Entangled Compressed Sensing for Highly Accelerated 4D Flow MRI
Adrian Emmanuel Georg Huber1, Christian Binter1, Claudio Santelli1, and Sebastian Kozerke1

1Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland

Synopsis

Entangled denoising (eSPARSE) was developed for highly undersampled 4D Flow MRI, combining both k-t SPARSE-SENSE and 3D-L1-Wavelets. Undersampling factors of 8 and 10 were studied in healthy volunteers. The proposed algorithm improves the reconstruction of fluid vector fields in the aorta compared to k-t SPARSE-SENSE. The relative RMSE velocity is reduced by up to 16% for an undersampling rate of R = 8 and by up to 19% for R = 10. Entangled denoising (eSPARSE) is a promising approach to accelerate 4D Flow MRI while preserving key features of the flow field.

Introduction

A number of approaches based on compressed sensing (1) have been presented to accelerate time-resolved phase-contrast velocity mapping (2,3). In 4D Flow MRI (3), scan time reduction is of critical importance to improve its clinical applicability and translation. To this end, various implementations of compressed sensing with and without joint parallel imaging have been described (4-8). A key challenge of present methods relates to finding an appropriate sparsifying transform that is suitable for data of limited spatial and temporal resolution. While spatial sparsification using Wavelets or other transforms (1) can compromise resolution in space, reconstruction based on temporal transforms may introduce temporal blurring. It is the objective of the present work to entangle spatial and temporal nonlinear denoising to better preserve spatiotemporal fidelity of 4D Flow MRI at high acceleration factors. The concept is demonstrated using in vivo data acquired in the aorta of healthy subjects.

Methods

In-vivo 4D Flow MRI data were acquired on a 3T Ingenia system (Philips Healthcare, Best, The Netherlands) equipped with a 28-channel cardiac coil array using the following scan parameters: spatial resolution: 2x2x2mm3, temporal resolution: 40ms, isotropic venc of 200cm/s, retrospective cardiac triggering and respiratory navigator gating (1.5mm gating window). Data were retrospectively undersampled by factors of 8 and 10 following a random 3D Poisson distribution which was varied for every time frame. Coil calibration data were obtained from a separate fully sampled pre-scan. Entangled compressed sensing (eSPARSE) reconstruction was implemented following ideas presented in (9). In brief, multiple reconstructions are performed interleaved and results thereof are combined patch-based using a weighted sum in each iteration step until final convergence is achieved. In this work, k-t SPARSE-SENSE (4) using both the temporal Fourier transform (FTtime) and Principal Component Analysis (PCA) along with 3D-L1-Wavelets operating separately on each time frame were implemented to sparsify the data prior to the nonlinear denoising step. The FISTA optimization method (10) was implemented in Matlab (Mathworks, Natick, MA) and used to solve both minimization problems. The result of each iteration of the eSPARSE framework was subdivided into spatially localized patches of 10x10x5 voxels while keeping all time frames. The centroid of the patches was determined and the individual patches were weighted by the inverse of the Euclidean distance between themselves and the centroid. The weighted patches were then recombined. To reduce temporal aliasing during 3D-L1-Wavelet reconstruction, this step was dynamically activated during the iteration process (Figure 1). Reconstruction results of the eSPARSE approach for 8- and 10-fold undersampling were compared to the fully sampled reference and relative to standard k-t SPARSE-SENSE reconstruction (4) by calculating root-mean-square errors (RMSE) of velocity along with an assessment of directional velocity error.

Results

Compared to k–t SPARSE-SENSE, flow data derived with eSPARSE reconstruction showed less noise and preserved flow patterns more faithfully (Figure 2). In Figure 3 it is seen that in-plane velocity vectors are more aligned with the reference data compared to data reconstructed with k-t SPARSE-SENSE. Figure 4 shows that both directional error and RMSE of the velocity field are lower for eSPARSE when compared to k-t SPARSE-SENSE: directional error (eSPARSE/k-t SPARSE-SENSE) 3.1%/4.6% in systole and 23.6%/34.7% in diastole and RMSE velocity 13.1%/15.5% and 38.9%/44.4% for 8-fold undersampling For R = 10 the directional error is 3.5%/5.5% in systole and 25.0%/38.2% in diastole and the RMSE velocity is 14.1%/17.5% and 39.7%/46.6%. Regression analysis in Figure 5 shows that on average eSPARSE approximates the hypothetical slope of 1 better when compared to k-t SPARSE-SENSE (slope: 0.94 vs. 0.93 with R2 0.96 vs. 0.93 for R = 8 and 0.94 vs. 0.92 with R2 0.95 vs. 0.91).

Discussion

In this work an entangled denosing approach to reconstruct undersampled 4D Flow MRI data has been implemented and compared against k-t SPARSE-SENSE. A reduction of error of both velocity magnitude (by up to 16% for R = 8 and 19% for R = 10) and velocity direction (by up to 33% for R = 8 and 36% for R = 10) was achieved. These undersampling rates are currently targeted for practical 4D Flow MRI protocols. In eSPARSE, patches are combined and the individual weights employed are therefore crucial. It is essential that the L1-Wavelet algorithm acts only after a few iterations of k-t SPARSE-SENSE to first reduce temporal aliasing and to ensure convergence.

Conclusion

Entangled denoising (eSPARSE) is a promising approach to accelerate 4D Flow MRI while preserving key features of the flow field.

Acknowledgements

No acknowledgement found.

References

1. Lustig M, Donoho D, Pauly JM. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn Reson Med. 2007; 58(6): 1182-1195.

2. Holland DJ, Malioutov DM, Blake A, Sederman AJ, Gladden LF. Reducing data acquisition times in phase-encoded velocity imaging using compressed sensing. J Magn Reson 2010;203(2):236-246.

3. Dyverfeldt P, Bissell M, Barker AJ, Bolger AF, Carlhäll CJ, Ebbers T, Francios CJ, Frydrychowicz A, Geiger J, Giese D, Hope MD, Kilner PJ, Kozerke S, Myerson S, Neubauer S, Wieben O, Markl M. 4D flow cardiovascular magnetic resonance consensus statement. J Cardiovasc Magn Reson. 2015 Aug 10;17(1):72.

4. Kim D, Dyvorne HA, Otazo R, Feng L, Sodickson DK, Lee VS. Accelerated phase-contrast cine MRI using k-t SPARSE-SENSE. Magn Reson Med 2012;67(4):1054-1064.

5. Liu J, Dyverfeldt P, Acevedo-Bolton G, Hope M, Saloner D. Highly accelerated aortic 4D flow MR imaging with variable-density random undersampling. Magn Reson Imaging. 2014 Oct;32(8):1012-20.

6. Basha TA, Akçakaya M, Goddu B, Berg S, Nezafat R. Accelerated three-dimensional cine phase contrast imaging using randomly undersampled echo planar imaging with compressed sensing reconstruction. NMR Biomed. 2015 Jan;28(1):30-9.

7. Santelli C, Loecher M, Busch J, Wieben O, Schaeffter T, Kozerke S. Accelerating 4D flow MRI by exploiting vector field divergence regularization. Magn Reson Med. 2015 Feb 13.

8. Hutter J, Schmitt P, Saake M, Stubinger A, Grimm R, Forman C, Greiser A, Hornegger J, Maier A. Multi-dimensional flow-preserving compressed sensing (MuFloCoS) for time-resolved velocity-encoded phase contrast MRI. IEEE Trans Med Imaging. 2015 Feb;34(2):400-14.

9. Schmidt JFM, Kozerke S. META: Multiple Entangled denoising and Thresholding Algorithms for suppression of MR image reconstruction artifacts. Proceedings of ISMRM 2015, Toronto.

10. Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2009; 2(1): 183-202.

Figures

Figure 1: Flow chart of eSPARSE algorithm.

Figure 2: Comparison of magnitude and phase images reconstructed with 8x eSPARSE relative to 8x k-t SPARSE-SENSE and the fully sampled reference.

Figure 3: Comparison of in-plane vector and flow magnitude from 8x eSPARSE versus 8x k-t SPARSE-SENSE and the fully sampled reference (taken in the ascending aorta as indicated in Figure 2).

Figure 4: Directional Error and RMSE of velocity fields as a function of cardiac phase for 8- and 10-fold undersampled (US) eSPARSE and k-t SPARSE-SENSE relative to the fully sampled reference. Shaded areas correspond to min/max across volunteers.

Figure 5: Scatterplots of reconstructed velocities for R = 8 and R = 10 in the ascending aorta for eSPARSE and k-t SPARSE-SENSE; mean and standard deviation of slope and y-intersection of regression line for eSPARSE and k-t SPARSE-SENSE for all three volunteers.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
4198