Automated tissue phase and QSM estimation from multichannel data
Berkin Bilgic1, Jonathan R Polimeni1, Lawrence L Wald1, and Kawin Setsompop1

1Martinos Center for Biomedical Imaging, Charlestown, MA, United States


An automated method for tissue phase and susceptibility estimation from multichannel data is proposed. Using ESPIRiT with virtual body coil calibration on multichannel data, phase-sensitive coil combination is achieved without an additional reference acquisition. This is shown to perform similarly to SNR-optimal Roemer combination that requires additional reference body and head coil acquisitions. Estimation of the tissue phase from the combined data is posed as a regularized inverse problem using the spherical mean value property. The extension of the technique to single-step Quantitative Susceptibility Mapping is also demonstrated on 2D, 3D and Simultaneous MultiSlice data.


We introduce an automated, data-driven coil combination method for high-quality phase and susceptibility imaging that obviates the need for an additional reference acquisition. The technique is shown to perform similarly to SNR-optimal Roemer combination (1,2) that requires additional body and head coil acquisitions. For tissue phase estimation, an inverse problem using the spherical mean value (SMV) property was adopted (3,4), and extended to allow single-step Quantitative Susceptibility Mapping (QSM) (5–7). Our reconstruction approach is shown to enable streamlined phase and QSM processing of multi-coil images from routinely acquired 2D, 3D and Simultaneous MultiSlice (SMS) protocols.


The magnetic field created by background susceptibility sources is harmonic inside the brain boundary, hence can be filtered out using an SMV kernel (3). Denoting the total and tissue phase as φtot and φtis, this can be expressed as M(s*L(φtot))=M(s*φtis), where M is the brain mask, s is an SMV filter and L is Laplacian unwrapping operator (8,9). RESHARP technique formulates SMV filtering as a regularized inverse problem (10):

minφtis ||M(s*L(φtot)) - M(s*φtis)||22 + α·||φtis||22

Expressing the convolution operations as multiplication with k-space kernel S=Fs, this formulation is readily extended to single-step QSM:

minχ ||M(F'SFL(φtot)) - M(F'SDFχ)||22 + λ·TV(χ)

Here, the susceptibility distribution χ is related to the tissue phase φtis via DFχ=φtis and λ is the Total Variation parameter. Nonlinear conjugate gradients (11) were employed for optimization.

Automated data-driven coil combination

Optimal-SNR coil combination requires estimation of coil sensitivities as well as the receiver phase offsets, which need to be removed from the coil images for constructive addition (1,2). This necessitates additional reference images acquired with the body coil and head coil array, where the head coil images are normalized by the body coil to remove anatomical information from the receiver phase estimates. Virtual body coil concept (12) derives a homogenous reference from the head array data, thus averting the need for an additional body coil acquisition. This is achieved by computing the singular value decomposition (SVD) across channels, and taking the dominant singular vector as the body coil reference, similar to a “uniform-mode birdcage combination”. We propose to combine this concept with ESPIRiT (13) for automated calibration of sensitivities. In ESPIRiT, the relative receiver phase offset is arbitrary; hence the first coil channel is assumed to be the reference. To make use of the virtual body coil concept, we apply SVD compression (14) on the head array, and sort the virtual channels in decreasing order of eigenvalues. This way, the first virtual channel corresponds to the dominant singular vector, and therefore is the virtual body coil. Supplying the SVD compressed data to ESPIRiT then uses the virtual body coil as the reference, thus allowing coil sensitivity estimation without an additional acquisition (Fig.1).

Data Acquisition & Reconstruction

Three volunteers were scanned with informed consent. Following BET brain masking (15) and Laplacian unwrapping, tissue phase and QSM images were reconstructed using α and λ chosen with L-curve (16). A 32-channel head array was used for reception and coil sensitivities were estimated from the central 16×16×16 k-space points of the acquired data using the proposed ESPIRiT with virtual body coil concept. The following datasets were acquired:

(i) 3D-GRE at 3T with 1mm isotropic resolution (Fig.2): FOV=240×192×120mm3, TE/TR=24.8/35ms. For comparison against Roemer combination, additional reference acquisitions with body and head coils were processed with ESPIRiT to compute coil sensitivities.

(ii) 2D-GRE at 3T with 1.5mm isotropic resolution (Fig.3): FOV=192×192×144mm3, TE/TR=20/2630ms.

(iii) SMS-EPI with blipped-CAIPI (17) at 7T with 2mm isotropic resolution (Fig.4): MultiBand 3× accelerated data were acquired at 3× in-plane acceleration with FOV=200×200×126mm3 and TE/TR=15/2040ms. To mitigate SMS slice-group boundary artifacts stemming from large acquisition time differences between adjacent slices at the slice-group boundaries, Laplacian unwrapping was applied separately for each slice-group.


Fig.2 demonstrates high-quality phase and QSM reconstructions where the difference from Roemer combination is 2.6% and 2.3% RMSE respectively. Fig.3 shows high-fidelity QSM images free of dipole artifacts. Arrows in Fig.4 point to the slice-group boundary artifacts in the SMS phase images, which were largely mitigated in the tissue phase and susceptibility results.

Discussion & Conclusion

Herein, an automated coil sensitivity estimation technique that does not require additional reference scans has been proposed. This is shown to yield detailed phase and QSM images with nearly identical quality as the Roemer combination. This approach can be particularly useful in cases where an adequate body coil reference is not available, such as ultra-high field scanners. The technique is applicable to raw coil images from 2D, 3D and SMS acquisitions and performs in a data-driven fashion from as few as 16×16 central k-space lines of the acquired data.


NIH NIBIB P41-EB015896, 1U01MH093765, R24MH106096, 1R01EB01943701A1


1. Pruessmann K, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI. Magn. Reson. Med. 1999;42.5:952–962.

2. Roemer P, Edelstein W, Hayes CE, Souza SP, Mueller OM. The NMR phased array. Magn. Reson. Med. 1990;16:192–225.

3. Schweser F, Sommer K, Deistung A, Reichenbach JR. Quantitative susceptibility mapping for investigating subtle susceptibility variations in the human brain. Neuroimage 2012;62:2083–100. doi: 10.1016/j.neuroimage.2012.05.067.

4. Wu B, Li W, Guidon A, Liu C. Whole brain susceptibility mapping using compressed sensing. Magn. Reson. Med. 2012;67:137–47. doi: 10.1002/mrm.23000.

5. Langkammer C, Bredies K, Poser BA, Barth M, Reishofer G, Fan AP, Bilgic B, Fazekas F, Mainero C, Ropele S. Fast quantitative susceptibility mapping using 3D EPI and total generalized variation. Neuroimage [Internet] 2015;111:622–30. doi: 10.1016/j.neuroimage.2015.02.041.

6. Liu T, Zhou D, Spincemaille P, Yi W. Differential approach to quantitative susceptibility mapping without background field removal. In: Proceedings of the 22nd Annual Meeting of ISMRM, Milan, Italy. ; 2014. p. 597.

7. Sharma S, Hernando D, Horng D, Reeder S. A joint background field removal and dipole deconvolution approach for quantitative susceptibility mapping in the liver. In: Proceedings of the 22nd Annual Meeting of ISMRM, Milan, Italy. ; 2014. p. 606.

8. Li W, Wu B, Liu C. Quantitative susceptibility mapping of human brain reflects spatial variation in tissue composition. Neuroimage 2011;55:1645–1656.

9. Schofield MA, Zhu Y. Fast phase unwrapping algorithm for interferometric applications. Opt. Lett. 2003;28:1194. doi: 10.1364/OL.28.001194.

10. Sun H, Wilman AH. Background field removal using spherical mean value filtering and Tikhonov regularization. Magn. Reson. Med. 2014;71:1151–7. doi: 10.1002/mrm.24765.

11. Lustig M, Donoho D, Pauly JM. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 2007;58:1182–95. doi: 10.1002/mrm.21391.

12. Buehrer M, Boesiger P, Kozerke S. Virtual Body Coil Calibration for Phased-Array Imaging. In: Proceedings of the 17th Annual Meeting of ISMRM, Honolulu, Hawaii, USA. ; 2009. p. 760.

13. Uecker M, Lai P, Murphy M, Virtue P, Elad M, Pauly JM, Vasanawala S, Lustig M. ESPIRiT—an eigenvalue approach to autocalibrating parallel MRI: Where SENSE meets GRAPPA. Magn. Reson. Med. 2014;71:990–1001.

14. Buehrer M, Pruessmann KP, Boesiger P, Kozerke S. Array compression for MRI with large coil arrays. Magn. Reson. Med. 2007;57:1131–9. doi: 10.1002/mrm.21237.

15. Smith S. Fast robust automated brain extraction. Hum. Brain Mapp. 2002;17:143–155.

16. Hansen PC. The L-Curve and its Use in the Numerical Treatment of Inverse Problems. WIT Press, Southampton; 2000.

17. Setsompop K, Gagoski B, Polimeni JR, Witzel T, Wedeen VJ, Wald LL. Blipped-controlled aliasing in parallel imaging for simultaneous multislice echo planar imaging with reduced g-factor penalty. Magn. Reson. Med. 2012;67:1210–1224.


Proposed data driven coil combination applies SVD coil compression on the head array data, where the first channel corresponds to the virtual body coil. Applying ESPIRiT calibration then employs the virtual body coil as the phase reference, thus yielding high quality, automated coil combination without the need for additional reference data.

Single step tissue phase and QSM reconstruction from coil combined 3D GRE volume at 1mm isotropic resolution. The data-driven channel combination yields near identical phase and susceptibility maps to the SNR-optimal Roemer combination that requires additional reference acquisitions with head and body coils.

Data-driven ESPIRiT calibration with virtual body coil concept is also applicable to 2D GRE acquisition, and yields high quality tissue phase and QSM images at 1.5 mm isotropic resolution.

Phase imaging with Simultaneous MultiSlice EPI acquisition is hampered by slab boundary artifacts stemming from the timing difference between the slice groups. This can be largely mitigated by separately unwrapping the slabs, which allows tissue phase and QSM reconstruction within a single step.

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