Introduction/Purpose

In patients with vertebral fractures or degenerative changes often CT and MR imaging are performed¹. A CT is performed to assess the fracture lines of the vertebra for potential surgery planning in acute cases. Acute vertebral fractures are often associated with bone marrow edema. To differentiate acute from chronic fractures MR imaging is the ‘gold standard’ for the investigation of bone marrow edema². Degenerative changes of the spine comprise soft-tissue as well as osseous tissue components^2,3. CT examinations of the spine are associated with radiation exposure, additional examination time and costs. To assess the soft-tissue and the osseous components it would be desirable to acquire all information in one examination. Ultrashort-echo time (UTE) imaging enables signal detection from tissues with short T₂^* components, such as cortical bone⁽⁴⁾. The purpose of this work was to develop a methodology for simultaneously extracting susceptibility-weighted imaging (SWI) and single point Dixon imaging (spDixon) based on a single-TE UTE scan in order to assess vertebral fractures and degenerative bone changes in the thoracolumbar spine.

Methods

The complex UTE S(x) data at TE=0.14ms was processed in the following manner:

SWI-processing
A phase mask f(x) was defined to enhance negative phase values as follows⁵:
$$S_{n}^{\prime}(x)=f(x)^{n}|S(x)|\;\;\;\;\text{with}\;\;f(x)=\left\{\begin{array}{cc}\frac{\pi+\phi(x)}{\pi}\text{for.}&-\pi<\phi(x)<0\\1&\text{otherwise}\end{array}\right.\;\;\;\;\text{[1]}$$
The phase mask was then n-times multiplied into the magnitude of the original UTE image |S(x)|.

spDixon-processing
spDixon approaches were previously proposed for rapid water-fat separation from a single TE^6,7. The water–fat separation is sensitive to unwanted phase components $$$\phi$$$. To remove unwanted components, previous methods either used calibration scans or implemented a region-growing algorithm. Unwanted phase components arise due to B₀ inhomogeneities, eddy currents, signal delays in the receiver chains, and the B₁ transmit/receive phase⁶. In UTE imaging the phase contribution due to B₀ inhomogeneities was expected to be small with respect to the short TE (0.14ms). Eddy currents and signal delays were corrected by means of a gradient impulse response function⁸. We observed a strong contribution of the B₁ phase which varied slowly and smoothly in the x-y plane (Figure 1A)^9,10. To demodulate unwanted phase components and separate water and fat, we propose to solve the following smoothness-constrained non-linear inverse problem:
$$\phi^{*}=\underset{\phi}{\operatorname{argmin}}\psi(\phi)=\underset{\phi}{\operatorname{argmin}} \frac{1}{2}\left\|\left(|W|+|F| e^{i\theta}\right)e^{i \phi}-S_{exp}\right\|_{2}^{2}+\lambda\|\nabla\phi\|_{2}^{2}\;\;\;\;\text{[2]}$$
where W: water image, F: fat image, $$$\theta=\angle\left(\sum_{i}\alpha_{i}e^{2\pi\,i\Delta\,f_{i}}\right)$$$: phase difference between water and fat due to the chemical shift, S_exp measured signal, $$$\lambda$$$ : regularization parameter and $$$\phi^*$$$: optimal solution which contains all unwanted phase components. $$$\psi$$$ was linearized as follows:
$$\psi(\phi+d \phi)=\frac{1}{2}\left\|\left(|W|+|F|e^{i \theta}\right)e^{i \phi}(1+id\phi)-S_{exp}\right\|_{2}^{2}+\lambda\|\nabla\phi+\nabla\,d\phi\|_{2}^{2}\;\;\;\;\text {[3]}$$
The update $$$d \phi$$$ was found by solving:
$$0=\nabla_{d\phi}\psi(\phi+d\phi)\;\;\;\;\text {[4]}$$
$$\left[\left(|W|^{2}+|F|^{2}+2|W||F|\cos(\theta)\right)+2\lambda\nabla^{H}\nabla\right]d\phi=-\operatorname{Im}\left(\left(|W|+|F|e^{i\theta}\right)e^{i\phi}S_{exp}^{H}\right)-2\lambda\nabla^{H} \nabla\phi\;\;\;\;\text{[5]}$$
Finally, equation [5] was solved using the conjugate gradient method (Figure 1B). The Gauss-Newton method is terminated when the relative update $$$\frac{\left\|d \phi_{n}\right\|_{2}}{\left\|\phi_{n}\right\|_{2}}$$$ was smaller than 0.01 with $$$\phi_{n}$$$ being the solution after the n-th iteration step.

UTE
UTE images were acquired with a 3D stack-of-stars sequence⁸ using a 3T-MRI (Ingenia Elition X, Philips Healthcare, Best, Netherlands) and following parameters: TR/TE=6.3/0.14ms, FA=5°, in‐plane resolution 0.45×0.45mm², slice thickness=3mm, FOV=250×250×279mm³, ramp length=0.08ms, maximum gradient strength 15.04mT/m, dwell time=3.12μs, acquisition window=1.77ms, 945 spokes, 568 samples, radial percentage 85%, half‐scan factor 0.6 in slice-direction, and scan time of 6.3min.

mDixon and STIR
A six-echo 3D monopolar time-interleaved multi-echo gradient-echo sequence was used¹¹ with following parameters: 2 interleaves with 3 echoes per TR and TR/TE1/ΔTE=8.2/1.3/1.1ms, FA=3°, voxel size=1.8×1.8×1.8mm³, FOV=626×511×102mm³, receiver bandwidth=1504 Hz/pixel, frequency direction A/P, scan time=3.7min. Water–fat maps were calculated using chemical shift encoding-based water-fat separation assuming a common T₂* for water and fat and a multi-peak fat model, tuned specifically to bone marrow^12,13. Further, a sagittal short-tau inversion recovery (STIR) was acquired which is used in the standard clinical routine to detect bone marrow edema.

Results

Figure 1 shows the observed smoothly varying B₁ phase and the resulting $$$\phi_{n}$$$ after n iteration steps. The demodulated phase showed no notable unwanted phase components or influences of the B₁ phase (Figure 1C).
Figure 2 shows the spDixon result for different regularization parameters. The best result was obtained for a $$$\lambda$$$ of 10⁵, where the water-fat contrast was high and subcutaneous fat was correctly identified as fat.
Figure 3 shows the spDixon results from a single UTE acquisition in comparison with water-fat images from a Cartesian 6-echo multi-echo scan (mDixon) and a STIR acquisition. The quality of the water–fat images from the spDixon was comparable with the mDixon maps. The red arrow highlights edema of an acute fracture, which was elevated in the STIR and was detectable in the spDixon maps.
Figure 4 shows that the SWI processing increased the contrast of osseous structures and the depiction of disc herniation into the vertebra.
Figure 5 shows an example of how the derived water-spDixon, SWI-UTE images can replace STIR and CT images in assessing edema and fracture lines, respectively.

Discussion & Conclusion

The proposed methodology allows the removal of the low-frequency background phase enabling water-fat separation and SWI from a single-echo complex UTE image. The water-fat separation can be challenging in anterior fat regions affected by respiratory motion and the UTE images are affected by fat blurring due to the radial k-space trajectory. The presented results showed that the proposed methodology enables the simultaneous assessment of vertebral fractures and edema of the thoracolumbar spine from a single MR sequence.

Acknowledgements

The present work was supported by the European Research Council (grant agreement No 677661, ProFatMRI). 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 also acknowledge research support from DAAD (Project number: 57514573) and Philips Healthcare.