Design and implementation of uniplanar gradient field coil for magnetic resonance imaging

We present a new approach to the design of uniplanar gradient coils for magnetic resonance imaging. The theoretical formulation involves a constraint cost function between the desired field in a particular region of interest in space and the current-carrying coil plane, based on Biot-Savart´s integral equation. An appropriate weight function in conjunction with linear approximation functions allows us to transform the problem formulation into a linear matrix equation whose iterative solution yields discrete current elements in terms of magnitude and direction within a specified coil plane. These current elements can be synthesized into an overall practical wire configuration by suitably adding individual wire loops. Numerical predictions and measurements for the G_y gradient coil show that this approach produces a highly linear field while maintaining low parasitic fields.