Table 1.

Outline of the Iterative reVERSE Algorithm

Inputs:

rfd(·): RF design function, returning an RF pulse

B1,max: peak-RF-magnitude target

Gmax: maximum gradient amplitude

α: attenuation factor of B1,max for the use in VERSE, e.g., α = 0.9

T: hardware update time

$B_1^{+}(\mathbf{r})$: transmit RF field

ΔB0(r): main-field inhomogeneity

Outputs:

B1[n], G[n]: reVERSE pulse waveforms

Algorithm: Initialize a pulse. design an excitation trajectory: G(t). set B1[n] = 0 (or a small-tip-angle solution). Design an RF pulse: $B_1[n]=\mathbf{rfd}(B_1[n],\mathbf{G}(t),B_1^{+}(\mathbf{r}),\mathrm{\Delta }{B}_0(\mathbf{r}))$. Stop if max{|B1[n]|} ≤ B1,max and sample the gradient waveform: G[n] = G(nT). Reduce the peak RF power via VERSE. interpolate RF waveforms: B1[n] ⇒ B1(t). calculate the RF-to-gradient amplitude ratio: W(s) = B1(t)/|G(t)|, $s=\gamma {\int }_0^t\mid \mathbf{G}(\tau )\mid d\tau$. calculate the gradient upper bound: Gu(s) = min{αB1,max/|W (s)|, Gmax}. find the time-optimal gradient waveform G(t), given Gu(s), using Eq. 10 of Ref. (19). recalculate the RF waveform: B1[n] = W (sn)|G(nT)|, $s_n=\gamma {\int }_0^{nT}\mid \mathbf{G}(\tau )\mid d\tau$. Goto 2.