Model-Order Reduction of Nonlinear Models of Electromagnetic Phased-Array Hyperthermia

IEEE Transactions on Biomedical Engineering

Volumn 50, Issue 11, 2003, Pages 1243-1254

  Kowalski, Marc E ^a   Jin, Jian Ming ^b  

^a Pennie and Edmonds LLP   (United States)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

Annular phased array; Bioheat transfer; Karhunen Lo ve transform; Proper orthogonal decomposition; Reduced order model

Indexed keywords

ARRAYS; FINITE DIFFERENCE METHOD; HEAT TRANSFER; HYPERTHERMIA THERAPY; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS;

NONLINEAR MODELS;

BIOMEDICAL ENGINEERING;

ARTICLE; ELECTROMAGNETIC RADIATION; HEAT TRANSFER; HYPERTHERMIC THERAPY; MATHEMATICAL MODEL; NONLINEAR SYSTEM; PHANTOM;

ADIPOSE TISSUE; BODY TEMPERATURE; COMPUTER SIMULATION; HEAT; HUMANS; HYPERTHERMIA, INDUCED; MODELS, BIOLOGICAL; MUSCLE, SKELETAL; NONLINEAR DYNAMICS; PHANTOMS, IMAGING; THERAPY, COMPUTER-ASSISTED; URINARY BLADDER NEOPLASMS;

EID: 0242300785     PISSN: 00189294     EISSN: None     Source Type: Journal    
DOI: 10.1109/TBME.2003.818468     Document Type: Article

References (56)

1. J. Overgaard, D. Gonzalez, M. Hulshof, G. Arcangeli, O. Dahl, O. Mella, and S. Bentzen, "Randomized trial of hyperthermia as an adjuvant to radiotherapy for recurrent or metastatic malignant melanoma," Lancet, vol. 345, pp. 540-543, 1995.
2. R. B. Roemer, "Engineering aspects of hyperthermia therapy," in Annual Review of Biomedical Engineering, M. L. Yarmush, K. R. Diller, and M. Toner, Eds. Palo Alto, CA: Annual Reviews, 1999, pp. 347-376.
3. P. Wust, M. Seebass, J. Nadobny, P. Deuflhard, G. Monich, and R. Felix, "Simulation studies promote technological development of radiofrequency phased array hyperthermia," Int. J. Hypertherm., vol. 12, no. 4, pp. 477-494, 1996.
4. D. Sullivan, "Mathematical methods for treatment planning in deep regional hyperthermia," IEEE Trans. Microwave Theory Tech., vol. 39, pp. 864-872, May 1991.
5. P. F. Turner, "Regional hyperthermia with an annular phased array," IEEE Trans. Biomed. Eng., vol. BME-31, pp. 106-113, Jan. 1984.
6. P. Wust, J. Nadobny, R. Felix, P. Deuflhard, A. Louis, and W. John, "Strategies for optimized application of annular-phased-array systems in clinical hyperthermia," Int. J. Hypertherm., vol. 7, no. 1, pp. 157-173, 1991.
7. F. Bardati, A. Borrani, A. Gerardino, and G. A. Lovisolo, "Sar optimization in a phased array radiofrequency hyperthermia system," IEEE Trans. Biomed. Eng., vol. 42, pp. 1201-1207, Dec. 1995.
8. K. S. Nikita, N. G. Maratos, and N. K. Uzunoglu, "Optimization of the deposited power distribution inside a layered lossy medium irradiated by a coupled system of concentrically placed waveguide applicators," IEEE Trans. Biomed. Eng., vol. 45, pp. 909-920, July 1998.
9. M. E. Kowalski and J.-M. Jin, "Determination of electromagnetic phased array driving signals for hyperthermia based on a steady-state temperature criterion," IEEE Trans. Microwave Theory Tech., vol. 47, pp. 1525-1533, Nov. 2000.
10. M. Mattingly, R. B. Roemer, and S. Devasia, "Optimal actuator placement for large scale systems: A reduced-order modeling approach," Int. J. Hypertherm., vol. 14, no. 4, pp. 331-345, 1998.
11. S. K. Das, S. D. Clegg, and T. V. Samulski, "Computational techniques for fast hyperthermia temperature optimization," Med. Phys., vol. 26, pp. 319-328, Feb. 1999.
12. J. K. Potocki and H. S. Tharp, "Reduced-order modeling for hyperthermia control," IEEE Trans. Biomed. Eng., vol. 39, pp. 1265-1273, Dec. 1992.
13. -, "Concurrent hyperthermia estimation schemes based on extended kalman filtering and reduced-order modeling," Int. J. Hypertherm., vol. 9, no. 6, pp. 849-865, 1993.
14. E. A. Bailey, A. W. Dutton, M. Mattingly, S. Devasia, and R. B. Roemer, "A comparison of reduced-order modeling techniques for application in hyperthermia control and estimation," Int. J. Hypertherm., vol. 14, no. 2, pp. 135-156, 1998.
15. M. Mattingly, E. A. Bailey, A. W. Dutton. R. B. Roemer, and S. Devasia, "Reduced-order modeling for hyperthermia: An extended balanced-realization-based approach," IEEE Trans. Biomed. Eng., vol. 45, pp. 1154-1162, Sept. 1998.
16. J. J. W. Lagendijk, G. C. V. Rhoon, S. N. Homsleth, P. Wust, A. C. C. de Leeuw, C. J. Schneider, J. D. P. V. Dijk, J. V. D. Zee, R. V. Heek-Romanowski, S. A. Rahman, and C. Gromoll, "ESHO quality assurance guidelines for regional hyperthermia," Int. J. Hypertherm., vol. 14, no. 2, pp. 125-133, 1998.
17. M. E. Kowalski and J.-M. Jin, "Modeling and control of transient temperature fields in electromagnetically-induced hyperthermia," J. Appl. Computat. Electromagn. Soc., vol. 16, pp. 126-137, July 2001.
18. D. T. Tompkins, R. Vanderby, S. A. Klein, W. A. Beckman, R. A. Steeves, D. M. Frye, and B. R. Paliwal, "Temperature-dependent versus constant-rate blood perfusion modeling in ferromagnetic thermoseed hyperthermia: Results with a model of the human prostate," Int. J. Hypertherm., vol. 10, no. 4, pp. 517-536, 1994.
19. J. Lang, B. Erdmann, and M. Seebass, "Impact of nonlinear heat transfer on temperature control in regional hyperthermia," IEEE Trans. Biomed. Eng., vol. 46, pp. 1129-1138, Sept. 1999.
20. M. Loéve, Probability Theory. Princeton, NJ: Van Nostrand, 1955.
21. K. Pearson, "On lines and planes of closest fit to points in space," Philosophical Mag., vol. 2, pp. 609-629, 1901.
22. I. T. Jolliffee, Principal Component Analysis. New York: Springer-Verlag, 1986.
23. R. C. Gonzalez and P. A. Wintz, Digital Image Processing. Reading, MA: Addison-Wesley, 1987.
24. J. L. Lumley, "The structure of inhomogeneous turbulence," in Atmospheric Turbulence and Wave Propagation, A. M. Yaglom and V. I. Tatarski, Eds. Moscow, U.S.S.R.: Nauka, 1967, pp. 166-178.
25. J. R. Phillips, "Automated extraction of nonlinear circuit macromodels," in Proc. IEEE Custom Integrated Circuits Conf., 2000, pp. 451-454.
26. P. K. Gunupudi and M. S. Nakha, "Nonlinear circuit-reduction of high-speed interconnect networks using congruent transformation techniques," IEEE Trans. Adv. Packag., vol. 24, pp. 317-325, Aug. 2001.
27. H. T. Banks, R. C. H. de Rosario, and R. C. Smith, "Reduced-order model feedback control design: Numerical implementation in a thin shell model," IEEE Trans. Automat. Contr., vol. 45, pp. 1312-1323, July 2000.
28. J. Baker and P. D. Christofides, "Output feedback control of parabolic PDE systems with nonlinear spatial differential operators," Ind. Eng. Chem. Res., vol. 38, pp. 4372-4380, 1999.
29. H. V. Ly and H. T. Tran, "Modeling and control of physical processes using propser orthogonal decomposition," Math. Comp. Model., vol. 33, pp. 223-236, 2001.
30. P. S, Lall, J. E. Marsden, and S. Glavaski, "A subspace approach to balanced truncation for model reduction of nonlinear control systems," Int. J. Robust Nonlinear Control, to be published.
31. C. A. Balanis, Advanced Engineering Electromagnetics. New York: Wiley, 1989.
32. K. R. Diller and T. P. Ryan, "Heat transfer in living systems: Current opportunities," Trans. ASME, vol. 120, pp. 810-829, November 1998.
33. C. Gabriel, S. Gabriel, and E. Corthout, "The dielectric properties of biological tissues: I. literature survey," Phys. Med. Biol., vol. 41, pp. 2231-2249, 1996.
34. S. Gabriel, R. W. Lau, and C. Gabriel, "The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues," Phys. Med. Biol., vol. 41, pp. 2271-2293, 1996.
35. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propagat., vol. AP-14, pp. 302-307, 1966.
36. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method. Boston, MA: Artech House, 1995.
37. A. Taflove and A. Taflove, Eds., Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method. Boston, MA: Artech House, 1998.
38. C.-Q. Wang and O. P. Gandhi, "Numerical simulation of annular phased arrays for anatomically based models using the FDTD method," IEEE Trans. Microwave Theory Tech., vol. 37, pp. 118-126, Jan. 1989.
39. D. Sullivan, "Three-dimensional computer simulation in deep regional hyperthermia using the finite-difference time-domain method," IEEE Trans. Microwave Theory Tech., vol. 38, pp. 204-211, Feb. 1990.
40. P. C. Cherry and M. F. Iskander, "FDTD analysis of power deposition patterns of an array of interstitial antennas for use in microwave hyperthermia," IEEE Trans. Microwave Theory Tech., vol. 40, pp. 1692-1700, Aug. 1992.
41. J.-Y. Chen and O. P. Gandhi, "Numerical simulation of annular-phased arrays of dipoles for hyperthermia of deep-seated tumors," IEEE Trans. Biomed. Eng., vol. 39, pp. 209-216, Mar. 1992.
42. D. Dunn, C. M. Rappaport, and A. J. Terzuoli, "FDTD verification of deep-set brain tumor hyperthermia using a spherical microwave source distribution," IEEE Trans. Microwave Theory Tech., vol. 44, pp. 1769-1777, Oct. 1996.
43. D. M. Sullivan, D. Buechler, and F. A. Gibbs, "Comparison of measured and simulated data in an annular phased array using an inhomogeneous phantom," IEEE Trans. Microwave Theory Tech., vol. 40, pp. 600-604, Mar. 1992.
44. J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, and R. Felix; "A high-resolution interpolation at arbitrary interfaces for the FDTD method," IEEE Trans. Microwave Theory Tech., vol. 46, pp. 1759-1766, Nov. 1998.
45. K. D. Paulsen, X. Jia, and J. M. Sullivan, "Finite element computations of specific absorption rates in anatomically conforming full-body models for hyperthermia treatment analysis," IEEE Trans. Biomed. Eng., vol. 40, pp. 933-945, Sept. 1993.
46. X. Jia, K. D. Paulsen, D. N. Buechler, F. A. Gibbs Jr., and P.M. Meany, "Finite element simulation of sigma 60 heating in the utah phantom: Computed and measured data compared," Int. J. Hypertherm., vol. 10, no. 6, pp. 755-774, 1994.
47. J. Tang, S. D. Geimer, and K. D. Paulsen, "Evaluation of prefectly matched layer mesh terminations in finite-element bioelectromagnetic scattering computations," IEEE Trans. Microwave Theory Tech., vol. 47, pp. 410-415, Apr. 1999.
48. H. H. Pennes, "Analysis of tissue and arterial blood temperatures in the resting human arm," J. Appl. Physiol., vol. 1, pp. 93-122, 1948.
49. W. Wulff, "The energy conservation equation for living tissue, " IEEE Trans. Biomed. Eng., vol. BME-21, pp. 494-495, Nov. 1974.
50. H. Arkin, L. X. Xu, and K. R. Holmes, "Recent developments in modeling heat transfer in blood perfused tissues," IEEE Trans. Biomed. Eng., vol. 41, pp. 97-107, Feb. 1994.
51. M. Fahl, "Computation of POD basis functions for fluid flows with Lanzcos methods," Math. Comp. Model, vol. 34, pp. 91-107, 2001.
52. M. E. Kowalski, B. Behnia, A. G. Webb, and J.-M. Jin, "Optimization of electromagnetic phased-arrays for hyperthermia using magnetic resonance temperature estimation," IEEE Trans. Biomed. Eng., vol. 49, pp. 1229-1241, Nov. 2002.
53. I. G. Zubal, C. R. Harrell, E. O. Smith, Z. Rattner, G. Gindi, and P. B. Hoffer, "Computerized three-dimensional segmented human anatomy," Med. Phys., vol. 21, no. 2, pp. 299-302, 1994.
54. F. A. Duck, Physical Properties of Tissue: A Comprehensive Reference. London, U.K.: Academics, 1990.
55. C. Q. Wang and O. P. Gandhi, "Numerical simulation of annular phased arrays for anatomically based models using the FDTD method," IEEE Trans. Microwave Theory Tech., vol. 37, pp. 118-126, Jan. 1989.
56. S. A. Sapareto and W. C. Dewey, "Thermal dose determination in cancer therapy," Int. J. Radiat. Oncol. Biol. Phys., vol. 10, pp. 787-800, 1984.