A numerical study of a 3D bioheat transfer problem with different spatial heating

Mathematics and Computers in Simulation

Volumn 68, Issue 4, 2005, Pages 375-388

  Karaa, Samir ^a   Zhang, Jun ^a   Yang, Fuqian ^a  

^a UNIVERSITY OF KENTUCKY   (United States)

Author keywords

Bioheat transfer; Hyperthermia; Pennes equation; Preconditioning

Indexed keywords

COMPUTER SIMULATION; FINITE DIFFERENCE METHOD; HEAT TRANSFER; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; THERMOMECHANICAL TREATMENT;

BIOHEAT TRANSFER; HYPERTHERMIA; PENNNES EQUATION; PRECONDITIONING;

HEATING;

EID: 18244409337     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2005.02.032     Document Type: Article

References (19)

1. G.T. Anderson, and G. Burnside A non-invasive technique to measure perfusion using a focused ultrasound heating source and a tissue surface temperature measurement Proc. Adv. Meas. Comput. Temp. Biomed. 147 1990 31 35
2. J.C. Chato Fundamentals of Bioheat Transfer 1989 Springer-Verlag Berlin
3. J. Crank, and P. Nicolson A practical method for numerical evaluation of solution of partial differential equations of the heat-conduction type Proc. Camb. Philos. Soc. 43 1947 50 67
4. Z.S. Deng, and J. Liu Analytical study on bioheat transfer problems with spatial or transient heating on skin surface or inside biological bodies ASME J. Biomech. Eng. 124 2002 638 649
5. K.R. Diller Modeling of bioheat transfer processes at high and low temperatures Adv. Heat Transfer 22 1992 157 167
6. M. Gautherie Clinical Thermology, vol. 1-4 1990 Springer-Verlag Heidelberg
7. K.R. Holmes, Biological structures and heat transfer, in: Allerton Workshop on the Future of Biothermal Engineering, 1997.
8. K.R. Killer, and L.J. Hayes Analysis of tissue injury by burning: comparison of in situ and skin flap models Int. J. Heat Mass Transfer 34 1991 1393 1406
9. J.B. Leonard, K.B. Foster, and T.W. Athey Thermal properties of tissue equivalent phantom materials IEEE Trans. Biomed. Eng. 31 1984 533 536
10. J. Liu Uncertainty analysis for temperature prediction of biological bodies subject to randomly spatial heating J. Biomech. 34 2001 1637 1642
11. J. Liu, and L.X. Xu Estimation of blood perfusion using phase shift in temperature response to sinusoidal heating at skin surface IEEE Trans. Biomed. Eng. 46 2001 1037 1043
12. P. Liu, and G. Liu Action Mechanisms of Laser Biology 1989 Science Press Beijing pp. 127-177 (in Chinese)
13. J.A. Meijerink, and H.A. van der Vorst An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix Math. Comput. 31 1977 148 162
14. H.H. Pennes Analysis of tissue and arterial blood temperature in the resting human forearm J. Appl. Physiol. 1 1948 93 122
15. Y. Saad Iterative Methods for Sparse Linear Systems 1996 PWS Publishing New York, NY
16. Y. Saad, and M.H. Schultz GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems SIAM J. Sci. Stat. Comput. 7 1986 856 869
17. S. Weinbaum, L.M. Jiji, and D.E. Lemons Theory and experiment for the effect of vascular microstructure on surface tissue heat transfer. Part I. Anatomical foundation and model conceptualization ASME J. Biomech. Eng. 106 2001 321 330
18. J.J. Zhao, J. Zhang, N. Kang, F. Yang, A two-level finite difference scheme for one dimensional Pennes' bioheat equation, Appl. Math. Comput., in press
19. (also as Technical Report No. 354-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002).