Closed-form solution for T₂ mapping with nonideal refocusing of slice selective CPMG sequences

Purpose: T₂ quantification with multiecho sequences is typically impaired by the contribution of stimulated echoes to the echo decay due to B₁+ inhomogeneity and slice profile effects. In this work, a compact signal model based on the generating functions approach, which accounts for both sources of error, is presented. Methods: The generating functions (GF) approach is used to obtain a closed solution to the evolution of the transverse magnetization in an echo train, however, not in the time domain, but in the transformed z-domain. The approach is generalized by the incorporation of flip angle distribution across the refocusing slice profiles. The approach is tested by fitting the model to simulated data as well as to phantom and in vivo measurements, followed by a comparison with the common monoexponential fitting approach. Results: The fitting simulations indicate that T₂ errors of up to 30% can be commonplace in a clinical setting using the monoexponential method. Conversely, the GF approach produced accurate results. Phantom and in vivo experiments showed a good agreement of the GF values with spectroscopic measurements and single-echo spin-echo sequences. Conclusion: A correction for stimulated echoes is necessary to compute comparable T₂ values. The presented approach provides a solution to this issue.