Use of Simulated Annealing for the Design of Fat-suppressed Multiple Repetition Time Balanced SSFP

Method We searched for an optimal parameter vector x = [α1 α2 α3 φ2 φ3 τ2 τ3], where αn are flip angles and φn the phase for the n RF pulse (intervals of 1°), and τn= TRn/TR1, with the range 0.05≤ τ ≤ 1.1 at intervals of 0.01 (Fig. 1). The SA algorithm used is described in [5]. The step adjustment of each parameter was adapted after every 20 iterations to maintain, as far as possible, a 1:1 rate between accepted and rejected configurations. The temperature was reduced by 0.99 after every 4000 iterations. The cost function C(x) to be minimized was defined as follows: First, the FRF(x) was computed by Bloch simulation over an offresonance range of –3000° to +3000° per TR1 (with T1/T2=300/300 ms for phantom and T1/T2=1000/200 ms for invivo). In general, the FRF will not show a repeating pattern, and it is therefore necessary to evaluate combinations of passand stopbands found within the FRF. For each pass/stopband pair, the offresonance angle between the centers of the passband and stopband was scaled to the fat chemical shift (434 Hz). This determined the TRn, as well as the passband width P and stopband width S in Hz, defined as the fullwidth at 90% and 20% of the passband amplitude, A. To take hardware constraints into account, only combinations with TR1 >2.5 ms for data collection were considered further. The signal efficiency was defined as: E = A√(TR1/ΣnTRn). The best pass/stopband pair was chosen as the one with the smallest value of p = –(1000E + 0.7P + 0.3S). To include the effect of B1 field inhomogeneity, p for the best pair was recalculated with αn changed by ±5%, to give p+ and p–. The cost function was taken as C(x)=(p + p+ + p–)/3. Thus, a low C(x) implies high signal efficiency, and large pass/stop bandwidths over a range of flip angles. Typically, the algorithm stops after ~10 iterations. Introduction Balanced steady-state free precession (bSSFP) is an ultrafast sequence with high SNR efficiency. However, it often generates a strong fat signal which can mask the water signal. To suppress this fat signal, it is possible to modify the Frequency Response Function (FRF) to create a stopband over the fat frequency, e.g. by using multiple repetition times (TR) [1-3]. Response functions with wide, flat bands at the water and fat frequencies give sequences that are robust against B0 field inhomogeneity. However, with three or more TRs, the number of parameters creates a vast search space with many local minima. Previously, parameters were chosen by hand or by using an approximate linear model [3]. Optimization methods like simulated annealing (SA) have been used to search such spaces efficiently [4]. We report on the initial results of using SA to find optimal sequences for fatsuppressed bSSFP at 3T with three TRs.