Synopsis

In this work we investigated the feasibility and assessed the performance of a bipolar compared to a unipolar gradient echo readout for a combined method of water-fat separation and quantitative susceptibility mapping for application in the carotid artery wall.

Introduction

Carotid atherosclerosis involves formation of plaques, which may rupture and cause ischemic stroke.¹ Plaques can become calcified and may contain haemorrhage¹, which makes them of interest for investigation using Quantitative Susceptibility Mapping (QSM). Application in the neck requires modification of the processing, to avoid errors in the field non-uniformity map ΔB, caused by the water-fat chemical shift, which propagate into susceptibility maps. We have previously implemented the IDEAL water-fat separation to correct for these errors when performing QSM in the neck.^2,3,4

IDEAL fits complex multi-echo gradient echo MR data to estimate water, fat, and ΔB. Increasing the number of echoes and shortening echo spacing have shown to improve SNR and reduce phase wraps in QSM,⁵ and to improve robustness of IDEAL processing.⁶ Using bipolar instead of unipolar readout gradients, improves acquisition efficiency while minimizing echo spacing. However, opposite readout gradient polarities cause phase discrepancies between odd and even echoes, that require compensation. We investigated the feasibility and potential benefits of acquiring data with bipolar sequences for simultaneous water-fat separation and QSM in the neck compared to the conventional unipolar echoes.

Methods

The phase φ of the multi-echo gradient echo sequence is a function of ΔB, echo time TE, initial phase offset φ₀, and the gradient polarity specific phase offsets Δθ_i(x,y), which are caused by gradient delays and eddy currents:

φ(x,y,TE_EVEN)=φ₀-γΔB(x,y)TE_EVEN+Δθ₁(x,y)

φ(x,y,TE_ODD)= φ₀-γΔB(x,y)TE_ODD+Δθ₂(x,y)

We subsequently implemented a correction to remove these offsets.^7-11 A nonlinear fit of the complex data from odd echoes gives the phase difference Φ=-γΔB(x,y)(TE₃-TE₁).^12-14 After spatial phase unwrapping¹⁵ and scaling by a factor of TE_i/(TE₃-TE₁), Φ corresponds to the phase at TE_i without any offset. The differences between Φ and the phase of the complex images S at echo times TE₁ and TE₂ give the gradient polarity specific offsets:

Δθ₁(x,y)+φ₀=∠(S(TE₁)conj(e^{i*Φ*TE₁/(TE₃-TE₁)}))

Δθ₂(x,y)+φ₀=∠(S(TE₂)conj(e^{i*Φ*TE₂/(TE₃-TE₁)}))

We assumed that the phase offset varies linearly in space^7-10 and can be described by two constants, m and n, and is modeled as Δθ_i(x,y)_fitted=mx+ny+b. This was used to correct the complex data so that even and odd echoes are without phase offset(Fig.1):

S(TE_ODD)_corr= S(TE_ODD)conj(e^{iΔθ₁(x,y)_fitted})

S(TE_EVEN­)_corr= S(TE_EVEN)conj(e^{jΔθ₂(x,y)_fitted})

Six healthy subjects were scanned using a 3D multi-echo gradient echo acquisition with bipolar gradients at 3T (MR 750, GE Healthcare, Waukesha, WI) and one patient with carotid artery stenosis at 1.5T (MR450w, GE Healthcare, Waukesha, WI)(Table1). Before performing QSM, the phase offsets from odd and even echoes were removed from the bipolar dataset. This is unnecessary when using odd echoes only, since they all have the same offset Δθ₁(x,y). The results from both datasets were compared using a large number of echoes (twelve bipolar/six unipolar), to assess feasibility of using bipolar acquisitions for QSM and IDEAL, and a smaller number (eight/four) to assess potential improvements of bipolar acquisitions if the results of the unipolar echoes are degraded. QSM consisted of estimating ΔB using IDEAL,^2,3 followed by background field removal^16-18 and dipole field inversion to estimate the susceptibility map.^19-23

Results

The unipolar and bipolar methods produced similar results, using six and twelve echoes respectively(Fig.2). Water-fat separation robustly estimated ΔB with minimal artifacts which resulted in clear visualization of anatomical features like fat and vessel wall on both susceptibility maps. The measured susceptibility difference between tissue and fat, 0.57ppm, agreed with previously published values, 0.61ppm.^3,26

When limiting the number of unipolar echoes to four, ΔB showed errors at the boundary between water and fat that resulted in streaking artifacts on the susceptibility map(Fig.3.a),c)). The use of all eight bipolar echoes acquired during the same time improved image quality on ΔB and removed streaking artifacts(Fig.3.b),d)) to allow for clear visualization of relevant anatomical features.

In the patient scan a bipolar acquisition produced susceptibility maps in which the vessel wall and a strongly diamagnetic region (thought to be vessel wall calcification) were clearly identifiable(Fig.4).

Discussion

Conclusion

Acknowledgements

References

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[12]Liu, Tian, et al. "Nonlinear formulation of the magnetic field to source relationship for robust quantitativesusceptibility mapping." Magnetic resonance in medicine 69.2 (2013): 467-476.

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[15] graph cut phase unwrapping, code available from "http://weill.cornell.edu/mri/pages/qsm.html"

[16] Zhou, Dong, et al. "Background field removal by solving the Laplacian boundary value problem." NMR inBiomedicine 27.3 (2014): 312-319.

[17] Liu, Tian, et al. "A novel background field removal method for MRI using projection onto dipole fields." NMR in Biomedicine 24.9 (2011): 1129-1136.

[18] de Rochefort, Ludovic, et al. "Quantitative susceptibility map reconstruction from MR phase data using bayesian regularization: validation and application to brain imaging." Magnetic Resonance in Medicine 63.1 (2010): 194-206.

[19] Liu, Tian, et al. "Nonlinear formulation of the magnetic field to source relationship for robust quantitativesusceptibility mapping." Magnetic resonance in medicine 69.2 (2013): 467-476.

[20] Liu, Jing, et al. "Morphology enabled dipole inversion for quantitative susceptibility mapping using structuralconsistency between the magnitude image and the susceptibility map." Neuroimage 59.3 (2012): 2560-2568.

[21] Liu, Tian, et al. "Morphology enabled dipole inversion (MEDI) from a single-angle acquisition: comparison withCOSMOS in human brain imaging." Magnetic resonance in medicine 66.3 (2011): 777-783.

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[23] Shmueli, Karin, et al. "Magnetic susceptibility mapping of brain tissue in vivo using MRI phase data." Magnetic Resonance in Medicine 62.6 (2009): 1510-1522.

[24] the codes referenced in [12-22] are available at "http://weill.cornell.edu/mri/pages/qsm.html"

[25] code from [23] from "Wang, Yi, and Tian Liu. "Quantitative susceptibility mapping (QSM): decoding MRI datafor a tissue magnetic biomarker." Magnetic resonance in medicine 73.1 (2015): 82-101."; available at"http://weill.cornell.edu/mri/pages/qsmreview.html"

[26] Szczepaniak, Lidia S., et al. "Bulk magnetic susceptibility effects on the assessment of intra‐and extramyocellular lipids in vivo." Magnetic resonance in medicine 47.3 (2002): 607-610.