Synopsis

In this work, we demonstrate the distinction and importance of two virtual time points during excitation for correct flow compensation and quantification: the centre of excitation ($$$t_0^\text{m}$$$) at which spins are excited and thus magnitude is generated, and the isophase time-point ($$$t_0^\text{ph}$$$) at which all excited spins are in phase. A general method to determine $$$t_0^\text{m}$$$ is presented and $$$t_0^\text{ph}$$$ and $$$t_0^\text{m}$$$ are shown to be not necessarily identical. Finally, phantom experiments demonstrate that the knowledge of $$$t_0^\text{m}$$$ is required to remove the displacement artefact in phase-encoding directions to enable correct flow compensation and imaging.

Introduction

2D-selective excitation has been employed to accelerate time-resolved flow measurements in 1D^1-3 and 3D⁴ by reducing the field-of-view. However, applying conventional flow quantification and compensation techniques straightforwardly to 2D-selective RF-pulses can lead to a) wrong velocity quantification and b) displacement⁵ of moving spins possibly into static tissue.

Here, we identify for the first time two distinct virtual time-points during excitation: the isophase time-point$$$\;(t_0^\text{ph})\;$$$at which all excited spins are in phase (cf. isodelay⁶) and the centre of excitation$$$\;(t_0^\text{m})\;$$$at which spins are effectively excited and thus magnitude is generated. While those points coincide for standard ‘SINC’-pulses at nearly half the RF-pulse duration, their distinction is indispensable for correct flow compensation and quantification using 2D-RF-pulses:

a)$$$\;t_0^\text{ph}\;$$$is needed for correct velocity quantification and has been identified for spiral 2D-selective excitation at the 2D-RF-pulse end^7,4. Here, we investigate how off-resonances affect phase and velocity quantification.

b)$$$\;t_0^\text{m}\;$$$has not been reported yet but is required to correct the displacement of moving spins caused by the time-delay between excitation and read-out in phase-encode (PE) directions.

The aim of this work is 1.) to present a general method to determine $$$t_0^\text{m}$$$, 2.) to show that$$$\;t_0^\text{ph}\;$$$and$$$\;t_0^\text{m}\;$$$are not necessarily identical, and 3.) to demonstrate in phantom experiments that precise knowledge of$$$\;t_0^\text{m}\;$$$is required to remove the displacement artefact in PE-directions.

Theory

Methods

2D-selective excitation

Two 3.5ms long 2D-selective RF-pulses with spiral k-space trajectory were designed⁷ as described in⁴ to excite a rectangular bar with 1) a large field-of-excitation FOX=$$$(\infty\times60\times60)\,\text{mm}\;$$$and bandwidth-time-product BWT=1.2 (RFL) and 2) a small FOX=$$$(\infty\times36\times36)\,\text{mm}\;$$$and BWT=0.9 (RFS).

Simulations

The velocity-dependent phase of the magnetisation at the 2D-RF-pulse end$$$\;T_\text{end}\;$$$was determined using Bloch-simulations. Additionally, the impact of off-resonance on velocity quantification was investigated by simulating the 2D-RF-pulses once with consecutive flow-encoding and second with flow-compensation gradients. Simulated spins move in a virtual tube oriented in $$$y$$$-direction (PE) with maximum velocities $$$v_y\in[-100:20:100]\,\text{cm}/\text{s}$$$ and are static elsewhere.

The location of $$$t_0^\text{m}$$$ was quantified by evaluating the spatial shifts of the magnitude pattern at $$$T_\text{end}$$$ in Bloch-simulations using moving spins in comparison to stationary spins. The spatial shift of the magnitude signal $$$|S(y,v_y)|$$$ was calculated by $$$\Delta y=\frac{\int|S(y,v_y)|\,y\,\text{d}y}{\int|S(y,v_y)|\text{d}y}$$$ for $$$v_y\in[-100:20:100]\,\text{cm}/\text{s}$$$ and RFS and RFL. The centre of excitation is then calculated by $$$t_0^\text{m}=T_\text{end}-\frac{\Delta y}{v_y}$$$.

Experiments

Flow phantoms containing two pipes with constant flow were scanned at 3T (Magnetom Verio, Siemens) using a 15-channel-knee-coil to verify the simulation results. RFL- and RFS-excitation pattern shifts were measured for $$$t_\text{exp}=t_0^\text{ph}$$$, $$$t_\text{exp}=t_0^\text{m}$$$, and $$$t_\text{exp}=t_\text{TE}$$$ in the presence and absence of flow. Imaging parameters of two datasets differing mainly in venc: dataset1/dataset2: venc(z)=2m/s/4.5m/s, TE=3.35ms/3.25ms, FA=8°/3°, matrix=64x64x192/96x96x192, resolution=2x2x1mm³/1.5x1.5x1mm³. Receive profiles were eliminated using separate acquisitions with non-selective excitations.

Results

Simulations

Since$$$\;t_0^\text{ph}=T_\text{end}\;$$$for moving spins and zero off-resonance⁴, phase at$$$\;T_\text{end}\;$$$is velocity-independent (Fig.1a). However, for 200 and 500Hz off-resonance, phase is varying non-linearly as a function of velocity (Fig.1b). Still, the same velocity is quantified for zero and 200Hz off-resonance (Fig.2a,bottom). Actually, a fit shows that quantified$$$\;v_\text{qu}\;$$$and actual velocity$$$\;v_\text{act}\;$$$match for 0 and 200Hz off-resonance (Fig.2b) with fit difference close to zero (Fig.2c).

The magnitude pattern is smoothened for 200Hz off-resonance and shifted in the moving tissue section (Fig.2a,top). Figure3 depicts the shift of the RFL- and RFS-excitation patterns at $$$T_\text{end}$$$ for different velocities along y-direction. Based on this velocity-dependent shift the magnitude’s centre of excitation was located before$$$\;T_\text{end}$$$ at $$$T_\text{end}-t_0^\text{m}=(0.52\pm0.01)\,\text{ms}$$$ and $$$(0.75\pm0.02)\,\text{ms}$$$ for RFL and RFS respectively, while $$$t_0^\text{ph}$$$ was identified at $$$T_\text{end}$$$.

Experiments

Figure4 illustrates that the flow-induced excitation pattern shift of up to $$$12.5\,\text{mm}\,$$$for$$$\;t_\text{exp}=t_\text{TE}\;$$$and$$$\;v=2.9\,\text{m}/\text{s}\;$$$is successfully suppressed choosing$$$\;t_\text{exp}=t_0^\text{m}$$$. Figure5 shows the RFL- and RFS-shift for different velocities and$$$\;t_\text{exp}$$$. The measurements agree with simulations predicting $$$\Delta\boldsymbol{r}=\boldsymbol{v}\cdot(t_\text{exp}-t_0^\text{m})$$$ and thus zero shift for $$$t_\text{exp}=t_0^\text{m}$$$.

Discussion and Conclusion

Acknowledgements

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