A simple iterative reduction method for optimization of quantitative magnetization transfer imaging

Introduction: Quantitative magnetization transfer imaging (QMTI) [1] yields the parameters – F, kf, R1f, T2f, and T2r – of the two-pool model for magnetization transfer (MT). Data are usually acquired using spoiled gradient-echo sequences with shaped off-resonance saturation pulses. The amplitude (or flip angle, α) and central frequency (Δ) of these saturation pulses are set according to the needs of the experiment, traditionally to cover the Z-spectrum uniformly [1,2]. Naturally, QMTI can benefit from optimized selection of the MT weightings. A previous study [3] used global Cramer-Rao Lower-Bound (CRLB) optimization of α-Δ pairs to yield sets of 10 and 15 MT weightings for brain white matter (WM) imaging, for the constant-wave-power-equivalent model of QMTI. We present a simple method for the selection of optimal MT weightings, by iterative reduction of the MT sampling from a discrete space. The optimal number of MT weightings is also investigated. Methods: The “reduction” method begins with a broad N-point sampling, X, of the Z-spectrum, and iteratively reduces the sampling by one point at a time, using an A-optimality criterion, to produce an optimized sampling. At each iteration, all sub-samplings Xj (j = 1...n), with n-1 points, of the current n-point sampling X are considered: the total estimate variance σn-1,j is computed for all Xj, using numerical propagation of error through the signal equation [4]. The Xj that results in the smallest increase in σn-1,j relative to σn (from X) is retained, thereby eliminating the α-Δ pair which provides the least information. The computation is repeated until the desired number of MT weightings is reached. In this study, the optimized sampling was derived based on typical MT model parameters for WM at 1.5 T [1] (F = 0.16, kf = 4 s, R1f = 1.7 s, T2f = 35 ms and T2r = 12 μs), from N = 320 MT weightings (2 TRs × 5 α × 32 Δ), for the rectangular-pulse model [1]. QMTI data were acquired on a 1.5 T scanner (Siemens, Erlangen, Germany) in a single female subject, using uniform and optimized 10-point samplings. The impact of sampling on reproducibility was retrospectively evaluated in 5 healthy adults (3M/2F, age 26-38) scanned four times each, with subsets of uniform 60-point data.