Sebastian Theilenberg1, Ben John Parkinson2, and Christoph Juchem1,3
1Department of Biomedical Engineering, Columbia University in the City of New York, New York, NY, United States, 2Robinson Research Institute, Victoria University of Wellington, Wellington, New Zealand, 3Department of Radiology, Columbia University in the City of New York, New York, NY, United States
Synopsis
As part of a
collaborative effort to create a novel compact high-temperature superconductor
1.5 T head-only scanner for improved accessibility of MRI and advanced
motor coordination studies, we are developing a 31-coil Multi-Coil (MC) array
for linear and non-linear image encoding and concomitant B0
shimming. Here we present a preliminary characterization of the expected eddy
currents generated by the unshielded MC array in the unusual scanner assembly
at hand based on finite element based electromagnetic simulations.
Introduction
To improve accessibility of magnetic resonance imaging (MRI)
and to enable advanced motor coordination studies, we are part of a
collaborative effort to develop a compact 1.5 T head-only scanner with the
shoulders completely excluded. The compact size of the scanner causes large B0
inhomogeneities1,2 and, therefore, necessitates novel imaging methods which in turn require
advanced B0 field modeling capabilities. To this end we developed a
Multi-Coil (MC) array capable of generating linear3 and non-linear4 MRI encoding fields and
concomitant complex B0 shim fields5. Our solution2 is uniquely suited to the limited
space and low power demand of this application (Figure 1).
The time-varying encoding fields for MRI create eddy
currents (EC) in conductive structures of the scanner, in particular in the
magnet thermal shield. ECs create secondary magnetic fields that alter the effective
encoding fields and thereby lead to various image artifacts. EC generation is commonly
minimized by designing shielded gradient coils and by characterizing the
remaining ECs in order to correct for them (so-called preemphasis). By
contrast, our MC array is an unshielded coil system. By using a cryogen-free
high-temperature superconductor magnet, we eliminated the magnet thermal
shield. However, ECs might instead be induced in the copper conduction
cooling bus of the magnet. Here we present simulations on the magnitude and
temporal behavior of ECs generated in the magnet cooling bus by switching
typical linear encoding fields6 along with strategies to minimize them.Methods
The geometry of the copper bus structure was transferred into a
transient electromagnetic FEA model (Figure 2A,
Opera, Dassault Systèmes, Vélizy-Villacoublay, France). The copper was modeled with an electrical conductivity of 2 GS/m corresponding to copper
at 30 K7. The 31 coil elements of the MC
array were added as Biot-Savart conductors (cf. Figure 1).
Individual currents needed to generate specific MC fields were simulated using
B0DETOX8,9 and applied to the respective
conductors in the FEA model. To assess the EC generation, these currents were
ramped down linearly from 100% to 0% over 500 µs resembling typical
gradient switches, and electromagnetic fields and currents across the cooling bus structure were calculated for
various time points after the start of this ramp. At every output time step the
z-component of the B0 field was characterized by calculating
spherical harmonic (SH) coefficients on a sphere of 100 mm radius around
the isocenter (Figure
2B).
Two exemplary fields were examined, a Z-gradient of 6 kHz/cm (14.1 mT/m)
and an X-gradient of 4 kHz/cm (9.4 mT/m).
EC minimization strategies were explored by repeating the EC field simulations for
the Z-gradient using a modified bus geometry with radial and circumferential
cuts through the copper bus (cf. Figure 2A).Results
Figure 3
shows the calculated SH coefficients for the unmodified geometry as a function
of time. Coefficients that were considered negligible (<5% of the largest EC
component) are not shown. The Z-gradient created a significant field offset and Zn terms with the self (Z) term reaching a maximum of 29%
of the original gradient strength. The X-gradient
created mainly XZn terms
with the self (X) term reaching 2% of
the original gradient strength. Additionally, this
field also created YZn
terms with the linear Y term reaching
about 30% of the strength of the X
term.
All SH terms were fitted with exponential functions of the
form $$$\sum_n\alpha_ne^{-t/\tau_n}$$$, whereupon n was chosen as 1 or 2 to yield the
largest adjusted $$$\bar{R}^2$$$. For the quality of
these fits compare Figure 3 and Table 1. The time constants $$$\tau_n$$$ of the self-term ECs of the Z- and X-gradient were 248 ms
and 41 ms, respectively, and the remaining time constants were in the same
order of magnitude.
EC generation of the Z-gradient in the
modified geometry was significantly reduced (Figure 4) with the dominant 0th and 1st
order terms <5% of the EC strength in the unmodified case, corresponding to a self-term strength of 1.4% of the gradient strength. The time
constants of the corresponding fits were reduced to less than 20% of the corresponding
values in the unmodified case (cf. Table
1).Conclusion & Outlook
The presented simulations revealed that significant eddy
currents can be generated in a solid cooling bus structure, leading to
spatio-temporal field alterations across the volume of interest and potentially
affecting the MRI experiment. ECs can be significantly reduced, however, by employing a slotted
design of the otherwise unchanged copper plates of the cooling bus. The copper structure considered in this analysis is expected to be the main source of ECs
due to its high conductivity and proximity to the MC array. Other conductive structures such
as the RF coil located inside the MC array, or the MC coils themselves have
been neglected here, but will need to be included for a comprehensive analysis.
Note that all MC channels are actively current compensated which is expected to
reduce the latter effect.
The ECs observed in this study are larger than values
reported in the literature for traditional whole-body systems10. However, the values obtained
with the slotted bus design are comparable to conventional MR systems, and it should
thus be possible to correct for them using standard methods like preemphasis.Acknowledgements
This research was supported by the National Institute of
Biomedical Imaging & Bioengineering of the National Institutes of Health under
award number U01EB025153.References
1. Hunter M, Bouloukakis K, Theilenberg S,
Kobayashi N, Juchem C, Parkinson BJ. Passive shimming for a Portable Head-Only
scanner. In: Proc. Intl. Soc. Magn. Reson. Med. 27, 1478 (2019).
2. Theilenberg S, Shang Y, Kobayashi N,
Parkinson BJ, Juchem C. Multi-Coil Array for Combined Imaging and B0 Shimming
in a Portable Head-Only Scanner. In: Proc. Intl. Soc. Magn. Reson. Med.
27, 1480 (2019).
3. Juchem C, Nixon TW, McIntyre S, Rothman
DL, de Graaf RA. Magnetic field modeling with a set of individual localized
coils. J Magn Reson. 2010;204(2):281-289.
4. Juchem C, Nixon TW, de Graaf RA.
Multi-Coil Imaging with Algebraic Reconstruction. In: Proc. Intl. Soc. Magn.
Reson. Med. 20, 2545 (2012).
5. Rudrapatna SU, Fluerenbrock F, Nixon
TW, de Graaf RA, Juchem C. Combined imaging and shimming with the dynamic
multi-coil technique. Magn Reson Med. 2019;81(2):1424-1433.
6. Juchem C, Mullen M, Kumaragamage C, et
al. Dynamic Multi-Coil Technique (DYNAMITE) MRI on Human Brain. In: Proc.
Intl. Soc. Magn. Reson. Med. 27, 0219 (2019).
7. Ekin J. Experimental Techniques for
Low-Temperature Measurements. Oxford University Press; 2006.
8. Juchem C, Herman P, Sanganahalli BG,
Brown PB, Mcintyre S, Nixon TW, Green D, Hyder F, de Graaf RA. DYNAmic
Multi-coIl TEchnique (DYNAMITE) shimming of the rat brain at 11.7T. NMR
Biomed. 2014;27(8):897-906.
9. MR Scientific Engineering for Clinical
Excellence (MR SCIENCE) Laboratory software download. http://juchem.bme.columbia.edu/software-and-tools.
10. Papadakis NG, Martin KM, Pickard JD, Hall
LD, Carpenter TA, Huang CL-H. Gradient preemphasis calibration in
diffusion-weighted echo-planar imaging. Magn Reson Med.
2000;44(4):616-624.