A FOURTH-ORDER COMPACT FINITE-DIFFERENCE SCHEME FOR SOLVING A 1-D PENNES' BIOHEAT TRANSFER EQUATION IN A TRIPLE-LAYERED SKIN STRUCTURE

REFERENCES

• Bechnke , W. P. 1984 . Predicting Flash Fire Protection of Clothing from Laboratory Tests Using Second-Degree Burn to Rate Performance . Fire Mater. , 8 : 57 – 63 .
   Web of Science ®Google Scholar
• Lecarpentier , G. L. , Motamedi , M. , Mcmath , L. P. , Rastegar , S. and Welch , A. J. 1993 . Continuous Wave Laser Ablation of Tissue: Analysis of Thermal and Mechanical Events . IEEE Trans. Biomed. Eng. , 40 : 188 – 200 .
   PubMed Web of Science ®Google Scholar
• Li , J. and Liang , H. 1989 . The Laser Medicine and Its Biomedical Applications Beijing, , China (in Chinese), Science Press
   Google Scholar
• Moritz , A. R. and Henriques , F. C. 1947 . Studies of Thermal Injuries II: The Relative Importance of Time and Surface Temperature in the Causation of Cutaneous Burns . Am. J. Pathol. , 23 : 695 – 700 .
   PubMed Web of Science ®Google Scholar
• Stoll , A. M. and Greene , L. C. 1959 . Relationship between Pain and Tissue Damage due to Thermal Radiation . J. Appl. Physiol. , 14 : 373 – 382 .
   PubMed Web of Science ®Google Scholar
• Torvi , D. A. and Dale , D. J. 1994 . A Finite Element Model of Skin Subjected to a Flash Fire . ASME J. Biomech. Eng. , 116 : 250 – 255 .
   PubMed Web of Science ®Google Scholar
• Killer , K. R. and Hayes , L. J. 1991 . Analysis of Tissue Injury by Burning: Comparison of in Situ and Skin Flap Models . Int. J. Heat Mass Transfer , 34 : 1393 – 1406 .
   Web of Science ®Google Scholar
• Pennes , H. H. 1948 . Analysis of Tissue and Arterial Temperature in the Resting Human Forearm . J. Appl. Physiol. , 1 : 93 – 122 .
   PubMed Web of Science ®Google Scholar
• Cai , R. and Zhang , N. 1998 . Unsteady One-Dimensional Analytical Solutions for Bioheat Transfer Equations . Prog. Nat. Sci. , 8 : 733 – 739 .
   Google Scholar
• Cattaneo , C. 1958 . A Form of Heat Conduction Equation which Eliminates the Paradox of Instantaneous Propagation . Compte Rendus , 247 : 431 – 433 .
   Google Scholar
• Chan , C. L. 1992 . Boundary Element Method Analysis for the Bioheat Transfer Equation . J. Biomech. Eng. , 114 : 358 – 365 .
   PubMed Web of Science ®Google Scholar
• Chato , J. C. , Eckburg , J. J. and Hurlburt , E. 1989 . Comparison of Three Bioheat Transfer Models Using Finite Difference Techniques . ASME Heat Transfer Div. , 126 : 17 – 21 .
   Google Scholar
• Doody , C. , Duck , F. A. and Humphrey , V. F. 2000 . Comparison of Finite Element and Heated Disc Models of Tissue Heating by Ultrasound . Ultrasound Med. Biol. , 26 : 1347 – 1355 .
   PubMed Web of Science ®Google Scholar
• Hall , E. J. and Roizin-Towle , L. 1984 . Biological Effects of Heat . Cancer Res. , 44 : 4708s – 4713s .
   PubMed Web of Science ®Google Scholar
• Huang , H. W. , Chan , C. L. and Roemer , R. B. 1994 . Analytical Solutions of Pennes Bioheat Transfer Equation with a Blood Vessel . J. Biomech. Eng. , 116 : 208 – 212 .
   PubMed Web of Science ®Google Scholar
• Kaminski , W. 1990 . Hyperbolic Heat Conduction Equation for Material with a Nonhomogeneous Inner Structure . ASME J. Heat Transfer , 112 : 555 – 560 .
   Web of Science ®Google Scholar
• Liu , J. , Chen , X. and Xu , L. X. 1999 . New Thermal Wave Aspects on Burn Evaluation of Skin Subjected to Instantaneous Heating . IEEE Trans. on Biomed. Eng. , 46 : 420 – 428 .
   PubMed Web of Science ®Google Scholar
• Liu , J. and Xu , L. X. 2000 . Boundary Information Based Diagnostics on the Thermal States of Biological Bodies . Int. J. Heat Mass Transfer , 43 : 2827 – 2839 .
   Web of Science ®Google Scholar
• Liu , J. , Zhang , X. and Wang , C. 1997 . Generalized Time Delay Bioheat Equation and Preliminary Analysis on its Wave Nature . Chinese Sci. Bull. , 42 : 289 – 292 .
   Google Scholar
• Majchrzak , E. and Mochnacki , B. 1999 . Numerical Model of Heat Transfer between Blood Vessel and Biological Tissue . Comput. Assist. Mech. Eng. Sci. , 6 : 439 – 447 .
   Google Scholar
• Mitra , K. , Kumar , S. , Vedavarz , A. and Moallemi , M. K. 1995 . Experimental Evidence of Hyperbolic Heat Conduction in Processes Meat . ASME J. Heat Transfer , 117 : 568 – 573 .
   Web of Science ®Google Scholar
• Newman , W. H. , Martin , G. T. and Sidney , D. A. 1995 . Evaluation and Application of the Basis Element Method: A Rapid, 3-D Algorithm for Bioheat Transfer Calculation . ASME Advances in Heat and Mass Transfer in Biotechnology , HTD-Vol. 322 : 49 – 55 .
   Google Scholar
• Weinbaum , S. and Jiji , L. M. 1985 . A New Simplifies Equation for the Effect of Blood Flow on Local Average Tissue Temperature . ASME J. Biomech. Eng. , 107 : 131 – 139 .
   PubMed Web of Science ®Google Scholar
• Xuan , Y. and Roetzel , W. 1997 . Bioheat Equation of the Human Thermal System . Chem. Eng. Technol. , 20 : 268 – 276 .
   Web of Science ®Google Scholar
• Xu , L. X. , Chen , M. M. , Holmes , K. R. and Arkin , H. 1991 . The Theoretical Evaluation of the Pennes, the Chen-Holmes and the Weinbaum-Jiji Bioheat Transfer Models in the Pig Rebal Cortex . Adv. Biol. Heat Mass Transfer , 189 : 15 – 21 .
   Google Scholar
• Xu , L. X. and Liu , J. 1998 . Discussion on Nonequilibrium Heat Transfer in Biological System . ASME Advances in Heat and Mass Transfer in Biotechnology , HDT-Vol. 362/BED-Vol. 40 : 13 – 17 .
   Google Scholar
• Yang , W. H. 1993 . Thermal (Heat) Shock Biothermomechanical Viewpoint . ASME J. Biomech. Eng. , 5 : 617 – 621 .
   Google Scholar
• Lele , S. K. 1992 . Compact Finite Difference Schemes with Spectral-like Resolution . J. Comput. Phys. , 103 : pp.16 – 42 .
   Web of Science ®Google Scholar
• Chatterjee , I. and Adams , R. A. 1994 . Finite Element Thermal Modelling of the Human Body under Hyperthermia Treatment for Cancer . Int. J. Comput. Appl. Technol. , 7 : 151 – 159 .
   Web of Science ®Google Scholar
• Clegg , S. T. and Roemer , R. B. 1989 . Predictions of Three-Dimensional Temperature Distributions during Hyperthermia Experiments . ASME Heat Transfer Div. , 126 : 29 – 35 .
   Google Scholar
• Liauh and Roemer , R. B. 1993 . A Semilinear State and Parameter Estimation Algorithm for Inverse Hyperthermia Problems . J. Biomech. Eng. , 115 : 257 – 261 .
   PubMed Web of Science ®Google Scholar
• Roemer , R. B. 1991 . Optimal Power Deposition in Hyperthermia I. The Treatment Goal: The Ideal Temperature Distribution: The Role of Large Blood Vessels . J. Hyperthermia , 7 : 317 – 341 .
   PubMed Web of Science ®Google Scholar
• Roemer , R. B. , Moros , E. G. and Hynynen , K. 1989 . A Comparison of Bioheat Transfer and Effective Conductivity Equation Predictions to Experimental Hyperthermia Data . ASME Heat Transfer Div. , 126 : 11 – 15 .
   Google Scholar
• Atkinson , K. E. 1988 . An Introduction to Numerical Analysis , 2d ed. , 489 – 495 . New York : Wiley .
   Google Scholar