Introduction

Magnetic resonance elastography (MRE) provides valuable quantitative information about the mechanical properties of human brain tissue. Commonly, this is done using multi-slice 2D acquisitions. A high signal-to-noise ratio (SNR) is required to be able to determine the stiffness values accurately. However, high SNR in MRE is often ensured by thick image slices, which limits the resolution of details in elastograms^[1].
Here we present a super-resolution reconstruction (SRR) approach which combines multiple stacks of multi-slice elastography scans with a resolution of (1×1×3) mm³ to a 3D high resolution elastogram with (1×1×1) mm³ isotropic resolution. Compared to a multi-slice acquisition with (1×1×1) mm³ isotropic resolution we obtain 1.8 times higher contrast-to-noise ratio (CNR) and consistent shear wave speed values without an increase in scan time.

Methods

Data acquisition:
Data was acquired using spin-echo echo planar imaging on a 3-Tesla MRI system (Lumina, Siemens Healthineers, Erlangen, Germany) with a 32-channel head coil: flip angle: 90°, resolution: (1×1×1) mm³, TE/TR = 125/5230 ms. Three stacks à 25 slices covering a volume of (192×192×75) mm³ were acquired within a total acquisition time of 7 minutes. Each stack was shifted by 1 mm relative to the other stacks along the slice-encoding direction. Consequently, the FOV covered by combining all stacks was (192×192×77) mm³. The following MRE parameters were used: number of MEG directions: 3, mechanical frequencies: 31.25 Hz, 8 time steps over a vibration period.
For comparison, a data set HV was acquired with isotropic resolution of (1×1×1) mm³ and a FOV of (192×192×75) mm³ within 7 minutes of acquisition time. A T1-weighted sequence was used as anatomical reference with a resolution of (1×1×1) mm³ and a FOV of (192×192×75) mm³.

Data postprocessing:
Complex wave fields were recovered from raw data by phase unwrapping, temporal Fourier transformation and spatial filtering^[2,3]. Interslice dejittering^[4] was applied to generate 3D stacks of complex wave fields which were further processed by SRR. After SSR, wave inversion was performed by wavenumber-based inversion^[5] to reconstruct maps of shear wave speed (SWS) as a surrogate marker of stiffness.
As shown in Figure 1, in the state of the art, all steps within the pipeline are applied independently to each acquired slice. In our approach, SRR mixes information of adjacent low-resolution slices of the complex wavefields and the resulting high-resolution wavefields are processed into a high-resolution elastogram.

Super-resolution reconstruction (SRR) of wave images:
The idea of SRR is to acquire several low-resolution stacks of the object from different points of view and to calculate a high-resolution volume from the differences between these^[6], as visualized in Figure 2. This can be implemented as an optimization problem, that minimizes the discrepancy between the acquired low-resolution data $$$\tilde{l}$$$ and the low-resolution data $$$l$$$ predicted from the high-resolution volume. Here, $$$s$$$ describes the individual stacks, $$$\tilde{l}$$$ the acquired complex low-resolution (3 mm slice thickness) wave fields, $$$d$$$ their individual spatial directions and $$$w$$$ the high-resolution volume. $$$A$$$ is the effective slice profile of the scanner, calculated from the RF pulse and resulting from the excitation and refocusing pulse^{[7, 8]}. The minimization problem was initialized by SV_init, the combination of the low-resolution stacks taking into account the slice profile of the scanner. It was solved with the Limited-memory BFGS solver^[9] and additional Total Variation regularization^[10].

$$$\hat w_{d} \ = \underset{w_{d}}{\mathrm{argmin}} \sum_{s=1}^{S} ||\tilde{l_{s,d}}-\underbrace{A_s w_{d}}_\text{$l_{s,d}$}||_2^2 +\lambda {TV}(w_{d})$$$

Results and discussion

SRR was evaluated qualitatively with respect to the visibility of small anatomical structures and quantitatively with respect to the SWS value. SV_init, as a linear combination of the low-resolution stacks, was used as a reference for the SWS values and the isotropically acquired elastogram high-resolution volume HV served as reference for spatial resolution.
The complex wavefields before and after SRR are shown in Figure 3: In the different MEG directions, an improved visibility of small structures can be seen, which are shown enlarged in a white box.
Figure 4 displays the resulting elastograms: The input volume SV_init and output volume SV­_final of the SRR are shown, next to HV. The visibility of small structures is improved with the proposed SRR.
To be able to quantitatively assess the visibility of small structures, the CNR in the sulcus (green box in Figure 4) was calculated. The CNR in SV­_final was 1.8 times higher than in HV, allowing us to better differentiate the sulcus from white matter.
The SWS values were compared between the SV_init, SV­_final and HV, once over the entire white matter and once in a small ROI, framed in orange in Figure 4. Table 1 shows that HV underestimates SWS compared to SV­_init, while reducing precision, as indicated by the increase in standard deviation when focusing on a small ROI. This can be explained by the decreased SNR of the complex HR wavefields which leads to an underestimation of the SWS values in the elastograms.

Conclusion

The proposed SRR approach generated (1×1×1) mm³ elastograms of the human brain from multiple wavefields acquired with 3 mm slice thickness and shifted by 1 mm along the head-feed axis. This SRR approach was successfully applied to a healthy volunteer, resulting in improved visualization of small details and consistent shear wave speed values of brain tissue.

Acknowledgements

The authors gratefully acknowledge funding from the German Research Foundation (GRK2260, BIOQIC).

References

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