The Equivalent Krogh Cylinder and Axial Oxygen Transport

  • Roy W. Schubert
  • Xuejun Zhang
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 411)

Abstract

The Krogh-Erlang model has served as a basis of understanding of oxygen supply to resting and working muscle. Considerable discrepancy was found between pO 2 microsensor data and results from that model. A modification was made to the transport mechanisms implied by the Krogh-Erlang model by averaging the tissue radially, using a mass-transfer coefficient to maintain radial transport, and adding axial diffusion in the capillary and tissue. This radially-averaged, axially distributed (RAAD) modified Krogh model is used to evaluate the hypothesis that axial transport is important in Krogh-geometry capillary-tissue structures. Analytic solutions for the modified model were developed. RAAD model histograms bear a striking resemblance to experimental data, while results from the classic model do not. The former has an SSE (sum of squared error) of 10.2 with respect to experimental histograms, while the Krogh model has an SSE of 238.6. The effect of using a radial mass-transfer coefficient was evaluated by comparing the RAAD model with a fully distributed model. It had been shown that the modified Krogh model predicts tissue level data well when the length-to-tissue radius ratio is 50. It was expected that the predictions would be degraded for smaller ratios and then the Krogh model would suffice. By supplying a fixed volume of tissue at different radius/length ratios, it will be shown that the modified Krogh model is superior in all aspects to the Krogh model. The results are slightly different from those of the distributed model, but these differences are limited to the first 10% of the arteriolar region. It is concluded that the RAAD model is a better overall predictor of oxygen distribution and may be useful in furthering our understanding of oxygen transport to tissue in hemoglobinless perfusion situations. We suggest that this radially-averaged, axially-distributed model be used in place of the classic Krogh cylinder model for all biological situations.

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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Roy W. Schubert
    • 1
  • Xuejun Zhang
    • 1
  1. 1.Biomedical EngineeringLouisiana Tech UniversityRustonUSA

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