Vol. 20
Latest Volume
All Volumes
PIERB 98 [2023] PIERB 97 [2022] PIERB 96 [2022] PIERB 95 [2022] PIERB 94 [2021] PIERB 93 [2021] PIERB 92 [2021] PIERB 91 [2021] PIERB 90 [2021] PIERB 89 [2020] PIERB 88 [2020] PIERB 87 [2020] PIERB 86 [2020] PIERB 85 [2019] PIERB 84 [2019] PIERB 83 [2019] PIERB 82 [2018] PIERB 81 [2018] PIERB 80 [2018] PIERB 79 [2017] PIERB 78 [2017] PIERB 77 [2017] PIERB 76 [2017] PIERB 75 [2017] PIERB 74 [2017] PIERB 73 [2017] PIERB 72 [2017] PIERB 71 [2016] PIERB 70 [2016] PIERB 69 [2016] PIERB 68 [2016] PIERB 67 [2016] PIERB 66 [2016] PIERB 65 [2016] PIERB 64 [2015] PIERB 63 [2015] PIERB 62 [2015] PIERB 61 [2014] PIERB 60 [2014] PIERB 59 [2014] PIERB 58 [2014] PIERB 57 [2014] PIERB 56 [2013] PIERB 55 [2013] PIERB 54 [2013] PIERB 53 [2013] PIERB 52 [2013] PIERB 51 [2013] PIERB 50 [2013] PIERB 49 [2013] PIERB 48 [2013] PIERB 47 [2013] PIERB 46 [2013] PIERB 45 [2012] PIERB 44 [2012] PIERB 43 [2012] PIERB 42 [2012] PIERB 41 [2012] PIERB 40 [2012] PIERB 39 [2012] PIERB 38 [2012] PIERB 37 [2012] PIERB 36 [2012] PIERB 35 [2011] PIERB 34 [2011] PIERB 33 [2011] PIERB 32 [2011] PIERB 31 [2011] PIERB 30 [2011] PIERB 29 [2011] PIERB 28 [2011] PIERB 27 [2011] PIERB 26 [2010] PIERB 25 [2010] PIERB 24 [2010] PIERB 23 [2010] PIERB 22 [2010] PIERB 21 [2010] PIERB 20 [2010] PIERB 19 [2010] PIERB 18 [2009] PIERB 17 [2009] PIERB 16 [2009] PIERB 15 [2009] PIERB 14 [2009] PIERB 13 [2009] PIERB 12 [2009] PIERB 11 [2009] PIERB 10 [2008] PIERB 9 [2008] PIERB 8 [2008] PIERB 7 [2008] PIERB 6 [2008] PIERB 5 [2008] PIERB 4 [2008] PIERB 3 [2008] PIERB 2 [2008] PIERB 1 [2008]
2010-04-15
A Divergence-Free BEM Method to Model Quasi-Static Currents: Application to MRI Coil Design
By
Progress In Electromagnetics Research B, Vol. 20, 187-203, 2010
Abstract
The modeling of quasi-static optimization problems often involves divergence-free surface current densities. In this paper, a novel technique to implement these currents by using the boundary element method framework is presented. A locally-based characterization of the current density is employed, to render a fully geometry-independent formulation, so that it can be applied to arbitrary shapes. To illustrate the versatility of this approach, we employ it for the design of gradient coils for MRI, providing a solid mathematical framework for this type of problem.
Citation
Clemente Cobos Sanchez Salvador Gonzalez Garcia Luis Diaz Angulo Carlos Moreno De Jong Van Coevorden Amelia Rubio Bretones , "A Divergence-Free BEM Method to Model Quasi-Static Currents: Application to MRI Coil Design," Progress In Electromagnetics Research B, Vol. 20, 187-203, 2010.
doi:10.2528/PIERB10011504
http://www.jpier.org/PIERB/pier.php?paper=10011504
References

1. Bandelier, B., C. Daveau, P. Haghi Ashtiani, A. Rais, and F. Rioux-Damidau, "Use of stream functions for the computation of currents in thin circuits determination of the impedances," IEEE Transactions on Magnetics, Vol. 36, No. 4, 760-764, 2000.
doi:10.1109/20.877558

2. Zacharopoulos, A., S. Arridge, O. Dorn, V. Kolehmainen, and J. Sikora, "3D shape reconstruction in optical tomography using spherical harmonics and BEM," PIERS Online, Vol. 2, No. 1, 48-52, 2006.

3. Ruan, B. and Y. Wang, "New topography inversion using EM field," Progress In Electromagnetics Research, Vol. 1, No. 1, 79-83, 2005.

4. Peeren, G. N., "Stream function approach for determining optimal surface currents," Journal of Computational Physics, Vol. 191, No. 1, 305-321, 2003.
doi:10.1016/S0021-9991(03)00320-6

5. Turner, R. and Gradient coil design: A review of methods, "Magn. Reson. Imaging,", Vol. 11, 903-920, 1993.

6. Li, X., D. Xie, and J. Wang, "A novel target field method for designing uniplanar self-shield gradient coils of fully open MRI device," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 12, 1635-1644, 2007.

7. Hong, L. and D. Zu, Shimming permanent magnet of MRI scanner, Progress In Electromagnetics Research Symposium, Vol. 3, No. 6, 859-864, 2007.

8. Pissanetzky, S., "Minimum energy MRI gradient coil of general geometry," Measurement of Science Technology, Vol. 3, 667-673, 1992.
doi:10.1088/0957-0233/3/7/007

9. Lemdiasov, R. A. and R. Ludwig, "A stream function method for gradient coil design," Concepts in Magnetic Resonance Part B: Magnetic Resonance Engineering, Vol. 26B, No. 1, 67-80, 2005.
doi:10.1002/cmr.b.20040

10. Marin, L., H. Power, R. W. Bowtell, C. Cobos Sanchez, A. A. Becker, P. Glover, and I. A. Jones, "Boundary element method for an inverse problem in magnetic resonance imaging gradient coils," Computer Methods in Engineering & Sciences, 2007.

11. Jackson, J. D., Classical Electrodynamics, Wiley, New York, 1962.

12. Pars, F. and J. Canas, Boundary Element Method: Fundamentals and Applications, Oxford Science Publications, 1997.

13. Brebbia, C. A., J. F. C. Telles, and L. C. Wrobel, Boundary Element Techniques, Springer-Verlag, 1984.

14. Holland, R., "Finite-difference solution of Maxwell's equations in generalized nonorthogonal coordinates ," IEEE Trans. Nucl. Sci., Vol. NS-30, 4586-4591, 1983.

15. Pozrikidis, C., A Practical Guide to Boundary-element Methods with the Software Library BEMLIB , Chapman & Hall/CRC, 2002.

16. Gill, P. E., W. Murray, and M. H. Wright, Practical Optimization , Academic Press, London, 1981.

17. Tiknonov, A. N. and V. Y. Arsenin, Methods for Solving Ill-posed Problems, Nauka, Moscow, 1986.

18. Goharian, M., M. Soleimani, and G. R. Moran, "A trust region subproblem for 3D electrical impedance tomography inverse problem using experimental data ," Progress In Electromagnetics Research, Vol. 94, 19-32, 2009.
doi:10.2528/PIER09052003

19. Brideson, M. A., L. K. Forbes, and S. Crozier, "Determining complicated winding patterns for shim coils using stream functions and the target-field method," Concepts in Magnetic Resonance, Vol. 14, No. 1, 9-18, 2002.
doi:10.1002/cmr.10000

20. Qi, F., X. Tang, Z. Jin, L. Wang, D. Zu, and W. Wang, A new target ¯eld method for optimizing longitudinal gradient coils' property , Progress In Electromagnetics Research Symposium, Vol. 3, No. 6, 865-869, 2007.

21. Eibert, T. F. and V. Hansen, "On the calculation of potential integrals for linear source distributions on triangular domains," IEEE Transactions on Antennas and Propagation, Vol. 43, No. 12, 1499-1502, 1995.
doi:10.1109/8.475946

22. Marin, L., H. Power, R. W. Bowtell, C. Cobos Sanchez, A. A. Becker, P. Glover, and I. A. Jones, "Numerical solution for an inverse MRI problem using a regularized boundary element method," (Special Issue) Engineering Analysis with Boundary Elements, 2007.

23. Kamon, M., M. J. Tsuk, and J. K. White, "Fasthenry: A multipole-accelerated 3-D inductance extraction program," IEEE Transactions on Microwave Theory and Techniques, Vol. 42, 1750-1758, 1994.
doi:10.1109/22.310584