A Brief Journey into Parallel Transmit Jason Su

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

Spiral Design

Spiral Design – FOV/2

Parallel Transmit System 4 channels 16cm 24cm

Parallel Transmit Design Design target profile –Based on full FOV spiral –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

Finer K-Space Sampling

Side Note: Receive Oversampling The excited profile is calculated as: E f b f The spatial resolution of E f can be as fine as desired Sample an 80x80 grid: The profile is quite different. Matching with Tx required?

RF Coil Considerations RF coils have finite bandwidth With hardest case of 2048 k-space pts., how does this affect excited volume?

Effects of RF Coil Modeled coil response as that of a windowed sinc Somewhat arbitrarily: BW half the k-space sampling rate = 100KHz

Resulting Profile Poor cancellation outside main lobe Main lobe profile is worsened Sidelobes reappear at edges Should be able to do better, consider 1024-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

Comparison

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