Interleaved Variable-Density 1D Fourier Velocity-Encoding
J. DiCarlo1, B. Hu2, D. Nishimura1, J. Pauly1
1
Stanford University, Stanford, CA, United States, 2Stanford University and Palo Alto Medical Foundation, Palo Alto, California, United States
Abstract One-shot Fourier velocity-encoding (FVE) has the ability to measure velocities up to 2.5 m/s in real-time. Two variable-density FVE trajectories are
interleaved to reconstruct images at the same resolution and 2x velocity field of view (FOV) to detect fast jet velocities. Alternatively, FOV can be held constant and
velocity resolution can be improved. The use of interleaved trajectories increases the number of velocity-frequency samples while minimizing off-resonance effects.
Introduction
The velocity-detecting tool that is the MR equivalent of Doppler ultrasound is an important component of a
comprehensive cardiac MR exam. When stenosis is present, velocities may peak between 4-5 m/s. Fourier-velocity
encoding (FVE) is a good choice to detect these velocities because it acquires a full velocity spectrum and does not
underestimate flow by averaging velocities over a voxel. To acquire a full velocity-position image in a single readout,
a 2D excitation pulse can be applied to restrict imaging to 1D along a cylinder producing a bowtie-shaped trajectory
in kv(z)-kz [1]. The use of variable-density k-space sampling further reduces imaging times or alternatively allows for
improvement of velocity resolution or field of view (FOV.) Since velocity varies smoothly over a voxel, higher
velocity-frequencies can be sampled more coarsely without generating significant aliasing artifact [2]. This aliasing
artifact can be further reduced by smoothly decreasing the density of k-space samples as a function of distance from
the k-space center. Aliasing artifact can also be reduced using an adaptive-averaging technique, which temporally
interleaves low and high velocity-frequency variable-density measurements [3].
In order to measure velocities at resolutions between 12-25 cm/s with readout times between 9-15 ms, velocity
FOV must be limited to 400-600 cm/s. This results in velocity aliasing when jet velocities are present. However, a
longer readout to increase the FOV greatly worsens off-resonance effects. By designing variable-density trajectories
that are interleaved in kv(z)-kz, the number of samples can be doubled over two frame acquisitions without increasing
off-resonance effects. In addition, a sliding window reconstruction can be used to produce images with a frame rate
that corresponds to the original real-time velocity measurement sequence.
Theory and Methods
One-shot FVE first uses a spiral 2D excitation in X and Y to restrict imaging to 1D along a cylindrical excitation.
A real-time imaging system is used to position the cylinder along the aortic axis [4]. A sawtooth-shaped readout
follows on the Z-axis to read back-and-forth along the length of the excitation. This readout produces a sinusoidally
oscillating kz trajectory. At the same time, the first moment of the gradient also produces a sinusoidally oscillating kvtrajectory that increases in magnitude along the length of the readout. When the k-space trajectory for the velocityposition image (kv(z) as a function of kz) is plotted, the result is a tilted bowtie with its center at the origin. A bipolar
prewinder gradient is played out prior to the readout to shift the trajectory so that the largest distribution of samples
acquired is centered about the kv(z)-kz origin. To use a variable-density readout, the sawtooth waveform’s bipolar lobes
linearly increase in area once low kv(z) has been acquired so that a wider portion of kz points are acquired. This causes
the first moment to increase more rapidly, and the spokes of the bowtie to be further spaced, resulting in movement to
a further distance in kv(z).
Once the first variable-density trajectory is created, the second gradient waveform is specifically designed to
traverse samples that fall halfway between the spokes of the first interleave. The magnitude of the second bipolar
prewinder is set to space the uniform-density (low kv(z)) samples accordingly. However, the change in the bipolar
prewinder first moment also changes the speed of the trajectory through high kv(z). Therefore, the factor by which the
density is varied for the second readout is also varied from the first interleave to space the higher kv(z) spokes between
those of the first interleave. The echo time for each trajectory is also slightly shifted to smooth the off-resonance
effects in the reconstructed frames. Additionally, since the readout time is kept to 10.4 ms, off-resonance effects are
no more significant than with the single-shot technique. Figure 1a shows the prewinder and readout gradients for both
interleaves, each with a 10.4 ms readout. The corresponding k-space trajectories covered by these gradients are
shown in Figure 1b. Although the number of reconstruction points has doubled, the number is still small enough that
a simple homodyne/IDFT reconstruction is used to create a velocity-position image that will be sampled to create a
velocity-time image.
Figure 1. a) Prewinder and readout gradient
waveforms for each of the interleaves.
b) Corresponding k-space trajectory points in
the reconstructed region.
Results
Figure 2a shows the uniform-density 1D-FVE image in the ascending aorta of a normal volunteer with a velocity
FOV of 400 cm/s and resolution of 25 cm/s. The readout duration was 9.1 ms. Figure 2b shows the single-shot
variable-density version with a velocity FOV of 450 cm/s. A trajectory with readout duration of 15 ms was used to
achieve a velocity resolution of 16 cm/s. Figure 2c shows the interleaved variable-density image reconstructed with a
sliding window. Each frame had a readout time of 10.4 ms. The velocity resolution is kept at 25 cm/s, but the
velocity FOV has been doubled to 10 m/s. Note that the FVE technique does not exhibit reduced signal at high
velocity-FOV. This is not the case for phase contrast because the use of such a large encoding velocity would lead to
a lower phase-SNR.
Conclusion
Interleaved variable-density 1D-FVE has been implemented with a real-time system. It can be used to measure
jets at the same velocity-resolution as the original single-shot sequence but with double the FOV to facilitate detection
of jet velocities without aliasing. Alternatively, the technique could be used to produce velocity images at the same
FOV with significant improvement in velocity resolution. Interleaved 1D-FVE is a promising technique to measure
the full range of velocities necessary to diagnose cardiovascular disease as part of a comprehensive MR exam.
References
[1] Luk-Pat, G. et al., MRM, 40:603, 1998.
[2] Sabataitis, J. et al., 9th ISMRM, 372, 2001.
Proc. Intl. Soc. Mag. Reson. Med. 11 (2003)
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[3] Macgowan, C. et al., 10 ISMRM, 603, 2002.
[4] DiCarlo, J. et al., 10th ISMRM, 1801, 2002.
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Figure 2. a) Velocity-time image, uniformdensity sequence. b) Velocity-time image,
variable-density sequence. c) Velocity-time
image, interleaved variable-density sequence.