Biplanar Coils Research Articles

A Novel Efficient Algorithm for Magnetic Biplanar Coils

A Novel Efficient Algorithm for Magnetic Biplanar Coils

Biplanar coils design for spatial nonlinear magnetic fields using an enhanced target field method

The demand for spatial nonlinear magnetic fields (SNMF) spans diverse domains, encompassing medical applications like drug transportation and aerospace applications such as attitude control. Existing designs of magnetic field coils predominantly focus on uniform and gradient fields as the complexity of nonlinear magnetic field distribution often leads to intricate solution processes. This paper presents a novel approach to coil design, addressing the challenge of SNMF distribution by reconstructing the characteristic matrix within the traditional target field method (TFM). To solve the overdetermined equations involved, we incorporate an improved particle swarm optimization algorithm into the TFM framework. A pair of symmetrical and asymmetrical coils are designed and the effectiveness of this method is verified by comparing the simulated and experimental results.

Measuring Human Auditory Evoked Fields with a Flexible Multi-Channel OPM-Based MEG System.

Magnetoencephalography (MEG) is a non-invasive imaging technique for directly measuring the external magnetic field generated from synchronously activated pyramidal neurons in the brain. The optically pumped magnetometer (OPM) is known for its less expensive, non-cryogenic, movable and user-friendly custom-design provides the potential for a change in functional neuroimaging based on MEG. An array of OPMs covering the opposite sides of a subject's head is placed inside a magnetically shielded room (MSR) and responses evoked from the auditory cortices are measured. High signal-to-noise ratio auditory evoked response fields (AEFs) were detected by a wearable OPM-MEG system in a MSR, for which a flexible helmet was specially designed to minimize the sensor-to-head distance, along with a set of bi-planar coils developed for background field and gradient nulling. Neuronal current sources activated in AEF experiments were localized and the auditory cortices showed the highest activities. Performance of the hybrid optically pumped magnetometer-magnetoencephalography/electroencephalography (OPM-MEG/EEG) system was also assessed. The multi-channel OPM-MEG system performs well in a custom built MSR equipped with bi-planar coils and detects human AEFs with a flexible helmet. Moreover, the similarities and differences of auditory evoked potentials (AEPs) and AEFs are discussed, while the operation of OPM-MEG sensors in conjunction with EEG electrodes provides an encouraging combination for the exploration of hybrid OPM-MEG/EEG systems.

Low noise magnetic field compensation based on differential biplanar coils with small coil constant

Magnetic field noise is a key factor limiting the resolution of quantum precise measurement. In active magnetic field compensation systems, the large coil constant and fixed noise of the coil and current source, respectively, cause excessive noise. This study proposes a differential biplanar coils (DBCs) design method by comprehensively optimizing two sets of biplanar coils with differential evolution (DE) algorithm, which can reduce the coil constant by two magnitude orders while ensuring high uniformity. The peak-to-peak magnetic field at the center point is reduced to 0.8 pT, and the magnetic field noise is reduced to 8 fT/Hz, which is a reduction of 94.4%. The low noise active magnetic compensation system based on the differential biplanar coils can improve the accuracy of the magnetic shielding room (MSR) internal magnetic field control and reduce magnetic field noise effectively. The proposed method contributes to generating a near-zero magnetic field environment with low magnetic field noise, which is critical to promoting magnetoencephalography (MEG) measurements.

Analysis and Design of Biplanar Coils Within Magnetic Shielding Room Considering Actual Ferromagnetic Boundaries

Analysis and Design of Biplanar Coils Within Magnetic Shielding Room Considering Actual Ferromagnetic Boundaries

Design and Optimization of Biplanar Coils for Active Magnetic Compensation System Inside the MINI-Magnetically Shielded Room

Design and Optimization of Biplanar Coils for Active Magnetic Compensation System Inside the MINI-Magnetically Shielded Room

In Situ Study of the Magnetic Field Gradient Produced by a Miniature Bi-Planar Coil for Chip-Scale Atomic Devices.

The miniaturization of quantum sensors is a popular trend for the development of quantum technology. One of the key components of these sensors is a coil which is used for spin modulation and manipulation. The bi-planar coils have the advantage of producing three-dimensional magnetic fields with only two planes of current confinement, whereas the traditional Helmholtz coils require three-dimensional current distribution. Thus, the bi-planar coils are compatible with the current micro-fabrication process and are quite suitable for the compact design of the chip-scale atomic devices that require stable or modulated magnetic fields. This paper presents a design of a miniature bi-planar coil. Both the magnetic fields produced by the coils and their inhomogeneities were designed theoretically. The magnetic field gradient is a crucial parameter for the coils, especially for generating magnetic fields in very small areas. We used a NMR (Nuclear Magnetic Resonance) method based on the relaxation of 131Xe nuclear spins to measure the magnetic field gradient in situ. This is the first time that the field inhomogeneities of the field of such small bi-planar coils have been measured. Our results indicate that the designed gradient caused error is 0.08 for the By and the Bx coils, and the measured gradient caused error using the nuclear spin relaxation method is 0.09±0.02, suggesting that our method is suitable for measuring gradients. Due to the poor sensitivity of our magnetometer under a large Bz bias field, we could not measure the Bz magnetic field gradient. Our method also helps to improve the gradients of the miniature bi-planar coil design, which is critical for chip-scale atomic devices.

Biplanar quadrature coil for versatile low-field extremity MRI

Biplanar magnets offer extended flexibility in MRI, particularly appealing due to unmatched accessibility to the patient. At low field strength (<0.2 T), such geometries could be particularly suitable for interventional settings or purpose-built applications such as musculoskeletal imaging. In the proposed work, we present a dual-channel, biplanar coil array for low-field MRI featuring almost fully open access when sited in a biplanar magnet. The proposed detector relies on the assembly of two orthogonal biplanar coils (single transmit channel, two receive channels in quadrature) respectively interfaced with custom inductive couplers. Simulations of the B1 field in each element were performed before the quadrature coil was built and used at ∼ 0.1 T (4.33 MHz). Once assembled, the best performance in our setup was achieved in undermatched conditions in place of conventional 50-Ω matching. Phantom images display the extended coverage of the quadrature coil, with similar SNR from each individual biplanar coil. The combined images show an expected SNR gain of 2 that confirms good decoupling between the two channels (−36 dB). To the best of our knowledge, the proposed coil represents the first implementation of a biplanar geometry at low field and the first quadrature detection for a biplanar design. The open design and overall good sensitivity of our biplanar design enabled fast and quasi-isotropic 3D imaging with (1.6 × 1.6 × 2.2) mm3 resolution in vivo in human extremities.

Iterative Optimization Algorithm to Design Biplanar Coils for Dynamic Magnetoencephalography

In this article, an iterative optimization algorithm is proposed to design biplanar coils, which is used for dynamic magnetoencephalography to compensate for residual fields in the magnetic shielding room. The effects of magnetic shielding layers and plane’s side length on the uniformity are both considered for designing coils. The iterative calculation is used to minimize the side length of the coil plane. The biplanar coils with 1.3-m side length are designed, which consist of three homogeneous-field coils ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$B_{x}, B_{y},\; { \rm and }\; B_{z}\; { \rm coils }$</tex-math></inline-formula> ) and five gradient-field coils ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dB_{x}/dy, dB_{x}/dz, dB_{y}/dy, dB_{y}/dz,\; { \rm and }\; dB_{z}/dz\; { \rm coils }$</tex-math></inline-formula> ). The coil system can produce homogeneous and gradient fields within 1% error over the volume of 40 cm × 40 cm × 40 cm. Through active magnetic shielding, the central field inside the magnetic room is reduced from 7.56 to 0.17 nT, and standard deviation from the mean value in the target area falls from 1.366 to 0.177 nT. The dynamic auditory stimulation experiment proves that the biplanar coil system will improve the quality of the evoked signals.

A Magnetic Compensation System Composed of Biplanar Coils Avoiding Coupling Effect of Magnetic Shielding

Magnetic compensation coils are often used to improve the effectiveness of a magnetically shielded room (MSR), but a distortion of the field is caused by the shielding layer consisting of high-permeability material, which leads to a reduction in compensation capacity. To solve this problem, a new method is presented in this article based on a target-field method, an image method, and particle swarm optimization. By this way, a magnetic compensation system composed of biplanar coils is designed and fabricated to compensate the background field for a wearable magnetoencephalography device inside the MSR, and the coupling effect between the magnetic shielding material and the compensation field is effectively avoided. Experimental data show that these compensation coils produce uniform fields and field gradients with the inhomogeneity of less than 3.8%, consistent with the simulation results. In addition, this system realizes a real-time compensation to the residual field and field gradient in the MSR.

Optimal Design of Self-Shielded Biplanar Coil Assembly With Miniaturized Structure

Optimal Design of Self-Shielded Biplanar Coil Assembly With Miniaturized Structure

Residual field suppression for magnetocardiography measurement inside a thin magnetically shielded room using bi-planar coil

For a magnetocardiography (MCG) system inside a magnetically shielded room (MSR), the residual field should be further suppressed to obtain high-quality MCG signals. In this paper, a compensation system has been developed based on the bi-planar coil and the proportional-integral-derivative (PID) controller. The bi-planar coil, derived from the target-field theory and the Tikhonov regularization method, is utilized to generate magnetic field with high uniformity in the pre-defined target region. And the PID controller is introduced to provide dynamic compensation current for the coil, according to the residual field change monitored by a reference SQUID magnetometer. The measurement results show that the noise suppression ratio (NSR) can reach above 20 dB in the low-frequency range from 0.1 Hz to 50 Hz. The DC component and the fluctuation of the residual field in time-domain can be respectively suppressed to 0 pT and 4 pT, indicating that this proposed compensation method is useful for the MCG measurement.

Design of Bi-Planar Coil for Acquiring Near-Zero Magnetic Environment

The magnetic source localization of the brain is very sensitive to artifacts caused by residual magnetic fields in space. Therefore, the high-uniformity magnetic coil is very important to acquire near-zero magnetic environment for magnetoencephalography (MEG). In this article, an optimized target field method (TFM) is proposed, in which bat algorithm (BA) is applied. The BA has excellent ability to search for the globally optimal solution, so the higher-uniformity coil can be designed with the same Fourier orders compare with traditional TFM. This novel method is used to design biplanar coil to compensate for residual magnetic field in space for MEG. Through the simulation and experimental result, the coil system designed by optimized TFM can produce uniform field (within ±5% error) over a volume of 11 cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times11$ </tex-math></inline-formula> cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times11$ </tex-math></inline-formula> cm. This volume is enough to contain a single brain functional region. Automated control of the coils allows reduction of the maximum component of field from 7.93 ± 0.29 to 0.32 ± 0.004 nT. The biplanar coil will suppress the drift field and bring more stable output signal of optical pumping magnetometers (OPMs). The auditory stimulation experiment proves that the biplanar coil system has significant effect on the MEG experiment.

Calibration of SQUID Magnetometers in Multichannel MCG System Based on Bi-Planar Coil

In a practical multichannel magnetocardiography (MCG) system based on superconducting quantum interference device (SQUID) magnetometers, the Tesla/Volt coefficient must be precisely calibrated for accurate analysis of heart diseases. In this article, we utilize the biplanar coil to calibrate the SQUID magnetometers in an MCG system for the first time. The coil design theory is discussed in detail, including the target-field theory and the Tikhonov regularization method. Also, the coil winding patterns can be obtained after discretization of the stream function, which is related to the current density. By defining the parameter of calibration uncertainty, the performance of the biplanar coil is analyzed and compared with a rectangular Helmholtz coil based on the COMSOL simulation method and experimental measurement. The measurement results are well in coincidence with the simulation ones, indicating that the biplanar coil has remarkable advantages over the Helmholtz coil. Also, Tesla/Volt coefficient calibrations of four SQUID magnetometers in an MCG system are conducted inside a magnetically shielded room (MSR) depending on these two coils. The final results show the superiority of the biplanar coil method in MCG system calibration.

A volumetric finite-difference method for the design of three-dimensional, arbitrary-structured MRI gradient coil.

A volumetric finite-difference based method is presented in this paper for the design of three-dimensional (3D), arbitrarily structured gradient coils in magnetic resonance imaging. In the proposed method, the coil space is discretized with quasi-rectangular elements, and the current density of each element is expressed by a finite-difference based numerical approximation of stream functions. The magnetic flux density at target field points can be calculated by those stream function values at all grids of the coil space. The optimization problem is constructed and solved to determine the stream function and coil patterns. This proposed method has been tested on several designs that include a shielded, ultra-short cylindrical coil, a partially shielded biplanar coil, and an asymmetric head coil with 3D geometries. The numerical results show that the proposed method is straightforward to implement and is versatile and suitable for designing complex structured gradient coils with high electromagnetic performance.

Design of Biplanar Coils for Degrading Residual Field in Magnetic Shielding Room

The uniform field and field gradient coils can be utilized for nulling the background field inside a magnetic shielding room (MSR), but the desired field produced by the coils is inevitably distorted due to the coupling effect of the magnetic shielding material. To overcome this problem, an improved method is proposed based on the image method and target field method (TFM). Directed by this method, a series of biplanar coils (BCs) are designed to produce the uniform fields and field gradients for an active compensation in an MSR. Then, their finite element models and practical experiment are established to verify the effectiveness. Compared with the conventional TFM, the proposed method shows significant effects for both uniform field coils and field gradient coils. Uniformities of the $\boldsymbol {B_{x}}$ and $\boldsymbol {B_{z}}$ increase by 79.9% and 72.5%, and the $\boldsymbol {dB_{x}/dz}$ and $\boldsymbol {dB_{z}/dz}$ improve by 89.6% and 63.2%, respectively. It demonstrates that this method is adopted to design the BCs fixed in MSR and holds great promise for the active compensation of environmental magnetic field in the measurement of magnetoencephalogram (MEG).

Hybrid Optimal Design of Biplanar Coils With Uniform Magnetic Field or Field Gradient

This article presents a hybrid optimal design of biplanar coils, which produce uniform fields and field gradients. It treats the coil design issue as a nonlinear programming problem, and seeks the best performance via the optimal algorithm. The target field method is first utilized to obtain the initial coefficients and ranges of searching areas in stream functions. Then, the magnetic field relative error is defined as the fitness function for minimization, and the particle swarm optimization algorithm is adopted to optimize the aforementioned coefficients. It not only overcomes the dependence on the position distribution of target field points, but also reduces the required computational dimensions without affecting the pursuit of the ultimate performance. Comparing this work with the traditional target field method, the field inhomogeneity error in the region of interest is reduced from 6.55% to 0.95% (B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> coil), 12.02% to 0.35% (B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</sub> coil), 16.54% to 0.57% (dB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> /dz coil), and 11.8% to 0.28% (dB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</sub> /dz coil). Numerical simulation and experimental results show the validity and significance of the proposed method. It has great improvements in both uniform fields and field gradients, which is beneficial to the perfect realization of nulling undesired magnetic fields.

Balanced, bi-planar magnetic field and field gradient coils for field compensation in wearable magnetoencephalography

To allow wearable magnetoencephalography (MEG) recordings to be made on unconstrained subjects the spatially inhomogeneous remnant magnetic field inside the magnetically shielded room (MSR) must be nulled. Previously, a large bi-planar coil system which produces uniform fields and field gradients was used for this purpose. Its construction presented a significant challenge, six distinct coils were wound on two 1.6 × 1.6 m2 planes. Here, we exploit shared coil symmetries to produce coils simultaneously optimised to generate homogenous fields and gradients. We show nulling performance comparable to that of a six-coil system is achieved with this three-coil system, decreasing the strongest field component Bx by a factor of 53, and the strongest gradient dBx/dz by a factor of 7. To allow the coils to be used in environments with temporally-varying magnetic interference a dynamic nulling system was developed with a shielding factor of 40 dB at 0.01 Hz. Reducing the number of coils required and incorporating dynamic nulling should allow for greater take-up of this technology. Interactions of the coils with the high-permeability walls of the MSR were investigated using a method of images approach. Simulations show a degrading of field uniformity which was broadly consistent with measured values. These effects should be incorporated into future designs.

A bi-planar coil system for nulling background magnetic fields in scalp mounted magnetoencephalography

Small, commercially-available Optically Pumped Magnetometers (OPMs) can be used to construct a wearable Magnetoencephalography (MEG) system that allows large head movements to be made during recording. The small dynamic range of these sensors however means that movement in the residual static magnetic field found inside typical Magnetically Shielded Rooms (MSRs) can saturate the sensor outputs, rendering the data unusable. This problem can be ameliorated by using a set of electromagnetic coils to attenuate the spatially-varying remnant field. Here, an array of bi-planar coils, which produce an open and accessible scanning environment, was designed and constructed. The coils were designed using a harmonic minimisation method previously used for gradient coil design in Magnetic Resonance Imaging (MRI). Six coils were constructed to null Bx, By and Bz as well as the three dominant field gradients dBx/dz, dBy/dz and dBz/dz. The coils produce homogeneous (within ±5%) fields or field gradients over a volume of 40 × 40 × 40 cm3. This volume is sufficient to contain an array of OPMs, mounted in a 3D-printed scanner-cast, during basic and natural movements. Automated control of the coils using reference sensor measurements allows reduction of the largest component of the static field (Bx) from 21.8 ± 0.2 nT to 0.47 ± 0.08 nT. The largest gradient (dBx/dz) was reduced from 7.4 nT/m to 0.55 nT/m. High precision optical tracking allowed experiments involving controlled and measured head movements, which revealed that a rotation of the scanner-cast by ±34° and translation of ±9.7 cm of the OPMs in this field generated only a 1 nT magnetic field variation across the OPM array, when field nulling was applied. This variation could be further reduced to 0.04 nT by linear regression of field variations that were correlated with the measured motion parameters. To demonstrate the effectiveness of the bi-planar coil field cancellation system in a real MEG experiment, a novel measurement of retinotopy was investigated, where the stimulus remains fixed and head movements made by the subject shift the visual presentation to the lower left or right quadrants of the field of view. Left and right visual field stimulation produced the expected responses in the opposing hemisphere. This simple demonstration shows that the bi-planar coil system allows accurate OPM-MEG recordings to be made on an unrestrained subject.

Oval gradient coils for an open magnetic resonance imaging system with a vertical magnetic field

Existing open magnetic resonance imaging (MRI) systems use biplanar gradient coils for the spatial encoding of signals. We propose using novel oval gradient coils for an open vertical-field MRI. We designed oval gradients for a 0.3T open MRI system and showed that such a system could outperform a traditional biplanar gradient system while maintaining adequate gradient homogeneity and subject accessibility. Such oval gradient coils would exhibit high efficiency, low inductance and resistance, and high switching capability. Although the designed oval Y and Z coils showed more heat dissipation and less cooling capability than biplanar coils with the same gap, they showed an efficient heat-dissipation path to the surrounding air, which would alleviate the heat problem. The performance of the designed oval-coil system was demonstrated experimentally by imaging a human hand.