Minhua Zhu

MRI Coil Design Using Boundary-Element Method With Regularization Technique: A Numerical Calculation Study

A new boundary element method (BEM) based method is described for the design of coils for magnetic resonance imaging (MRI) systems. BEM is an effective approach for solving the electromagnetic forward problem and has been used in the design of MRI gradient coils. However, BEM-based gradient coil design faces an ill-posed mathematical problem, which is conventionally handled by means of a Lagrange multiplication method. This work attempts to improve the BEM method for MRI coil designs by applying the Tikhonov regularization scheme to solve the ill-posed matrix system formulated by the BEM forward model. The objective of the study is not to design some specific gradient or radio-frequency (RF) coils for MRI system, but to discuss the design scheme with practical regularization and constraints. The proposed approach was explained in the design of MRI coils including biplanar transverse gradient coils and RF phased array coils. With the consideration of the practical engineering requirements, physical constraints such as wire intervals are transformed into mathematical constraints and formulated into BEM equations. The examples demonstrate that the proposed method is efficient and flexible for the design of MRI coils with arbitrary geometries and engineering constraints.

A Finite Difference Method for the Design of Gradient Coils in MRI—An Initial Framework

This paper proposes a finite-difference (FD)-based method for the design of gradient coils in MRI. The design method first uses the FD approximation to describe the continuous current density of the coil space and then employs the stream function method to extract the coil patterns. During the numerical implementation, a linear equation is constructed and solved using a regularization scheme. The algorithm details have been exemplified through biplanar and cylindrical gradient coil design examples. The design method can be applied to unusual coil designs such as ultrashort or dedicated gradient coils. The proposed gradient coil design scheme can be integrated into a FD-based electromagnetic framework, which can then provide a unified computational framework for gradient and RF design and patient-field interactions.

Deformation-Space Method for the Design of Biplanar Transverse Gradient Coils in Open MRI Systems

We propose an efficient real-space algorithm for the design of biplanar transverse gradient coils for use in open magnetic resonance imaging (MRI) systems. In our method, each wire arc is represented by a closed contour (Limacon). Using parametric equations, we deform/reshape an ensemble of closed contours in a simple manner, controllable by just a few parameters. These parameters are used to define system rearrangements in the design procedure. We use an iterative optimization procedure to adjust the control parameters in order to minimize cost functions such as gradient homogeneity and inductance. Here, we compare the coil pattern designed by our deformation-space method with a pattern designed by the conventional stream function approach, and we discuss the merit of the new method.

A novel passive shimming method for the correction of magnetic fields above the patient bed in MRI.

This paper presents a novel passive shimming method for the effective correction of static magnetic field (B0) inhomogeneities in Magnetic Resonance Imaging (MRI) systems. Passive shimming is used to find an optimum configuration for the placement of iron pieces applied to improve the B0 uniformity in the predefined imaging region referred to as the diameter of spherical volume (DSV). However, most passive shimming methods neglect to recognize that the space under the patient bed is not in use for imaging. In this work, we present a new algorithm that attempts to avoid the unnecessary shimming of the space under the patient bed. During implementation, the B0 field is still measured over the DSV surface and then mapped onto the effective imaging volume surface; a dedicated sensitivity matrix is generated only for the imaging area above the patient bed. A linear programming optimization procedure is performed for the determination of thicknesses and locations the shim pieces. Our experimental results showed that by revising the shimming target area, the new method provides superior optimization solutions. Compared to a conventional approach, the new method requires smaller amount of iron to correct the B0 inhomogeneities in the imaging area which has the effect of improving thermal stability to the B0 field. It also reduces the complexity of the optimization problem. Our new shimming strategy helps to improve the magnetic field homogeneity within the realistic imaging space, and ultimately improve image quality.

Passive shimming of a superconducting magnet using the L1-norm regularized least square algorithm.

The uniformity of the static magnetic field B0 is of prime importance for an MRI system. The passive shimming technique is usually applied to improve the uniformity of the static field by optimizing the layout of a series of steel shims. The steel pieces are fixed in the drawers in the inner bore of the superconducting magnet, and produce a magnetizing field in the imaging region to compensate for the inhomogeneity of the B0 field. In practice, the total mass of steel used for shimming should be minimized, in addition to the field uniformity requirement. This is because the presence of steel shims may introduce a thermal stability problem. The passive shimming procedure is typically realized using the linear programming (LP) method. The LP approach however, is generally slow and also has difficulty balancing the field quality and the total amount of steel for shimming. In this paper, we have developed a new algorithm that is better able to balance the dual constraints of field uniformity and the total mass of the shims. The least square method is used to minimize the magnetic field inhomogeneity over the imaging surface with the total mass of steel being controlled by an L1-norm based constraint. The proposed algorithm has been tested with practical field data, and the results show that, with similar computational cost and mass of shim material, the new algorithm achieves superior field uniformity (43% better for the test case) compared with the conventional linear programming approach.

Improved halbach magnets by particle swarm optimization for mobile nuclear magnetic resonance systems

The Halbach magnets have been widely used in engineering especially for the mobile NMR (Nuclear Magnetic Resonance) systems. The homogeneity of the magnetic field generated by the magnet affects the imaging quality of NMR. In this paper, we have proposed two improved 2D constructions of the Halbach magnet, which can improve the magnetic field uniformity greatly. The improved constructions of Halbach magnet are optimized by the modified PSO (particle swarm optimization) algorithm and the simulations are based on the 2D Finite Element Method (FEM) analysis.

A Finite-Difference Method for the Design of Biplanar Transverse Gradient Coil in MRI

This paper presents a finite difference method for the design of gradient coil in MRI. In this method, a linear matrix equation is formulated using a finite-difference approximation of the current density in the source domain and an optimization procedure is then carried out to solve the resulting inverse problem and the coil winding pattern are found. The developed algorithm is tested with a transverse biplanar gradient coil design example. Compared with conventional design methods such as target-field, standard stream function or boundary element schemes, the new design approach is relatively easy to implement and flexible to manage the local winding pattern for 2D or 3D geometries.