1. In vivo sodium (23Na) magnetic resonance imaging of human knee using a
pseudo-random k-space sampling scheme
Alireza Akbari1, Konrad Anand2, Christopher Anand3,4, and Michael D. Noseworthy1,4
3-dimensional center-out k-space sampling
schemes are at the heart of in vivo sodium
(23Na) magnetic resonance imaging (MRI).
These sampling methods offer ultra-short
echo times making them ideal for short T2
species such as 23Na. Some schemes, such as
spectrally weighted twisted projection
imaging (TPI)[1], require fewer number of
projections in order to fulfill the Nyquist
sampling criterion thus leading to shorter
scan times. In order to lessen scan time, the
number of projections can even be reduced
further (i.e. undersampling) at the cost of
inducing aliasing artifacts. However,
coherent aliasing can be minimized if
undersampling is done randomly as it leads
to incoherent summation of the aliasing
artifacts. This was the basis of the DURGA
sequence using in proton imaging [2]. In this
work, we demonstrate the feasibility of
pseudo-random k-space sampling (fig.1d) for
in vivo 23Na MRI that allows shorter scan
times.
The effects of aliasing using fully-sampled,
regularly-, and randomly-under-sampled
Cartesian, and pseudo-random non-Cartesian
schemes were simulated. A resolution
phantom (Model ECT/DLX/MP, Data
Spectrum Corp., Durham, North Carolina)
immersed in 6% saline and doped with 2.9 g/
L copper sulfate was used to measure the
actual achievable resolution when applying
pseudo-random sampling. In vivo knee 23Na
MR images of two subjects were
subsequently obtained. All imaging was
done using a GE MR750 3T (General Electric
Healthcare, Milwaukee WI) and an in-house-
made 12-pole quadrature transmit/receive
sodium birdcage coil. The pulse sequence
consisted of a single 500!s hard pulse, TE/
TR = 0.46/75 ms, flip angle = 90°, NEX= 64,
400 trajectories, 2000 samples per trajectory,
sampling rate of 4!s/sample, leading to a
total scan time of 32 minutes.
a
The effects of under-sampling using the two
sampling schemes are shown (fig.2). Figure 3
shows the actual achievable resolution using
the proposed sampling scheme. Figure 4
demonstrates the in vivo sodium knee MR
images acquired using the pseudo-random
sampling scheme. The SNR in patellar,
femoro-tibial, and posterior condyle cartilage
was measured as 10.6±1.1, 10.5±2.0, 9.6 ± 1.2
(mean ± SE), respectively.
Figure 1. K-space acquisition schemes used to investigate
how different under-sampling patterns produce image aliasing
artifacts. 3-dimensional views of a) fully sampled, b) regularly,
and c) randomly under-sampled Cartesian, and d) pseudo-
randomly under-sampled non-Cartesian schemes along with
their 2-dimensional views through the ky-kz plane (e-h),
respectively, are depicted. For better visualization, only a
subset of randomly under-sampled non-Cartesian trajectories
is shown in the 3D view.
Figure 2. A 2D representation through the zy-plane of point
spread function (PSF) simulations of: a) fully sampled; b)
regularly under-sampled; c) randomly under-sampled
Cartesian; and d) randomly under-sampled non-Cartesian k-
space sampling. The 1D PSF representation through the y-
direction are shown in (e-h), respectively. The reconstructed
images sampled from the simulated phantom using the k-
space sampling schemes (top), respectively, are shown (i-l).
Figure 4. In vivo axial, coronal, and sagittal views of 23Na MRI of a healthy subject obtained by the
pseudo-random non-Cartesian k-space acquisition.
The results indicate that pseudo-random non-
Cartesian sampling remarkably reduces the
aliasing artifacts caused by undersampling.
The in vivo results confirm the feasibility of
this scheme for 23Na MRI. This scheme will
help reduce the total scan time through a
high sampling-duty cycle with fewer
trajectories, while keeping aliasing artifacts
minimal due to the randomness of the
sampling scheme.
[1] Boada FE, et al. Magn Reson Med. 1997;38(6):1022–8. [2] Curtis
AT, Anand CK. Int J Biomed Imaging. 2008;2008.
akbaria@mcmaster.ca
Introduction
Methods
Results Conclusion
More Information
References
F i g u r e 3 . M R I r e s o l u t i o n
measurement. Axial proton (a)
and corresponding sodium (b)
images of a resolution phantom
with rods of 1.2, 1.6, 2.4, 3.2, 4.0,
and 4.8 mm in diameter. The
actual resolution achieved by
randomly sampled non-Cartesian
acquisition was 4.0 mm.