volume | PIER Journals

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.

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 Google Scholar

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. Google Scholar

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

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 Google Scholar

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

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. Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

Dr. Clemente Cobos Sanchez

Professor Salvador Gonzalez Garcia

Mr. Luis Diaz Angulo

Dr. Carlos Moreno De Jong Van Coevorden

Dr. Amelia Rubio Bretones