Christoph Stefan Aigner^{1}, Armin Rund^{2}, Christina Graf^{1}, Karl Kunisch^{2}, and Rudolf Stollberger^{1}

This work demonstrates a constrained joint design of minimum duration RF pulse and slice selective gradient waveforms for combined SMS excitation, refocusing and inversion scenarios. A hybrid trust-region semismooth Newton/quasi-Newton method with exact derivatives via adjoint calculus is used to solve the time optimal problem on fine spatial and temporal grids. Specific hardware and safety constraints, including maximal RF, slice selective gradient, slew rate amplitudes as well as global SAR estimates, guarantee practical applicability. High-resolution GRE, crushed SE and inversion recovery GRE slice profile measurements on a 3T MR system validate the numerical results.

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Figure 1: Initial (row 1) and time
optimal (row 2) excitation, refocusing and inversion pulse duration for a
variation of different parameters including multiband factor (MB),
time-bandwidth-product (TBWP) and slice thickness (THK).

Figure
2: Time
optimal RF and slice selective gradient shape for MB3 excitation (90°, 2mm
thickness, time bandwidth product of 4 and 40mm slice gap). Row 2 and 3 show
the simulated excitation profiles |2a(z)b*(z)| for each spatial
position z in the spin domain and the cross section of the measured slice
profile depicted in row 1 with frequency encoding in left-right
(LR) and phase encoding in feet-head (FH) direction.

Figure 3: Time
optimal RF and slice selective gradient shape for MB5 refocusing (180°, 2mm
thickness, time bandwidth product of 4 and 24mm slice gap). Row 2 and 3 show
the simulated (perfectly crushed) refocusing profiles |b(z)|^{2} using
the simulated excitation profile |2a(z)b*(z)| for each spatial
position z in the spin domain and the cross section of the measured slice
profile depicted in row 1 with frequency encoding in left-right
(LR) and phase encoding in feet-head (FH) direction.

Figure 4: Time
optimal RF and slice selective gradient shape for MB9 inversion (180°, 2mm
thickness, time bandwidth product of 4 and 13.3mm slice gap). Row 2 and 3 show
the simulated inversion profiles 1-2|b(z)|^{2} using the simulated
excitation profile |2a(z)b*(z)| for each spatial position z in the
spin domain and the cross section of the measured slice profile depicted in row 1 with frequency encoding in left-right (LR) and phase encoding
in feet-head (FH) direction.

Figure 5: B_{1} (85-125%) and B_{0} (+/-
200Hz) influences on the optimized examples shown in Figures 1-3 in terms of
the excitation |2a(z)b*(z)|, crushed refocusing |b(z)|^{2}
and inversion 1-2|b(z)|^{2} profile for each spatial position z in the
spin domain. For each example the most distant slice is depicted. The other not
shown slices have a comparable behavior.