Magnetic resonance imaging gradient coil design by combining optimization techniques with the finite element method

In this paper, the optimization techniques of complex method, steepest descent, and conjugate gradient are investigated in terms of their convergence behaviors. The conjugate gradient method is then combined with finite element analysis techniques to develop a magnetic resonance imaging (MRI) G_z gradient coil design strategy which maximizes the field linearity within a specified region of interest. It is found that conjugate gradient optimization in conjunction with the finite element method is a powerful and flexible coil design approach with the potential to incorporate complex coil geometries, inhomogeneous media, and transient current excitation