Tissue layer
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♦ For terminology and basic concepts, refer to the pages about
Principles of diffusion and
Facilitation Pressure.
In a tissue layer, there is oxygen consumption, irreversible
reaction with oxygen, M, in moles per volume per time, and the solution of
steady state diffusion through a flat layer is:
| P = P0 + ΔP |
x | −
| M |
x (L − x) |
| L | 2℘ |
where P is oxygen (O2) partial pressure, x is distance into the layer
ranging from 0 to L, ΔP is pressure difference across the layer
= PL−P0, and ℘ is O2
permeability. The flux J is:
So, measurements of fluxes in both chambers lead to results for both determinants:
| ℘ = ½L |
J0 + JL |
M = |
J0 − JL |
| P0 − PL
| L |
But there are some preconditions:
– P must be high enough to maintain M at the same value erverywhere;
– no facilitation by myoglobin or can be neglected
– J can be measured - this is not obvious in case of layer bulging.
The second condition can be handled by replacing P by P+PFS
inside the layer and assuming saturation S to be in equilibrium with P.
If M stays maximal up to a location x=d where all oxygen has been consumed,
both pressure P and flux J will be zero there and the solution for P becomes:
which after some math leads to:
J02 =
2℘M(P0 + PFS0)
But these simple solutions are limited to simple model situations. Read more
in the reference (1), also about
how to handle the preconditions both mathematically and experimentally,
and conclusion drawn from graphs.
For the Appendix to this paper contact me throught the Contact page
of the homepage menu.
(1) de Koning J Hoofd LJC Kreuzer F:
Oxygen transport and the function of myoglobin.
Theoretical model and experiments in chicken gizzard smooth muscle.
Pflügers Arch Eur J Physiol 389(3): 211-217. (1981)
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