Magnetic field estimation with ultrashort echo time (UTE) imaging.
Jiazheng Zhou1,2, Ali Aghaeifer1,2,3, Jonas Bause1,2,3, Alexander Loktyushin1,4, Gisela Hagberg1,3, and Klaus Scheffler1,3

1High-Field Magnetic Resonance, Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2Graduate Training Center of Neuroscience, IMPRS, University of Tübingen, Tübingen, Germany, 3Biomedical Magnetic Resonance, University Hospital Tübingen (UKT), Tübingen, Germany, 4Empirical Inference, Max Planck Institute for Intelligent Systems, Tübingen, Germany


We have used UTE sequence to obtain the subject-specific susceptibility distribution, which was then used to simulate motion-induced B0 change at two head positions. A Fourier-based dipole-approximation method was used to map susceptibility to B0. We have evaluated the simulation results against the measured B0 at the same positions and observed a good agreement between the simulated and real data.


Echo Planar Imaging(EPI) and balanced Stead-Stated Free Precession(bSSFP) are limited in their application for real-time fMRI by both subject motion and main magnetic field(B0) inhomogeneities. Motion-related B0 variations result from changing position and orientation of susceptibility interfaces relative to the B0 field; this causes ghosting and ringing artifacts in structural imaging and time-series phase instability in functional scans. Alternatively, the B0 field inhomogeneities have to be determined for each large-scale movement of the imaged object during acquisitions1. However, it is impractical to acquire the B0 field for every possible positions and orientations of the object. Previously, field probes have been used to correct for this, but they cannot fully estimate B0 in the brain as they are outside the brain2

Here, we estimate the motion-related B0 variations using a Fourier-based dipole-approximation method3-5 and combine with ultrashort echo time(UTE) imaging for computing the subject’s susceptibility model. The UTE sequence allows delineating the cortical bone and air cavities; and thus provides susceptibility models specific to each subject.


UTE sequence was applied to a healthy subject after applying the scanner’s second-order Spherical Harmonic (SH) global shimming. We took 192 slices of dual-echo UTE(1.5mm3voxel; TE1=0.05ms; TE2= 2.46ms; TR=6ms; flip-angle=8°, FOV=288mm3) on a 3T scanner(Prisma, Siemens, Erlangen, Germany). As a reference, off-resonance field map was measured using dual-echo GRE sequence(1.5mm3voxel; TE1=6.66ms; TE2=9.12ms; TR=1630ms; flip-angle=60°, FOV=288x288x192mm). The reference field map, “Measured ΔB0 (x,y,z)”, was calculated by measuring the phase accrued between two echo times at each image voxel.

A 3-classes(air, cortical bones, and soft tissues) UTE based susceptibility model was processed through 3 steps, as shown in Figure.1. First the magnitude images at the first(TE1) and second(TE2) echo times were used to calculate the air mask. An empirically determined threshold was chosen to segment the air cavities6. Then the bone and soft tissue were segmented using inverse of the transverse effective relaxation rate(R2*) estimated from TE1 and TE2, where cortical bone has high R2* values(R2*bone≥0.3ms-1) and soft tissue expected to have low R2* values(0ms-1<R2*soft-tissue<0.3ms-1)7. Finally, the air mask was multiplied back to the R2* map(R2*air=0ms-1) and corresponding magnetic susceptibilities $$$(\chi_{soft-tissue}\approx-9.2ppm, \chi_{bone}\approx-11.4ppm, \chi_{air}\approx0.36ppm)$$$8,9 were assigned to the R2* map.

The simulated off-resonance field map, “Simulated ΔB0 (x,y,z)”, was calculated using a Fourier-based method(Eq.1),

$${Estimated}\triangle{B_0^{z}}({\bf{x}})=\underbrace{FT^{-1}\left\{B_0\left[\frac{1}{3}-\frac{k_z^2}{k_x^2+k_y^2+k_z^2}\right]\cdot{\tilde{\chi}({\bf{k}})}\right\}}_{simulated\triangle{B_0^z}}+B_{in} \quad{(1)}$$

Where the tilde denotes a 3-dimensional Fourier transform of susceptibility model and k indicates k-space vector. Susceptibility is weighted by a k-space scaling factor(the terms in brackets)10. The Bin is measured background inhomogeneities, We measured Bin in a spherical phantom with identical SH shimming setting as measured ΔB0. The resulting “estimated ΔB0 (x,y,z)” is the sum of simulated ΔB0 and Bin. The standard deviation of B0(σB0) within a brain mask was used to assess the simulation performance. Image processing and simulations were performed in MATLAB(Mathwork, Natick, MA).

Two different head positions were measured. We used the first position(pos.1) as reference position. The scanner’s second-order SH shimming was calculated and then applied to the first position. For the second position(pos.2), we kept the identical SH shimming values as position one during measurements. Then second position’s field maps were registered to the first position using the FMRIB Software Library package11 of FLIRT12. We calculated the difference between pos.1 and registered pos.2 for “Estimated ΔB0” and “Measured ΔB0”, in order to demonstrate that the B0 field estimated with our method could be used to predict the motion-induced B0 variations


Figure.2 shows the ΔB0 maps estimated from UTE scan. Compared to the measured ΔB0(σB0=36.9Hz), the estimated ΔB0 increased the σB0 to 64.1Hz, potentially due to a mismatch between the simulated and actual susceptibility distribution. Estimated ΔB0 share some similarities with measured ΔB0 in field distribution. Figure.3 compares the histogram from estimated ΔB0 and measured ΔB0 at both two positions. Note that the histogram from measured ΔB0 has a narrower and higher peak, suggesting that the measured ΔB0 were more centrally distributed. Figure 4 shows the discrepancy between pos.1 and registered pos.2. Note that global σB0 for simulated and measured scenarios are 22.1Hz and 15.2Hz, respectively.


In this study, we used the UTE and a Fourier-based method to estimate the position-dependent B0 variations. In brief, the field maps matched. The difference between simulation and empirical measurements might be due to 1) underestimation of air cavities inside the implemented susceptibility distribution and 2) the magnetic field of the body(for example, lung, where is mostly air) influencing the field in the brain13. Figure.4 shows that it is possible to calculate position-change induced B0 variations from estimated field map. Future work is linking field map estimation with motion camera and multi-coil shimming for dynamic shimming.


This work was supported by DFG SCHE658/13 and the Max Planck Society. The authors thank Dr.Rainer Boegle for helpful discussions on simulation and Dr.Petros Martirosian for help with the UTE measurement protocol.


1 D. F. Hillenbrand K. M. L., W. F. B. Punchard , T. G. Reese, and P. M. Starewicz I.Applied Magnetic Resonance.2005; 29:39-64.

2 Gross S, Duerst Y, Vionnet LM, Barmet C and Pruessmann KP, B0-Atlas with Field-Probe Guidance: Application in Real-Time Field Control, In Proceedings of the 24th Annual Meeting of ISMRM, Melbourne, Singapore, 2016. p. 0930

3 Marques J. P. & Bowtell R.Concepts in Magnetic Resonance Part B: Magnetic Resonance Engineering.2005; 25B:65-78.

4 Boegle R., Maclaren J. & Zaitsev M.Magnetic Resonance Materials in Physics, Biology and Medicine.2010; 23:263-273.

5 Koch K. M., Papademetris X., Rothman D. L. et al.Phys Med Biol.2006; 51:6381-6402.

6 Catana C., van der Kouwe A., Benner T. et al.Journal of Nuclear Medicine.2010; 51:1431-1438.

7 Keereman V., Fierens Y., Broux T. et al.Journal of Nuclear Medicine.2010; 51:812-818.

8 Collins C. M., Yang B., Yang Q. X. et al.Magnetic Resonance Imaging.2002; 20:413-424.

9 Hopkins J. A. & Wehrli F. W.Magnetic Resonance in Medicine.1997; 37:494-500.

10 Cheng Y. C., Neelavalli J. & Haacke E. M.Phys Med Biol.2009; 54:1169-1189.

11 Smith S. M., Jenkinson M., Woolrich M. W. et al.NeuroImage.2004; 23 Suppl 1:S208-219.

12 Jenkinson M., Bannister P., Brady M. et al.NeuroImage.2002; 17:825-841.

13 Sostheim R, Maclaren J, Testud F, Zaitsev M. In Proceedings of the 20th Annual Meeting of ISMRM, Melbourne, Australia, 2012, p.3386


Figure 1. Image processing workflow. The Air mask derived from UTE TE1 and TE2 magnitude images using the transformation (TE1+TE2)/(TE12). An empirical threshold was determined to segment corresponding air cavities voxels. The R2* map was calculated for distinguishing bone and soft tissue. The binary air mask was multiplied with the R2* map to segment the air from soft tissue. Finally, the susceptibility model is obtained by assigning corresponding susceptibility values to the corrected R2* map.

Figure 2. Visual comparison of estimated ΔB0 map and measured ΔB0 map for two positions. The estimated ΔB0 map is the sum of simulated ΔB0 and measured background inhomogeneities Bin. Note that the σB0 across the brain mask is 28Hz larger in the estimated model than in measured field map. Potentially because the voxels near air cavities in simulated ΔB0 have a larger frequency offset than those in measured ΔB0

Figure 3. Histograms from estimated ΔB0 and measured ΔB0 at both positions. The histograms were plotted in same coordinates. The voxels distribution is calculated in a range of ±1kHz (only ±200Hz are shown). Estimated ΔB0 is less centralized than measured ΔB0. This phenomenon is due to the voxels near air cavities have a relatively large offset (~±400Hz) than those in measured ΔB0(~±200Hz), which “drag out” the histogram of estimated ΔB0

Figure 4. A comparison of position-change induced B0 variations in estimated field map (left) and measured field map (middle). The frequency-offset profiles (right) through the dotted white lines in simulated and measured field maps set in left.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)