2008-12-30
Comparison of Methods for Modeling Uncertainties in a 2D Hyperthermia Problem
By
Progress In Electromagnetics Research B, Vol. 11, 189-204, 2009
Abstract
Uncertainties in biological tissue properties are weighed in the case of a hyperthermia problem. Statistic methods, experimental design and kriging technique, and stochastic methods, spectral and collocation approaches, are applied to analyze the impact of these uncertainties on the distribution of the electromagnetic power absorbed inside the body of a patient. The sensitivity and uncertainty analyses made with the different methods show that experimental designs are not suitable in this kind of problem and that the spectral stochastic method is the most efficient method only when using an adaptative algorithm.
Citation
Damien Voyer, Laurent Nicolas, Ronan Perrussel, and Francois Musy, "Comparison of Methods for Modeling Uncertainties in a 2D Hyperthermia Problem," Progress In Electromagnetics Research B, Vol. 11, 189-204, 2009.
doi:10.2528/PIERB08112104
References

1. Hurt, W. D., J. M. Ziriax, and P. A. Mason, "Variability in EMF permittivity values: Implications for SAR calculations," IEEE Trans. on Biomedical Engineering, Vol. 47, No. 3, 396-401, 2000.
doi:10.1109/10.827308        Google Scholar

2. Garcia-Diaz, A. and D. Philips, Principles of Experimental Design and Analysis, Chapman & Hall, 1995.

3. Koehler, J. and A. Owen, Handbook of Statistics, 261-308, Chapter Computer experiments, Elsevier Science, 1996.

4. Ghanem, R. G. and P. D. Spanos, Stochastic Finite Elements: A Spectral Approach, Springer-Verlag, 1991.

5. Xiu, D. and J. S. Hesthaven, "High-order collocation methods for differentialequations with random inputs," SIAM Journal on Scientific Computing, Vol. 27, No. 3, 1118-1139, 2005.
doi:10.1137/040615201        Google Scholar

6. Gerstner, T. and M. Griebel, "Dimension-adaptive tensor-product quadrature," Computing, Vol. 71, No. 1, 65-87, Springer-Verlag, New York, Inc., 2003.
doi:10.1007/s00607-003-0015-5        Google Scholar

7., IFAC, Institute For Applied Physics, http://niremf.ifac.cnr.it/tissprop/.
doi:10.1007/s00607-003-0015-5

8. Stoneman, M. R., M. Kosempa, W. D. Gregory, C. W. Gregory, J. J. Marx, W. Mikkelson, J. Tjoe, and V. Raicu, "Correction of electrode polarization contributions to the dielectric properties of normaland cancerous breast tissues at audio/radiofrequencies," Physical Medecine and Biology, Vol. 52, 6589-6604, 2007.
doi:10.1088/0031-9155/52/22/003        Google Scholar

9. Renard, Y. and J. Pommier, "Getfem finite element library,", http://home.gna.org/getfem/.        Google Scholar

10. OHagan, T. and M. Kennedy, "Gaussian emulator machine software,", http://www.tonyohagan.co.uk /academic/GEM/index.html.        Google Scholar

11. Sobol, I. M., "Sensitivity estimates for non linear mathematical models," Mathematical Modelling and Computational Experiments, Vol. 1, 407-414, 1993.        Google Scholar

12. Xiu, D. and G. E. Karniadakis, "The Wiener-Askey polynomial chaos for stochastic differentialequations," SIAM Journal on Scientific Computing, Vol. 24, No. 2, 619-644, 2002.
doi:10.1137/S1064827501387826        Google Scholar

13. Zeng, Z. Y. and J. M. Jin, "An efficient calculation of scattering variation due to uncertain geometricaldeviation," Electromagnetics, Vol. 27, No. 7, 387-398, 2007.
doi:10.1080/02726340701572975        Google Scholar

14. Klimke, A., "Sparse grid interpolation toolbox,", http://www.ians.uni-stuttgart.de/spinterp/.        Google Scholar

15. Klimke, A., Uncertainty modeling using fuzzy arithmetic and sparse grids, Ph.D. thesis, Fakult¨at Mathematik und Physik der Universit¨at Stuttgart, 2006.