Adaptively regularized gradient coils for reduced local heating

Gradient and shim coil design is an inverse problem in which the objective is to generate a magnetic field with an error that falls within acceptable limits while optimizing some other property of the coil. This problem can be solved using a boundary element method via regularized matrix inversion. However, it is not possible to optimize properties that are not linear‐least‐squares with respect to the solutions using this method. In this work, we employ adaptive regularization to design coils with reduced maximum local current density, which is not a linear‐least‐squares problem. Reducing the maximum local current density allows the design of coils with lower maximum local Joule heating for the same gradient field strength and uniformity. Excessive local heating can be the cause of thermal drift and localized gradient failure. The minimum spacing between wires is increased by this method, permitting the design of more efficient coils for a given minimum wire spacing constraint as dictated by the method of manufacture. The adaptive regularization method, as formulated within the inverse boundary element method (IBEM) coil design framework, is described and results from three types of adaptively regularized coils are presented. The maximum local current densities of the coils are shown to be significantly reduced by adaptive regularization at the expense of some increase in their inductances and resistances. © 2008 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 33B: 220–227, 2008