In this paper, we present a novel nonlinear optimization algorithm for designing a shim coil system, especially a high-order axial shim coil, for a magnetic resonance imaging (MRI) system. In an MRI equipment, in order to eliminate higher-order harmonic components of the magnetic field within the volume of interest (VOI), passive shimming (PS) is adopted in traditional methods. However, such a method is suitable for the global shimming with low accuracy and poor target. Active shimming (AS) makes up for the shortcomings from PS with a set of shim coils which are designed to generate a specific magnetic fields to improve magnetic field homogeneity within the VOI. Because the complexity of wire pattern increases with the order of AS coil increasing, conventional optimization model cannot meet the design requirements for producing the complicated magnetic field. In this paper, we propose a nonlinear optimization method of designing the axial shim coils for an open-style bi-planar MRI system, based on boundary element method. The optimization model is built in light of influence extents of the various parameters on the coil characteristics for different shim coils. In such a new method, the field error between the magnetic field produced by designed shim coil and the desired target value is selected to be an optimal value subjected to some constraints including line spacing and coil radius, which makes it possible to realize the manufacture process. Meanwhile, the more design parameters, which involve not only the stream function values at each node, but also the compensation parameters and/or the number of grid nodes, are regarded as optimized variables to control the magnetic deviation and characteristics of designed coil. By using some designed shim coils for a 0.5 T open style bi-planar superconducting MRI, including Z1, Z2, Z3 and Z4, the efficiency of such a numerical design method is displayed. Especially for high-order shim coils, more optimized parameters are involved to control the magnetic deviation of the coils, thereby providing a more flexible and straightforward method of designing the axial shim coils.%在磁共振成像设备中，为了消除目标区域内的高阶谐波磁场分量，传统方法采用无源匀场，但该方法匀场精度较低，针对性较差，适用于全局匀场，而有源匀场则可以通过优化线圈分布来产生所需要的特定的磁场分布.但是，由于匀场线圈线型的复杂度会随着线圈阶数的增加而增加，难以满足设计需要，因此本文提出了一种用于磁共振成像超导匀场线圈系统的多变量非线性优化设计方法.该方法基于边界元方法，将匀场线圈所产生的磁场与目标磁场之间的偏差作为目标函数，线匝间距、线圈半径等作为约束条件，通过非线性优化算法，得到满足设计要求的线圈分布.通过一个中心磁场为0.5 T的开放式双平面磁共振成像超导轴向匀场线圈的设计案例，说明本方法具有计算效率高、灵活性好的特点.
展开▼
