A Vascular Model for Heat Transfer in an Isolated Pig Kidney During Water Bath Heating

[+] Author and Article Information
Cuiye Chen

School of Mechanical Engineering, Purdue University, USA

Lisa X. Xu

School of Mechanical Engineering, Department of Biomedical Engineering, Purdue University, USASchool of Life Science and Technology, Shanghai Jiao Tong University, People’s Republic of China

J. Heat Transfer 125(5), 936-943 (Sep 23, 2003) (8 pages) doi:10.1115/1.1597625 History: Received January 14, 2002; Revised May 12, 2003; Online September 23, 2003
Copyright © 2003 by ASME
Your Session has timed out. Please sign back in to continue.


Dyce, K. M., Sack, W. O., and Wensing, C. J. G., 1996, Textbook of Veterinary Anatomy, W. B. Saunders Company, Philadelphia, PA.
Holmes,  K. R., Ryan,  W., Weinstein,  P., and Chen,  M. M., 1984, “A Fixation Technique for Organs to be Used as Perfused Tissue Phantoms in Bioheat Transfer Studies,” ASME Adv. in Bioeng., 11, pp. 9–10.
Zaerr,  J., Roemer,  R. B., and Hynynen,  K., 1990, “Computer-Controlled Dynamic Phantom for Ultrasound Hyperthermia Studies,” IEEE Trans. Biomed. Eng., 37(11), pp. 1115–1120.
Xu, L. X., 1999, “New Developments in Bioheat and Mass Transfer,” Ann. Rev. Heat Trans., C. L. Tien, ed., Begell House, Chap. 1.
Brown,  S. L., Li,  X. L., Pai,  H. H., Worthington,  A. E., Hill,  R. P., and Hunt,  J. W., 1992, “Observations of Thermal Gradients in Perfused Tissues During Water Bath Heating,” Int. J. Hyperthermia, 8(2), pp. 275–287.
Kolios,  M. C., Worthington,  A. E., Sherar,  M. D., and Hunt,  J. W., 1998, “Experimental Evaluation of Two Simple Thermal Models Using Transient Temperature Analysis,” Phys. Med. Biol., 43, pp. 3325–3340.
Kolios,  M. C., Worthington,  A. E., Holdsworth,  D. W., Sherar,  M. D., and Hunt,  J. W., 1999, “An Investigation of the Flow Dependence of Temperature Gradients Near Large Vessels During Steady State and Transient Tissue Heating,” Phys. Med. Biol., 44(6), pp. 1479–149.
Pennes,  H. H., 1948, “Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm,” Appl. Physiol., 1(2), pp. 93–122.
Weibaum,  S., Jiji,  L. M., and Lemons,  D. E., 1984, “Theory and Experiment for the Effect of Vascular Microstructure on Surface Heat Transfer-Part I: Anatomical Foundation and Model Conceptualization,” ASME J. Biomech. Eng., 106, pp. 321–330.
Valvano,  J. W., Nho,  S., and Anderson,  G. T., 1994, “Analysis of the Weinbaum-Jiji Model of Blood Flow in the Canine Kidney Cortex for Self-Heated Thermistors,” ASME J. Biomech. Eng., 116, pp. 201–207.
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(10), pp. 2275–2284.
Chen, C., and Xu, L. X., 2000, “Theoretical and Experimental Studies of Heat Transfer in the Vascularized Tissue Hyperthermic Conditions Using Preserved Pig Kidney,” Proc. 34th National Heat Transfer Conference, Pittsburgh, PA, pp. 683–689.
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(4), pp. 1073–1083.
Weinbaum,  S., Xu,  L. X., Zhu,  L., and Ekpene,  A., 1997, “A New Fundamental Bioheat Equation for Muscle Tissue: Part I—Blood Perfusion Term,” ASME J. Biomech. Eng., 119, pp. 278–288.
Xu,  L. X., Holmes,  K. R., Moore,  B., Chen,  M. M., and Arkin,  H., 1994, “Microvascular Architecture Within the Pig Kidney Cortex,” Microvasc. Res., 47, pp. 293–307.
Murray,  C. D., 1926, “The Physiological Principle of Minimum Work Applied to the Angle of Branching of Arteries,” J. Gen. Phys., 9, pp. 835–841.
Murray,  C. D., 1926, “The Physiological Principle of Minimum Work. I. The Vascular System and the Cost of Blood Volume,” Proc. Natl. Acad. Sci. U.S.A., 12, pp. 207–214.
Arkins,  H., Holmes,  K. R., Chen,  M. M., and Bottje,  W. G., 1986, “Thermal Pulse Decay Method for Simultaneous Measurement of Local Thermal Conductivity and Blood Perfusion: A Theoretical Analysis,” ASME J. Biomech. Eng., 108, pp. 208–214.


Grahic Jump Location
Schematic of kidney vasculature. a. artery; v. vein (adopted from Frandson Anatomy and Physiology of Farm Animals, Philadelphia, PA, Lea and Febiger, 1986)
Grahic Jump Location
Schematic of the inverted conical tissue unit and the vessel spacing
Grahic Jump Location
Schematic of the experimental setup
Grahic Jump Location
Contour plot of the analytical solutions of the steady state temperature distribution at the cross-section at z=6 mm. The kidney surface temperature Ts=43.0°C, the arterial inlet flow temperature Ta0=37.0°C, and the blood perfusion rate ωb=0.007 m3/s/m3.
Grahic Jump Location
Steady state temperature distributions in the pig kidney during water bath heating. The kidney surface temperature was Ts=43°C, the arterial inlet flow rate Qin=1.55×10−6m3/s, and the initial kidney temperature and the arterial inlet flow temperature were the same, Ti=Ta0=37°C.
Grahic Jump Location
The analytical predictions of the steady state bulk temperature distributions with respect to different blood perfusion rates. The kidney surface temperature Ts=43.0°C and the arterial inlet flow temperature Ta0=37.0°C.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In