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Samy Abo Seada, Joseph V Hajnal and Shaihan J Malik

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1 Samy Abo Seada, Joseph V Hajnal and Shaihan J Malik
A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients Samy Abo Seada, Joseph V Hajnal and Shaihan J Malik

2 Motivation Aim Problem: Multiband RF pulses for SMS have long pulse durations [1,2] Solution: Use Time-Optimal VERSE to reduce pulse duration [3] Result: Not suitable for gradient system due to gradient imperfection Our solution: Iterative VERSE optimization with gradient correction Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations Experiment Conclusion A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients [1] Larkman et al. 2001 [2] Wong E. 2012 [3] Lee et al. 2009

3 Theory (1) - VERSE algorithm
Aim For flip angle πœƒ RF flips Magnetization down by an angle πœƒ and gradient ensures spatial selection Ultimately, net rotation πœƒ determined by angular precession [4] To achieve same signal, preserve net rotation πœƒ. Net rotation preserved if field strengths are halved and played out twice as long Theory VERSE TO-VERSE GIRF-effect πœƒ=πœ” dt Iterative RF-correction Methods Results Simulations Experiment Same net rotation πœƒ Conclusion A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients [4] Conolly 1988

4 Theory (2) Time Optimal VERSE
Aim Use VERSE to Minimise pulse duration, given System specification [5] Max gradient amplitude, max slew rate, max B1 Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations Experiment Conclusion Define arc-length parameter 𝑠 𝑑 =𝛾 0 𝑑 𝐺 𝜏 π‘‘πœ Excitation profiles preserved if π‘Š 𝑠 = 𝐡 1 𝑠 𝐺(𝑠) = 𝐡 1 𝑣 (𝑠) 𝐺 𝑣 (𝑠) A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients [5] Lee et al 2009

5 Theory (3) GIRF-effect Aim Previous work: Use VERSE to Minimise pulse duration, given hardware specs Does: Maximum peak RF (13πœ‡π‘‡), Maximum peak Gradient (40 π‘šπ‘‡ π‘š ), Maximum slew-rate (200 π‘šπ‘‡ π‘š π‘šπ‘  ) Does not take into account: Eddy currents, RF/G time-mismatch etc.. A measured Gradient Impulse Response function (GIRF) does! Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations 𝐺 π‘œπ‘’π‘‘ (𝑑)= 𝐺 𝑖𝑛 (𝑑)βˆ—πΊπΌπ‘…πΉ(𝑑) Experiment Conclusion A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients [6] Vannesjo 2013

6 Theory (3) GIRF-effect Simulated Profiles Gradient after TO-VERSE
RF after TO-VERSE Aim Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Simulated Profiles Results Simulations Experiment Conclusion A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients

7 Theory (4) Iterative correction
Aim Holds for But Magnetization experiences Correct by substituting 𝑠 π‘Žπ‘π‘‘ into (1) and find 𝐡 1,π‘Žπ‘π‘‘π‘’π‘Žπ‘™ 𝑣 𝑠 π‘Žπ‘π‘‘ =π‘Š 𝑠 π‘Žπ‘π‘‘ 𝐺 π‘Žπ‘π‘‘π‘’π‘Žπ‘™ 𝑣 ( 𝑠 π‘Žπ‘π‘‘ ) Excitation profiles preserved if π‘Š 𝑠 = 𝐡 1 𝑠 𝐺(𝑠) = 𝐡 1 𝑣 (𝑠) 𝐺 𝑣 (𝑠) (1) Theory VERSE Corrected RF pulse overshoots initial 𝐡 1 constraint TO-VERSE GIRF-effect 𝑠 𝑑 =𝛾 0 𝑑 𝐺 π‘‘π‘’π‘šπ‘Žπ‘›π‘‘ 𝑣 𝜏 π‘‘πœ Iterative RF-correction Methods Simulated Profiles Results Simulations | 𝑀 π‘₯𝑦 | 𝑠 π‘Žπ‘π‘‘ 𝑑 =𝛾 0 𝑑 𝐺 π‘Žπ‘π‘‘π‘’π‘Žπ‘™ 𝑣 𝜏 π‘‘πœ Experiment Conclusion Space [cm] A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients

8 Theory (4) Iterative correction
Aim Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations Experiment Conclusion A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients

9 Methods Aim Simulations: Phase-optimized [Wong 2012] 180 π‘œ refocusing pulses Maximum gradient 40 π‘šπ‘‡ π‘š . Peak 𝐡 1 : 13πœ‡π‘‡ Maximum slew-rate: 200 π‘šπ‘‡ π‘š π‘šπ‘  GIRF: Measured for our Philips Achieva 3T Experiments: Philips Achieva 3T. Gradient echo sequence Spherical water phantom ( 𝑇 1 =270ms) Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations Experiment Conclusion A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients

10 Results (1): Simulations
Aim Effective duration defined as 𝑇 𝑒𝑓𝑓 = 𝛾 𝐡 1,π‘šπ‘Žπ‘₯ 𝑑𝑑 πœƒ where 𝛾:gyromagnetic ratio. dt: dwell-time. πœƒ: Flip angle Errorsbars show range of duration across different slice-separations Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations Experiment Conclusion VERSE:80% reduction VERSE + GIRF: 70 reduction VERSE:46% reduction VERSE + GIRF: 31% reduction A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients

11 Results (2) – In-vitro experiment
Aim Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations Experiment Conclusion A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients

12 Conclusion Aim Effective method to make Time-optimal VERSE-Multiband pulses feasible Applicable for any 1D pulse which suffers from gradient BW problems Three-stage design is sub-optimal High compression factor for Higher Time-bandwidth pulses Further work: Incorporate GIRF directly into VERSE for optimal design Is a measured GIRF necessary? Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations Experiment Conclusion A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients

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