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Highly Accelerated Compressed-Sensing-Based Field-mapping is Possible for Body QSM Applications
Christof Böhm1, Julio Oscanoa1,2, Sophia Kronthaler1, Maximilian N. Diefenbach1,3, Alexandra Gersing1, Jakob Meineke4, and Dimitrios C. Karampinos1
1TUM, Munich, Germany, 2Stanford University, Stanford, CA, United States, 3Division of Infectious Diseases and Tropical Medicine, University Hospital, LMU, Munich, Germany, 4Philips Research, Hamburg, Germany

Synopsis

Body QSM relies on accurate magnetic field-mapping that particularly accounts for the presence of fat. Due to the need to account for T2* effects and perform water–fat separation, water–fat-imaging-based field-mapping typically acquires multiple echoes with appropriate echo time step, increasing the total required scan time especially for high-resolution body QSM. To reduce scan time, several acceleration schemes have been proposed, such as parallel imaging and compressed sensing (CS). This work demonstrates the feasibility of high CS acceleration factors to distinguish strong para- and diamagnetic susceptibility sources in body regions with CS acceleration factors of 10 and higher.

Introduction

QSM is an established method to study brain physiology (1), pathology (2) and function (3). QSM has also gained popularity in applications outside the brain, e.g. for measuring cartilage (4), organ microstructure (5) and bone density (6, 7). For body applications, the QSM processing needs to address the presence of fat with its chemical shift effect. Due to the need to account for $$$T_2^*$$$ decay effects and perform water-fat separation, water-fat-imaging-based field-mapping typically acquires multiple echoes with appropriate echo time step, increasing the total required scan time for high-resolution body QSM. To reduce scan time several acceleration schemes have been proposed, such as parallel imaging (8, 9) and compressed sensing (CS) (10). Compressed sensing has been demonstrated to be feasible to significantly accelerate data acquisition for quantitative susceptibility mapping (QSM) in water only regions (11). Compressed sensing has also been demonstrated to be feasible to accelerate water–fat imaging (12, 13). However, the accuracy of the non-linear and non-convex field-map parameter in the water–fat signal model in CS reconstruction and subsequently performed QSM has yet to be investigated. The purpose of this work is therefore to investigate the feasibility of high CS acceleration factors for body QSM.

Methods

Simulation
For the estimation of the error evolution with increasing CS acceleration factors a simulation based on in-vivo data was set up. A scan of a spine with degenerative disease including an intradiscal air inclusion and a vascular calcification was used. Field-mapping and water–fat separation was performed using a single-min-cut graph-cut algorithm (14, 15). The background field was removed using the Laplacian boundary value method (LBV) (16). With the water- and fat-image $$$\rho_W,\rho_F$$$, a shared relaxation $$$R_2^*$$$-map and the local tissue field $$$f_B$$$, the complex signal at the $$$n$$$-th echo was forward simulated using the well-established water–fat voxel signal model:$$s_{\text{model}}(t_n)=\left(\rho_W+c_n\rho_F\right)e^{(i2\pi{f_B}-R_2^*)t_n},\quad{c_n}=\sum_{p=1}^{P}a_pe^{i2\pi\Delta{f_p}t_n},\quad\text{with}\quad\sum_{p=1}^{P} a_p=1.$$A fat spectrum with $$$P=10$$$ peaks specific to bone marrow with relative amplitudes $$$a_p$$$ and chemical shifts $$$\Delta f_p$$$ was used (17). On the echo data the undersampling pattern provided in the vendor’s k-space undersampling routines was applied to obtain the same undersampling pattern as an actual scan (Ingenia Elition, Philips Healthcare, Release 5.4, Best, The Netherlands). The compressed sensing reconstruction was performed using the BART-toolbox (18). The reconstructed images were separated into field-map and water–fat images and the normalized root mean square error (NRMSE) to the reference was measured.
In-vivo
Three aged spine data sets with abnormalities such as intradiscal air-inclusions and osteophytes were scanned using a monopolar time-interleaved multiecho gradient echo sequence, acquiring 3 echoes per interleave and TR and 6 echoes in total. Scanning was performed on a 3$$$\:$$$T scanner (Ingenia, Philips Healthcare, Release 5.4, Best, The Netherlands). The imaging parameters were set to TE$$$_{\text{min}}=1.33\:$$$ms, $$$\Delta$$$TE$$$=1.05\:$$$ms, orientation = sagittal, readout direction = anterior-posterior, FOV = $$$220\times 220\times79.2\:$$$mm$$$^3$$$ and acquisition voxel size = $$$1.8\:$$$mm$$$^3$$$ isotropic. The CS undersampling pattern provided by the vendor was applied and reconstructed with the BART-toolbox for each data set. Field-mapping was performed using the above mentioned graph-cut algorithm. The background field was removed using LBV. For the field-to-susceptibility inversion the following $$$\ell_1$$$-regularized cost-function was minimized:$$\chi(\mathbf{r})=\underset{\chi'}{\arg\min}\big|\big|\text{w}(f_{B}-d*\chi')\big|\big|_2^2+\lambda\big|\big|\nabla\chi'\big|\big|_1,$$where the maximum intensity projection over echo times was set as the weighting factor w, $$$d$$$ is the dipole kernel and the regularization factor $$$\lambda{=}0.002$$$ for all CS acceleration factors.

Results

The error and its slope of the non-linear local field-map term in the water–fat signal model is significantly smaller than of the magnitude water and fat images, as shown in Figures 1 and 2. CS-accelerated QSM can distinguish a paramagnetic air-inclusion from a diamagnetic vascular calcification in a spine with an acceleration factor from up to 20, as shown in Figure 3. High CS acceleration factors are feasible for different subjects with pathologies such as intradiscal air inclusions and osteophytes (calcified bone regions) as shown in Figure 4.

Discussion & Conclusion

The local field-map and consequently the information of susceptibility sources within the water–fat voxel signal model is shown to be a more stable parameter than magnitude water and fat images within compressed sensing reconstruction. Multi-echo data are multi-dimensional data and the extraction of the water–fat-fieldmap parameters should in general benefit from the multi-dimensionality of the data when applying CS techniques. However, in addition the local field-maps and $$$\chi$$$-maps in the body seem to be driven primarily by regions with large susceptibility differences, include less high-resolution information than water-images and could thus tolerate higher CS acceleration factors.
In this work high acceleration factors greater than 10 are shown to be feasible to correctly distinguish between para- and diamagnetic body structures located in regions with no MR visible signals (calcifications and air inclusions).

Acknowledgements

The present work was supported by the European Research Council (grant agreement No 677661, Pro-FatMRI). This work reflects only the authors view and the EU is not responsible for any use that may be made of the information it contains. The authors acknowledge finally research support from Philips Healthcare.

References

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Figures

Figure 1: Simulation results for different CS acceleration factors. The reference -map shows three distinct susceptibility sources, a vascular calcification (white arrow), air in the chest (red circle) and an intradiscal air inclusion (white rectangular). In the water images, the calcification can not be seen and the intradiscal air inclusion can be clearly delineated only in the reference image. However, in the local field-map the distinct variations persist even for high CS acceleration factors.

Figure 2: Normalized root mean square error analysis of the simulated data depicted in Figure 1. The errors of magnitude water- and fat-images are consistently higher than the error of the local field-map. Furthermore, the slope of the error of the water- and fat-images is significantly steeper than of the local field-map, supporting the visual reading of the images in Figure 1.

Figure 3: Water images and susceptibility maps from a spine data set for different CS acceleration factors. The vascular calcification, highlighted by an arrow, can not be seen in any water-image. The air inclusion in the spine, highlighted by an rectangle, is blurred into the vertebral body in the water image already for CSx5. The susceptibility maps can pick up the strong susceptibility values in the ROIs for very high acceleration factors up to CSx20.

Figure 4: QSM results of three pathological spine data sets for different CS acceleration factors. The susceptibility values within the ROIs highlighted by arrow, rectangle or circle, respectively, persist even for high CS acceleration factors. The para- or diamagnetic nature of the abnormalities within the ROIs are verified by corresponding CT scans.

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)
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