Prediction of magnetically induced electric fields in biologicaltissue

There are many potential medical applications in which it is desirable to noninvasively induce electric fields. One such application that serves as the backdrop of this work is that of stimulating neurons in the brain. The magnetic fields necessary must be quite high in magnitude, and fluctuate rapidly in time to induce the internal electric fields necessary for stimulation. Attention is focused on the calculation of the induced electric fields commensurate with rapidly changing magnetic fields in biological tissue. The problem is not a true eddy current problem in that the magnetic fields induced do not influence the source fields. Two techniques are introduced for numerically predicting the fields, each employing a different gauge for the potentials used to represent the electric field. The first method employs a current vector potential (analogous to A in classical magnetic field theory where DEL x A = B) and is best suited to two-dimensional (2-D) models. The second represents the electric field as the sum of a vector plus the gradient of a scalar field; because the vector can be determined quickly using Biot Savart (which for circular coils degenerates to an efficient evaluation employing elliptic integrals), the numerical model is a scalar problem even in the most complicated three dimensional geometry. These two models are solved for the case of a circular current carrying coil near a conducting body with sharp corners.     

Superconducting receiver coils for sodium magnetic resonanceimaging

Presents the results from sodium magnetic resonance imaging (MRI) experiments using high-temperature superconducting (HTS) receiver coils. Sodium imaging has been shown to have great potential for the assessment of cell integrity but suffers from substantially lower signal-to-noise ratio (SNR) than that of hydrogen imaging. The use of an HTS receiver coil was found to significantly increase the SNR relative to an equivalent copper receiver coil at room temperature. The SNR gains afforded by HTS coils can also be used to decrease the imaging time     

Quantitative spectral/spatial analysis of phased array coil in magnetic resonance imaging based on method of moment

A new approach for analysis of RF coils in magnetic resonance (MR) experiments is reported. Instead of assuming current distribution in conventional quasi-static algorithm, this approach transforms the coil geometry into an equivalent circuit for complex current calculation. Self and mutual inductance are taken into consideration. Frequency responses of RF coils and transverse magnetic field (B1) maps can be simulated. This approach is especially efficient for phased array coil design for its small matrix size when implemented on computers. Experiments on both single surface coil and phased array coils are consistent with simulation results. Index Terms-Magnetic resonance, method of moment, phased array coil, RF coil.     

Performance of large-size superconducting coil in 0.21T MRI system

A high-temperature superconductor (HTS) was used on magnetic resonance imaging (MRI) receiver coils to improve image quality because of its intrinsic low electrical resistivity. Typical HTS coils are surface coils made of HTS thin-film wafers. Their applications are severely limited by the field of view (FOV) of the surface coil configuration, and the improvement in image quality by HTS coil is also reduced as the ratio of sample noise to coil noise increases. Therefore, previous HTS coils are usually used to image small in vitro samples, small animals, or peripheral human anatomies. We used large-size HTS coils (2.5-, 3.5-, and 5.5-in mean diameter) to enhance the FOV and we evaluated their performance through phantom and human MR images. Comparisons were made among HTS surface coils, copper surface coils, and cool copper surface coils in terms of the signal-to-noise ratio (SNR) and sensitivity profile of the images. A theoretical model prediction was also used to compare against the experimental result. We then selected several human body parts, including the wrist, feet, and head, to illustrate the advantage of HTS coil over copper coil when used in human imaging. The results show an SNR gain of 200% for 5.5-in HTS coil versus same size copper coils, while for 2.5- and 3.5-in coils it is 250%. We also address the various factors that affect the performance of large size HTS coils, including the coil-to-sample spacing due to cryogenic probe and the coil-loading effect.     

Toroidal coil models for transcutaneous magnetic stimulation of nerves

A novel design of coils for transcutaneous magnetic stimulation of nerves is presented. These coils consist of a toroidal winding around a high-permeability material (Supermendur) core embedded in a conducting medium. Theoretical numerical calculations are used to analyze the effect of the design parameters of these coils, such as coil width, toroidal radius, conducting layer thickness and core transversal shape on the induced electric fields in terms of the electric field strength and distribution. Results indicate that stimulation of nerves with these coils has some of the advantages of both electrical and magnetic stimulation. These coils can produce localized and efficient stimulation of nerves with induced electric fields parallel and perpendicular to the skin similar to surface electrical stimulation. However, they retain some of the advantages of magnetic stimulation such as no risk of tissue damage due to electrochemical reactions at the electrode interface and less uncomfortable sensations or pain. The driving current is reduced by over three orders of magnitude compared to traditional magnetic stimulation, eliminating the problem of coil heating and allowing for long duration and high-frequency magnetic stimulation with inexpensive stimulators     

Practical induction heating coil designs for clinical hyperthermiawith ferromagnetic implants

Interstitial techniques for hyperthermia therapy of cancer continue to evolve in response to requirements for better localization and control over heating of deep seated tissues. Magnetic induction heating of ferromagnetic implants is one of several available techniques for producing interstitial hyperthermia, using thermal conduction to redistribute heat within an array of controlled temperature “hot sources.” This report describes seven induction heating coil designs that can be used for producing strong magnetic fields around ferromagnetic seed implants located in different sites in the body. The effect of coil design on the extent and uniformity of the magnetic field is characterized, and appropriate electrostatic shield designs for minimizing electric field coupling to the patient are described. Advantages and disadvantages of each coil type are discussed in terms of the radiated fields, coil efficiency, and ease of use, and appropriate applications are given for each design. This armamentarium of induction coils provides the ability to customize magnetic field distributions for improved coupling of energy into ferromagnetic implant arrays located at any depth or orientation in the body. Proper selection of heating coil configuration should simplify patient setup, improve the safety of patient treatments, and pave the way for future applications of interstitial heating in sites that were previously untreatable     

An improved near- to far-zone transformation for thefinite-difference time-domain method

Near- to far-zone transformation for the finite-difference time-domain (FDTD) method can be performed by integration of the equivalent electric and magnetic currents originating from scattered electric and magnetic fields on a surface enclosing the object. Normally, when calculating the surface integrals, either the electric or magnetic fields are averaged since the electric and magnetic fields are spatially shifted in the FDTD grid. It is shown that this interpolation is unnecessary and also less accurate than if an integration is performed on two different surfaces. It is also shown that the accuracy of the far-zone transformation can be further improved if the phase is compensated with respect to a second-order dispersion corrected wavenumber. For validation, scattering results for an empty volume, a circular disk, and a sphere are compared with analytical solutions     

Mutual coupling analysis of a finite planar waveguide array

This paper deals with mutual coupling in a finite planar array antenna, composed of open-ended circular waveguides in a ground plane. The element-by-element approach is used and the problem is formulated as an integral equation, by requiring the transverse electric and magnetic fields to be continuous across the apertures. The equation is then solved by the method of moments and the mutual coupling in a 127-element array is computed. Excellent agreement with measurements and with the active reflection coefficient for the corresponding infinite array is found. The presented method of coupling analysis can be considered as a supplement to the established periodic-structure approaches for infinite arrays and may be useful for the analysis of small or nonperiodic arrays.     

Analysis of circular waveguide arrays on cylinders

An analysis is given of the mutual coupling effects in a finite array antenna of circular waveguide elements on a conducting cylinder. The array is described in terms of a scattering matrix and the multimode aperture fields of the elements are solved for by moment methods. Mutual coupling through wave propagation along the surface is treated according to GTD, since for most cases of interest the surface curvature is small in terms of wavelength. Appropriate asymptotic expansions for the magnetic field Green's function are derived for the two basic cases of an axial and a circumferential magnetic current element on the cylinder, the latter being a new case. The method, which allows the array elements to be nonuniformly spaced, applies to cylinders with radii>2lambdaand thus also includes planar arrays. Illustrative numerical examples and comparisons with infinite cylindrical and planar arrays are included.     

Reducing the Electric Field in Coil Systems Used for Environmental Research

Series resonant coil systems are being used to study the effects of ELF magnetic fields on living systems. High inductive voltages generate electric fields that prevent the separation of magnetic and electric field effects. These electric fields can be reduced by using multiple capacitor banks and connecting the coils and capacitors so that the electric fields cancel each other.     

MR flow measurement using RF phase gradients in receiver coilarrays

Radio frequency (RF) phase gradients in the receiver coil field pattern can encode flow velocity information in magnetic resonance (MR) images in the form of phase variations. These phase variations are not readily observed in MR images because they are relatively small compared to phase variations caused by static magnetic field (B₀) inhomogeneities, susceptibility variations, and other sources. However, the phase contributions from these other sources are independent of the receiver coil. Therefore, the RF phase gradient encoded flow information can be recovered by subtracting images obtained simultaneously using arrays of independent receiver coils and a multiple channel receiver. This flow velocity information can be extracted retrospectively from standard imaging sequences, including flow-compensated sequences. No additional time is required for the flow study as the flow measurements are made using sequences chosen for optimal imaging, and the images from each coil are obtained simultaneously. Initial results indicate that sufficient sensitivity is obtained to make flow measurements in the range of velocities commonly found in the carotid arteries and other major vessels. In principle, the method works with only two receiver coils. However, additional elements provide additional phase measurements that can be used to increase accuracy, remove ambiguities in flow direction or velocity calculations, and increase the region over which velocity measurements can be accurately made     

A 3-D differential coil design for localized magnetic stimulation

A novel three-dimensional (3-D) differential coil has been designed for improving the localization of magnetic stimulation. This new coil design consists of a butterfly coil with two additional wing units and an extra bottom unit, both perpendicular to the plane of the butterfly coil. The wing units produce opposite fields to restrict the spread of induced fields while the bottom unit enhances the induced fields at the excitation site. The peak induced field generated by this new design is located at the center of the coil, providing an easy identification of the excitation site. The field localization of the new coil is comparable with that of much smaller coils but with an inductance compatible to current magnetic stimulators. Numerical computations based on the principles of electromagnetic induction and using a human nerve model were performed to analyze the induced fields and the stimulation thresholds of new coil designs. The localization of the coil design was assessed by a half power region (HPR), within which the magnitude of the normalized induced field is greater than 1/square root of 2. The HPR for a 3-D differential coil built is improved (decreased) by a factor of three compared with a standard butterfly coil. Induced fields by this new coil were measured and in agreement with theoretical calculations.     

Design of coils for millimeter- and submillimeter-sized biotelemetry

Biotelemetric systems, especially those that employ implanted devices, work with inductive links, where usually large circular external coils are separated by relatively large distances (dimensions of centimeters) from the small (millimeter- or submillimeter-size) implanted coils. This paper shows that, under these conditions, a simplified method for calculation of the mutual inductance (M) between the coils, avoiding elliptic integrals, can be obtained. A procedure for coil design, with maximum M between them, is also described.     

Magnetic Field Coils for Gradiometer Balancing

We present a design of a compact set of biplanar coils which produces magnetic fields of eight different profiles for the purpose of gradiometer balancing. The magnetic field profiles correspond to uniform magnetic fields in three orthogonal directions and five linearly independent first-order gradients. The coils are made by etching square printed circuit boards that have dimensions of 0.5 m times 0.5 m. The typical inhomogeneity of the magnetic fields and gradients produced by the ideally assembled coil set in a cylindrically shaped volume that measures 50 mm in diameter and 225 mm in height is of the order of 10 ^-5. The coils yield uniform fields and first-order gradients of at least 1(muT/A) and 1(muT/Amiddotm), respectively. The influence of manufacturing tolerances on the performance of the set is investigated by means of Monte Carlo simulations. Based on these simulations, we concluded that the coil set needs to be assembled with a tolerance of 0.1 mm in order to reach a required uniformity of order of 10^-5-10^-4     

Peripheral nerve stimulation by gradient switching fields in magnetic resonance imaging

A heterogeneous model of the human body and the scalar potential finite difference method are used to compute electric fields induced in tissue by magnetic field exposures. Two types of coils are considered that simulate exposure to gradient switching fields during magnetic resonance imaging (MRI). These coils producing coronal (y axis) and axial (z axis) magnetic fields have previously been used in experiments with humans.The computed fields can, therefore, be directly compared to human response data. The computed electric fields in subcutaneous fat and skin corresponding to peripheral nerve stimulation (PNS) thresholds in humans in simulated MRI experiments range from 3.8 to 5.8 V/m for the fields exceeded in 0.5% of tissue volume (skin and fat of the torso). The threshold depends on coil type and position along the body, and on the anatomy and resolution of the human body model. The computed values are in agreement with previously established thresholds for neural stimulation.     

An inverted-microstrip resonator for human head proton MR imaging at 7 tesla

As an extension of the previously developed microstrip transmission line (MTL) RF coil design, a high-frequency RF volume coil using multiple inverted MTL (iMTL) resonators for human head imaging at high magnetic field strength of 7 tesla (T) is reported. Compared to conventional MTL resonators, iMTL resonators can operate at higher frequency with lower losses and, thus, are suitable for designs of high-frequency RF volume coils with large coil size for human MR imaging and spectroscopy at high fields. An approach using capacitive terminations was analyzed and applied to the design of the iMTL volume coil for improving RF field homogeneity and broadening frequency-tuning range. A performance-comparison study was conducted between the prototype iMTL volume coil and a custom-built TEM volume coil at 7 T. The iMTL volume coil presents a comparable SNR and intrinsic B1 homogeneity to the TEM volume coil. Phantom and the human head images acquired using the iMTL volume coil are also presented. The proposed iMTL volume coil provides an efficient and alternative solution to design high-frequency and large-size volume coils for human MR applications at very high fields.     

The signal-to-noise ratio of nuclear magnetic resonance surfacecoils and application to a lossy dielectric cylinder model. I. Theory

Surface coils are used in magnetic resonance imaging (MRI) for their high signal-to-noise ratio (S/N) when placed near the-region to be imaged. However, their optimization for high field MRI systems is hampered by the lack of understanding of the electromagnetic effects taking place at high frequencies when a coil is placed near the human body. The aim of this work was to calculate the S/N of surface coils using complete solutions to Maxwell's equations and also to study the high frequency effects and parameters determining the S/N. Here the authors present a general approach to the computation of the S/N of surface coils using the reciprocity principal and the complex Poynting vector for arbitrary coil and body geometries. This approach is then applied to the case of the human body modeled as an infinitely long homogeneous dielectric cylinder exhibiting both conductive and dielectric losses. The S/N of a coil of unspecified geometry facing the cylinder is derived using a dyadic Green's function. Complete solutions for the fields of a dipolar source arbitrarily located in the cylinder are first derived, and applying the reciprocity principle, the authors deduce the fields created at the dipole position by a coil excited with a unit radiofrequency current. These yield the expressions for the power dissipated in the cylinder, for its reciprocal the noise picked up by the coil, and also for the signal received. Any coil geometry and any coil or source position can be evaluated with this infinite cylinder model. It is valid at all frequencies and for any tissue parameter. The general approach to the computation of the S/N of MRI coils can be applied to other body geometries as well     

双注电子枪中最小二乘法拟合磁场的研究

用粒子仿真软件EGUN和MAGIC仿真电子枪时,需设置一组线圈来拟合磁控注入电子枪的磁场.为了提高设计效率,采用最小二乘法计算线圈参数,拟合电子枪磁场,计算结果用于34GHz双注磁控注入电子枪的仿真中,仿真结果表明:最小二乘法能够直接计算出拟合磁场的线圈组合,提高设计电子枪的效率;仿真的双注磁控注入电子枪电子速度零散小,横纵速度比适中,满足回旋管对电子枪的要求.     

Magnetic coil design considerations for functional magnetic stimulation

Our studies have demonstrated effective stimulation of the bladder, bowel, and expiratory muscles in patients with spinal cord injury using functional magnetic stimulation. However, one limitation of the magnetic coils (MC) is related to their inability to specifically stimulate the target tissue without activation of surrounding tissue. The primary goal of this study was to determine the governing parameters in the MC design, such as coil configuration, diameter, and number of turns in one loop of the coil. By varying these parameters, our approach was to design, construct, and evaluate the induced electric field distributions of two sets of novel MC's. Based on the slinky coil design, the first set of coils was constructed to compare their abilities in generating induced electric fields for focal nerve excitation. The second set of coils was built to determine the effect that changes in two parameters, coil diameter and number of turns in one loop, had on field penetration. The results showed that the slinky coil design produced more focalized stimulation when compared to the planar round coils. The primary-to-secondary peak ratios of the induced electric field from slinky 1 to 5 were 1.00, 2.20, 2.85, 2.62, and 3.54. We also determined that coils with larger diameters had better penetration than those with smaller diameters. Coils with less number of turns in one loop had higher initial field strengths; when compared to coils that had more turns per loop, initial field strengths remained higher as distance from the coil increased. In our attempt to customize MC design according to each functional magnetic stimulation application and patients of different sizes, the parameters of MC explored in this study may facilitate designing an optimal MC for a certain clinical application.     

Electrical conductivity imaging via contactless measurements: an experimental study

A data-acquisition system has been developed to image electrical conductivity of biological tissues via contactless measurements. This system uses magnetic excitation to induce currents inside the body and measures the resulting magnetic fields. The data-acquisition system is constructed using a PC-controlled lock-in amplifier instrument. A magnetically coupled differential coil is used to scan conducting phantoms by a computer controlled scanning system. A 10000-turn differential coil system with circular receiver coils of radii 15 mm is used as a magnetic sensor. The transmitter coil is a 100-turn circular coil of radius 15 mm and is driven by a sinusoidal current of 200 mA (peak). The linearity of the system is 7.2% full scale. The sensitivity of the system to conducting tubes when the sensor-body distance is 0.3 cm is 21.47 mV/(S/m). It is observed that it is possible to detect a conducting tube of average conductivity (0.2 S/m) when the body is 6 cm from the sensor. The system has a signal-to-noise ratio of 34 dB and thermal stability of 33.4 mV/degrees C. Conductivity images are reconstructed using the steepest-descent algorithm. Images obtained from isolated conducting tubes show that it is possible to distinguish two tubes separated 17 mm from each other. The images of different phantoms are found to be a good representation of the actual conductivity distribution. The field profiles obtained by scanning a biological tissue show the potential of this methodology for clinical applications.