Revisiting excitation pattern design for magnetic resonance imaging through optimisation of the signal contrast efficiency

The design of excitation signals for Magnetic Resonance Imaging (MRI) is cast as an optimal control problem. Here, we demonstrate that signals other than pulse excitations, which are ubiquitous in MRI, can provide adequate excitation, thus challenging the optimality and ubiquity of pulsed signals. A class of on-resonance piecewise continuous amplitude modulated signals is introduced. It is shown that despite the bilinear nature of the Bloch equations, the spins system response is largely analytically tractable for this class of signals, using Galerkin approximation methods. To challenge the optimality of the pulse excitation, an appropriate cost criterion, the Signal Contrast Efficiency (SCE), is developed. It is to be optimised subject to dynamics expressed by the Bloch equations. To solve the problem the Bloch equation is transferred to the excitation dependent rotating frame of reference. The numerical solutions to the problem for different tissue types show that for a short period of time, pulse excitations provide the maximum signal contrast. However, the problem should be solved for longer periods of time which may result in a different answer than a pulse. For this purpose, the approximate analytic solution which is derived based on averaging the Bloch equation in the excitation dependent rotating frame of reference will be used to find the optimal excitation pattern. The solution to the optimisation problem is potentially useful for all forms of MRI including structural and functional imaging. The objective of this paper is to show that while classically transient response of pulses have been monitored so far, the optimal excitation pattern may be the steady state response of a non-pulse excitation.