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.

梯度线圈用于生成空间变化的梯度磁场，用于对核磁共振 (NMR) 信号进行相位和频率调制，并在磁共振成像 (MRI) 中实现位置编码。基于连续电流密度的梯度线圈设计方法在数学建模中得到了很好的发展，但是，实际设计与模拟梯度线圈设计的实验实现及其最终性能有关，尚未得到很好的研究。在这项工作中，我们设计并构建了一个平面梯度线圈系统，由 X、Y 和 Z 梯度线圈组成，用于 6.5 mT 超低场 MRI (ULF MRI) 系统。具体来说，我们使用等效磁偶极子法（EMDM）设计了每个梯度线圈，并通过分析梯度线圈几何参数进一步研究了其实现，包括尺寸、间隙、导体图案和导体密度。在优化梯度线圈的设计过程中，几何参数会发生变化，然后使用有限元法 (FEM) 模拟进行分析，以揭示几何参数与梯度线圈性能之间的关系。基于EMDM和几何参数分析，我们得出了一个最佳梯度线圈系统，其性能通过有限元模拟和磁场测量进行了评估。