An analytical study of heat transfer in finite tissue with two blood vessels and uniform dirichlet boundary conditions

Journal of Heat Transfer

Volumn 127, Issue 2, 2005, Pages 179-188

  Shrivastava, Devashish ^a   McKay, Benjamin ^b   Roemer, Robert B ^a  

^a Department of Electrical and Computer Engineering   (United States)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BLOOD VESSELS; BOUNDARY CONDITIONS; MATHEMATICAL MODELS; POISSON EQUATION; TEMPERATURE; TISSUE;

DOMAINS; LIVING SYSTEMS; TEMPERATURE FIELDS; TRANSFER RATE;

HEAT TRANSFER;

HEAT TRANSFER;

EID: 17444397731     PISSN: 00221481     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1842788     Document Type: Article

References (38)

1. Hahn, G. M., 1982, Hyperthermia and Cancer, Plenum Press, New York.
2. Xu, L. X., Holmes, K. R., Moore, B., Chen, M. M., and Arkin, H., 1994, "Microvascular Architecture With in the Pig Kidney Cortex," Microvase. Res., 47, pp. 293-307.
3. Rommel, S. A., and Caplan, H., 2003, "Vascular Adaptations for Heat Conservation in the Tail of Florida Manatees (Trichechus Manatus Latirostris)," J. Anat., 202, pp. 343-353.
4. Pabst, D. A., Rommel, S. A., McLellan, W. A., Williams, T. M., and Rowles, T. K., 1995, "Thermoregulation of the Intra-Abdominal Testes of the Bottlenose Dolphin (Tursiops Truncatus) During Exercise," J. Exp. Biol., 198, pp. 221-226.
5. Geist, N. R., 2000, "Nasal Respiratory Turbinate Function in Birds," Physiol. Biochem. Zoolo., 73(5), pp. 581-589.
6. Mitchell, J. W., and Myers, G. E., 1968, "An Analytical Model of the Counter-Current Heat Exchange Phenomena," Biophys. J., 8, pp. 897-911.
7. Zhu, L., 2000, "Theoretical Evaluation of Contributions of Heat Conduction and Counter-Current Heat Exchange in Selective Brain Cooling in Humans," Ann. Biomed. Eng., 28, pp. 269-277.
8. DiFelice, Jr., R. F., and Bau, H. H., 1983, "Conductive Heat Transfer Between Eccentric Cylinders With Boundary Conditions of the Third Kind," ASME J. Heat Transfer, 105, pp. 678-680.
9. Lemons, D. E., Chien, S., Crawshaw, L. I., Weinbaum, S., and Jiji, L. M., 1987, "Significance of Vessel Size and Type in Vascular Heat Transfer," Am. J. Phys., 253, pp. R128-R135.
10. Chato, J. C., 1980, "Heat Transfer to Blood Vessels," J. Biomech. Eng., 102, pp. 110-118.
11. Wissler, E. H., 1988, "An Analytical Solution Countercurrent Heat Transfer Between Parallel Vessels With a Linear Axial Temperature Gradient," J. Biomech. Eng., 110, pp. 254-256.
12. Shitzer, A., Stroschein, L. A,, Gonzalez, R. R., and Pandolf, K. B., 1997, "Numerical Analysis of an Extremity in Cold Environment Including Counter-Current Arterio-Venous Heat Exchange," J. Biomech. Eng., 119 179-186.
13. Baish, J. W., and Ayyaswamy, P. S., 1986, "Small-Scale Temperature Fluctuations in Perfused Tissue During Local Hyperthermia," J. Biomech. Eng., 108, pp. 246-250.
14. Baish, J. W., Ayyaswamy, P. S., and Foster, K. R., 1986, "Heat Transport Mechanisms in Vascular Tissues: A Model Comparison," J. Biomec. Eng., 108, pp. 324-331.
15. Zhu, M., Weinbaum, S., and Jiji, L. M., 1990, "Heat Exchange Between Unequal Countercurrent Vessels Asymmetrically Embedded in a Cylinder With Surface Convection," Int. J. Heat Mass Transfer, 33, pp. 2275-2283.
16. Zhu, M., Weinbaum, S., Jiji, L. M., and Lemons, D. E., 1988, "On the Generalization of the Weinbaum-Jiji Bioheat Equation to Microvessels of Unequal Size; The Relation Between the Near Field and Local Average Tissue Temperatures," J. Biomech. Eng., 110, pp. 74-81.
17. Wu, Y. L., Weinbaum, S., and Jiji, L. M., 1993, "A New Analytic Technique for 3-D Heat Transfer From a Cylinder With Two or More Axially Interacting Eccentrically Embedded Vessels With Application to Countercurrent Blood Flow," Int. J. Heat Mass Transfer, 36, pp. 1073-1083.
18. Zhu, L., Lemons, D. E., and Weinbaum, S., 1996, "Microvascular Thermal Equilibration in Rat Cremaster Muscle," Ann. Biomed. Eng., 24, pp. 109-123.
19. Song, J., Xu, L. X., Lemons, D. E., and Weinbaum, S., 1997, "Enhancement in the Effective Thermal Conductivity in Rat Spinotrapezius Due to Vasoregulation," J. Biomech. Eng., 119, pp. 461-468.
20. Song, J., Xu, L. X., Lemons, D. E., and Weinbaum, S., 1997, "Microvascular Thermal Equilibration in Rat Spinotrapezius Muscle," Ann. Biomed. Eng., 27, pp. 56-66.
21. Van Leeuwen, G. M. J., Kotte, A. N. T. J., Crezee, J., and Lagendijk, J. J. W., 1997, "Tests of the Geometrical Description of Blood Vessels in a Thermal Model Using Counter-Current Geometries," Phys. Med. Biol., 42, pp, 1515-1532.
22. Zhu, L., and Weinbaum, S., 1995, "A Model for Heat Transfer From Embedded Blood Vessels in 2-D Tissue Preparations," J. Biomech. Eng., 117, pp. 64-73.
23. He, Q., Zhu, L., Lemons, D. E., and Weinbaum, S., 2002, "Experimental Measurements of the Temperature Variation Along Artery-Vein Pairs From 200 to 1000 μm Diameter in Rat Hind Limb," J. Biomech. Eng., 124 pp. 656-661.
24. Zhu, L., Xu, L. X., He, Q., and Weinbaum, S., 2002, "A New Fundamental Bioheat Equation for Muscle Tissue-Part 2: Temperature of SAV Vessels," J. Biomech. Eng., 124, pp. 121-132.
25. He, Q., Zhu, L., and Weinbaum, S., 2003, "Effect of Blood Flow on Thermal Equilibration and Venous Rewarming," Ann. Biomed. Eng., 31 pp. 659-666.
26. Lebedev, N. N., Skalskaya, I. P., and Uflyand, Y. S., 1979, Worked Problems in Applied Mathematics, Dover, New York.
27. El-Saden, M. R., 1961, "Heat Conduction in an Eccentrically Hollow. Infinitely Long Cylinder With Internal Heat Generation," ASME J. Heat Transfer, 83, pp. 510-512.
28. El-Shaarawi, M. A., and Mukheimer, I., 1995, "Unsteady Conduction in Eccentric Annuli," Heat Mass Transfer, 30, pp. 249-257.
29. Shrivastava, D., and Roemer, R. B., 2004, "An Analytical Derivation of Source Term Dependent, 2-D Generalized Poisson Conduction Shape Factors," Int. J. Heat Mass Transfer, 47(19-20), pp. 4293-4300.
30. Roemer, R. B., and Dutton, A. W., 1998, "A Generic Tissue Convective Energy Balance Equation: Part 1-Theory and Derivation," J. Biomech. Eng., 120, pp. 395-404.
31. Shrivastava, D., and Roemer, R. B., 2004, "An Analytical Study of Heat Transfer in Finite Tissue With Two Blood Vessels and General Dirichlet Boundary Conditions," Int. J. Heat Mass Transfer, (accepted).
32. Pennes, H. H., 1948, "Analysis of Tissue and Arterial Blood Temperatures in Resting Human Forearm," J. Appl. Phys., 1, pp. 93-122.
33. Brown, J. W., and Churchill, R. V., 1996, Complex Variables and Applications, McGraw-Hill, New York.
34. Devashish, 2004, "Development and Evaluation of Tissue Convective Energy Balance Equation," Ph.D. dissertation, University of Utah, Salt Lake City, UT.
35. Wehner, H., Ardenne, A. V., and Kaltofen, S., 2001, "Whole-Body Hyperthermia With Water-Filtered Infrared Radiation; Technical-Physical Aspects and Clinical Experiences," Int. J. Hyperthermia, 17, pp. 19-30.
36. Landry, J., and Marceau, N., 1978, "Rate-Limiting Events in Hyperthermic Cell Killing," Radial. Res., 75, pp. 573-585.
37. Milnor, W. R., 1990, Cardiovascular Physiology, Oxford University Press, New York.
38. Gray, H., 1978, Gray's Anatomy, Descriptive and Surgical, Barnes andd Nobel Inc., New York.