Magnetic induction tomography (MIT) is a non-invasive medical imaging technique with promising applications such as brain imaging and cryosurgery monitoring. Despite its potential, the realisation of medical MIT application is challenging. The computational complexity of both the forward and inverse problems, and specific MIT hardware design are the major limitations for the development of MIT research in medical imaging. The MIT forward modeling and linear system equations for large scale matrices are computationally expensive. This paper presents the implementation of GPU (graphics processing unit) for both forward and inverse problems in MIT research. For a given MIT mesh geometry composed of 167,488 tetrahedral elements, the GPU accelerated Biot-Savart Law for solving the free space magnetic field and magnetic vector potential is proved to be over 200 times faster compared to the time consumption of a CPU (central processing unit). The linear system equation arising from the forward and inverse problem, can also be accelerated using GPU. Both simulations and experimental results are presented based on a new GPU implementation. Laboratory experimental results are shown for a phantom study representing potential cryosurgery monitoring using an MIT system.
"Magnetic Induction Tomography with High Performance GPU Implementation," Progress In Electromagnetics Research B,
Vol. 65, 49-63, 2016. doi:10.2528/PIERB15101902
2. Griffiths, H., W. R. Stewart, and W. Gough, "Magnetic induction tomography: A measuring system for biological tissues," Annals of the New York Academy of Sciences, Vol. 873, 335-345, 1999. doi:10.1111/j.1749-6632.1999.tb09481.x
3. Otten, D. M. and B. Rubinsky, "Cryosurgical monitoring using bioimpedance measurements - A feasibility study for electrical impedance tomography," IEEE Transactions on Biomedical Engineering, Vol. 47, No. 10, 1376-1381, 2000. doi:10.1109/10.871411
4. Soleimani, M., O. Dorn, and W. R. B. Lionheart, "A narrow-band level set method applied to eit in brain for cryosurgery monitoring," IEEE Transactions on Biomedical Engineering, Vol. 53, No. 11, 2257-2264, 2006. doi:10.1109/TBME.2006.877112
5. Zlochiver, S., M. M. Radai, M. Rosenfeld, and S. Abboud, "Induced current impedance technique for monitoring brain cryosurgery in a two-dimensional model of the head," Annals of Biomedical Engineering, Vol. 30, 1172-1180, 2002. doi:10.1114/1.1521932
6. Zlochiver, S., M. Rosenfeld, and S. Abboud, "Contactless bio-impedance monitoring technique for brain cryosurgery in a 3D head model," Annals of Biomedical Engineering, Vol. 33, No. 5, 616-625, 2005. doi:10.1007/s10439-005-1639-8
7. Ma, L., H.-Y. Wei, and M. Soleimani, "Cryosurgical monitoring using electromagnetic measurements: A feasibility study for magnetic induction tomography," 13th International Conference in Electrical Impedance Tomography, 2012-05-23-2012-05-25, Tianjin University, Tianjin, 2012.
8. Gabriel, C., A. Peyman, and E. H. Grant, "Electrical conductivity of tissues at frequencies below 1 MHz," Physics in Medicine and Biology, Vol. 54, No. 16, 4863-4878, 2009. doi:10.1088/0031-9155/54/16/002
9. Gencer, N. G. and M. N. Tek, "Imaging tissue conductivity via contactless measurements: A feasibility study," Elektrik, Vol. 6, No. 3, 183-200, 1998.
10. Bagshaw, A. P., A. D. Liston, R. H. Bayford, A. Tizzard, A. P. Gibson, A. T. Tidswell, M. K. Sparkes, H. Dehghani, C. D. Binnie, and D. S. Holder, "Electrical impedance tomography of human brain function using reconstruction algorithms based on the finite element method," Neuro Image, Vol. 20, No. 2, 752-764, 2003.
11. Hwu, W.-M. W., GPU Computing Gems, Emerald Ed., Morgan Kaufmann, 2011.
12. Steuwer, M. and S. Gorlatch, "High-level programming for medical imaging on multi-GPU systems using the skelcl library," 2013 International Conference on Computational Science, Vol. 18, 749-758, 2013.
13. Shi, L., W. Liu, H. Zhang, Y. Xie, and D. Wang, "A survey of gpu-based medical image computing techniques," Quantitative Imaging in Medicine and Surgery, Vol. 2, No. 3, 188-206, 2012.
14. Borsic, A., E. A. Attardo, and R. J. Halter, "Multi-GPU jacobian accelerated computing for soft field tomography," Physiological Measurements, Vol. 33, 1703-1715, 2012. doi:10.1088/0967-3334/33/10/1703
15. Eklund, A., P. Dufort, D. Forsberg, and S. M. LaConte, "Medical image processing on the GPU: Past, present and future," Medical Image Analysis, Vol. 17, No. 8, 1073-1094, 2013. doi:10.1016/j.media.2013.05.008
16. Jia, X., B. Dong, Y. F. Lou, and S. B. Jiang, "GPU-based iterative cone-beam CT reconstruction using tight frame regularization," Physics in Medicine and Biology, Vol. 56, No. 13, 3787, 2011. doi:10.1088/0031-9155/56/13/004
17. Tavares, R. S., T. C. Martins, and M. S. G. Tsuzuki, "Electrical impedance tomography reconstruction through simulated annealing using a new outside-in heuristic and GPU parallelization," Journal of Physics Conference Series, Vol. 407(Conference 1), 012015, 2012. doi:10.1088/1742-6596/407/1/012015
18. Kapusta, P., M. Majchrowicz, D. Sankowski, and R. Banasiak, "Application of GPU parallel computing for acceleration of finite element method based 3D reconstruction algorithms in electrical capacitance tomography," Image Processing and Communications, Vol. 17, No. 4, 339-346, 2013.
19. Maimaitijiang, Y., M. A. Roula, S. Watson, R. Patz, R. J. Williams, and H. Griffiths, "Parallelization methods for implementation of a magnetic induction tomography forward model in symmetric multiprocessor systems," Parallel Computing, Vol. 34, No. 9, 497-507, 2008. doi:10.1016/j.parco.2008.03.008
20. Maimaitijiang, Y., M. A. Roula, S. Watson, G. Meriadec, K. Sobaihi, and R. J. Williams, "Evaluation of parallel accelerators for high performance image reconstruction for magnetic induction tomography," Journal of Selected Areas in Software Engineering (JSSE), January 2011.
21. Wei, H.-Y. and M. Soleimani, "Hardware and software design for a national instrument-based magnetic induction tomography system for prospective biomedical applications," Physiological Measurement, Vol. 33, No. 5, 863-879, 2012. doi:10.1088/0967-3334/33/5/863
22. Bíró, O., "Edge element formulations of eddy current problems," Computer Methods in Applied Mechanics and Engineering, Vol. 169, 391-405, 1999. doi:10.1016/S0045-7825(98)00165-0
23. Bíró, O. and K. Preis, "An edge finite element eddy current formulation using a reduced magnetic and a current vector potential," IEEE Transactions on Magnetics, Vol. 36, No. 5, 3128-3130, 2000. doi:10.1109/20.908708
24. Golias, N. A., C. S. Antonopoulos, T. D. Tsiboukis, and E. E. Kriezis, "3D eddy current computation with edge elements in terms of the electric intensity," The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 17, No. 5/6, 667-673, 1998. doi:10.1108/03321649810221062
25. Barber, D. C. and B. H. Brown, "Applied potential tomography," Journal of Physics E: Scientific Instruments, Vol. 17, No. 9, 723-734, 1984. doi:10.1088/0022-3735/17/9/002
26. Soleimani, M. and W. R. B. Lionheart, "Absolute conductivity reconstruction in magnetic induction tomography using a nonlinear method," IEEE Transactions on Medical Imaging, Vol. 25, No. 12, 1521-1530, 2006. doi:10.1109/TMI.2006.884196
27. Dyck, D. N., D. A. Lowther, and E. M. Freeman, "A method of computing the sensitivity of the electromagnetic quantities to changes in the material and sources," IEEE Transactions on Magnetics, Vol. 30, 3415-3418, 1994. doi:10.1109/20.312672
28. Soleimani, M. and W. R. B. Lionheart, "Image reconstruction in three-dimensional magnetostatic permeability tomography," IEEE Transactions on Magnetics, Vol. 41, 1274-1279, 2005. doi:10.1109/TMAG.2005.845158
29. Calvetti, D., S. Morigi, L. Reichel, and F. Sgallari, "Tikhonov regularization and the L-curve for large discrete ill-posed problems," Journal of Computational and Applied Mathematics, Vol. 123, No. 1, 423-446, 2000. doi:10.1016/S0377-0427(00)00414-3
30. Kirk, D. B. and W-M. W. Hwu, Programming Massively Parallel Processors: A Hands on Approach, Elsevier, 2010.
31. Bernstein, A. J., "Program analysis for parallel processing," IEEE Transactions on Electronic Computers, Vol. 15, 757-762, October 1966.
32. Arora, M., "The architecture and evolution of CPU-GPU systems for general purpose computing,", University of California, 2012.
33. Soleimani, M., C. E. Powell, and N. Polydorides, "Improving the forward solver for the complete electrode model in eit using algebraic multigrid," IEEE Transactions on Medical Imaging, Vol. 24, No. 5, 577-583, 2005. doi:10.1109/TMI.2005.843741
34. Lezar, E. and D. Davidson, "GPU-based LU decomposition for large method of moments problems," Electronics Letters, Vol. 46, No. 17, 1194-1196, 2010. doi:10.1049/el.2010.1680
35. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 3rd Ed., 1992.
36. Humphrey, J. R., D. K. Price, K. E. Spagnoli, A. L. Paolini, and E. J. Kelmelis, "Cula: Hybrid GPU accelerated linear algebra routines," SPIE Defense and Security Symposium (DSS), April 2010.
37. Wei, H.-Y. and M. Soleimani, "Three-dimensional magnetic induction tomography imaging using a matrix free Krylov subspace inversion algorithm," Progress In Electromagnetics Research, Vol. 122, 29-45, 2012. doi:10.2528/PIER11091513
38. Cheney, M., D. Isaacson, J. C. Newell, S. Simske, and J. Goble, "Noser: An algorithm for solving the inverse conductivity problem," International Journal of Imaging Systems and Technology, Vol. 2, No. 2, 1990. doi:10.1002/ima.1850020203