Approximate B1+ scaling of the SSFP steady state

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 B-1(+) . 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 Cramer-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 R-1 and B-1(+) , whereas good R-2 estimates can be obtained without even knowing the correct actual flip angle.Conclusion: Simultaneous estimation of R-1 and B-1(+) from a set of SSFP steady states alone is not advisable. Apart from separate B-1(+) measurements, the problem can be addressed by adding transient state information, but, depend-ing on the situation, residual effects due to the scaling may still require some attention.

Automated summary

It is shown that the steady state of rapid TR-periodic SSFP sequences at small to moderate flip angles follows a universal scaling law with respect to variations of B-1(+). The accuracy and precision of relaxometry experiments are discussed through analytical solutions, Cramer-Rao bound, and Monte Carlo simulations. Simultaneous estimation of R-1 and B-1(+) from SSFP steady states alone is not recommended, and additional transient state information is needed to address the issue.