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Rapid MR-guided-HIFU using Convolution-based Reconstruction and Parallel Imaging (CORE-PI)
Efrat Shimron1 and Haim Azhari1

1Department of Biomedical Engineering, Technion - Israel Institute of Technology, Haifa, Israel

### Synopsis

A novel reconstruction method for accelerated Magnetic Resonance guided High Intensity Focused Ultrasound (MRgHIFU) thermometry is presented. This method utilizes multi-coil acquisition, k-space undersampling and the recently introduced Convolution-based Reconstruction for Parallel Imaging (CORE-PI) technique. The proposed method utilizes data sparsity in the Stationary Wavelet Transform (SWT) domain. It is a parameter-free, non-iterative and calibrationless method. Retrospective experiments with in-vivo data from clinical human prostate ablation treatments show that the proposed method produces accurate temperature maps from two-fold and three-fold subsampled k-space data. The method is therefore suitable for real time application.

### Background

MR thermometry is a safe, non-invasive efficient modality for guiding High Intensity Focused Ultrasound (HIFU) treatments1,2. MR-guided-HIFU (MRgHIFU) is clinically used for treating prostate3,4, brain5,6, breast7,8 liver9–11 and heart11. However, common MRgHIFU has a very limited spatial coverage, which currently includes only several few 2D slices12,13. To improve the temperature monitoring, MRgHIFU can be accelerated by k-space undersampling.

### Purpose

A novel method for accelerated MRgHIFU from subsampled k-space is proposed. This method utilizes the recently introduced Convolution-based Reconstruction for Parallel MRI (CORE-PI)17 technique. In contrast to previous methods, CORE-PI utilizes parallel MRI acquisition, exploits data sparsity and offers simple non-iterative computations. The proposed method is also parameter-free, i.e. does not require tuning of any parameters, and operates in a calibrationless manner.

### Theory

The proposed method assumes the existence of one fully sampled baseline dataset. This dataset is acquired at $t=0$ , prior to heating onset, by an array of $N_c$ coils. Sensitivity maps of the coils are estimated from that data, and a complex-valued baseline image $f_0(x,y)$ is computed from the data using Roemer’s optimal method18.

During heating $(t>0)$, subsampled k-space data are acquired. The method’s goal is to reconstruct $f_t(x,y)$ (the unknown complex-valued MR image) from the subsampled data using the CORE-PI method. Then, the temperature change can be obtained using the well-established Proton Resonance Frequency (PRF) shift thermometry1.

In contrast to most PI methods, which reconstruct $f_t(x,y)$ either in the image domain or the Fourier domain (or their hybrid domain), CORE-PI reconstructs the image representation in the Stationary Wavelet Transform (SWT) domain. Since SWT-domain data are highly sparse and redundant, CORE-PI obtains the full SWT of $f_t(x,y)$ from the subsampled k-space data, using only estimated sensitivity maps.

The proposed method steps are:

1. Applying CORE-PI17 for computation of $\Psi f_t(x,y)$, which is the SWT of $f_t(x,y)$, directly from the subsampled k-space data. This step is performed in a two-channel process, which includes a low-pass and a high-pass channel, according to the wavelet filter bank method19. This step produces the full set of SWT coefficients representing $f_t(x,y)$ in the $\Psi$ domain.
2. Reconstruction of $f_t(x,y)$ from the recovered coefficeints using $\Psi^{-1}$, which is the Inverse SWT.
3. Reconstruction of the temperature rise from the temporal phase change using the well-established PRF shift method1, with $\Delta \angle\phi_t = \angle f_t(x,y) - \angle f_0(x,y)$ .

### Methods

Imaging. The method was validated using MR data acquired in two clinical in-vivo human prostate treatments using 8-coils, a 3Tesla MR scanner (GE Healthcare, WI) and ExAblate 2100 prostate array (InSightec, Israel). Data was provided by InSightech. The data was fully sampled in 2D Cartesian k-space, deidentified and retrospectively subsampled offline with a regular subsampling scheme.

Reconstruction. CORE-PI was implemented using a Daubechies-2 SWT. Coils sensitivity maps were estimated from baseline data using a Sum Of Squares (SOS). The temperatures reconstructed from the subsampled data were compared to those obtained from the full k-space data using the Normalized Root Mean Square Error (NRMSE). Computations were performed in Matlab™ on a personal computer.

### Results & Discussion

CORE-PI was implemented to the in-vivo data which was subsampled with a reduction factor of R=2. Figure 1 shows the SWT coefficients that were computed by CORE-PI, i.e. the $\Psi f_t(x,y)$ representation, and the coefficients obtained form the fully sampled data. Clearly, CORE-PI produced a highly accurate reconstruction of the SWT coefficients, both in magnitude and in phase, in both the low-pass and high-pass channels. The CORE-PI images include all the anatomical structures and HIFU-induced phase modifications that are present in the gold standard images, without discernible artifacts.

Figure 2 shows the results of the temperature changes reconstructed by CORE-PI from the SWT decomposition, for both R=2 and R=3. Evidently, the CORE-PI reconstructions of the HIFU-induced temperature rise are similar both in value and shape to the gold standard. Similar results are shown in Figure 3, which shows CORE-PI reconstructions for data of a different patient. Markedly, in both Figure 2 and Figure 3, there are no severe errors of temperature reconstruction with in the HIFU-heated zone. This high accuracy of CORE-PI is reflected by the low NRMSE values (0.05-1.4).

### Conclusion

This work proposes the implementation of CORE-PI for accelerated MRgHIFU. CORE-PI exploits data sparsity, offers simple non-iterative computations, and is a parameter-free calibrationless method. The in-vivo results show that: (1) CORE-PI reconstructs $\Psi f_t(x,y)$ accurately and directly from the multicoil subsampled k-space data, and (2) it produces highly accurate temperature rise maps. It is therefore highly suitable for accelerating MRgHIFU.

### Acknowledgements

The authors thank InSightech for providing the in-vivo data, and Dr. Yoav Levy from InSightech for useful discussions.

### References

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17. Shimron, E., Webb G., A. & Azhari, H. CORE-PI: Non-iterative Convolution-based Reconstruction for Parallel MRI in the Wavelet Domain. Med. Phys. (2018). DOI:10.1002/MP.13260

18. Roemer, P. B., Edelstein, W. A., Hayes, C. E., Souza, S. P. & Mueller, O. M. The NMR phased array. Magn. Reson. Med. 16, 192–225 (1990).

19. Mallat, S. G. A wavelet tour of signal processing. (Academic Press, 1999).

### Figures

Figure 1. In-vivo validation experiment. CORE-PI was implemented to subsampled k-space data with an acceleration factor of R=2. The SWT coefficients representing ft(x,y) are presented in (a) magnitude and (b) phase, for the low-pass channel (top row) and the high-pass channel (bottom row). Note that the coefficients computed by CORE-PI from 50% of the data are highly similar to the gold standard ones obtained from the full data.

Figure 2. Temperature maps reconstructed from in-vivo data using the proposed CORE-PI method (patient #1). Top, left: gold standard reconstruction from full k-space data. Top, right: CORE-PI reconstructions obtained with the proposed method from k-space data subsampled with reduction factors of R=2 and R=3. Bottom row: reconstruction errors with their NRMSE values.

Figure 3. Temperature maps reconstructed from in-vivo data using the proposed CORE-PI method (patient #2). Top, left: gold standard reconstruction from full k-space data. Top, right: CORE-PI reconstructions obtained with the proposed method from k-space data subsampled with R=2 and R=3. Bottom row: reconstruction errors with their NRMSE values.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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