Gradient Coil Design and Optimization for an Ultra-Low-Field MRI System

Gradient coils are used to generate the spatially varying gradient magnetic fields used to phase- and frequency-modulate the nuclear magnetic resonance (NMR) signal and enable position encoding in magnetic resonance imaging (MRI). The continuous-current–density-based method of gradient coil design has been well developed in mathematical modeling, however, practical design as it relates to the experimental realization of simulated gradient coil designs and their ultimate performance has not been well studied. In this work, we design and build a planar gradient coil system, consisting of X, Y, and Z gradient coils, for use in a 6.5 mT ultra-low-field MRI (ULF MRI) system. Specifically, we designed each gradient coil using the equivalent magnetic dipole method (EMDM), and further studied its realization by analyzing gradient-coil geometric parameters, including size, gap, conductor pattern, and conductor density. The geometric parameters are varied during the design of an optimal gradient coil and then analyzed using finite-element-method (FEM) simulations to reveal the relationship between the geometric parameters and gradient coil performance. Based on EMDM and the geometric parameter analysis, we arrive at an optimal gradient coil system whose performance was evaluated by FEM simulation and magnetic field measurement.