Simultaneous multislice (SMS) has been recently described as a method for significantly reducing acquisition time, decreasing TR or increasing slice coverage. The major challenge in SMS pulse design is to reduce peak power to abide by hardware limitations. At high field strengths, in-slice flip angle inhomogeneity (FAI) and local SAR hotspots are additional criteria that must be considered in the pulse design. Prior efforts to develop SAR-aware SMS-pTx pulse design algorithms [1] only focused on optimizing channel weightings. The composite RF waveform for the SMS-pTx pulse was formed through summation of a conventional slice-selective subpulse modulated by appropriate slice frequencies, which results in high peak power especially for large multiband acceleration factors. Here we introduce two related approaches for SMS-pTx based on an extension of the SAR-aware pulse design algorithm, IMPULSE [2], and describe a strategy for using the two methods to design optimal SMS-pTx pulses even for large number of slices with demanding peak power constraints.

We propose two methods, termed IMPULSE-SMS1 and IMPULSE-SMS2, that are each formulated to maximize pulse performance depending on whether the FAI tolerance or peak power limit is the more demanding constraint.

Both variations extend the IMPULSE algorithm which finds the minimum SAR pTx pulse that satisfies a tolerance on FAI by splitting the pTx pulse design problem into two subproblems, a SAR-update and an FAI-update, each of which can be solved efficiently. Two major benefits of IMPULSE, which are retained here, include elimination of the need for SAR compression (eg. VOPs [3]) and the ability to optimize k-space trajectory (eg. spokes locations).

IMPULSE-SMS1 (Figure 1) involves first using SLR design to find the RF waveform for the pTx sub-pulse, $$${\beta_{sub,1}(t)}$$$, that achieves the desired single-slice profile (1a). Then IMPULSE is used to optimize the C*K*N channel weightings, $$${b_{c,k}^{(n)}}$$$, corresponding to a different set of channel weightings for each slice (1b). The composite SMS-pTx pulse is then formed as: $$${\beta_{SMS,1}^{(c,k)}(t)=\sum_{n=1}^N{b_{c,k}^{(n)}\beta_{sub,1}(t)e^{-\gamma G_z z_n t}}}$$$ (1c).

IMPULSE-SMS2 (Figure 2) involves first designing a single subpulse, $$${\beta_{sub,2}(t)}$$$, to excite all slices in a way that limits peak power (2a). We chose to use the optimal control approach for accomplishing this [4]. Then IMPULSE is used to optimize the C*K channel weightings, $$${b_{c,k}}$$$, corresponding to a single set of channel weightings for all slices (2b). The composite SMS-pTx pulse is then formed as: $$${\beta_{SMS,2}^{(c,k)}(t)={b_{c,k}\beta_{sub,2}(t)}}$$$ (2c).

We use both methods to optimize pTx pulses for two different design cases. For the first case, representing an FAI-limited problem, we seek to excite 2 slices spaced 6 cm apart with FAI≤5%. For the second case, representing a peak power-limited problem, we seek to excite 6 slices spaced 2 cm apart with FAI≤10%. We simulated B1+ and E fields using an 8-channel loop array (SEMCAD, ZMT, Zurich) operating at 298 MHz (7T) and the Duke head model (IT’IS Foundation, Zurich) to design SMS pulses to minimize SAR subject to a 600W peak power constraint.

For the case with 2 slices and a 5% FAI tolerance (Fig 3), IMPULSE-SMS1 is able to achieve a peak local SAR of 1.24 W/kg which is better than IMPULSE-SMS2 (2.13 W/kg). However, for 6 slices and a 10% FAI tolerance (Fig 4), IMPULSE-SMS2 performs better with a peak local SAR of 8.47 W/kg compared to 9.92 W/kg for IMPULSE-SMS1.For low acceleration factors where peak power is of less concern, IMPULSE-SMS1 is better able to achieve in-slice homogeneity because of the fact that there are more degrees of freedom in the optimization since the channel weightings for each slice are determined separately. However, for higher acceleration factors, IMPULSE-SMS1 proves to be inadequate as it results in undesirable high SAR. A significantly novel contribution of this work is IMPULSE-SMS2 which is an effective method for addressing the problem of high peak power that results from summation of the waveforms corresponding to each slice. By intelligently designing the RF waveform upfront to excite all slices in a way that limits peak power, the composite SMS-pTx pulse will be less likely to violate the hardware power constraint. The results for the acceleration factor of 6 indicate that this benefit outweighs the limited degrees of freedom in the IMPULSE-SMS2 optimization.We have presented a general pulse design strategy, composed of two extensions of the IMPULSE pTx design algorithm, that enables combined SMS-pTx to achieve acceptable flip angle homogeneity over multiple simultaneous slices. This method can be used to perform significantly accelerated high field imaging without sacrificing in plane flip angle homogeneity while abiding by SAR and peak power constraints.