Krogh model

Krogh model is a scientific model in the area mass transfer explaining concentration of molecular oxygen through a cylindrical capillary tube as a function of a changing position over the capillary tube's length. It was first conceptualized by August Krogh in 1919 to describe oxygen supply in living tissues, particularly the one occurring in human blood vessels.^[1] Its applicability has been extended to various academic fields, and has been successful explaining drug diffusion, water transport, and ice formation in tissues.^[2]

Mathematical modeling

Krogh model is derived by applying Fick's laws of diffusion and the law of conservation of mass over a radial interval ${\displaystyle Rc\leq r\leq Rt}$

Limitations

Although Krogh model is a good approximation, it underestimates oxygen consumption^[2] because the cylinder model does not include all the tissue surrounding the capillary.^[3]

Notes

1. Wei & Anderson 1995, p. 176.
2. "Axial oxygen diffusion in the Krogh model: modifications to account for myocardial oxygen tension in isolated perfused rat hearts measured by EPR oximetry.". PubMed.gov. Retrieved 2015-12-22.
3. Truskey, Fan & Katz 2009, p. 643.

References

• Truskey, George; Fan, Yuan; Katz, David (2009), Transport phenomena in biological systems, ISBN 978-0131569881
• Wei, James; Anderson, John (1995), Advances in chemical engineering, Volume 19, ISBN 978-0120085194