Clarissa Wink^{1}, Giulio Ferrazzi^{1}, Jean Pierre Bassenge^{1}, Sebastian Flassbeck^{2}, Simon Schmidt^{2}, Tobias Schaeffter^{1}, and Sebastian Schmitter^{1}

4D flow MRI suffers from long scan times which limit maximum spatial resolutions. A promising approach is to restrict the field-of-excitation (FOX) to the region of interest and therefore reduce the field-of-view (FOV) not only in partition/slab direction, but also in phase encoding direction. In this work, we replace the slab-selective excitation of a 4D flow sequence by a 2D spatially-selective excitation with reduced FOX to enable reduced FOV imaging. We investigate the impact of the excitation on velocity encoding and demonstrate correct velocity quantification with $$$10\%$$$ reduced scan times in phantoms and in-vivo.

4D flow MRI^{1} is the only technique allowing velocity vector field
quantification in-vivo. However, the 3D slab-selective acquisition of the velocity
vector field requires long scan times and thus limits the spatial resolution. A
promising approach is to restrict the field-of-excitation (FOX) to the region of interest and
therefore allow to image a reduced field-of-view (FOV) not only in partition/slab
direction, but also in phase encoding direction.

In this
work, we replace the slab-selective excitation of a 4D flow sequence by a 2D
spatially-selective excitation with spiral trajectory and demonstrate correct
velocity quantification in a reduced FOX (rFOX) and reduced FOV (rFOV) in a phantom and intracranial vessels.

**2D Selective Excitation**

We designed a 2D selective RF-pulse with spiral k-space trajectory (Fig.1a) and bandwidth-time-product $$$\text{BWTP}=1.2$$$
in the small flip angle (FA) regime as proposed by Pauly^{2}. The
spiral starts at $$$k_{\text{max}}=2.51\,\frac{\text{rad}}{\text{cm}}$$$ and moves in $$$T=3.5\,\text{ms}$$$ with $$$n=10$$$ turns inwards to $$$\boldsymbol{k}$$$-space
center.

The actual
$$$\boldsymbol{k}$$$-space trajectory was measured according to Duyn^{3} prior to scanning
(parameters: Tab.1, line1). Two
RF-pulses were calculated to excite a FOX of $$$(6\times6\times\infty)\,\text{cm}^3$$$:
i) based on nominal gradient waveforms (RF_{nom}); ii) based on
measured gradient waveforms (RF_{meas}).

**4D Flow MRI Combined with 2D Selective Excitation**

In order to quantify flow by phase-contrast imaging the phase of moving
spins $$$\phi(v)=\gamma\,M_1\,v$$$ is manipulated by bipolar gradients such
that the total first gradient moment between the effective center of excitation
$$$t_0$$$ and echo-time $$$t_{\text{TE}}$$$ is $$$M_1=\int_{t_0}^{t_{\text{TE}}}G(s)\,s\,\text{d}s=\frac{\pi}{\gamma\,v_{\text{enc}}}$$$. While for symmetric SINC pulses $$$t_0$$$ is nearly at
the center of the RF-pulse^{4}, there are controversial reports about
$$$t_0$$$ of 2D pulses^{5,6}.

Therefore, we performed Bloch-simulations of our 2D spiral excitation using moving spins with varying velocities $$$v_{x,y}\in[-20,20]\,\text{m/s}$$$ to obtain the phase as a function of velocity at the end of excitation $$$T$$$. Thereby, we obtained $$$M_1^{v_i}(T)=\frac{\phi(T)}{\gamma\,v_i}$$$, where $$$i=x,y$$$. Finally, we compared it to the respective gradient moment $$$M^{v_i}_1(T) = \int_{t_0}^TG_{i}(s)\,s\,\text{d}s$$$ for $$$t_0\in[0,T]$$$.

Based on our findings, we included the 2D excitation pulse in a gradient echo 4D flow
ECG-triggered MR sequence^{1}.

**Phantom and In-Vivo Experiments**

Two phantom and one in-vivo
measurement were performed at 3T (Magnetom Verio, Siemens, Erlangen, Germany). First,
we included RF_{nom} and RF_{meas} in a GRE sequence to
investigate the squared excitation and non-excitation region in a large FOV
using three adjacent phantom bottles (parameters: Tab.1, line2&4). To eliminate
proton density and receive profiles, we normalized the data with the
corresponding slab-selective acquisition (parameters: Tab.1, line3&5).

Next, the excitation performance and accuracy of flow quantification was
investigated non-time-resolved in a flow phantom with constant flow. For
comparison, we imaged all possible four combinations of full/reduced FOV and
selective/non-selective excitation with RF_{meas} (parameters: Tab.1, line6-9).

Finally, a volunteer was scanned according to an approved ethical protocol
and with full informed consent. A flow sequence (parameters: Tab.1, line10&11)
was acquired in cerebral vessels with two different excitations targeting the
Circle-of-Willis: i) 1D slab-selective excitation and ii) 2D $$$(6\times6\times\infty)\,\text{cm}^3$$$-selective
excitation using RF_{meas}.

In all flow acquisitions, read-out was along the non-selective axis ($$$k_z$$$)
and both phase-encodings perpendicular to it. Acquisition parameters are summarized in Tab.1.

Fig.1c-e show the excitation profile obtained with RF_{nom} and RF_{meas}.
The residual excitation of RF_{meas} outside the excitation window of
$$$(10\times10)\,\text{cm}^2$$$ in Fig.1d is $$$(0.6\pm0.6)\%$$$.

The Bloch-simulations of moving spins show nearly velocity-independent phase at the end of the RF-pulse $$$T$$$ (Fig.2), implying $$$t_0=T$$$.

Fig.3a-d show all four combinations of 2D/non-selective excitation of the flow phantom in a full/reduced FOV. For the rFOV with non-selective excitation, biased velocities are measured, as seen quantitatively in the Bland-Altman-plot (Fig.3f). This is not seen with 2D-selective excitation (Fig.3e,g). The mean velocity difference to non-selective excitation in a full FOV is for 2D-selective excitation with full FOV $$$\Delta\,v/v_{\text{ref}}=(1.1\pm5.5)\%$$$ and with rFOV $$$\Delta\,v/v_{\text{ref}}=(2.9\pm5.9)\%$$$.

Fig.4 shows the absolute velocity and its three components during systole $$$130\,\text{ms}$$$ after ECG-trigger in the Circle-of-Willis for both 1D- and 2D-selective excitation. Qualitatively no aliasing of regions outside the FOX was observed.

Quantitatively, the flow through the internal carotids and basilar artery over the cardiac cycle is compared for both different FOXs and corresponding FOVs in Fig.4a. The maximum difference is reached during systole, $$$130\,\text{ms}$$$ after ECG-trigger, with $$$\Delta\,v/v_{\text{ref}}=6.6\%$$$.

The acquisition time with 2D excitation and rFOV was reduced by $$$10\%$$$.

1. Markl M et al. 4D flow MRI, J. Magn. Reson. Imaging 2012;36:1015-1036.

2. Pauly J et al. A k-Space Analysis of Small-Tip-Angle Excitation. J. Magn. Reson. Imaging 1989;81:43-56.

3. Duyn J H et al. Simple Correction Method for k-Space Trajectory Deviations in MRI. J. Magn. Reson. 1998;132:150-153.

4. Bernstein M A et al. Handbook of MRI pulse sequences, John Wiley & Sons, Ltd 2005

5. Hardy C J et al. Rapid NMR Cardiography with a Half-Echo M-Mode Method. J. Comput. Assist. Tomogr. 1991;15:868-874.

6. Cline H E, et al. Fast MR cardiac profiling with two-dimensional selective pulses. Magn. Res. Med. 1991;17:390-401.

**Figure 1**

(**a**) Nominal (solid line) and measured k-space trajectory (dashed) of our 2D
RF-pulse.

(**b**) Respective RF and gradient diagram with RF-field envelope based on
nominal (RF_{nom}, solid line) and measured gradients (RF_{meas}, dashed).

(**c-e**) Resulting excitation profile of RF_{nom} (c, e dashed line) and RF_{meas} (d,
e solid line).

**Figure 2**

Phase of excited spins in isocenter as a function of spin velocity right after excitation at t=T for an exemplary pulse with spiral k-space trajectory. The inset zooms in to show the residual phase variation with velocity. The phase variation of excited spins outside the isocenter is of the same order as in isocenter.

**Figure 3
**

(**a-d**) Magnitude (gray) and through plane flow (colored) images of our flow
phantom containing two pipes of d=10mm diameter.

(**a**) full
FOV, non-selective excitation, (**b**) full FOV, selective excitation, (**c**) rFOV,
non-selective excitation, and (**d**) rFOV, selective excitation.

(**e-g**) Bland-Altman plots of
the velocities quantified within the pipes corresponding to images (b-d)
compared to full FOV, non-selective excitation. Solid lines indicate the mean
velocity deviation and dashed lines the three-fold standard deviation.

Arrows indicate where signal from non-selectively excited spins is aliased into the rFOV, which results in biased velocity quantification.

**Figure 4**

(**a-b,d**) Comparison of GRE
magnitude (gray-scale) and velocity images (color-coded) between 1D- (bottom row)
and 2D-selective excitation (top row) in the Circle-of-Willis during
systole, 129.6ms after ECG-trigger.

(**c**) Comparison of time-resolved flow through the basilar artery and
internal carotids between a full FOX/FOV- (solid line) and a rFOX/rFOV-acquisition
in PE-direction (dashed line). The error bars are the standard deviation of all 37 voxels of the
basilar artery and internal carotids including the physiological velocity
profile. The figures on the right show a respective slice of a full
FOX/FOV-acquisition (bottom) and rFOX/rFOV-acquisition (top).

**Table 1**

Table of acquisition parameters.

For the RF-pulses RF_{meas} & RF_{nom} the given flip
angles are nominal flip angles. If no number of cardiac phases is given, the
scan is time-unresolved. The given acquisition time is a nominal value for an
acquisition window of 778ms.