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Practical Applications of Models of Oxygen Supply, Diffusion, and Consumption

Past, Perspectives, and Problems

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Book cover Oxygen Transport to Tissue XVII

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 388))

Abstract

It is the objective of this paper to describe, what models of oxygen supply, diffusion, and consumption have been and can be used for and to discuss some common problems in employing mathematical models of O2 transport. In a first part, four typical fields for model applications are selected from the wide variety of former investigations and are illustrated with some recent examples.

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References

  • Batra, S. and Rakusan, K., 1992, Capillary length, tortuosity, and spacing in rat myocardium during cardiac cycle, Am. J. Physiol. 263:H1369–H1376.

    PubMed  CAS  Google Scholar 

  • Bouwer, S., 1987, Facilitated oxygen diffusion through hemoglobin solutions. Measurement of diffusion and reaction parameters, Doctoral Thesis, University of Nijmegen.

    Google Scholar 

  • Bruley, D.F., 1995, Empirical modeling for oxygen transport processes and related physiological systems, this volume.

    Google Scholar 

  • Clark, P.A.A., Kennedy, S.R, and Clark, A., 1989, Buffering of muscle tissue PO 2 levels by the superposition of the oxygen field from many capillaries, Adv. Exp. Med. Biol. 248:165–174.

    PubMed  CAS  Google Scholar 

  • Egginton, S. and Ross, H.E, 1987, Quantifying capillary distribution in four dimensions, Adv. Exp. Med. Biol. 248:271–280.

    Google Scholar 

  • Ellis, C.G., Potter, R.F., and Groom, A.C., 1983, The Krogh cylinder geometry is not appropriate for modeling O2 transport in contracted skeletal muscle, Adv. Exp. Med. Biol. 159:253–268.

    PubMed  CAS  Google Scholar 

  • Federspiel, W.J., 1986, A model study of intracellular oxygen gradients in a myoglobin-containing skeletal muscle fiber, Biophys. J. 49:857–868.

    Article  PubMed  CAS  Google Scholar 

  • Gayeski, T.E.J, and Honig, CR., 1986, O2 gradients from sarcolemma to cell interior in red muscle at maximal VO 2, Am. J. Physiol. 251:H789–H799.

    PubMed  CAS  Google Scholar 

  • Gayeski, T.E.J., Connett, R.J., and Honig, CR., 1987, Minimum intracellular PO 2 for maximum cytochrome turnover in red muscle in situ, Am. J. Physiol. 252:H906–H915.

    PubMed  CAS  Google Scholar 

  • Gayeski, T.E.J., Honig, CR., 1988, Intracellular PO2 in long axis of individual fibers in working dog gracilis muscle, Am. J. Physiol. 254:H1179–H1186.

    PubMed  CAS  Google Scholar 

  • Groebe, K., 1990, A versatile model of steady state O2 supply to tissue. Application to skeletal muscle, Biophys. J. 57:485–498.

    Article  PubMed  CAS  Google Scholar 

  • Groebe, K., Erz, S., and Müller—Klieser, W., 1994, Glucose diffusion coefficients determined from concentration profiles in EMT6 tumor spheroids incubated in radioactively labeled 1-glucose, Adv. Exp. Med. Biol, in press.

    Google Scholar 

  • Hellums, J.D., 1977, The resistance to oxygen transport in the capillaries relative to that in the surrounding tissue, Microvasc. Res. 13:131–136.

    Article  Google Scholar 

  • Honig, CR., Odoroff, C.L., and Frierson, J.L., 1980, Capillary recruitment in exercise: rate, extent, uniformity, and relation to blood flow, Am. J. Physiol 238:H31–H42.

    PubMed  CAS  Google Scholar 

  • Honig, CR., Odoroff, CL., and Frierson, J.L., 1982, Active and passive capillary control in red muscle at rest and in exercise, Am. J. Physiol 243:H196–H206.

    PubMed  CAS  Google Scholar 

  • Hoofd, L., Turek, Z., and Olders, J., 1989, Calculation of oxygen pressures and fluxes in a flat plane perpendicular to any capillary distribution, Adv. Exp. Med. Biol. 248:187–196.

    PubMed  CAS  Google Scholar 

  • Kayar, S.R., Hoppeler, H., Jones, J.H., Longworth, K., Armstrong, R.B., Laughlin, M.H., Lindstedt, S.L., Bicudo, J.E.P.W., Groebe, K., Taylor, and CR., Weibel, E.R., 1994, Capillary blood transit time in muscles in relation to body size and aerobic capacity, J. Exp. Biol, in press.

    Google Scholar 

  • Klitzman, B. and Johnson, P.C., 1982, Capillary network geometry and red cell distribution in hamster cremaster muscle, Am. J. Physiol 242:H211–H219.

    PubMed  CAS  Google Scholar 

  • de Koning, J., Hoofd, L.J.C, and Kreuzer, F, 1981, Oxygen transport and the function of myoglobin, Pflügers Arch. 389:211–217.

    Article  PubMed  Google Scholar 

  • Krogh, A., 1918a, The rate of diffusion of gases through animal tissues with some remarks on the coefficient of invasion, J. Physiol (London) 52:391–408.

    Google Scholar 

  • Krogh, A., 1918b, The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue, J. Physiol. (London) 52:409–415.

    Google Scholar 

  • Krogh, A., 1918c, The supply of oxygen to the tissues and the regulation of the capillary circulation, J. Physiol. (London) 52:457–474.

    Google Scholar 

  • Mathieu—Costello, O., Ellis, CG., Potter, R.F., MacDonald, I.C, and Groom, A.C., 1991, Muscle capillary-to-fiber perimeter ratio: morphometry, Am. J. Physiol. 261:H1617–H1625.

    PubMed  CAS  Google Scholar 

  • Müller—Klieser, W, 1984, Method for determination of oxygen consumption rates and diffusion coefficients in multicellular spheroids, Biophys. J. 46:343–348.

    Article  Google Scholar 

  • Potter, R.F. and Groom, A.C., 1983, Capillary diameter and geometry in cardiac and skeletal muscle studied by means of corrosion casts, Microvasc. Res. 25:68–84.

    Article  PubMed  CAS  Google Scholar 

  • Turek, Z., Hoofd, L., and Rakusan, K., 1987, A comparison of the methods for assessment of the heterogeneity of myocardial capillary spacing, Adv. Exp. Med. Biol. 215:13–19.

    PubMed  CAS  Google Scholar 

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© 1996 Plenum Press, New York

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Groebe, K. (1996). Practical Applications of Models of Oxygen Supply, Diffusion, and Consumption. In: Ince, C., Kesecioglu, J., Telci, L., Akpir, K. (eds) Oxygen Transport to Tissue XVII. Advances in Experimental Medicine and Biology, vol 388. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0333-6_20

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  • DOI: https://doi.org/10.1007/978-1-4613-0333-6_20

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-8002-3

  • Online ISBN: 978-1-4613-0333-6

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