Shim design using a linear programming algorithm.

The advent of open magnetic resonance imaging (MRI) scanners and dedicated MRI scanners tailored to specific body parts has led to an increasing number of noncylindrical MRI scanner geometries, for which noncylindrical gradients and shims are needed. These new scanner geometries are driving the need for fast, flexible shim design methods that can design shim coils for any geometry. A linear programming (LP) algorithm was developed to design minimum-power resistive shim coils on an arbitrary surface. These coils can be designed to produce any order shim field over an arbitrarily shaped target region, which can be placed anywhere within the coil. The resulting designs are relatively sparse and can be readily constructed. This algorithm was used to design and construct a seven-coil cylindrical shim set for a knee imaging magnet with a cylindrical homogeneous region. The algorithm was then used to design shim coils for a biradial head imager with an asymmetrically located spherical target region for brain imaging.