VPM Technical Discussion

[Robert C. Helling]

On 08 Mar 2014, at 12:01, Gopichand Paturi <gopichandpaturi at gmail.com> wrote:

Gopichand,

> 
> I'm sure we have ambient pressure data during ascent or descent.

Yes, that’s basically given by the depth.

How do you determine the radius r? My guess is that it is the actual unknown in this equation and we have some knowledge of the pressure inside the bubble in terms of how much gas is in the bubble. Is this true? Then, how exactly is the pressure in the bubble determined/the amount of gas? How is that related to the amount of gas in the tissue (the ‘tension’)?

> Next,  As you asked, as far as my knowledge about VPM is concerned, we put a single bubble in each compartment to simulate the actual bubble formation.
> 

OK, then at which size? I though there are is a distribution of bubbles of all sizes.

> Next, Regarding the radius of the bubble,we will have to initialize it at the surface                (this one point I read from Eric Baker's research paper)…

But how is it initialised? What determines the value?

> It is actually initialized this way at the surface.
> Every compartment has it's own pressure(we use this as pressure inside bubble at surface) i.e they are at equilibrium.

I think you are confusing the pressure in the tissue and the pressure in the bubble. Or are they the same somehow?

> 
> Next we use the formula P inside = Pambient + (2*gamma)/r.....where we solve this equation for every compartment to find the initial radius®

Really? At the surface without prior gas loading the pressure in the tissue is the ambient pressure. That would lead to an infinite radius.

> No-bubble Growth Equation:
> 
> So this is all about "Controlling the supersaturated state"
> 
> So here compartmental pressure (called Tissue tension) is critical.
> Let this value be called PTC.
> 
>          So Pressure inside compartment < pressure inside the bubble
> This helps maintain No-growth because whenever Pressure inside compartment goes above Pressure of bubble, diffused gases go inside the bubble, expanding it.
> 
> So to avoid this we control pressure of compartment by the below
> 
> PTC < Pressure inside bubble   (theoritically this is possible to be at Equilibrium)
> 
> ->    PTC < Ambient pressure + (S/r)
> 
> -> PTC-Pa < S/r    (This term PTC-Pa  shows the supersaturation and upper bound on their difference)
> 
> This was the term I was talking about in my previous mail.
> The above equation for No-Growth helps maintain our Compartmental pressures.
> 
> Now THIS is the whole point,
> As you implemented supersaturation using half life times and getting Maximum Compartmental Pressure,
>  I will reverse map this to the M-values that are possible while decompression/ascent. This helps us in formulating the deco table for finding the acceptable ascents with an upperbound based on the pressures that we get from the No-bubble growth equation.
> 

I don’t get this. Could you be more specific? I know of course how to calculate the ambient pressure as a function of time as well as I know how to compute the ‘tension’ in the compartments as a function of time (this is the same as in Buehlmann).

Best
Robert

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Robert C. Helling     Elite Master Course Theoretical and Mathematical Physics  
                      Scientific Coordinator                                   
                      Ludwig Maximilians Universitaet Muenchen, Dept. Physik    
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