VPMechanics 2

Copyright 1999-2001 Eric Maiken

Tracking the Supersaturation Gradient

This notebook continues the discussion of VPMechanics 1 (VPM1).

The integrals of the converged supersaturation gradients, shown as the last figure in VPM1,  are evaluated

The Integral: ; r(t) >=0 is considered for each ZHL-16 compartment.

While the integral r(t) is fundamental to the VPM,  r(t) is also commonly used to describe the risk of a decompression schedule. r(t) thereby describes the time dependence of the risk of DCI for each compartment. The probability of DCI has been taken by some modelers to be related to a further integration of the risk functions over all compartments and times.
While only the positive portions of the integral are displayed, it's important to note that both the positive and negative regions of Pss(t) contribute to the integral. For no-stop dives, the maximum of each compartment's r(t) corresponds very nearly to the zero-crossing of the compartment's Pss. This can be seen by using the click,Ctrl method for viewing quantitative numerical values from the plots with the mouse's cross-hairs.
An interesting interpretation of the maximum of r(t) is that it predicts a delayed on-set of DCI by predicting maximum risk at a time some-what after completion of the dive.
So, the gradient function's zero-crossings are important to decompression modeling in a number of ways:
- They are used to predict the time of maximum risk (neglecting a small contribution prior to surfacing)
- The zero-crossing of the fastest compartment (4 min here) sets the depth of the deepest possible stop in conventional compartment based decompression modeling

Plots of r(t) for the 8 compartments with regions of r(t)>=0