Abstract
The cylindrical steady-state model developed by Krogh with Erlang has served as the basis of understanding oxygen supply in living tissue for over eighty years. Due to its simplicity and agreement with some observations, it has been extensively used and successfully extended to new fields, especially for situations such as drug diffusion, water transport, and ice formation in tissues. However, the applicability of the model to make even a qualitative prediction of the oxygen level of specific volumes of the tissue is still controversial. We recently have developed an approximate analytical solution of a steady-state diffusion equation for a Krogh cylinder, including oxygen concentration in the capillary. This model was used to explain our previous experimental data on myocardial pO2 in isolated perfused rat hearts measured by EPR oximetry. An acceptable agreement with the experimental data was obtained by assuming that a known limitation of the existing EPR methods—a tendency to over-weight low pO2 values—had resulted in an under-estimate of the pO2. These results are consistent with recent results of others, which stress the importance of taking into account the details of what is measured by various methods.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
A. S. Popel, Theory of oxygen transport to tissue, Crit. Rev. Biomed. Eng. 17(3), 257–321 (1989).
J. D. Hellums, P. K. Nair, N. S. Hugang, and N. Ohshima, Simulation of intraluminal gas transport process in microcirculation, Ann. Biomed. Eng. 24(1), 1–24 (1996).
M. Sharan, and A. Popel, A compartmental model for oxygen transport in brain microcirculation in the presence of blood substitutes, J. Theor. Biol. 216(4), 479–500 (2002).
F. Hyder, R. G. Shulman, and D. L. Rothman, A model for the regulation of cerebral oxygen delivery, J. Appl. Physiol. 85(2), 554–564 (1998).
C. A. Lodi, A. T. Minassian, L. Beydon, and M. Ursino, Modeling cerebral outoregulation and CO2 reactivity in patients with severe head injury, Am. J. Physiol. 274(5 Pt. 2), H1729–H1741 (1998).
S. S. Kety, Determination of tissue oxygen tension, Fed. Proc. 16, 666–670 (1957).
J. E. Fletcher, and R.W. Schubert, Axial diffusion and wall permeability effects in perfused capillary-tissue structures, Biosystems 20(2), 153–174 (1987).
T. D. Lagerlund, and P. A. Low, Axial diffusion and Michaelis-Menten kinetics in oxygen delivery in rat peripheral-nerve, Am. J. Physiol. 260(2 Pt. 2), R430–R440 (1991).
R. W. Schubert, and X. Zhang, The equivalent Krogh cylinder and axial oxygen transport, Oxygen Transport to Tissue XVIII, Adv. Exper. Med. Biol. 411, 191–202 (1997).
L. Gabet, Capillary net and injection modeling, Int. J. BioMed. Comp. 31(1), 25–36 (1992).
C. A. Millard, and A. D. Gorman, A model for substrate concentrations in tissue surrounding single capillaries, Math. Comp. Model. 25(11), 1–7 (1997).
B. Rubinsky, and D. E. Pegg, A mathematical-model for the freezing process in biological tissue, Cryobiol. 25(6), 546 (1988).
J. C. Bischof, C. M. Ryan, R. G. Tompkins, M. L. Yarmush, and M. Toner, Ice formation in isolated human hepatocytes and human liver tissue, ASAIO J. 43(4), 271–278 (1997).
R. V. Devireddy, and J. C. Bischof, Measurement of water transport during freezing in mammalian liver tissue: Part II-The use of differential scanning calorimetry, J. Biomech. Eng. (Transactions of the ASME) 120(5), 559–569 (1998).
R. V. Devireddy, J. E. Coad, and J. C. Bischof, Microscopic and calorimetric assessment of freezing processes in uterine fibroid tumor tissue, Cryobiol. 42(4), 225–243 (2001).
B. J. Friedman, O. Y. Grinberg, K. A. Isaacs, T. M. Walczak, and H. M. Swartz, Myocardial oxygen-tension and relative capillary density in isolated-perfused rat hearts, J. Mol. Cell. Cardiol. 27(12), 2551–2558 (1995).
I. Tomas-Das, A. Waites, A. Das, and J. Denekamp, Theoretical simulation of oxygen tension measurement in tissues using a microelectrode: I. The response function of the electrode, Physiol. Measur. 22(4),713–725 (2001).
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this paper
Cite this paper
Grinberg, O., Novozhilov, B., Grinberg, S., Friedman, B., Swartz, H.M. (2005). Axial Oxygen Diffusion in the Krogh Model. In: Okunieff, P., Williams, J., Chen, Y. (eds) Oxygen Transport to Tissue XXVI. Advances in Experimental Medicine and Biology, vol 566. Springer, Boston, MA. https://doi.org/10.1007/0-387-26206-7_18
Download citation
DOI: https://doi.org/10.1007/0-387-26206-7_18
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-25062-5
Online ISBN: 978-0-387-26206-2
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)