Steady-state free precession signals of arbitrary dephasing order and their sensitivity to T2∗

A simple approach how to calculate analytical expressions for unbalanced steady-state free precession (ubSSFP) signals of arbitrary dephasing order is presented. Dephasing order is the number of effective gradient dephasing cycles that magnetization immediately after an RF-pulse has experienced during the ubSSFP sequence. Based on the obtained equations, which are in accordance with existing literature, the sensitivity of ubSSFP signals to T₂^∗ is derived under the assumption of a Lorentzian frequency distribution resulting from static field inhomogeneities. Further, the phases of all ubSSFP signals are calculated and a general expression of how to use them for B₀-fieldmapping is given. The derivation is supported by the extended phase graph (EPG) model, and as such the work also acts as a comprehensive introduction to the formal description of SSFP. In addition, the balanced SSFP (bSSFP) sequence is explored. The connection of bSSFP to ubSSFP is shown, and potential T₂^∗-sensitivity of bSSFP is examined based on numerical simulations. It is shown that ubSSFP signals with negative dephasing order have a refocusing character and behave similar to spin-echo signals. Conversely, ubSSFP signals with zero or positive dephasing order can be regarded as T₂^∗-weighted. The behavior of bSSFP depends largely on the exact distribution of frequencies. For instance, for a narrow spherical distribution, bSSFP acts like a spin-echo sequence, while for a Lorentzian distribution a refocusing behavior does not occur.