Kilian Weiss^{1,2}, David Maintz^{2}, and Daniel Giese^{2}

^{1}Philips Healthcare, Hamburg, Germany, ^{2}Department of Radiology, University Hospital of Cologne, Cologne, Germany

### Synopsis

**In this work a new multi shell
variable density k-t space sampling scheme for highly accelerated acquisitions
with sheared grid k-t space sampling and an adapted reconstruction framework
based on a linear reconstruction is proposed. The proposed method is evaluated
on numerical phantom data and compared to a conventional k-t PCA acceleration. The
proposed method is shown to be comparable to conventional k-t PCA for moderate
acceleration factors while outperforming conventional k-t PCA for high
accelerations factors allowing for ultra-fast dynamic MRI.**### Purpose

Fast
dynamic MRI plays an essential role for a variety of clinical applications such
as dynamic contrast enhanced imaging, dynamic magnetic resonance angiography or
dynamic imaging of motion or flow. Because MRI is an intrinsic slow technique,
image acceleration is key for a high spatio-temporal resolution and short scan
times. A variety of acceleration techniques has been suggested to address these
limitations. Due to their linear reconstruction, techniques such as k-t GRAPPA

^{1}, k-t SENSE

^{2} or its derivate
k-t PCA

^{3}
are widely used for dynamic MRI applications. These techniques are
conventionally based on a fully sampled central region of k-space and a
constant undersampling of the higher frequencies on a sheared grid in the k-t
domain, allowing for a fast and stable linear reconstruction process. However,
variable density sampling in k-space, with high density in the k-space center
to lower density in the k-space periphery, has been shown to be beneficial for
fast imaging techniques such as compressed sensing

^{4}.
Herein a new type of variable density k-t space sampling scheme for acquisitions
with sheared grid k-t space sampling and an adapted reconstruction framework
based on a linear reconstruction is proposed.

### Methods

In typical ‘linear’ k-t acquisitions,
data is sampled on a sheared grid in the k-t domain with a fully sampled region
in the central k-space, which provides the so called training data, and a
constantly undersampled region in the k-space peripheral (Fig. 1A). The
proposed method uses a modified sampling scheme, which includes a fully sampled
central region of the k-t space and undersampling of the k-space periphery with
variable density on multiple shells (Fig. 1B), resulting in constantly
increasing undersampling factors (e.g. 2, 4, 8, 16, 32) while moving towards the
k-space periphery. The sampling pattern can be divided into training data and
the different undersampling factors covering different ranges of k-space (Fig.
2C). Data reconstruction is started on the most central undersampling shell
which is reconstructed using k-t PCA resulting in a low resolution image. The
next undersampling layer is then reconstructed using the reconstructed images
from the previous shell as training data. This process is repeated until the
most outer undersampling shell is reached and the final images are
reconstructed. A scheme of the proposed reconstruction framework is shown in
Fig. 2.
To evaluate the proposed method, a numerical phantom
for dynamic contrast enhanced imaging was designed using signal curves as based
on a Tofts model with a maximal signal to noise ratio of 50. Data was
undersampled on a sheared grid as used for convention k-t type of sequences
(Fig. 1A) and using the proposed method with variable k-space density (Fig. 1B).
Data was reconstructed according to the scheme shown in Fig. 2, based on a k-t
PCA reconstruction.

### Results

Fig.
3A shows a single time point of the dynamic numerical phantom (Fig. 3 left
panel) and reconstructions using k-t PCA (Fig. 3 middle panel) and the proposed
method (Fig. 3 right panel) from the same time point for net acceleration
factors of R

_{eff} = 7.7 and 8.0, respectively. Time intensity plots
are shown for the different reconstructions along with time-intensity profiles
and their error. Fig. 4 shows the same data as Fig. 3 for acceleration factors
of R

_{eff} = 15.8 and 16.1.

### Discussion

The reconstructed dynamic curves and
spatio-temporal plots for R

_{eff} = 7.7 and 8.0 show good agreement to
the reference for the k-t PCA and the proposed method with only slight
differences. For higher acceleration factors of R

_{eff} = 15.8 and 16.1
the advantage of the proposed multi shell variable k-space method becomes
apparent. The dynamic curves reconstructed with the proposed method show good
agreement to the reference curves, while the k-t PCA reconstruction shows
strong deviations (temporal blurring) from the reference curves (Fig 4B). This
advantage of the proposed method over the conventional k-t PCA reconstruction
is also apparent it the spatio-temporal signal variations shown in Fig. 4C,
despite the slightly higher acceleration factor. This emphasizes the benefit of
the proposed multi shell variable k-space density method for highly accelerated
dynamic MRI.

### Conclusion

The
herein prosed method for fast dynamic MRI is based on a multi shell variable
k-space sampling in combination with a linear reconstruction. The proposed
method is shown to be comparable to conventional k-t PCA for moderate
acceleration factors while outperforming conventional k-t PCA for high
accelerations factors allowing for ultra-fast dynamic MRI. Future work will
concentrate on prospectively accelerated data acquisition using the proposed
method.

### Acknowledgements

No acknowledgement found.### References

1. Huang et al., MRM 2005

2. Tsao et al., MRM 2003

3. Pedersen et al., MRM 2009

4. Lustig et al., MRM 2007