Approximate B1+ scaling of the SSFP steady state

Abstract

Purpose: It is shown that the steady state of rapid, TR-periodic steady-state free precession (SSFP) sequences at small to moderate flip angles exhibits a universal, approximate scaling law with respect to variations of (Formula presented.). Implications for the accuracy and precision of relaxometry experiments are discussed. Methods: The approximate scaling law is derived from and numerically tested against known analytical solutions. To assess the attainable estimator precision in a typical relaxometry experiment, we calculate the Cramér–Rao bound (CRB) and perform Monte Carlo (MC) simulations. Results: The approximate universal scaling holds well up to moderate flip angles. For pure steady state relaxometry, we observe a significant precision penalty for simultaneous estimation of (Formula presented.) and (Formula presented.), whereas good (Formula presented.) estimates can be obtained without even knowing the correct actual flip angle. Conclusion: Simultaneous estimation of (Formula presented.) and (Formula presented.) from a set of SSFP steady states alone is not advisable. Apart from separate (Formula presented.) measurements, the problem can be addressed by adding transient state information, but, depending on the situation, residual effects due to the scaling may still require some attention.