An Analytic Framework for the Evaluation of Coil Configurations for Parallel Transmission MRI With Subsampled Cartesian Excitation k-Space

The use of multiple independent simultaneous radio-frequency (RF) transmitters and coils, known as parallel transmission, has the potential to make multidimensional excitation applicable to a wide range of magnetic resonance imaging applications. The sensitivity profile of the RF coils in a parallel transmission system determines the performance of the system. We present a theoretical framework, allowing the evaluation of the performance of a coil array for parallel transmission. We show through theoretical analysis and Monte Carlo simulation that the proposed framework predicts the fidelity of excitation that can be achieved by a given coil configuration in the presence of noise in the measured coil sensitivity profiles. We evaluate the fidelity of excitation achieved by four candidate coil configurations for a four-channel parallel transmission system with noisy coil sensitivity estimates. Theoretical results are confirmed with Monte Carlo simulation. The results give insight into the design of coil configurations for parallel transmission. In particular, optimal fidelity of excitation for subsampled Cartesian excitation k -space is achieved with a coil sensitivity profile having uniform amplitude and increasing linear phase for each channel. Such sensitivity profiles may be achieved with twisted birdcage coil designs.