中文摘要：

梯度线圈是磁共振系统的核心部件之一,其产生的梯度磁场是成像空间定位的物理基础。在开放式磁共振系统中,大量铁磁介质会导致实际梯度磁场偏离设计值,因此需要对实际梯度磁场进行校验。本文针对开放式磁共振的结构特点,提出了一种基于扇环形状单元的积分方程法,可以计算二维/三维模型中的梯度磁场。针对两种常见的开放式磁共振结构,通过将本文方法的计算结果与其他三种方法（直接法、镜像法和有限元法）进行对比,证明了本文方法在保证计算精度的同时,可以大幅减少计算时间,在重复计算和迭代优化中具有显著优势。实验结果证明了该算法具有良好的可靠性。

英文摘要：

Gradient coil is one of the key components in the magnetic resonance imaging（ MRI） system. The effect of gradient magnetic field is to provide the spatial orientation of imaging. In biplanar MRI system,a large number of ferromagnetic materials would destroy the gradient magnetic field,so it is necessary to calibrate the gradient magnetic field. Aiming at the structural characteristics of biplanar MRI,a new method to calculate the gradient magnetic field in three dimensional model based on the integral equation method and sector-ring element is presented in this paper. In two different MRI structures,simulation results of the proposed method is compared with the method without ferromagnetic materials,mirror method and finite element method. It is proved that the proposed method can effectively reduce the computing time and has a significant advantage in the repeated calculation and iterative optimization while ensuring the accuracy. Experimental results also show that the proposed method has good reliability.