imaging and spectroscopy for all pulse sequences. The problematic interactions among nearby surface coils is eliminated (a) by overlapping adjacent coils to give zero mutual inductance, hence zero interaction, and (b) by attaching low input impedance preamplifiers to all coils, thus eliminating interference among next nearest and more distant neighbors. We derive an algorithm for combining the data from the phased array elements to yield an image with optimum SNR. Other techniques which are easier to implement at the cost of lower SNR are explored. Phased array imaging is demonstrated with high resolution (512 x 512, 48-cm FOV, and 32-cm FOV) spin-echo images of the thoracic and lumbar spine. Data were acquired from four-element linear spine arrays, the first made of 12-cm square coils and the second made of 8-cm square coils. When compared with images from a single 15 x 30-cm rectangular coil and identical imaging parameters, the phased array yields a 2X and 3X higher SNR at the depth of the spine (approximately 7 cm).
The fundamental limit for NMR imaging is set by an intrinsic signal-to-noise ratio (SNR) for a particular combination of rf antenna and imaging subjects. The intrinsic SNR is the signal from a small volume of material in the sample competing with electrical noise from thermally generated, random noise currents in the sample. The intrinsic SNR has been measured for a number of antenna-body section combinations at several different values of the static magnetic field and is proportional to B0. We have applied the intrinsic and system SNR to predict image SNR and have found satisfactory agreement with measurements on images. The relationship between SNR and pixel size is quite different in NMR than it is with imaging modalities using ionizing radiation, and indicates that the initial choice of pixel size is crucial in NMR. The analog of "contrast-detail-dose" plots for ionizing radiation imaging modalities is the "contrast-detail-time" plot in NMR, which should prove useful in choosing a suitable pixel array to visualize a particular anatomical detail for a given NMR receiving antenna.
Simple theoretical estimates of the average, maximum, and spatial variation of the radiofrequency power deposition (specific absorption rate) during hydrogen nuclear magnetic resonance imaging are deduced for homogeneous spheres and for cylinders of biological tissue with a uniformly penetrating linear rf field directed axially and transverse to the cylindrical axis. These are all simple scalar multiples of the expression for the cylinder in an axial field published earlier (Med. Phys. 8, 510 (1981]. Exact solutions for the power deposition in the cylinder with axial (Phys. Med. Biol. 23, 630 (1978] and transversely directed rf field are also presented, and the spatial variation of power deposition in head and body models is examined. In the exact models, the specific absorption rates decrease rapidly and monotonically with decreasing radius despite local increases in rf field amplitude. Conversion factors are provided for calculating the power deposited by Gaussian and sinc-modulated rf pulses used for slice selection in NMR imaging, relative to rectangular profiled pulses. Theoretical estimates are compared with direct measurements of the total power deposited in the bodies of nine adult males by a 63-MHz body-imaging system with transversely directed field, taking account of cable and NMR coil losses. The results for the average power deposition agree within about 20% for the exact model of the cylinder with axial field, when applied to the exposed torso volume enclosed by the rf coil. The average values predicted by the simple spherical and cylindrical models with axial fields, the exact cylindrical model with transverse field, and the simple truncated cylinder model with transverse field were about two to three times that measured, while the simple model consisting of an infinitely long cylinder with transverse field gave results about six times that measured. The surface power deposition measured by observing the incremental power as a function of external torso radius was comparable to the average value. This is consistent with the presence of a variable thickness peripheral adipose layer which does not substantially increase surface power deposition with increasing torso radius. The absence of highly localized intensity artifacts in 63-MHz body images does not suggest anomalously intense power deposition at localized internal sites, although peak power is difficult to measure.
A theoretical derivation of the equivalent loading resistance of an annular volume conductor within a magnetic resonance imaging radio frequency (RF) coil is presented. Theoretical predictions of the magnitude of the load resistance agree well with measurement over a range of frequencies. The loading resistance is proportional to the sample conductivity, the frequency and coil sensitivity squared, and depends strongly upon the sample dimensions. The orientation of the magnetic vector potential for the specific coil geometry is also important. An experimental comparison of loading by annular and cylindrical objects with the human head over the imaging frequency range is made. Cylindrical test objects are adversely affected by the skin effect. The optimum means of simulating RF induced losses for quality assurance and performance evaluation is discussed in the light of these results.