Driving mutually coupled gradient array coils in magnetic resonance imaging

Abstract

Purpose In contrast to conventional linear gradients, gradient coil arrays with arbitrary spatial dependency might experience strong mutual coupling. Although conventional gradient power amplifiers with feedback loop might compensate the effect of coupling, required voltages for the compensation are generally unknown and has to be considered beforehand to ensure that amplifier voltage limits are not exceeded. A first‐order circuit model is proposed to be used as a feedforward model which enables analytical formulas of required voltages to drive the mutually coupled gradient coil arrays.

Theory and Methods A first‐order circuit model including the mutual couplings is provided to analytically calculate the input voltages and minimum achievable rise times for a given set of gradient array currents and amplifier limitations. Previously designed 9‐channel Z‐gradient coil array and home‐built gradient amplifiers (50 V and 20 A) are used in the experiments. Three sets of currents optimized for linear Z‐gradient, second‐order Z2, and third‐order Z3 fields are used in the bench‐top experiments. The current weightings for the linear Z‐gradient are also used as the readout gradient in the 3T MRI experiments.

Results Current measurements for the example magnetic field profiles with minimum rise times are demonstrated for the simultaneous use of 9‐channel gradient coils and amplifiers. MRI experiments verify that a linear Z‐gradient field with a desired time waveform can be generated using a mutually coupled array coils.

Conclusion Bench‐top and MRI experiments demonstrate the feasibility of the proposed circuit model and analytical formulas to drive the mutually coupled gradient coils.