基于目标场法的磁共振成像小尺寸射频线圈设计

Design of Small-size Magnetic Resonance Imaging Radio-frequency Coils by Target Field Approach

为得到分辨率较高的实蝇磁共振图像(MRI),将目标场法引入小尺寸射频(RF)线圈设计,设计了一种磁场均匀性较好、适合实蝇磁共振成像的小尺寸圆柱体射频线圈。首先采用目标场法求出线圈表面的电流密度分布,利用流函数将电流密度离散为Fourier级数;然后基于Tikhonov正则化的方法,引入最小曲率惩罚函数和最小化电流密度的散度惩罚函数,解决了积分方程的高度病态问题,获得了线圈的绕线形状和感兴趣区域(ROI)内的磁场强度。结果表明,2种惩罚函数对应的惩罚因子λ1和λ2均会对线圈的绕线形状和磁场分布均匀性造成影响;对于不同尺寸的线圈,其合适的λ1和λ2的取值不同。因此,选取λ1和λ2时应综合考虑线圈绕线结构和磁场分布均匀性的要求。

To realize high-resolution magnetic resonance imaging（MRI） of fruit fly, we introduced the target field method into the design process of small size radio-frequency（RF） coils, and designed a small cylindrical RF coil which had uniform magnetic field distribution and suited for MRI of fruit fly. Firstly, we applied the target field method to calculate the current density distributing on the coil surface, and used the stream function to discretize current density functions into Fourier series. Then, by using the Tikhonov regularization method, we introduced the minimum curvature penalty function and minimum divergence of current densities penalty function to solve the highly ill-conditioned integral equations, and hence obtained the winding pattern of coils and the induced magnetic field in the region of interest（ROI）. It is concluded that the two penalty factors related to the two penalty functions both affect the winding pattern of coils and the homogeneity of induced magnetic field in ROI. Different RF coils have different fitting penalty factors. Therefore, the selection of penalty factors should comprehensively take the simplicity of coil＇s winding pattern and the homogeneity of induced magnetic field in ROI into consideration.