A generic tissue convective energy balance equation: Part I--theory and derivation.

A new equation for calculating temperatures in living tissues, the tissue convective energy balance equation (TCEBE), is derived using only a few assumptions. The resulting equation is basic, general and applicable to any tissue. The (unsolved) TCEBE is used: (a) to relate both Pennes' BHTE perfusion-related parameter (W) and the effective thermal conductivity equation's perfusion-related parameter (keff) to the true capillary perfusion Pcap, and (b) to show that both W and keff are defined, nonphysiological variables, which are only related to Pcap in a problem-dependent manner. Finally, the derivation of the relationship between W and Pcap provides a complete derivation of Pennes' BHTE, something that has not been previously done.

[1]  Kenneth R. Holmes,et al.  MICROVASCULAR CONTRIBUTIONS IN TISSUE HEAT TRANSFER , 1980, Annals of the New York Academy of Sciences.

[2]  C. K. Charny,et al.  Mathematical Models of Bioheat Transfer , 1992 .

[3]  H. H. Pennes.  Analysis of tissue and arterial blood temperatures in the resting human forearm. 1948. , 1948, Journal of applied physiology.

[4]  Kenneth R. Diller,et al.  Modeling of Bioheat Transfer Processes at High and Low Temperatures , 1992 .

[5]  S. Weinbaum,et al.  A new fundamental bioheat equation for muscle tissue: Part I--Blood perfusion term. , 1997, Journal of biomechanical engineering.

[6]  S. Weinbaum,et al.  A new simplified bioheat equation for the effect of blood flow on local average tissue temperature. , 1985, Journal of biomechanical engineering.

[7]  J. C. Chato,et al.  Fundamentals of Bioheat Transfer , 1990 .

[8]  H. Arkin,et al.  Recent developments in modeling heat transfer in blood perfused tissues , 1994, IEEE Transactions on Biomedical Engineering.

[9]  D E Lemons,et al.  Theory and experiment for the effect of vascular microstructure on surface tissue heat transfer--Part II: Model formulation and solution. , 1984, Journal of biomechanical engineering.

[10]  R L Levin,et al.  An evaluation of the Weinbaum-Jiji bioheat equation for normal and hyperthermic conditions. , 1990, Journal of biomechanical engineering.

[11]  W. Wulff,et al.  The Energy Conservation Equation for Living Tissue , 1974 .

[12]  W Wulff,et al.  DISCUSSION PAPER: ALTERNATIVES TO THE BIO‐HEAT TRANSFER EQUATION , 1980, Annals of the New York Academy of Sciences.

[13]  J. Whitelaw,et al.  Convective heat and mass transfer , 1966 .

[14]  D E Lemons,et al.  Theory and experiment for the effect of vascular microstructure on surface tissue heat transfer--Part I: Anatomical foundation and model conceptualization. , 1984, Journal of biomechanical engineering.