RGBM model questions

[lamont]

I'm trying to learn RGBM from BRWs _RGBM in depth_, and I've got some questions about the variables in the model.

specifically:

dV/dt_diffusion = 4 pi DS int[ n r ( Pi - P - 2 gamma / r ) dr ]
dV/dt_Boyle = int [ n ( T / P d/dt ( P V / T ) ) dr ]
dV/dt_excitation = d/dt ( 4 pi int [ n r^2 dr ] )

First of all, are the pressures in all of these equations not ambient pressure, but the ambient pressure minus inherant unsaturation? (ambient pressure in the tissues? what do you call this?) And in the equation for inherant unsaturation as it is given:

nu = f_O2 P - 2.04 ( 1 - f_O2 ) - 5.47

Is the inherant unsaturation there just the unsaturation of ppO2, so you have to take into account ppH2O and ppCO2 in the lungs just like ZHL16B explicitly before this, or is that folded into the given equation so that you can take ambient pressure at depth minus nu?

And, Pi is the "total gas tension" (aka "tissue tension"?) and is going to be coming from exponential loading of dissolved gasses just like in ZHL16B?

 

[Dr Deco]

Hello lamont:

As far as I can tell, the pressures are the gas pressures in the tissues. I do not know where the “inherent unsaturation” fits in the great scheme of things.

The truth is, I have never studied the RGBM model in great depth. It is not applicable to the conditions of decompression that we use at NASA, and we have our own models.

The books are not easy reading, as many have noted. A lot more work would need to go into deciphering all of the material than I am willing to do.

I spent some time trying to find a good answer for your questions and realized that it would require a lot more time than I have. Sorry.

Dr Deco :doctor:

Readers, please note the next class in Decompression Physiology September 10 – 11, 2005 :1book:
http://wrigley.usc.edu/hyperbaric/advdeco.htm

 

[Tavi]

I think Dr Wienke is a member here. You could try to PM him.

User name BRW

 

[lamont]

thanks for giving it some thought....

i think i just need to read a bit more of the background literature so that i absorb more of the 'lingo'... i'm doing it backwards right now and trying to teach myself the concepts from the math...

 

[lamont]

i've been reading through _physiology and medicine of diving_ and some online references and i think i may be able to phrase my questions in terms of just basic issues with the terminology of decompression models.

first, there is going to be Pambient which is just pressure depth measured in ATA (not gauge). and diving on air, the gas in the regulator is:

PN2 = Pamb / 0.79 and PO2 = Pamb / 0.21

then, in the lungs you have H2O and CO2 introduced such that:

PN2 + PO2 + PH2O + PCO2 = Ptot = Pamb

oxygen, however, gets bound to hemoglobin and metabolized so that in tissue in the gas phase PO2 drops so that:

PN2 + PO2 + PH2O + PCO2 = Ptot < Pamb

where Pamb - Ptot = "oxygen window" or "inherant unsaturation". but now we know the gas phase pressures of the different gases in our tissue compartment and we know the total gas phase pressure.

the tension is the dissolved 'pressure' in the tissues and is 'p' instead of 'P'. and we apply:

d pN2 / dt = ( PN2 - pN2 ) / tau

and that gets us our tissue tension compartment loading.

now, there is the dissolved phase tension (measured in pressure units) of the components and the total gas, the free phase pressure of the components and the total gas, and there is still the ambient pressure. in general the total tissue tension, total free phase pressure and ambient pressure will not be the same.

my confusion was coming over if the P in most of the RGBM equations was the free phase pressure or the ambient pressure. since the equations are essentially just things like Boyle's law i believe the pressure must simply be ambient pressure, since via hydrostatic equilibrium that is the pressure that the compartment is under -- the blood or tissues will push on the walls of a bubble with that much force. for gas diffusion the tissue tension or free-phase pressure would be important (respectively for free-dissolved and free-free diffusion) but for boyle's law applied to a bubble it should just be Pambient...

do i have the basic concepts there mostly right?

 

[Dr Deco]

Hello lamont:

RGBM

That is about it. Remember that there is gaseous nitrogen (free-gas phase) and dissolved nitrogen (dissolved-gas phase). There is not a “free-dissolved” and a “free-free” phase.

All of the terms are the same as any other model. The RGBM adds a free-gas component from the start, in the form of micronuclei, and tracks this during the ascent.

Others

While the RGBM is one algorithm that is used to produce dive tables, it is of interest to note that there are other models. They are referenced below.

Dr Deco :doctor:

Readers, please note the next class in Decompression Physiology September 10 – 11, 2005 :1book:
http://wrigley.usc.edu/hyperbaric/advdeco.htm

References :book3:

Srinivasan RS, Gerth WA, Powell MR. Mathematical model of diffusion-limited evolution of multiple gas bubbles in tissue. Ann Biomed Eng. 2003 Apr;31(4):471-81.

Srinivasan RS, Gerth WA, Powell MR. Mathematical model of diffusion-limited gas bubble dynamics in unstirred tissue with finite volume. Ann Biomed Eng. 2002 Feb;30(2):232-46.

Foster PP, Feiveson AH, Boriek AM. Predicting time to decompression illness during exercise at altitude, based on formation and growth of bubbles. Am J Physiol Regul Integr Comp Physiol. 2000 Dec;279(6):R2317-28.

Srinivasan RS, Gerth WA, Powell MR. A mathematical model of diffusion-limited gas bubble dynamics in tissue with varying diffusion region thickness. Respir Physiol. 2000 Oct;123(1-2):153-64.

Nikolaev VP. Effects of heterogeneous structure and diffusion permeability of body tissues on decompression gas bubble dynamics. Aviat Space Environ Med. 2000 Jul;71(7):723-9.

Srinivasan RS, Gerth WA, Powell MR. Mathematical models of diffusion-limited gas bubble dynamics in tissue.J Appl Physiol. 1999 Feb;86(2):732-41.

Gernhardt, M.L. Development and Evaluation of a Decompression Stress Index Based on Tissue Bubble Dynamics. Ph.D. Dissertation in Bioengineering. Philadelphia, PA: University of Pennsylvania, 1991.

 

[lamont]

Hello lamont:

RGBM

That is about it. Remember that there is gaseous nitrogen (free-gas phase) and dissolved nitrogen (dissolved-gas phase). There is not a “free-dissolved” and a “free-free” phase.

The "free-dissolved" and "free-free" nomenclature in RGBM is different kinds of diffusion from-to the different phases. I think I have a good picture of what BRW is talking about with "free-dissolved diffusion" which is gas in a bubble coming out of the bubble, shrinking it, and going into dissolved tissues because the tissue tension of the dissolved phase is lower than the pressure of the gas in the bubble (or, presumably, vice-versa if the tensions are higher than the pressure in the bubble). I don't know if I fully understand what 'free-free diffusion" refers to because that implies that there is a free gas phase in the tissue other than the bubble for the gas in the buble to diffuse into -- but BRW uses that term.

 

[Dr Deco]

Hello lamont:

???

I see what you mean. On page nine, last paragraph, of the book RGBM In Depth , he does use that term. I could not find an explanation either.

Dr Deco :doctor:

Readers, please note the next class in Decompression Physiology September 10 – 11, 2005 :1book:
http://wrigley.usc.edu/hyperbaric/advdeco.htm