Improving temporal resolution in fMRI using 3D spiral acquisition and low-rank plus sparse image reconstruction
Andrii Y Petrov1, Michael Herbst1,2, and V Andrew Stenger1

1Department of Medicine, University of Hawaii, Honolulu, HI, United States, 2Department of Radiology and Medical Physics, University Medical Center Freiburg, Freiburg, Germany

### Synopsis

Recent advances in dynamic MRI propose low-rank plus sparse (L+S) matrix decomposition for image reconstruction from reduced data acquisition. The L+S method has been successfully applied to multiple applications including cardiac MRI, perfusion, angiography and recently to denoise resting-state fMRI data, suggesting that it might be promising for improving temporal resolution in task-based fMRI. We propose to use 3D spiral acquisition, undersampled in kz-t domain, and L+S method for image reconstruction. Our results indicate that proposed approach allows 4x acceleration for the data acquisition and improved statistical significance of activation maps in the S component from an increased temporal resolution and eliminating physiological noise in the L component.

### Purpose

Recent progress in dynamic MRI propose low-rank plus sparse (L+S) matrix decomposition for image reconstruction from undersampled data 1,2. The L+S method has been successfully applied to multiple applications including cardiac MRI, perfusion, angiography 3 and recently to denoise resting-state fMRI data 4, suggesting that it might be promising for accelerating the task-based fMRI. We propose to use a 3D Stack of Spirals (SoS) sequence and achieve acceleration via excluding phase encoding planes in the kz-t domain. We then use the L+S method to (1) reconstruct aliasing artifact corrected images and (2) improve statistical significance of activation due to the increased temporal resolution. We further hypothesize that activation maps in S are a more realistic representation of the true BOLD signal after eliminating the physiologic noise in the L component.

### Theory

The L+S reconstruction is defined by the following convex optimization problem:

$$\arg \min_{L,S} \frac 12 \parallel E(L+S)-d\parallel_F^2 +\lambda_L\parallel L\parallel_* +\lambda_S\parallel S\parallel_1$$

where E is the encoding operator, $d$ is the k-space data, $T$ is the sparsifying transform for $S$, $\parallel . \parallel_*$ and $\parallel . \parallel_1$ are the nuclear norm and $l_1$ norm of the matrices $L$ and $TS$. $\lambda_L$ and $\lambda_S$ are the regularization parameters that balance the contributions of $L$ and $S$. $L$ represents the highly correlated background information that slowly changes over time (cardiac pulsation, respiratory movement), while $S$ captures spatially localized dynamic information. Linear combination of $L$ and $S$ results in a matrix $M$ representing the slowly changing background with localized dynamic components.

### Methods

We applied the L+S method to fMRI data on a healthy adult volunteer on a 3T scanner (Siemens, Tim Trio) with a 12-channel head coil. A 3D SoS trajectory was used to acquire fully sampled fMRI data in the whole brain. The imaging parameters were: FOV=22 cm, 64x64 matrix resolution, 40 2 mm thick slices, TR/TE=50/30ms, flip angle 15 degrees and 120 temporal frames. The paradigm was a flashing checkerboard consisting of four 30 sec “on” and 30 sec “off” blocks for a total duration of 4 minutes. The data were then retrospectively undersampled with x2 and x4 factors in the kz-t domain by fully sampling the centre lines of k-space and randomly excluding remaining planes at every time point (Fig. 1). For x4 undersampling, three different sampling patterns were examined. After the pattern providing the best reconstruction result was selected, a prospectively 4x undersampled fMRI scan was performed providing increased temporal resolution of 480 time points. All L+S reconstructions were performed using a temporal FFT as a sparsifying transform. Statistical analysis of the BOLD based activation was accomplished using a generalized linear model (GLM).

### Results and Discussion

Fig. 2 shows L+S reconstruction results of one slice within the visual cortex with overlaid activation scaled from t=6 to 8. Fig. 2 (a) is fully sampled data, (b) data retrospectively under sampled x2, (c-e) x4 undersampling using three different sampling patterns (as shown), and (f) prospectively undersampled data using a 4x acceleration. For retrospective undersampling, the L+S algorithm was able to eliminate aliasing artifacts and reconstruct structural brain images in the L component and retrieve BOLD signal in the S and M components that is only partially seen in the B images computed from the undersampled data. The activation patterns from the x2 and x4 retrospectively undersampled data are qualitatively consistent to that of the fully sampled data. For prospective under sampling, although L+S was less successful in eliminating artifacts, good recovery of the activation maps was observed. Fig. 3 shows reconstruction of multiple slices in the vicinity of the visual cortex from the 4x prospectively accelerated fMRI scan shown in Fig. 2 (f). Better statistical significance of activation regions is observed in the S components compared with the B images. Fig. 4 shows different types of separation into L and S components using different weights of the regularization parameters. It can be seen that L+S decomposition is highly sensitive to regularization values. Finally, Fig. 5 illustrates GLM fitting into the average BOLD signal across all activated voxels in the prospective data. It can be seen that physiological "slow drift" noise is absorbed by the L component, while S mainly captures the localized time-varying BOLD signal. Furthermore, spectral analysis confirms that the activation peak is absorbed by the S component as indicated by the arrow.

### Conclusion

An approach for prospectively accelerating fMRI using an under sampled 3D SoS acquisition and L+S image reconstruction is presented. Experimental fMRI results demonstrate the ability of the approach in obtaining aliasing artifact corrected functional images with improved statistical significance of the activation maps.

### Acknowledgements

Work supported by the NIH grants R01DA019912, R01EB011517, and K02DA020569.

### References

1. Lingala S, Hu Y, DiBella E, Mathews J. Accelerated Dynamic MRI Exploiting Sparsity and Low-Rank Structure: k-t SLR. IEEE Trans Med Imag. 2011; 30:1042-1054

2. Zhao B. et al., Image Reconstruction From Highly Undersampled Space Data With Joint Partial Separability and Sparsity Constraints, IEEE Trans Med Imag. 2012; 31:1809–18203.

3. Otazo R., et al., Low-Rank Plus Sparse Matrix Decomposition for Accelerated Dynamic MRI with Separation of Background and Dynamic Components, MR in Medicine. 2014; 73:1125–1136

4. Otazo R, et al., Low-Rank plus Sparse (L+S) matrix decomposition for separation of subsampled physiological noise in fMRI, OHBM, 2015, Honolulu, Hawaii.

### Figures

Figure 1. Example of kz-t under sampling for the SOS technique. (a) Central phase encoding planes are always fully sampled while remaining planes are randomly skipped in the kz-t domain facilitating different aliasing artifacts in the image domain. (b) Schematic diagrams of x2 and x4 kz-t under sampling patterns.

Figure 2. L+S reconstruction results with overlaid activation t-maps scaled from 6 to 8 for (a) the fully sampled fMRI data, (b) retrospectively undersampled fMRI data x2, (c-e) x4 under sampling using different sampling strategies, and (f) prospectively x4 undersampled fMRI data with an increased temporal resolution of 480 points.

Figure 3. L+S reconstruction results of multiple slices in the vicinity of the visual cortex from the 4x prospectively undersampled fMRI data with increased temporal resolution of 480 points. Improved statistical significance of the activation maps can be observed across all the S and M images compared to the B images.

Figure 4. Different types of separation into L and S components within one slice of the x4 prospectively undersampled fMRI data using different regularization parameters. It can be seen that decomposition is highly sensitive to the regularization weights which need to be carefully adjusted for optimal performance as shown in (f,g).

Figure 5. (a) GLM fit to the average of the activated voxels. It can be observed that physiological or slowly drifting noise is in the L component while S captures spatially localized time-varying BOLD response. (b) Temporal spectrum of the average of the activated voxels. Activation is clearly seen in S .

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