Liu H, Truwit C L
Center for MR-guided Therapy, University of Minnesota, Minneapolis 55455, USA.
IEEE Trans Med Imaging. 1998 Oct;17(5):826-30. doi: 10.1109/42.736052.
Finite-sized high-performance planar magnetic field gradient coils in today's open configuration magnetic resonance imaging (MRI) systems have always been desirable for ever demanding imaging applications. We present a Lagrange multiplier technique for designing a minimum-energy gradient coil under a finite-size planar geometry constraint in addition to a set of magnetic field constraints. In this new design methodology, the surface current density on a finite size plane is represented by a two-dimensional (2-D) Fourier series expansion. Following the standard approach, we construct a functional F in terms of the stored magnetic energy and a set of field constraint points which are chosen over the desired imaging volume. Minimizing F, we obtain the continuous current density distribution for the finite-size planar gradient coil. Applying the stream function technique to the resulting continuous current distribution, the discrete current pattern can be generated. Employing the Biot-Savart law to the discrete current loops, the gradient magnetic field has been re-evaluated in order to validate the theory. Using this approach, we have been able to design a finite-size biplanar z-gradient coil which is capable of generating a gradient field of 40 mT/m @ 266 A. The excellent agreement between the analytical and numerical results has been achieved.
在当今的开放式配置磁共振成像（MRI）系统中，有限尺寸的高性能平面磁场梯度线圈一直是满足日益增长的成像应用需求所期望的。我们提出了一种拉格朗日乘数技术，用于在有限尺寸平面几何约束以及一组磁场约束条件下设计最小能量梯度线圈。在这种新的设计方法中，有限尺寸平面上的表面电流密度由二维（2-D）傅里叶级数展开表示。按照标准方法，我们根据存储的磁能和在期望成像体积上选择的一组场约束点构建一个泛函F。通过最小化F，我们得到了有限尺寸平面梯度线圈的连续电流密度分布。将流函数技术应用于所得的连续电流分布，可以生成离散电流模式。对离散电流环应用毕奥 - 萨伐尔定律，为了验证该理论，对梯度磁场进行了重新评估。使用这种方法，我们能够设计出一个有限尺寸的双平面z梯度线圈，该线圈能够在266 A时产生40 mT/m的梯度场。在分析结果和数值结果之间实现了极好的一致性。
