Abstract
A new experimental approach was developed to obtain the first direct measurements of the axial countercurrent thermal equilibration in a microvascular tissue preparation using high resolution infrared thermography. Detailed surface temperature measurements were obtained for an exteriorized rat cremaster muscle in which pharmacological vasoactive agents were used to change the local blood flow Peclet number from 1 to 14 in the feeding artery. Under normal conditions, only the 1A arteries (>70 μm diameter) showed thermal nonequilibration with the surrounding tissue. The theoretical model developed by Zhu and Weinbaum (28) for a two-dimensional tissue preparation with arbitrarily embedded countercurrent vessels was modified to include axial conduction and the presence of the supporting glass slide. This modified model was used to interpret the experimental results and to relate the surface temperature profiles to the bulk temperature profiles in the countercurrent artery and vein and the local average tissue temperature in the crosssectional plane. Surface temperature profiles transverse to the vessel axis are shown to depend significantly on the tissue inlet temperature. The eigenfunction for the axial thermal equilibration depends primarily on the blood flow Peclet number and the environmental convective coefficient. The theoretical results predict that when ρ ar *Pe is less than 1 mm (the range in our experiments), axial conduction is the dominant mode of axial thermal equilibration. For 1 < ρ ar *Pe < 3 mm, countercurrent blood flow becomes comparable to axial conduction, whereas, when ρ ar *Pe > 3 mm, countercurrent blood flow is the dominant mode of axial thermal equilibration. Therefore, for ρ ar *Pe > 3 mm the axial equilibration length is proportional to the blood flow Peclet number, as predicted previously by Zhu and Weinbaum in a study in which axial conduction was neglected. It also is shown that the axial decay of the tissue temperature at low perfusion rates can be described by a simple one-dimensional Weinbaum-Jiji equation with a newly derived conduction shape factor.
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References
Anderson G. T., and J. W. Valvano. A small artery heat transfer model for self-heated thermistor measurements of perfusion in the kidney cortex.J. Biomech. Eng. 116:71–78, 1994.
Baez, S. An open cremaster muscle preparation for the study of blood vessels byin vivo microscopy.Microvasc. Res. 5:384–394, 1973.
Baish, J. W., P. S. Ayyaswamy, and K. R. Foster. Heat transport mechanism in vascular tissues: a model comparison.J. Biomech. Eng. 108:324–331, 1986a.
Baish, J. W., P. S. Ayyaswamy, and K. R. Foster. Smallscale temperature fluctuations in perfused tissue during local hyperthermia.J. Biomech. Eng., 108:246–250, 1986b.
Baker, M., and H. Wayland. On-line volume flow rate and velocity profile measurement for blood in microvessels.Microvasc. Res. 7:131–134, 1974.
Bau, H. H., and S. S. Sadhal. Heat losses from a fluid flowing in a buried pipe.Int. J. Heat Mass Transfer 25: 1621–1629, 1982.
Bazett, H. C., I. Love, M. Newton, I. Eisenberg, R. Day, and R. Forest. Temperature changes in blood flowing in the arteries and veins in man.J. Appl. Physiol. 1:3–19, 1948.
Charny, C. K., S. Weinbaum, and R. L. Levin. An evaluation of the Weinbaum-Jiji bioheat equation for normal and hyperthermic conditions.J. Biomech. Eng. 112:80–87, 1990.
Chato, J. C., Heat transfer to blood vessels.J. Biomech. Eng. 102:110–118, 1980.
Chen, M. M., and K. R. Holmes. Microvascular contributions in tissue heat transfer. Ann. NY Acad. Sci. 335:137–150, 1980.
Crezee, J., and J. J. W. Lagendijk. Experimental verification of bioheat transfer theories: measurement of temperature profiles around large artificial vessels in perfused tissue.Phys. Med. Biol. 37:905–923, 1990.
Crezee, J., J. Mooibroek, C. K. Bos, and J. J. W. Lagendijk. Interstitial heating: experiments in artificially perfused bovine tongues.Phys. Med. Biol. 36:823–833, 1991.
DiFelice, R. F., Jr., and H. H. Bau. Conductive heat transfer between eccentric cylinders with boundary conditions of the third kind.J. Heat Transfer 105:678–680, 1983.
Faber, J. E.,In situ analysis of α-adrenoceptors on arteriolar and venular smooth muscle in rat skeletal muscle microcirculation.Circ. Res. 62:37–50, 1988.
Lemons, D. E., S. Chien, L. I. Crawshaw, S. Weinbaum, and L. M. Jiji. The significance of vessel size and type in vascular heat transfer.Am. J. Physiol. 253:R128-R135, 1987.
Mitchell, J. W., and G. R. Myers. An analytical model of the counter-current heat exchange phenomena.Biophys. J. 8:897–911, 1968.
Pennes, H. H.. Analysis of tissue and arterial blood temperatures in the resting human forearm.J. Appl. Physiol. 1: 93–122, 1948.
Roemer, R. B., E. G. Moros, and K. Hynynen. A comparison of bio-heat transfer and effective conductivity equation predictions to experimental hyperthermia data.Adv. Bioeng. ASME Winter Annual Meeting, 11–15, 1989.
Scholander P. F., and J. Krog. Countercurrent heat exchange and vascular bundles in sloths.J. Appl. Physiol. 10:405–411, 1957.
Thiyagarajan, R., and M. M. Yovanovich. Thermal resistance of a buried cylinder with constant flux boundary condition.J. Heat Transfer 96:249–250, 1974.
Weinbaum, S., and L. M. Jiji. A new simplified bioheat equation for the effect of blood flow on local average tissue temperature.J. Biomech. Eng. 107:131–139, 1985.
Weinbaum, S., and L. M. Jiji. The matching of thermal fields surrounding countercurrent microvessels and the closure approximation in the Weinbaum-Jiji bioheat equation.J. Biomech. Eng. 111: 271–275, 1989.
Weinbaum, S., L. M. Jiji, and D. E. Lemons. Theory and experiment for the effect of vascular microstructure on surface tissue heat transfer. I. Anatomical foundation and model conceptualization.J. Biomech. Eng. 106:321–330, 1984.
Wissler, E. H. An analytical solution countercurrent heat transfer between parallel vessels with a linear axial temperature gradient.J. Biomech. Eng. 110:254–256, 1988.
Wu, Y. L., S. Weinbaum, and L. M. Jiji. 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 flowInt. J. Heat Mass Transfer 36:1073–1083, 1993.
Xu, L. X., M. M. Chen, K. R. Holmes and H. Arkin. The theoretical evaluation of the Pennes, the Chen-Holmes and the Weinbaum-Jiji bioheat transfer models in the pig renal cortex. ASME Winter Annual Meeting, Atlanta, HTD, Vol. 189, pp. 15–22, 1991.
Zhu, L., D. E. Lemons, and S. Weinbaum. A new approach for prediction the enhancement in the effective conductivity of perfused muscle tissue due to hyperthermia.Ann. Biomed. Eng. 23:1–12, 1995.
Zhu, L., and S. Weinbaum. A model for heat transfer from embedded blood vessels in two-dimensional tissue preparations.J. Biomech. Eng. 117:64–73, 1995.
Zhu, M., S. Weinbaum, and L. M. Jiji. Heat exchange between unequal countercurrent vessels asymmetrically embedded in a cylinder with surface convection.Int. J. Heat Mass Transfer 33:2275–2284, 1990.
Zhu, M., S. Weinbaum, L. M. Jiji, and D. E. Lemons. On the generalization of the Weinbaum-Jiji bioheat equation to microvessels of unequal size; the relation between the near field and local average tissue temperature.J. Biomech. Eng. 110:74–81, 1988.
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Zhu, L., Lemons, D.E. & Weinbaum, S. Microvascular thermal equilibration in rat cremaster muscle. Ann Biomed Eng 24 (Suppl 1), 109–123 (1995). https://doi.org/10.1007/BF02771000
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DOI: https://doi.org/10.1007/BF02771000