# VPM Overview

Gopichand Paturi gopichandpaturi at gmail.com
Mon Mar 10 00:41:08 PDT 2014

```Hi Robert,
With lots of effort and understanding that was needed, I am writing this.
It might look to you that I'm rushing, yes , because I have exams starting
from wednesday. But I'm not compromising on my efforts for understanding
VPM.

*This is my brief understanding of the VPM*

*About bubble & it's role: *

So, We will relate decompression sickness to number of bubbles formed,
which is dependent on a threshold radius value called rmin.

This value is significant in determining number of bubbles because all the
nuclei in solution above this value of radius are capable of forming
bubbles on application of pressure.

So, our main aim is to simulate the course of bubble so that we can assess
a safe number of bubbles that are allowed.

This value is found by an integration of f(r) i.e distribution of radii
over dr, from rmin to infinity.

This is how we get the number of bubbles formed.

So as rmin becomes significant in determining number of bubbles, it helps
in indicating the severity of the DCS.

The value of rmin is initialized to 0.8 Micrometer initially, this is a
constant and is same across compartments.

*Course of the bubble: *

Bubble has two phases in VPM,

1) First phase is that bubble is permeable while compressing(which is till
8 ATA pressure), in which the laws are governed by only Laplace equation
which helps in calcualating new radius.

2) Second phase is that bubble is impermeable for the next range of
pressure, here Boyle's law helps in determining the pressure.

Boyle's law and Laplace's equation both give us the value of new radius.

We assume that after sudden compression in permeable phase, radius is same
after compression in impermeable phase. (this is assumed because this
process is usually very slow).

So now the value of rmin changes due to the application of pressure.So
this value is set to a new rmin for that pressure.

This value as stated above is computed using different laws applicable in
different situations.

After saturation pressures are computed using the Laplace equation with
the prior radius taken as the one after permeable compression. (Just prior
and after decompression we assume bubble is permeable, so Laplace eqn
holds, and we compute the pressures also).

By solving some equations that arise, we get the super saturation
pressure and Crushing pressures.

Also there lot of constants involved in these calcualtions.

This supersaturation varies across compartments, so we need to calculate
them individually and take least pressure gradient permissible.

*VPM for diving:*

Now, all these were assumed to be in a situation where only one gas exists.
But usually all the gases we take are mixtures, we will adjust it to suit
our requirements.

*Assumptions: *

1) There is an amount of bubbles N safe, that can be tolerated by diver's
body irrespective all other parameters, whcih is dependent as stated
earlier on rmin.

2)The N actual value can be higher than N safe, as long as total volume of
free gas remains below critical value called V crit.

This is critical Volume hypothesis (a new r new less than r min is assigned)

3) Volume of free gas inflates at a rate proportional to (super saturation
pressure)*(Nactual - Nsafe).

Note: We need not explicitly calculate the number of safe bubbles. It is a
value that can imagined in the form of rmin which provides a quantitative
assessment.

Also, unlike other algos, VPM uses tissue tension value to be sum of
pressures of (inert gases+oxygen+CO2+water vapor) rather than individual
inert gas.

Also there is small enhancement in reformulated VPM.

The new saturation radius value that was assumed to be same in impermeable
phase and permeable phase is modified.

We use an equation involving regeneration time, and calculate he radius
based on the time elapsed if the diver stops at that point.

*CONCLUSION: *

So now we will use the information generated above to form dive tables.

step1: we will have all constants acquired.

step2: As stated above, we will calculate a supersaturated pressure for
every compartment, since half times vary we get different values for
different compartments which varies partial pressures.

step3: we will calcualte with this value a decompression profile, and hence
a decompression time.

step4: Next we need to calculate next super saturated pressure (I have
doubts regarding this, I will put this in my next email)

Although I am not giving math part of it, please assume that I can do
them, because I have all equations and constants with me.

Thanks & Regards,

Gopichand.
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