Discrete Design Method of a Transverse Gradient Coil for Magnetic Resonance Imaging

S. Shvartsman, G. DeMeester, M. Morich Philips Medical Systems, Cleveland, Ohio, United States Introduction In this work we describe a discrete gradient coil design method that does not include some of the essential steps of continuous current based minimum energy design methods. The key concept is that all characteristics of a transverse gradient, such as coil inductance, spatial distribution of the magnetic field, coil resistance, and slew rate of the coil, are expressed through the set of z-intercepts where the coil current pattern intersects the cardinal axes, for example Zi along φ=0 and φ=π for an X-gradient. We illustrate the advantages of the discrete design method with the example of a whole body gradient. Method Conventional methods of shielded gradient coil design [1,2] include two important steps: 1) find the continuous current distributions on the primary and shield coils that provides the required field quality characteristics such as gradient strength at the isocenter of the coil, gradient field linearity and uniformity within the Field-of-View (FoV), minimum coil inductance, and good shielding. In the case of finite length coils the current density is represented by a finite length series expansion; 2) discretize the continuous current distribution with an integer number of turns to match the power amplifier current-voltage characteristics. Constraints can be built into the analytical formalism [2] to achieve these goals. Depending on the size of the FoV, the size of the coil, and the field quality characteristics it often happens that the coil turns on the primary coil are most concentrated along the lines φ=0 and φ=π. The spacing between the turns centroids along these lines determines the allowed conductor widths and positions. Regions with smallest spacing have the highest power density. Power density or turns density is an important factor for short coils with relatively large FoV. We propose a method of shielded transverse gradient design that provides direct control of turns density. Suppose one wants to design a gradient coil that has S P N , number of turns in each of four quadrants on the primary/shield coil. Our method starts with a “pre-discretized” primary coil that carries