Thank you, certainly more approachable thru explicit terms.
So this paper/concept begins by assuming the tissue/venous system is subject to "inherent unsaturation," even under a 'steady state' (stated as such; the equations are static)
Eq. 1 is defined based on this assumption (perhaps prematurely?)
P
w = P
B - (P
tisN2 + P
tisO2 + P
tisCO2 + P
tisU + P
H2O) [Eq. 1]
But we know that total tissue gas pressure is the sum of gas partial pressures (Dalton's Law?)
P
B = (P
tisN2 + P
tisO2 + P
tisCO2 + P
tisU + P
H2O) [Eq. 0?]
Eq. 0 already accounts for whatever the P
tisO2 happens to be. No P
w 'oxygen window' term is required to explain that for a low P
tisO2, P
tisN2 will be a higher proportion of total tissue (bubble) gas pressure. P
B will not be "unsaturated"--it will be equilibrated to ambient pressure, which for tissue/veins is actually slightly
above ambient/'barometric' pressure (it's why we bleed..)
So why do we need to explicitly invent a P
w, and why do we think arterial oxygen pressures change this?
Eq. 2 is folded into Eq. 1 to generate Eq. 3, which
removes P
tisN2 and now weirdly implies that P
bubN2 depends on P
AO2, but
not on P
B, the ambient pressure, which was "canceled out" in the operation. I don't think this can be right.
I am not sure this is valid algebra. For one, ambient pressure in the arteries is probably not actually the same term as the ambient pressures in the tissues, veins, or lungs, and perhaps not so simply canceled out.
Eq. 2 (as used) doesn't help the Eq. 3 rationale on pure oxygen either, regardless of depth or ppO2:
P
tisN2 = P
AN2 = P
B - P
AO2 - P
ACO2 - P
H2O [Eq. 2]
P
tisN2 = P
AN2 = 1.6 - 1.6 - ~0 - ~0 = 0 [6 metres / 20 ft]
P
tisN2 = P
AN2 = P
B - P
AO2 - P
ACO2 - P
H2O [Eq. 2]
P
tisN2 = P
AN2 = 1.3 - 1.3 - ~0 - ~0 = 0 [3 metres / 10 ft]
The result in both cases of "P
tisN2 = 0" certainly changes what happens to the algebra used to make Eq. 3.
The relevant part of Eq. 2 is to prevent inspired P
AN2, especially when staying deeper. Not sure I follow or agree with the rest of the maths (Eq. 3 ...)
I don't see how the math actually justifies that maxing out the P
AO2 itself while on oxygen (by staying deeper) magically "vacuums" more nitrogen out of the tissues. But keeping bubbles smaller, or from forming at all makes sense.
Maybe there is a more decompression-relevant treatment of the gas dynamics somewhere... might need to include explicit rate equations, and separate and distinct terms for the pressures of various spaces/compartments.