Abstract
Most modelling of oxygen transport in tissue has been based on the classical Krogh-Erlang equation (Krogh, 1919), which describes oxygen diffusion in any circular cross-section of a spherical cylinder around a capillary. Extensions like facilitated diffusion and non-zero-order oxygen consumption can be built in and combined with blood flow and capillary spacing heterogeneity (Turek et al., this volume). Other models are based on computer simulations (Federspiel, 1986; Popel et al., 1986; Groebe, 1987), with the disadvantage of describing only specific situations; thus making application in real heterogeneous tissue impossible.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Clark, P.A., Kennedy, S.P., Clark Jr., A.C., Buffering of muscle Po2 levels by the superposition of the oxygen field from many capillaries, this volume.
De Koning, J., Hoofd, L.J.C., Kreuzer, F., 1981, Oxygen transport and the function of myoglobin: theoretical model and experiments in chicken gizzard smooth muscle, Pflügers Arch., 389: 211–217.
Federspiel, W.J., 1986, A model study of intgracellular oxygen gradients in a myoglobin-containing skeletal muscle fiber, Biophys. J., 49: 857–868.
Gayeski, T.E.J., 1982, “A cryogenic microspectrophotometric method for measuring myoglobin saturation in subcellular volumes: Application to resting dog gracilis muscle”, Dissertation Thesis, University of Rochester, Rochester, NY, USA.
Groebe, K., 1987, “Theoretische Untersuchung des Sauerstofftransportes in der Skeletmuskulatur bei maximaler Sauerstoffaufnähme”, Dissertation Thesis, University of Mainz, Mainz, FRG.
Honig, C.R., Gayeski, T.E.J., 1987, Comparison of intracellular Po2 and conditions for blood-tissue O2 transport in heart and working red skeletal muscle, in: “Oxygen Transport to Tissue IX (Adv. Exp. Med. Biol. 215),” I. A. Silver and A. Silver, eds., Plenum Press, New York & London, pp. 309–321.
Hoofd, L., 1987, “Facilitated diffusion of oxygen in tissue and model systems”, Dissertation Thesis, University of Nijmegen, Nijmegen, the Netherlands.
Hoofd, L., Turek, Z., Kubat, K., Ringnalda, B.E.M., Kazda, S., 1985, Variability of intercapillary distance estimated on histological sections of rat heart, in: “Oxygen Transport to Tissue VII (Adv. Exp. Med. Biol. 191),” F. Kreuzer, S. M. Cain, Z. Turek and T. K. Goldstick, eds., Plenum Press, New York & London, pp. 239–247.
Hoofd, L., Turek, Z., Rakusan, K., 1987, Diffusion pathways in oxygen supply of cardiac muscle, in: “Oxygen Transport to Tissue IX (Adv. Exp. Med. Biol. 215),” I. A. Silver and A. Silver, eds., Plenum Press, New York & London, pp. 171–177.
Krogh, A., 1919, The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue. J. Physiol., 52: 409–415.
Popel, A.S., Charny, C.K., Dvinsky, A.S., 1986, Effect of heterogeneous oxygen delivery on the oxygen distribution in skeletal muscle, Math. Biosci. 81: 91–113.
Rakusan, K., Hoofd, L., Turek, Z. 1984, The effect of cell size and capillary spacing on myocardial oxygen supply, in: “Oxygen Transport to Tissue VI (Adv. Exp. Med. Biol. 180).” D. Bruley, H. I. Bicher and D. Reneau, eds., Plenum Press, New York & London, pp. 463–477.
Turek, Z., Olders, J., Hoofd, L., Egginton, S., Kreuzer, F., Rakusan, K., PO2 histograms in various models of tissue oxygenation in skeletal muscle, this volume.
Turek, Z., Rakusan, K., 1981, Lognormal distribution of intercapillary distance in normal and hypertrophic rat heart as estimated by the method of concentric circles: its effect on tissue oxygenation, Pflü-gers Arch., 391: 17–21.
Van Haelst, A.C.T.A., Hoofd, L., Turek, Z., 1985, Lognormal distribution of capillary domains in the rat myocardium. J. Physiol. (London), 366: 114P.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Plenum Press, New York
About this chapter
Cite this chapter
Hoofd, L., Turek, Z., Olders, J. (1989). Calculation of Oxygen Pressures and Fluxes in a Flat Plane Perpendicular to Any Capillary Distribution. In: Rakusan, K., Biro, G.P., Goldstick, T.K., Turek, Z. (eds) Oxygen Transport to Tissue XI. Advances in Experimental Medicine and Biology, vol 248. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5643-1_23
Download citation
DOI: https://doi.org/10.1007/978-1-4684-5643-1_23
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-5645-5
Online ISBN: 978-1-4684-5643-1
eBook Packages: Springer Book Archive