A time domain signal equation for multi-echo spin-echo sequences with arbitrary excitation and refocusing angle and phase

Accurate T2 mapping using multi-echo spin-echo is usually impaired by non-ideal refocusing due to B1+ inhomogeneities and slice profile effects. Incomplete refocusing gives rise to stimulated echo and so called "T1-mixing" and consequently a non-exponential signal decay. Here we present a time domain formula that incorporates all relaxation and pulse parameters and enables accurate and realistic modelling of the magnetization decay curve. By pulse parameters here we specifically mean the actual refocusing angle and axis, and phase angle of both the excitation and refocusing pulse. The method used for derivation comprises the so called Generating functions approach with subsequent back-transformation to the time domain. The proposed approach was validated by simulations using realistic RF pulse shapes as well as by comparison to phantom measurements. Excellent agreement between simulations and measurements underpin the validity of the presented approach. Conclusively, we here present a complete time domain formula ready to use for accurate T2 mapping with multi-echo spin-echo sequences.