The Bloch equation revisited through averaging under adiabatic passages

Abstract

In order to derive a simplified solution to a bilinear system originating from the Bloch equation under adiabatic excitation, we have employed a nonlinear averaging technique for the first time in magnetic resonance context. We achieve an averaged solution with an acceptable level of error by transferring the dynamics of the Bloch equation to a novel rotating frame of reference through a rotation and a proper time-scaling. In this frame, the states of the system which represent the components of magnetic resonance signal are slowly varying and thus can be averaged to achieve an approximate solution. Error analysis of the averaged solution as well as the simulation results clearly show that t..