中文摘要：

射频（RF）线圈是磁共振成像（MRI）系统的关键部件之一,用于射频信号的发射或接收,乳腺3 T MRI中采用专用的射频线圈可进一步提高磁共振成像的质量。为了获得简单的线圈绕线形状并使得射频磁场分布均匀,研究利用了L曲线自动选取和手动选取惩罚因子对线圈绕线形状和磁场分布均匀性的影响,并结合目标场方法和流函数方法,提出了一种用于3 T（磁感应强度为3 T）乳腺磁共振成像的射频线圈设计方法。研究结果表明：1×1、2×1、2×2、4×1等4种半球形相控阵射频线圈的绕线形状随着阵列增加而变复杂;惩罚因子取利用L曲线自动选取的值时,磁感应强度线性方程的解最精确,阵列1×1在[10-25,10-18]区间内无论怎样选取惩罚因子,灵敏区内的磁场分布误差（即实际值与理想值之间的误差）都〉40%,阵列2×2和4×1的磁场分布误差〈10%,但是线圈绕线形状非常复杂,工程上难以实现;手动选取惩罚因子的值,可以使得磁场分布误差〈40%,而且线圈的绕线形状简单;与相同半径和高度的圆柱型射频线圈相比,所提出的半球型射频线圈磁场分布更为均匀。可得结论：惩罚因子越小,则线圈绕线越复杂,而磁场分布越均匀;反之,惩罚因子越大,则线圈绕线越简单,而磁场分布越不理想。在简单的线圈绕线形状和保证射频磁场分布均匀之间取得平衡需要根据L曲线手动调节选取惩罚因子的值。

英文摘要：

As one of the key components in MRI systems, radio-frequency（RF） coil is used for transmitting or receiving RF signals. In 3 T breast MRI, using dedicated breast RF coils could further improve the image quality. To obtain simple winding patterns for this dedicated coil while assuring the homogeneity of its RF magnetic field, we studied the effect of using penalty factors automatically chosen by L-curve method and manually selected on the winding patterns and the field homogeneity, and proposed an inverse design method for the 3 T breast RF that combines the target field method and the stream function method. Several conclusions can be drawn as follows： The winding patterns for 1×1, 2×1, 2×2, 4×1 array become more complex with increasing array number. Using penalty factor automatically selected with the L-curve method, we can obtain the most precise solution of magnetic field intensity＇s linear equations. The error of 1×1 arrays between real and ideal magnetic fields is over 40% when the penalty factor is chosen between 10-25 and 10-18. Meanwhile, the errors of 2×2 and 4×1 arrays are less than 10% when the penalty factor is automatically selected, but in this case the winding pattern gets too complex to be implemented in engineering applications. Manually selecting the penalty factor can make the winding pattern simple while keeping the error between real and ideal magnetic fields within 40%. Compared with the cylindrical RF coil which has the same radius and height, the hemispherical breast RF coil proposed in this paper has magnetic field with better homogeneity. It is concluded that when the penalty factor decreases, the winding pattern becomes more complex but the magnetic field gets more homogeneous. Conversely, when the penalty factor increases, the winding pattern becomes simpler but the magnetic field becomes less ideal. To balance the simplicity and the homogeneity of magnetic field, it is better to determine the penalty factor manually according to the L-curve.