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This document outlines my exploration of parallel transmission (pTx) techniques in MRI, focusing on practical design and implementation strategies. The goal is to replicate in-class results, delve into 3D spoke design, and explore "inversion" design principles. Key considerations include optimizing spatial and k-space points, regularization, and addressing challenges of RF coil limitations. The results demonstrate significant insights regarding sidelobe cancellation and mainlobe uniformity, emphasizing the importance of RF coil bandwidth and regularization for improved excitation profiles.
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Description • Goal: expose myself to some of the basic techniques of pTx • Replicate in-class results • Explore some possibilities • Learn about spokes design – 3D design • Implement “inversion” design, as detailed in class notes
Small Tip-Angle Inversion Design • Freedoms in design: • Number of spatial points • Number of k-space points • Regularization and smoothing • Traditional design is sometimes too fast for RF coil to keep up
Basic Design • Jinc-weighted spiral design as in HW3 • Resolution = 0.2cm • FOV = 10cm • Gradient amplitude max = 6 G/cm • Gradient slew rate max = 20 G/cm/ms • Desired slice width = 4cm • Pulse length = 18ms for full FOV, 9ms for FOV/2
Parallel Transmit System • 4 channels 24cm 16cm
Parallel Transmit Design • Design target profile • Based on full FOVspiral • Cut out sidelobes • Flattened profile • 2x accelerated • This is actually infeasible • 64x64 spatial points, 512 spiral k-space points
Result • Good sidelobe cancellation • Uniformity of mainlobe is poor
Finer K-Space Sampling • We can improve the design by depositing more energy into k-space over the same trajectory • i.e. sample more finely in k-space • The penalty is that we need a better RF coil to keep up with the sampling rate
Side Note: Receive Oversampling • The excited profile is calculated as: Efbf • The spatial resolution of Ef can be as fine as desired • Sample an 80x80 grid: • The profile is quitedifferent. Matchingwith Tx required?
RF Coil Considerations • RF coils have finitebandwidth • With hardest caseof 2048 k-space pts.,how does this affectexcited volume?
Effects of RF Coil • Modeled coil response as that of a windowed sinc • Somewhat arbitrarily: BWhalf the k-space samplingrate = 100KHz
Resulting Profile • Poor cancellation outside main lobe • Main lobe profile is worsened • Sidelobes reappearat edges • Should be able todo better, consider1024-sample
Smoothing w/ Regularization • Try to minimize the high frequency energy • J = ||Eb-M||^2 + μ||Fb||^2, where F is the DFT matrix for high frequencies • Changed to 32x32,512-sample due to memory limitations
Conclusion • Here, there is a knee in the RMSE vs. # k-space pts. profile at around 1024 pts., may not be always be the case • RF coil bandwidth greatly affects the quality of the resulting excitation profile • Regularization improves profile, especially out-of-mainlobe uniformity