Matrix gradient coils with up to 84 coil elements were recently introduced for magnetic resonance imaging. Ideally, each element is driven by a dedicated amplifier, which may be technically and financially infeasible. Instead, several elements can be connected in series (called a "cluster") and driven by a single amplifier. In previous works, a set of clusters, called a "configuration," was sought to approximate a target field shape. Because a magnetic resonance pulse sequence requires several distinct field shapes, a mechanism to switch between configurations is needed. This can be achieved by a hypothetical switching circuit connecting all terminals of all elements with each other and with the amplifiers. For a predefined set of configurations, a switching circuit can be designed to require only a limited amount of switches. Here we introduce an algorithm to minimize the number of switches without affecting the ability of the configurations to accurately create the desired fields. The problem is modeled using graph theory and split into 2 sequential combinatorial optimization problems that are solved using simulated annealing. For the investigated cases, the results show that compared to unoptimized switching circuits, the reduction of switches in optimized circuits ranges from 8% to up to 44% (average of 31%). This substantial reduction is achieved without impeding circuit functionality. This study shows how technical effort associated with implementation and operation of a matrix gradient coil is related to different hardware setups and how to reduce this effort.
Keywords: combinatorial optimization; magnetic resonance imaging; matrix gradient coil; nonlinear encoding; switching circuit.