Design of Gradient Magnetic Field Coil Based on an Improved Particle Swarm Optimization Algorithm for Magnetocardiography Systems

Abstract

An improved particle swarm optimization method with multistage inertia weights is proposed for the design of gradient coils for use in magnetocardiography systems. With this method, the design of the gradient coils is transformed into a constrained nonlinear objective optimization problem, and the particle swarm optimization method with multistage inertia weights is used to solve this problem and thus obtain optimized size parameters for the coils. Furthermore, through comprehensive use of several parameters in combination, including the magnetic field derivative, the target field information, and the optimization algorithm, a highly linear magnetic field is produced by considering the constraints of the coil structure and the turns ratio. Simulation results show that the linearity spatial deviation of the designed gradient coil is one order of magnitude lower than that of the Maxwell coil with a sphere of a radius of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.5~R$ </tex-math></inline-formula> . Using the proposed method, two optimized gradient coils are manufactured for magnetocardiography system applications with magnetic fields that are matched well with those produced by the theoretical simulation model. Experimental results show that the maximum of the linearity spatial deviation of the proposed gradient coils reaches <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.2\times 10^{-3}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.4\times 10^{-3}$ </tex-math></inline-formula> along the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$ </tex-math></inline-formula> -axis within ± <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.5~R$ </tex-math></inline-formula> , respectively.