Advertisement

Transients of Gas Exchange Processes in the Upper Skin Calculated by the Capillary Loop Model

  • U. Grossmann
  • P. Winkler
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 180)

Abstract

The use of transcutaneous PO2 measuring techniques in clinics induces an enhanced need to understand the oxygen exchange processes within the upper skin. Several authors (Eberhard, 1976; Quinn, 1978; Lübbers, 1979; Thunstrom et al., 1979) used the combined approach of a Krogh model for stratum papillare and a layer model for epidermis to analyze the oxygen exchange processes within this part of the skin. The capillary loop model (Grossmann et al., 1980; Grossmann, 1982) was developed to simulate steady states of oxygen exchange within the upper skin. This model has the advantage of taking into account the loop shaped capillary structure of stratum papilläre and the nonlinear effects of the binding of oxygen by hemoglobin. In order to simulate processes varying with time we modified this steady state model. The numerical treatment of the basic parabolic initial boundary value problem was performed by the “Hopscotch”-method. The following sections show a short review of the model, a presentation of the method and some results.

Keywords

Steady State Model Breathing Oxygen Original Article Series Stop Blood Flow Oxygen Exchange Process 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Eberhard, P., 1976, Continuous oxygen monitoring of newborns by skin sensors, Dissertation, Basel.Google Scholar
  2. Gourlay, A.R., 1970, Hopscotch: A fast second-order partial differential equation solver, J. Inst. Maths. Applics, 6:375–390.CrossRefGoogle Scholar
  3. Grossmann, U., 1980, Existence and uniqueness of solutions of quasilinear transmission problems of both elliptic and pseudo-parabolic type simulating oxygen transport in capillary and tissue, Math. Meth. Appl. Sci., 2:34–47.CrossRefGoogle Scholar
  4. Grossmann, U., 1982, Simulation of combined transfer of oxygen and heat through the skin using a capillary loop model, Math. Biosci., 61:205–236.CrossRefGoogle Scholar
  5. Grossmann, U., Huber, J., Fricke, K., and Lübbers, D.W., 1980, A new method for simulating the oxygen pressure field of skin, in: “Oxygen Transport to Tissue”, Adv. Physiol. Sci., Vol. 25, A.G.B. Kovach, E. Dora, M. Kessler, I.A. Silver, eds., Pergamon Press, Akademiai Kiado, Budapest, pp. 319–320.Google Scholar
  6. Lübbers, D.W., 1979, Cutaneous and transcutaneous PO2 and PCO2 and their measuring conditions, in: “Continuous Transcutaneous Blood Gas Monitoring”, A. Huch, R. Huch, J.F. Lucey, eds., Birth Defects, Original Article Series, Volume XV, 4, The National Foundation March of Dimes, A.R. Liss, New York, pp. 13–31.Google Scholar
  7. Peaceman, D.W., and Rachford, H.H., 1955, The numerical solution of parabolic and elliptic differential equation, J. Soc. Indust. Appl. Math., 3:28–41.CrossRefGoogle Scholar
  8. Quinn, J.A., 1978, Gas transfer through the skin: A two layer model relating transcutaneous flux to arterial tension, in: “Oxygen Transport to Tissue III”, I.A. Silver, M. Erecinska, H.I. Bicher, eds., Plenum Press, New York, pp. 175–181.CrossRefGoogle Scholar
  9. Roache, P.J., 1972, “Computational Fluid Dynamics”, Hermosa Publishers, Alburquerque.Google Scholar
  10. Spaan, J.A.E., 1976, Oxygen transfer in layers of hemoglobin, Thesis, Eindhoven.Google Scholar
  11. Thunstrom, A.M., Stafford, M.J., and Severinghaus, J.W., 1979, A two temperature, two PO2 method of estimating the determinations of tcPO2, in: “Continuous Transcutaneous Blood Gas Monitoring” A. Huch, R. Huch, J.F- Lucey, eds., Birth Defects, Original Article Series, Volume XV, 4, The National Foundation March of Dimes, A.R. Liss, New York, pp. 167–182.Google Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • U. Grossmann
    • 1
  • P. Winkler
    • 1
  1. 1.Max-Planck-Institut für SystemphysiologieDortmund 1Germany

Personalised recommendations