Solution of an Inverse Heat Conduction Problem in a Bi-Layered Spherical Tissue

REFERENCES

• L. Zhang , W. Dai , and R. Nassar , A Numerical Method for Obtaining an Optimal Temperature Distribution in a 3-D Triple-Layered Cylindrical Skin Structure Embedded with a Blood Vessel , Numer. Heat Transfer A , vol. 49 , pp. 765 – 784 , 2006 .
   Web of Science ®Google Scholar
• J. Wren , D. Loyd , and M. Karlsson , Investigation of Medical Thermal Treatment using a Hybrid Bioheat Model , Proceedings of the 26th Annual International Conference of the IEEE EMBS , San Francisco , CA , USA , September 1–5 , 2004 .
   Google Scholar
• A. V. Luikov , Analytical Heat Diffusion Theory , Academic Press , New York , 1968 .
   Google Scholar
• W. Kaminski , Hyperbolic Heat Conduction Equation for Material with a Non-Homogenous Inner Structure , ASME J. Heat Transfer , vol. 112 , pp. 555 – 560 , 1990 .
   Web of Science ®Google Scholar
• A. M. Braznikov , V. A. Karpychev , and A. V. Luikova , One Engineering Method of Calculating Heat Conduction Process , Inzhenerno Fizicheskii Zhurnal , vol. 28 , pp. 677 – 680 , 1975 .
   Google Scholar
• K. Mitra , S. Kumar , A. Vedavarz , and M. K. Moallemi , Experimental Evidence of Hyperbolic Heat Conduction in Processed Meat , ASME J. Heat Transfer , vol. 117 , pp. 568 – 573 , 1995 .
   Web of Science ®Google Scholar
• W. Roetzel , N. Putra , and S. K. Das , Experiment and Analysis for Non-Fourier Conduction in Materials with Non-Homogeneous Inner Structure , Int. J. Therm. Sci. , vol. 42 , pp. 541 – 552 , 2003 .
   Web of Science ®Google Scholar
• W. H. Yang , Thermal (Heat) Shock Biothermomechanical Viewpoint , J. Biomedical Engi. , vol. 115 , pp. 617 – 621 , 1993 .
   Google Scholar
• T. C. Shih , H. S. Kou , C. T. Liauh , and W. L. Lin , The Impact of Thermal Wave Characteristics on Thermal Dose Distribution During Thermal Therapy: A Numerical Study , Med. Physi. , vol. 32 , pp. 3029 – 3036 , 2005 .
   PubMed Web of Science ®Google Scholar
• Ş. Özen , S. Helhel , and O. Çerezci , Heat Analysis of Biological Tissue Exposed to Microwave by using Thermal Wave Model of Bioheat Transfer , Burns , vol. 34 , pp. 45 – 49 , 2008 .
   PubMed Web of Science ®Google Scholar
• K. C. Liu , Thermal Propagation Analysis for Living Tissue with Surface Heating , Int. J. Thermal Sci. , vol. 47 , pp. 507 – 513 , 2008 .
   Web of Science ®Google Scholar
• D. Y. Tzou , The Generalized Lagging Response in Small-Scale and High-Rate Heating , Int. J. Heat Mass Transfer , vol. 38 , pp. 3231 – 3240 , 1995 .
   Web of Science ®Google Scholar
• S. Godoy and L. S. García-Colín , Nonvalidity of the Telegrapher's Diffusion Equation in Two and Three Dimensions for Crystalline Solids , Phys. Rev. E , vol. 55 , pp. 2127 – 2131 , 1997 .
   Web of Science ®Google Scholar
• C. Körner and H. W. Bergman , The Physical Ddefects of the Hyperbolic Heat Conduction Equation , Appl. Phys. A , vol. 67 , pp. 397 – 401 , 1998 .
   Web of Science ®Google Scholar
• T. J. Bright and Z. M. Zhang , Common Misperceptions of the Hyperbolic Heat Equation , J. Thermophys. and Heat Transfer , vol. 23 , pp. 601 – 607 , 2009 .
   Web of Science ®Google Scholar
• P. J. Antaki , New Interpretation of Non-Fourier Heat Conduction in Processed Meat , ASME J. Heat Transfer , vol. 127 , pp. 189 – 193 , 2005 .
   Web of Science ®Google Scholar
• K. C. Liu and H. T. Chen , Analysis for the Dual-Phase-Lag Bioheat Transfer during Magnetic Hyperthermia Treatment , Int. J. Heat and Mass Transfer , vol. 52 , pp. 1187 – 1192 , 2009 .
   Web of Science ®Google Scholar
• J. Zhou , Y. Zhang , and J. K. Chen , An Axismmetric Dual-Phase-Lag Bioheat Model for Laser Heating of Living Tissues , Int. J. Thermal Sci. , vol. 48 , pp. 1477 – 1485 , 2009 .
   Web of Science ®Google Scholar
• Y. Zhang , Generalized Dual-Phase Lag Bioheat Equations Based on Nonequilibrium Heat Transfer in Living Biological Tissues , Int. J. Heat and Mass Transfer , vol. 52 , pp. 4829 – 4834 , 2009 .
   Web of Science ®Google Scholar
• W. Andrä , C. G. d'Ambly , R. Hergt , I. Hilger , and W. A. Kaiser , Temperature Distribution as Function of Time Around a Small Spherical Heat Source of Local Magnetic Hyperthermia , J. Magnetism and Magnetic Materials , vol. 194 , pp. 197 – 203 , 1999 .
   Web of Science ®Google Scholar
• S. K. Kim and I. M. Daniel , Solution to Inverse Heat Conduction Problem in Nanoscale using Sequential Method, Numer. Heat Transfer A , vol. 44, pp. 439–456, 2003.
   Google Scholar
• H. T. Chen and X. Y. Wu , Estimation of Heat Transfer Coefficient in Two-Dimensional Heat Conduction Problems , Numer. Heat Transfer B , vol. 50 , pp. 375 – 394 , 2006 .
   Web of Science ®Google Scholar
• H. T. Chen and X. Y. Wu , Estimation of Surface Conditions for Nonlinear Inverse Heat Conduction Problems using the Hybrid Inverse Scheme , Numer. Heat Transfer B , vol. 51 , pp. 159 – 178 , 2007 .
   Web of Science ®Google Scholar
• Y. Favennec , Hessian and Fisher Matrices for Error Analysis in Inverse Heat Conduction Problems , Numer. Heat Transfer B , vol. 52 , pp. 323 – 340 , 2007 .
   Web of Science ®Google Scholar
• S. K. Kim , Resolving the Final Time Singularity in Gradient Methods for Inverse Heat Conduction Problems , Numer. Heat Transfer B , vol. 57 , pp. 74 – 88 , 2010 .
   Web of Science ®Google Scholar
• H. T. Chen , S. Y. Peng , P. C. Yang , and L. C. Fang , Numerical Method for Hyperbolic Inverse Heat Conduction Problems , Int. Commun. in Heat and Mass Transfer , vol. 28 , pp. 847 – 856 , 2001 .
   Web of Science ®Google Scholar
• C. Y. Yang , Direct and Inverse Solutions of Hyperbolic Heat Conduction Problems , J. Thermophys. and Heat Transfer , vol. 19 , pp. 217 – 225 , 2005 .
   Web of Science ®Google Scholar
• C. Y. Yang , Estimation of the Period Thermal Conditions on the Non-Fourier Fin Problem , Int. J. Heat and Mass Transfer , vol. 48 , pp. 3506 – 3515 , 2005 .
   Google Scholar
• C. H. Huang and H. H. Wu , An Inverse Hyperbolic Heat Conduction Problem in Estimating Surface Heat Flux by Conjugate Gradient Method , J. Phys. D: Appl. Phys. , vol. 39 , pp. 4087 – 4096 , 2006 .
   Web of Science ®Google Scholar
• C. H. Huang and C. Y. Lin , Inverse Hyperbolic Conduction Problem in Estimating Two Unknown Surface Heat Fluxes Simultaneously , J. Thermophys. and Heat Transfer , vol. 22 , pp. 766 – 774 , 2008 .
   Google Scholar
• M. N. Özisik , Heat Conduction , John Wiley and Sons , New York , 1993 .
   Google Scholar
• D. Y. Tzou , Macro- to Microscale Heat Transfer: The Lagging Behavior , Taylor & Francis , Washington , DC , 1996 .
   Google Scholar
• H. G. Bagaria and D. T. Johnson , Transient Solution to the Bioheat Equation and Optimization for Magnetic Fluid Hyperthermia Treatment , Int. J. Hyperthermia , vol. 21 , pp. 57 – 75 , 2005 .
   PubMed Web of Science ®Google Scholar
• S. Maenosono and S. Saita , Theoretical Assessment of FePt Nanoparticles as Heating Elements for Magnetic Hyperthermia , IEEE Trans. on Magnetics , vol. 42 , pp. 1638 – 1642 , 2006 .
   Web of Science ®Google Scholar
• G. Honig and U. Hirdes , A Method for the Numerical Inversion of Laplace Transforms , J. Comp. Appl. Math. , vol. 10 , pp. 113 – 132 , 1984 .
   Web of Science ®Google Scholar
• Y. Rabin , A General Model for the Propagation of Uncertainty in Measurements into Heat Transfer Simulations and its Application to Cryosurgery , Cryobiology , vol. 46 , pp. 109 – 120 , 2003 .
   PubMed Web of Science ®Google Scholar