An analytical solution for the SSFP signal in MRI

Among previous analyses of the steady-state free-precession (SSFP) signal in rapid MRI, one treatment resulted in equations that require the evaluation of infinite binomial series. Here, an analytical solution is derived by a transformation into the power series expansion of the derivative of the inverse sine function, which is essentially a root. The treatment is extended to include higher-order signals. The results demonstrate the identity of the vastly different equations for the SSFP signals reported so far. Applications consist of the derivation of closed expressions for the signal in echo-shifted MRI and a corresponding analysis of TrueFISP sequences.