Design of small-scale gradient coils in magnetic resonance imaging by using the topology optimization method

A topology optimization method based on the solid isotropic material with penalization interpolation scheme is utilized for designing gradient coils for use in magnetic resonance microscopy. Unlike the popular stream function method, the proposed method has design variables that are the distribution of conductive material. A voltage-driven transverse gradient coil is proposed to be used as micro-scale magnetic resonance imaging（MRI） gradient coils, thus avoiding introducing a coil-winding pattern and simplifying the coil configuration. The proposed method avoids post-processing errors that occur when the continuous current density is approximated by discrete wires in the stream function approach. The feasibility and accuracy of the method are verified through designing the z-gradient and y-gradient coils on a cylindrical surface.Numerical design results show that the proposed method can provide a new coil layout in a compact design space.

Gradient coil design with enhanced shielding constraint for a cryogen-free superconducting MRI system

The relatively fragile low-temperature stability of cryogen-free superconducting magnetic resonance imaging(MRI)magnets requires the careful management of exogenous heat sources.A strongly shielded gradient magnetic field is important for the optimal operation of cryogen-free MRI systems.In this study,we present an enhanced shielding method incorporating a regionalized stray field constraining strategy.By optimizing the constraint parameters,we could develop engineering-feasible gradient coil schemes without increasing system complexity but with the stray field intensity reduced by half.In real measurement in an integrated MRI system,the developed gradient assembly demonstrated good performance and supported to output images of excellent quality.Our findings suggested that the proposed method could potentially form a useful design paradigm for cryogen-free MRI magnets.

Accurate surface normal representation to facilitate gradient coil optimization on curved surface

The design methods for gradient coils are mostly based on discrete extrinsic methods(e.g.,the BioteSavart integration calculation),for which the surface normal vector strongly influences any numerical calculation of the discretized surface.Previous studies are mostly based on regular or analytical surfaces,which allow normal vectors to be expressed analytically.For certain applications,design methods for extending currentcarrying surfaces from developable or analytic geometries to arbitrary surfaces generated from a scanned point cloud are required.The key task is to correctly express the discretized normal vectors to ensure geometrical accuracy of the designed coils.Mathematically,it has been proven that applying a Delaunay triangulation to approximate a smooth surface can result in the discrete elemental normal vectors converging to those of the original surface.Accordingly,this article uses Delaunay triangulation to expand upon previous design methods so that they encompass arbitrary piecewise continuous surfaces.Two design methods,the stream function and the so-called solid isotropic material with penalization(SIMP)method,are used to design circumvolute and noncircumvolute gradient coils on general surfaces.

Multi-objective optimization of gradient coil for benchtop magnetic resonance imaging system with high-resolution

Significant high magnetic gradient field strength is essential to obtaining high-resolution images in a benchtop mag- netic resonance imaging （BT-MRI） system with permanent magnet. Extending minimum wire spacing and maximum wire width of gradient coils is one of the key solutions to minimize the maximum current density so as to reduce the local heating and generate higher magnetic field gradient strength. However, maximum current density is hard to optimize together with field linearity, stored magnetic energy, and power dissipation by the traditional target field method. In this paper, a new multi-objective method is proposed to optimize the maximum current density, field linearity, stored magnetic energy, and power dissipation in MRI gradient coils. The simulation and experimental results show that the minimum wire spacings are improved by 159% and 62% for the transverse and longitudinal gradient coil respectively. The maximum wire width increases from 0.5 mm to 1.5 mm. Maximum gradient field strengths of 157 mT/m and 405 mT/m for transverse and lon- gitudinal coil are achieved, respectively. The experimental results in BT-MRI instrument demonstrate that the MRI images with in-plane resolution of 50 ~tm can be obtained by using the designed coils.

Equivalent magnetic dipole method used to design gradient coil for unilateral magnetic resonance imaging

The conventional magnetic resonance imaging（MRI） equipment cannot measure large volume samples nondestructively in the engineering site for its heavy weight and closed structure. In order to realize the mobile MRI, this study focuses on the design of gradient coil of unilateral magnet. The unilateral MRI system is used to image the local area above the magnet. The current density distribution of the gradient coil cannot be used as a series of superconducting nuclear magnetic resonance gradient coils, because the region of interest（ROI） and the wiring area of the unilateral magnet are both cylindrical side arc surfaces. Therefore, the equivalent magnetic dipole method is used to design the gradient coil, and the algorithm is improved for the special case of the wiring area and the ROI, so the X and Y gradient coils are designed.Finally, a flexible printed circuit board（PCB） is used to fabricate the gradient coil, and the magnetic field distribution of the ROI is measured by a Gauss meter, and the measured results match with the simulation results. The gradient linearities of x and y coils are 2.82% and 3.56%, respectively, less than 5% of the commercial gradient coil requirement.

Modulation of the plasma uniformity by coil and dielectric window structures in an inductively coupled plasma

The effects of coil and dielectric window structures on the plasma distribution are examined in a cylindrically symmetric planar inductively coupled plasma(ICP).A two-dimensional(2 D)fluid model is employed to investigate the design issues of ICP source for etching.When the gradient coil structure is applied at 400 W and 20 mTorr,the ionization rate caused by the power deposition decreases at the reactor center as compared to that in a reactor with a planar coil above the planar dielectric window,and a rather uniform plasma is obtained.However,for the vertical coil geometry,all the coils move to the position of the outermost coil,and the peaks of the power deposition and ionization rate appear at the radial edge of the substrate.In this case,the plasma density is characterized by an edge-high profile.Further,it is observed that the plasma uniformity is improved by increasing the source power under a gas pressure of 20 mTorr and becomes better when the gas pressure increases to 30 mTorr with the source power being fixed at400 W in the gradient coil configuration,but the uniformity of plasma worsens with the rising source power or pressure due to the strong localization in the vertical coil geometry.Moreover,when the discharge is sustained in a reactor with a stepped dielectric window at r=0.135 m,the best plasma uniformity is obtained at 400 W and 20 m Torr because the ionization rate is enhanced at the outermost coil,and the dielectric window at r=0.135 m blocks the diffusion of plasma towards the axis.In addition,higher source power and lower gas pressure produce more uniform plasma for the designs with a stepped window near the symmetry axis.When the dielectric window is stepped at r=0.135 m,the non-uniformity of plasma initially decreases and then increases with the increase in source power or gas pressure.When the dielectric window is stepped at the radial edge of the chamber,the plasma uniformity is improved by increasing the source power and gas pressure due to the enhanced ionization at the larger radius caused by the severe localization.