Small gradient delays with respect to radiofrequency (RF) pulses can have disastrous effects on the performance of bipolar spokes RF pulses employed in parallel transmission (pTx) to mitigate RF field inhomogeneity problems. This work reports a new method to characterize this delay with a precision of ~20 ns, shown to appear necessary for high performance pTx. By the same token, the same physics principles underlying the method suggest a way to correct for it by simply phase-shifting every second spoke RF pulse. The technique is validated with measurements on a water phantom and on an adult volunteer at 7T.
The delay characterization measurement is depicted in Fig.1. The blips shown in the figure correspond to zero-order eddy-currents (ΔB0(t) envelopes) inherent to the presence of slice selection gradient ramps and which need to be modelled for an accurate analysis. With spoiled GRE sequences, the first (red blip in Fig.1) and last (blue blip) eddy-currents, the refocusing gradient lobe, the first rising gradient slope before the first RF pulse and the descending gradient slope after the second pulse do not affect the flip angle and thus shall be ignored. During the first gradient lobe and with a gradient delay Δt, the gradient during Tp−Δt induces a rotation Rz,Tp−Δt on the spins around z with an angle of rotation proportional to Tp−Δt. The RF pulse during the first plateau generates the rotation Rϕ=0 where, importantly, ϕ corresponds to the global phase of the RF pulse and not the axis of rotation (which may be pointing between the z-axis and the transverse plane). The second pulse, except for the phase change, should be the time-reversed of the first. The rotation induced by the second pulse thus is Rϕ=π+Δϕ. The residual eddy-current between the two RF sub-pulses (green envelope in Fig.2) generates Rz(−ϕEC), i.e. a rotation of angle −ϕEC around z. In the absence of a static ΔB0 offset, the rotation matrix can be shown to be equal to:
RTOT=R−z,Tp−ΔtRϕ=π+Δϕ+ϕEC−2δRϕ=0Rz,Tp−Δt,
where δ=γGzΔt, G being the gradient amplitude and z the slice position. The eddy-current and gradient delay thus effectively induce a phase-shift on the second RF pulse. If Δϕ=2δ−ϕEC, then the rotation matrix above becomes Identity and there should be no signal. Thus by determining at different slice locations the Δϕ value which returns a minimum of signal, the delay Δt can be recovered by linear regression of Δϕ versus z. Axial measurements were performed at 7T at -25,-20,-10,0,10,20 and 25 mm from the isocenter on a water phantom and Δϕ was swept across the interval [−90∘;90∘]. Once the delay and zero order eddy-current terms Δt and ϕEC were recovered, their prospective correction was implemented in tailored bipolar 2-spoke configurations2 on the same phantom and in vivo with multi-slice T2*-weighted GRE protocols (25 slices, TE=15 ms, TR=936 ms, FA=30°, 0.5×0.5×2 mm3 voxels), by phase-shifting the second sub-pulse according to the slice locations. The results were compared to the unipolar 2-spoke implementations as a reference.The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Program (FP7/2013-2018), ERC Grant Agreement n. 309674.