Skip to main content
SpringerLink
Log in

Analysis on matrix gradient coil modeling

  • Research Article
  • Published:
Magnetic Resonance Materials in Physics, Biology and Medicine Aims and scope Submit manuscript

A Correction to this article was published on 01 July 2022

This article has been updated

Abstract

Objective

The current distribution of the matrix gradient coil can be optimized via matrix gradient coil modeling to reduce the Lorentz force on individual coil elements. Two different modeling approaches are adopted, and their respective characteristics are summarized.

Methods

The magnetic field at each coil element is calculated. Then, the Lorentz force, torque, and deformation of the energized coil element in the magnetic field are derived. Two modeling approaches for matrix gradient coil, namely, optimizing coil element current (OCEC) modeling and optimizing coil element Lorentz force (OCEF) modeling, are proposed to reduce the Lorentz force on individual coil elements. The characteristics of different modeling approaches are compared by analyzing the influence of the weighting factor on the performance of the coil system. The current, Lorentz force, torque, and deformation results calculated via different modeling approaches are also compared.

Results

Coil element magnetic fields are much weaker than the main magnetic field, and their effect can be ignored. Matrix gradient coil modeling with different regularization terms can help to decrease the current and Lorentz force of coil elements. The performance of the coil system calculated via different modeling approaches is similar when suitable weighting factors are adopted. The two modeling approaches, OCEC and OCEF, can better reduce the maximum current and Lorentz force on individual coil elements compared with the traditional modeling approach.

Conclusions

Different modeling approaches can help to optimize the current distribution of coil elements and satisfy various requirements while maintaining the performance of the coil system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Change history

References

  1. Hidalgo-Tobon SS (2010) Theory of gradient coil design methods for magnetic resonance imaging. Concepts Magn Reason Part A 36A(4):223–242

    Article  Google Scholar 

  2. Winkler SA, Schmitt F, Landes H, de Bever J, Wade T, Alejski A, Rutt BK (2018) Gradient and shim technologies for ultra high field MRI. Neuroimage 168:59–70

    Article  Google Scholar 

  3. Konzbul P, Svéda K, Srnka A (2000) Design of matrix shim coils system for nuclear magnetic resonance. IEEE Trans Magn 36(4):1732–1735

    Article  Google Scholar 

  4. Juchem C, Nixon TW, McIntyre S, Rothman DL, de Graaf RA (2010) Magnetic field modeling with a set of individual localized coils. J Magn Reson 204:281–289

    Article  CAS  Google Scholar 

  5. Wintzheimer S, Driessle T, Ledwig M, Jakob PM, Fidler F (2010) A 50-channel matrix gradient system: a feasibility study. In: Proceedings of the joint annual meeting ISMRM-ESMRMB, Stockholm, Sweden, p 3937

  6. Juchem C, Brown PB, Nixon TW, McIntyre S, Rothman DL, de Graaf RA (2011) Multicoil shimming of the mouse brain. Magn Reson Med 66:893–900

    Article  Google Scholar 

  7. Stockmann JP, Wald LL (2018) In vivo B0 field shimming methods for MRI at 7 T. Neuroimage 168:71–87

    Article  Google Scholar 

  8. Kroboth S, Layton KJ, Jia F, Littin S, Yu H, Hennig J, Zaitsev M (2018) Optimization of coil element configurations for a matrix gradient coil. IEEE Trans Med Imaging 37(1):284–292

    Article  Google Scholar 

  9. Turner R (1993) Gradient coil design: a review of methods. Magn Reson Imaging 11(7):903–920

    Article  CAS  Google Scholar 

  10. Dietz P, Schmitt F, Hennig J (2011) Gradients in ultra high field (UHF) MRI. High-Field MR Imaging Med Radiol Diagn Imaging 27–40

  11. While PT, Korvink JG (2014) Designing MR shim arrays with irregular coil geometry: theoretical considerations. IEEE Trans Biomed Eng 61:1614–1620

    Article  Google Scholar 

  12. Jia F, Littin S, Layton KJ, Kroboth S, Yu H, Hennig J, Zaitsev M (2017) Design of a shielded coil element of a matrix gradient coil. J Magn Reson 281:217–228

    Article  CAS  Google Scholar 

  13. Littin S, Jia F, Layton KJ, Kroboth S, Yu H, Hennig J, Zaitsev M (2018) Development and implementation of an 84-channel matrix gradient coil. Magn Reson Med 79:1181–1191

    Article  Google Scholar 

  14. Chen W, Chen J, Sun H, Chen Z (2019) Simulation and analysis of irregular multicoil B0 shimming in C-type permanent magnets using genetic algorithm and simulated annealing. Appl Magn Reson 50(1–3):227–242

    Article  CAS  Google Scholar 

  15. Zivkovic I, Tolstikhin I, Schölkopf B, Scheffler K (2016) B0 matrix shim array design-optimization of the position, geometry and the number of segments of individual coil elements. In: 33rd annual scientific meeting of the European society for magnetic resonance. Medicine and biology. Vienna, Austria, 2016, p 36

  16. Xu Y, Yu P, Jia F, Wang Y, Yu Y, Yang X, Zaitsev M (2021) A Spherical harmonics decomposition method (SHDM) for irregular matrix coils design. IEEE Trans Biomed Eng. https://doi.org/10.1109/TBME.2021.3111656

    Article  PubMed  PubMed Central  Google Scholar 

  17. Aghaeifar A, Zhou J, Heule R, Tabibian B, Schölkopf B, Jia F, Zaitsev M, Scheffler K (2020) A 32-channel multi-coil setup optimized for human brain shimming at 9.4T. Magn Reson Med 83:749–764

    Article  Google Scholar 

  18. Delves LM, Mohamed JL (1985) Computational methods for integral equations. Cambridge University Press, Cambridge

    Book  Google Scholar 

  19. Forbes LK, Brideson MA, Crozier S, While PT (2007) Calculating the movement of MRI coils, and minimizing their noise. ANZIAM J 49(EMAC2007):C17–C35

    Article  Google Scholar 

  20. Jackson JM, Brideson MA, Forbes LK, Crozier S (2010) Tikhonov regularization approach for acoustic noise reduction in an asymmetric, self-shielded MRI gradient coil. Concepts Magn Reson Part B (Magn Reason Eng) 37B(3):167–179

    Article  Google Scholar 

  21. Forbes LK, Crozier S (2001) A novel target-field method for finite-length magnetic resonance shim coils. J Phys D Appl Phys 34(24):3447–3455

    Article  CAS  Google Scholar 

  22. Cooley CZ, Stockmann JP, Witzel T, LaPierre C, Mareyam A et al (2020) Design and implementation of a low-cost, tabletop MRI scanner for education and research prototyping. J Magn Reson 310:106625

    Article  CAS  Google Scholar 

  23. Juchem C, Green D, de Graaf RA (2013) Multi-coil magnetic field modelling. J Magn Reson 236:95–104

    Article  CAS  Google Scholar 

  24. Forbes LK, Brideson MA, Crozier S, While PT (2010) An analytical approach to the design of quiet cylindrical asymmetric gradient coils in MRI. Concepts Magn reason Part B Magn Reason Eng 31B(4):218–236

    Article  Google Scholar 

  25. Wang S, Huang S, Zhang Y, Zhao W (2016) Multiphysics modeling of a Lorentz force-based meander coil electromagnetic acoustic transducer via steady-state and transient analyses. IEEE Sens J 16(17):6641–6651

    Article  Google Scholar 

  26. Poole M, Bowtell R (2007) Novel gradient coils designed using a boundary element method. Concepts Magn Reason Part B (Magn reason Eng) 31B(3):162–175

    Article  Google Scholar 

  27. Li L, Cheng J, Ni Z, Wang H, Dai Y, Wang Q (2015) Preliminary mechanical analysis of a 9 4-T whole-body MRI magnet. IEEE Trans Appl Supercond 25(2):1–7

    Article  Google Scholar 

  28. Mansfield P, Glover P, Bowtell R (1994) Active acoustic screening: design principles for quiet gradient coils in MRI. Meas Sci Technol 5:1021–1025

    Article  Google Scholar 

  29. Chapman BLW, Mansfield P (1995) Quiet gradient coils: active acoustically and magnetically screened distributed transverse gradient designs. Meas Sci Technol 6:349–354

    Article  CAS  Google Scholar 

  30. Brideson MA, Jackson J, Forbes LK, Crozier S (2008) Computing Lorentz forces generated by gradient coils in an open MRI system. ANZIMA J 49(EMAC2007):C423–C438

    Article  Google Scholar 

  31. Roozen NB, Koevoets AH, den Hamer AJ (2008) Active vibration control of gradient coils to reduce acoustic noise of MRI systems. IEEE/ASME Trans Mechatron 13(3):325–334

    Article  Google Scholar 

Download references

Funding

Funding support was provided by the Major Science and Technology Innovation Program of Shandong (No. 2019TSLH0410), the Major Science and Technology Innovation Program of Shandong (No. 2021CXGC010504), and the Scientific Instrument and Equipment Development Project of Chinese Academy of Sciences (No. YJKYYQ20210004).

Author information

Authors and Affiliations

  1. Institute of Electrical of Engineering, Chinese Academy of Sciences, Beijing, 100190, China

    Hongyan He, Shufeng Wei, Huixian Wang & Wenhui Yang

  2. Chinese Academy of Sciences, Beijing, 100049, China

    Hongyan He & Wenhui Yang

  3. School of Information and Electrical Engineering, Hebei University of Engineering, Handan, 056038, China

    Hongyan He

Authors
  1. Hongyan He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shufeng Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huixian Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wenhui Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

HH: designed studies, analyzed the results, and wrote the manuscript. SW: assisted studies, analyzed the results, and wrote the manuscript. HW: assisted studies, analyzed the results, and wrote the manuscript. WY: obtained funding, designed studies, analyzed the results, and wrote the manuscript. All authors contributed to the discussion of the manuscript.

Corresponding author

Correspondence to Wenhui Yang.

Ethics declarations

Conflict of interest

All other authors declare that they have no conflicts of interest.

Ethical standards

The manuscript does not contain clinical studies, or patient or volunteer data.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, H., Wei, S., Wang, H. et al. Analysis on matrix gradient coil modeling. Magn Reson Mater Phy 35, 953–963 (2022). https://doi.org/10.1007/s10334-022-01022-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10334-022-01022-6

Keywords

Search

Navigation