Gradient Coil Design and Realization for a Halbach-Based MRI System

The LSM, or linear synchronous motor, with permanent magnet Halbach array and ironless coil possesses the dominant advantages of direct linear movement and being energy-saving. To analytically investigate the characteristics of this innovative LSM, its magnetic field and magnetic force are analyzed in this work. Based on the magnetic field of a single surface current, the field of a single permanent magnet with arbitrary magnetization angle is deduced. And the air-gap field of the motor is obtained by calculating the vector summation of the field generated by all the magnets in the array utilizing Denavit-Hartenberg transform technique. Given the form of three-phase current in the coil, the propulsion and normal force can be obtained. Finally, finite element method is introduced to validate the effedtiveness of the proposed analytical method, the result of which verifies the efficiency of the analytical method and the calculation error is within 5%. Also, it is concluded that the LSM composed of permanent magnet Halbach array and ironless coil is applicable for transportation. Compared to the widely utilized finite element method, the analytical method proposed in this work provides a faster and more convinent solution to analysis and design of the LSM with permanent magnet Halbach array and ironless coil.

Static magnetic fields (SMFs) and time-varying electromagnetic fields exposure is necessary to obtain the diagnostic information regarding the structure of patient's tissues, by the use of magnetic resonance imaging (MRI) scanners. A diagnostic procedure may also include the administration of pharmaceuticals called contrast, which are to be applied to a patient during the examination. The nurses involved in administering contrast into a patient during the pause in examination are approaching permanently active magnets of MRI scanners and are exposed to SMF. There were performed measurements of spatial distribution of SMF in the vicinity of MRI magnets and parameters of personal exposure of nurses (i.e. individual exposimetric profiles of variability in time of SMF affecting the nurse who is performing tasks in the vicinity of magnet, characterized by statistical parameters of recorded magnetic flux density affecting the nurse). The SMF exposure in the vicinity of various MRI magnets depends on both magnetic flux density of the main field B 0 (applicable to a patient) and the construction of the scanner, but the most important factor determining the workers' exposure is the work practice. In the course of a patient's routine examination in scanners of B 0 = 1.5 T, the nurses are present over ∼0.4–2.9 min in SMF exceeding 0.03% of B 0 (i.e. 0.5 mT), but only sometimes they are present in SMF exceeding 5% of B 0 (i.e. 75 mT). When patients need more attention because of their health status/condition, the nurses' exposure may be significantly longer – it may even exceed 10 min and 30% of B 0 (i.e. 500 mT). We have found that the level of exposure of nurses to SMF may vary from < 5% of the main field (a median value: 0.5–1.5%; inter-quartile range: 0.04–8.8%; max value: 1.3–12% of B 0) when a patient is moved from the magnets bore before contrast administration, up to the main field level (B 0) when a patient stays in the magnets bore and nurse is crawling into the bore.

Static weak magnetic field measurements based on low-field nuclear magnetic resonance.

A modified target field method is presented to the construction of shim and gradient coils for Halbach-type magnet featuring cylindrical magnet and transversal magnetic field direction. With Biot–Savart law, magnetic field is deduced from current density distribution, and two solutions corresponding to relations between spherical harmonic functions degree m and current density degree k, namely $$m=k\pm 1$$ are derived. Then combined with magnetic field distribution of target points, current density coefficient $$U_{\rm q}$$ is adopted to calculate stream function, based on which the coils' structure can be obtained. An appropriate objective function integrating dissipated energy and relative error is utilized to further improve the design. Examples of X2–Y2 and Y coils indicate that solution corresponding to $$m=k-1$$ exhibits good agreement with theory in terms of obtaining lower dissipated energy and smaller error rate, suggesting that the algorithm provides an effective, preferable approach for the design of Halbach shim coils.

Water electrolysis is an essential electrochemical process for both oxygen production in space as well as green hydrogen production on Earth. The presence of bubbles on electrodes increases the resistivity of the electrolytic cell and hinders mass-transport of the liquid electrolyte to the electrode surface. On Earth, efficiency losses due to the presence of bubbles can be as high as 30%, and potentiostatic parabolic plane experiments have shown a further decrease by 11% at current densities up to 100 mA/cm2.Among a variety of methods for accelerating bubble evacuation from the electrode surface, magnetohydrodynamic (MHD) pumping via a magnetically-induced Lorentz force has shown promise in controlled lab trials. The MHD effect reduced bubble coverage by 50% under a 1 T field and increased hydrogen-evolution current density by 25% at 700 mA/cm2 under a 5 T field. Experiments employing permanent magnets have shown a 5% decrease in cell overpotential from B-fields of 0.2 T at 150 mA/cm2.In this work, we describe the modeling and testing of alkaline water electrolysis conducted in the presence of a magnetic field produced by a scalable Halbach array of permanent magnets. Unlike many prior efforts, the field is produced by off-the-shelf rare-Earth N52 magnets of various sizes. These arrays are located just behind the electrodes in a “Halbach” sinusoidal pattern which serves to amplify the magnetic field strength. Bench-top tests of a pair of 1.6 cm2 electrodes show an 18.4% efficiency increase at current densities between 25-300 mA/cm2. Since the magnets are permanent, there is no additional power required for generating the MHD swirling, aside from a trivial overpotential of ~0.05% of cell power. This architecture presents a promising solution for scalability for industrial electrolyzers. Figure 1

A uniform axial or transverse magnetic field is applied on the silicon oil based ferrofluid of high Prandtl number fluid (Pr ? 111.67), and the effect of magnetic field on the thermocapillary convection is investigated. It is shown that the location of vortex core of thermocapillary convection is mainly near the free surface of liquid bridge due to the inhibition of the axial magnetic field. A velocity stagnation region is formed inside the liquid bridge under the axial magnetic field (B = 0.3-0.5 T). The disturbance of bulk reflux and surface flow is suppressed by the increasing axial magnetic field. There is a dynamic response of free surface deformation to the axial magnetic field, and then the contact angle variation of the free surface at the hot corner is as following, ?hot, B = 0.5 T = 83.34? &gt; ?hot, B = 0.3 T = 72.16? &gt; &gt; ?hot,B = 0.1 T = 54.21? &gt; ?hot, B = 0 T = 43.33?. The results show that temperature distribution near the free surface is less and less affected by thermocapillary convection with the increasing magnetic field, and it presents a characteristic of heat-conduction. In addition, the transverse magnetic field does not realize the fundamental inhibition for thermocapillary convection, but it transfers the influence of thermocapillary convection to the free surface.

In the last few years there has been rapid progress in the application of nuclear magnetic resonance clinical imaging as a diagnostic aid (Partain et al, 1983; Steiner, 1983; Worthington, 1983). Records kept by the operators of NMR imaging equipment indicate that about 1800 individuals have now been examined without incident within the United Kingdom. In view of this progress, an advisory group (Appendix) appointed by the National Radiological Protection Board recommends some modifications to the original advice given in 1981 (NRPB, 1981). The principal modifications are that: (1) It is no longer considered necessary to exclude volunteers with a history of epilepsy or cardiac disease. (2) It is not obligatory that a registered medical practitioner trained in resuscitation techniques be present during an exposure. (3) Higher limits are recommended for rates of change of magnetic flux density when the period of change is less than 10 ms. (4) The radiofrequency limit of 15 MHz has been removed. Theoretical considerations indicate that the interaction of an applied magnetic field with the intrinsic magnetic moments of protons and electrons within a molecule could alter its rate of chemical reaction (McLauchlan, 1981). Chemical reactions involving radical pair intermediates are expected to be sensitive to magnetic fields for this reason and a number of enzyme reactions that might be expected to be affected have been identified (A. Cass, personal communication). However, there is no experimental confirmation of these theoretical possibilities at present.

Medical staff working near magnetic resonance imaging (MRI) scanners are exposed both to the static magnetic field (SMF) itself and also to electric currents that are induced in the body by motion within the SMF. Currently available data on induced electric currents for realistic movements are limited. This study computationally investigates the movement-induces electric fields for realistic movements in the magnetic field of a 1.5 T MRI scanner.

The distribution and dissipation of neutral atoms are crucial for understanding the dielectric recovery process after interrupting direct current (DC) vacuum arcs. This article aims to investigate the dissipation of copper atoms after a forced extinction of the vacuum arc experimentally, adopting the plane laser-induced fluorescence method. The change in the 2-D distribution of copper atoms with time is presented. The results show that the magnetic fields, the axial magnetic field (AMF), and the transverse magnetic field (TMF) have a limited effect on the initial density of copper atoms. For both the AMF and the TMF, the copper atom densities at current zero (CZ) vary in the range (6– $8) \times 10^{17}\,\,\text{m}^{-3}$ when 3-kA vacuum arcs are forced to 0 in 0.2 ms. Contrary to the TMF case, in the AMF case, the evaporation on the anode after the CZ results in long-existing atoms near it. Consequently, the atom density of the TMF decays faster than that of the AMF, which indicates that a vacuum interrupter with the TMF contacts has a better performance when interrupting a DC load. The difference between the two magnetic fields originates from the arc control patterns. Namely, the AMF tends to keep vacuum arcs in a stable mode, which is unfavorable for a DC interruption; on the contrary, the TMF drives the vacuum arcs to move at high velocities resulting in faster dissipation of copper atoms after the CZ. In addition, the composition proportion of CuCr contacts has a limited effect on the diffusion of copper atoms when a low-vacuum arc is interrupted.

Based on the target-field method of solving Fredholm integral equations of the first kind, a new approach is presented in the paper for designing gradient coils that can be used in a permanent-magnet magnetic resonance imaging (MRI) system with biplanar poles. To restrict the current distribution on the coil plane within a finite radius, the current density is pre-expanded into Fourier series by orthogonal basis functions. By setting the target-field points and Bz values over the imaging region of interest, corresponding integral equations are derived from the Biot–Savart law to calculate the current densities. They form a matrix equation, in which the unknown elements of the column vector are the Fourier coefficients for the unknown current density. As long as these target-field points are well chosen, the Fourier coefficients can be solved by inverse matrix calculation instead of the regularization method for Fredholm integral equations of the first kind. Then the current density is discretized using the stream-function method to generate the winding patterns. To verify the feasibility of this approach, the gradient magnetic field generated by the current density is calculated via the Biot–Savart law. Optimized parameters are obtained through computer simulations for some shielded and unshielded transverse gradient coils. The performance of this approach has been demonstrated as well.

Aim: To study the effects of static magnetic fields (SMF) on the electrophysiological properties of voltage-gated sodium and calcium channels on trigeminal ganglion (TRG) neurons. Methods: Acutely dissociated TRG neurons of neonatal SD rats were exposed to 125-mT and 12.5-mT SMF in exposure devices and whole-cell patch-clamp recordings were carried out to observe the changes of voltage-gated sodium channels (VGSC) and calcium channels (VGCC) currents, while laser scanning confocal microscopy was used to detect intracellular free Ca2+ concentration in TRG neurons, respectively. Results: (1) No obvious change of current–voltage (I–V) relationship and the peak current densities of VGSC and VGCC currents were found when TRG neurons were exposed to 125-mT and 12.5-mT SMF. However, the activation threshold, inactivation threshold and velocity of the channel currents above were significantly altered by 125-mT and 12.5-mT SMF. (2) The fluctuation of intracellular free Ca2+ concentration within TRG neurons were slowed by 125-mT and 12.5-mT SMF. When SMF was removed, the Ca2+ concentration level showed partial recovery in the TRG neurons previously exposed by 125-mT SMF, while there was a full recovery found in 12.5-mT-SMF-exposed neurons. Conclusions: Moderate-intensity SMF could affect the electrophysiological characteristics of VGCS and VGCC by altering their activation and inactivation threshold and velocity. The fluctuations of intracellular free Ca2+ caused by SMF exposure were not permanent in TRG neurons.

Azimuthal surface waves are eigenmodes of cylindrical plasma–dielectric–metal structures both in the presence of and without an axial static magnetic field. They are actively studied due to possible applications in plasma electronics, nanotechnologies and biomedical diagnostics. Higher radial modes are known to propagate at higher frequencies and shorter wavelengths compared to those of the zeroth mode, a feature which is of interest for practical applications. To gain the advantage of the excitation of higher radial modes of azimuthal surface waves one has first to know their dispersion properties. This paper generalizes the results of earlier papers by including a static axial magnetic field and considering the higher radial modes. The presence of the constant axial magnetic field removes the degeneracy in the wave spectrum with respect to the sign of the azimuthal wavenumber.

The health care staff operating magnetic resonance imaging (MRI) scanners are exposed to static magnetic field of significant spatial heterogenity and high level of flux density—usually existing permanently during the shift. The personnel can also be exposed to pulses of magnetic field of high rate of rise/fall, so-called gradient fields, which exist only during examination of patients. The level of workers’ exposure depends both on the type of the magnet and on the ergonomical characteristic of design of the particular MRI scanner. This paper presents the current state of the art on occupational exposure to static magnetic field health effects, gaps in scientific data, MRI workers’ exposure characteristics, research needs, and suggestions for the exposure assessment protocol for future investigations.

Magnetic resonance imaging is a popular non-invasive technique for investigating soft tissue structures within the human body. Many design methods now exist for their principle hardware components, such as the radio frequency (RF) coils. A popular RF coil type is the RF phased array, comprised of many closely spaced coils covering a large volume. A time harmonic inverse method is presented for the theoretical design of RF phased arrays. The method allows any array size to be considered where the focus is on optimal coil geometry and position of individual coils. An ill-conditioned integral equation is solved using a regularisation strategy in which the error between induced and target magnetic fields is minimised along with an additional constraint related to the curvature of the coil windings. The method is demonstrated for a number of design considerations and includes the ability to focus the RF field to arbitrary locations within the coil volume. The effect of the choice of magnetic field polarisation direction is also investigated using the model. References Jin J. 1999. Electromagnetic Analysis and Design in Magnetic Resonance Imaging, Florida: CRC Press. Lawrence B. G., Crozier S., Yau D. D. and Doddrell D. M. 2002. A time-harmonic inverse methodology for the design of rf coils in mri, IEEE Transactions on Biomedical Engineering 49(1), 64--71. doi:10.1109/10.972841 Li B. K., Liu F. and Crozier S. 2005. Focused, eight-element transceive phased array coil for parallel magnetic resonance imaging of the chest --- theoretical considerations, Magnetic Resonance in Medicine 53, 1251--1257. doi:10.1002/mrm.20505 Ramo S., Whinnery J. R. and van Duzer T. 1967. Fields and waves in communication electronics, New York: John Wiley and Sons, Inc. Roemer P. B., Edelstein W. A., Hayes C. E., Souza S. P. and Mueller O. M. 1990. The nmr phased array, Magnetic Resonance in Medicine 16(2), 192--225. doi:10.1002/mrm.1910160203 Sodickson D. K., McKenzie C. A., Ohliger M. A., Yeh E. N. and Price M. D. 2002. Recent advances in image reconstruction, coil sensitivity calibration, and coil array design for SMASH and generalized parallel mri, Magnetic Resonance Materials in Physics, Biology and Medicine 13, 158--163. Turner R. 1986. A target field approach to optimal coil design, Journal of Physics D: Applied Physics 19, L147--L151. doi:10.1088/0022-3727/19/8/001 While P. T., Forbes L. K. and Crozier S. 2005a. A time-harmonic target-field method for designing unshielded rf coils in mri, Measurement Science and Technology 16, 997--1006. doi:10.1088/0957-0233/16/4/012 While P. T., Forbes L. K. and Crozier S. 2005b. A time-harmonic target-field method for designing shielded rf coils in mri, Measurement Science and Technology 16, 1381--1393. doi:10.1088/0957-0233/16/6/021 While P. T., Forbes L. K. and Crozier S. 2006. An inverse method for designing loaded rf coils in mri, Measurement Science and Technology 17, 2506--2518. doi:10.1088/0957-0233/17/9/019 Brideson M. A., Forbes L. K. and Crozier S. 2002. Determining complicated winding patterns for shim coils using streamfunctions and the target-field method, Concepts in Magnetic Resonance 14(1), 9--18. doi:10.1002/cmr.10000 While P. T., Forbes L. K. and Crozier S. 2007. An inverse method for designing rf phased array coils in mri --- theoretical considerations, Measurement Science and Technology 18, 245--259. doi:10.1088/0957-0233/18/1/031 Delves L. M. and Mohamed J. L. 1985. Computational methods for integral equations, Cambridge: Cambridge University Press. Forbes L. K. and Crozier S. 2002. A novel target-field method for finite-length magnetic resonance shim coils: II. tesseral shims, Journal of Physics D: Applied Physics 35, 839--849. doi:10.1088/0022-3727/35/9/303 Hardy C. J., Cline H. E., Giaquinto R. O., Niendorf T., Grant A. K. and Sodickson D. K. 2006. 32-element receiver-coil array for cardiac imaging, Magnetic Resonance in Medicine 55, 1142--1149. doi:10.1002/mrm.20870

We evaluated radiofrequency (RF) heating of a humerus implant embedded in a gel phantom during magnetic resonance (MR) imaging for the specific absorption rate (SAR), angle between the implant and static magnetic field (B(0)), and position of the implant in the irradiation coil. We embedded a stainless steel humerus implant 2 cm deep in tissue-equivalent loop and mass phantoms, placed it parallel to the static magnetic field of a 1.5T MR scanner, and recorded the temperatures of the implant surface with RF-transparent fiberoptic sensors. We measured rises in temperature at the tips of the implant by varying the SAR from 0.2 to 4.0 W/kg and evaluated RF heating of the implant for its angle to B(0) and its displacement along B(0) from the center of the RF irradiation coil. RF heating was similar for the loop and mass phantoms because the eddy current flows through the periphery of both. As the SAR increased, the temperature at the implant tip increased, and there was a linear relationship between the SAR and temperature rise. The values were 6.4 degrees C at 2.0 W/kg and 12.7 degrees C at 4.0 W/kg. Rise in temperature decreased steeply as the angle between the implant and B(0) surpassed 45 degrees . In addition, as the implant was displaced from the center of the RF coil to both ends, the rise in temperature decreased. The rise in temperature in deep tissue was estimated to be higher than 1.0 degrees C for SAR above 0.4 W/kg. RF heating was greatest when the implant was set parallel to B(0). In MR imaging of patients with implants, there is a risk of RF heating when the loop of the eddy current is formed inside the body.