Krogh cylinder model

The Krogh-cylinder model initially describes the diffusion of oxygen from a blood capillary into the surrounding tissue and the tissue at the oxygen partial pressure . The model was designed by August Krogh and worked out mathematically by Agner Krarup Erlang . Due to its simplicity and because it often allows a good approximation of the real conditions, it is often used in various modifications and extensions to simulate other, similar diffusion processes. For example, it is considered the basis of hyperbaric oxygen treatment .

Assumptions and mathematical description

The model assumes that diffusion takes place from a capillary cylinder into a larger but limited cylinder lying around it. The mathematical description is based on a number of other assumptions that greatly simplify the situation compared to the real facts:

• Only diffusion from the capillary to the outside is considered and this is symmetrical
• The capillaries are straight with a constant radius, run parallel, are evenly distributed and their wall does not affect diffusion. No oxygen is consumed within the capillary.
• Diffusion and oxygen consumption in the tissue are homogeneous and independent of the cellular structure or local oxygen partial pressure
• There is only diffusion, no active transport and no turbulence
• The model describes a steady state without dynamic changes

The following formula results:

${\displaystyle \mathrm {\Delta P} =P_{c}-P_{x}={\frac {M}{K}}({\frac {R^{2}}{2}}ln{\frac {x}{r}}-{\frac {x^{2}-r^{2}}{4}})}$

Here P _{c is} the partial pressure (in mmHg) in the capillary with radius r, P _x the partial pressure in the tissue at a distance x from the center of the capillary, M the oxygen consumption in ml O ₂ per ml tissue, K Krogh's diffusion coefficient in ml O ₂ / (cm sec mmHG) and R the radius of the entire tissue cylinder considered.

literature

• Ferdinand Kreuzer: Oxygen supply to tissues: The Krogh model and its assumptions . In: Experientia . tape 38 , 1982, pp. 1415–1426 ( full text (pdf)).
• Timothy W. Secomb: Krogh-Cylinder and Infinite-Domain Models for Washout of an Inert Diffusible Solute from Tissue . In: Microcirculation. tape 22 , no. 1 , 2015, p. 91-98 .