The Varying Permeability Model

The Varying Permeability Model (VPM) was developed to model laboratory
observations of bubble formation and growth in both inanimate (never been alive)
and in vivo (soon dead) systems exposed to pressure. In 1986, this model
was applied by researchers at the University of Hawaii to calculate Diving
Decompression Tables (Reference 1). Although the original VPM is considered
dated by specialists in hyperbaric medicine, the time lag between the
formulation and public release of the latest decompression methods has left many
divers following ascent schedules that are justified by obsolete Victorian era
physical models. Further compounding the problem is the widespread use of
commercial decompression software with excessive arbitrary parameters hiding
behind siren-song front-ends that allow programmers to dish out crucial
physiological advice. Finally, the mathematical and physical bases of the bubble
models have kept them inaccessible to all without degrees in physics or math and so, apart
from reports filtering back from the front lines, few have understood, seen or
used this stuff. So, caveat emptor --and beware too!

The VPM presumes that microscopic voids, cavities, nuclei exist in water, and
tissues that contain water before the start of a dive. Any nuclei larger than a
specific "critical" size, which is related to the maximum dive
depth (exposure pressure), will grow upon decompression. The VPM aims to
minimize the total volume of these growing bubbles by keeping the external
pressure large, and the inspired inert gas partial pressures low during
decompression.

The appendix to Reference 1 outlines simplifications to the full VPM, and therefore
models a restricted set of dive profiles. These restrictions are detailed in the
NOTES sections of the pages describing the various versions of the open source VPM program.
The simplification to the full VPM comes from assumptions that allow the nGt
integral, which tracks the volume of free gas, to be evaluated analytically
rather than numerically. This causes the program to be conservative from both supersaturation
and bubble-mechanical points of view because G and n are held constant during
the dive and each deco stage. Note that many of the
statistical decompression models
also associate the Gt product with the "risk" of a dive.

It is important to note that the total decompression times generated by the
simplified VPM were *FORCED* to be similar to the US NAVY
Standard/Exceptional Air deco times in ref 1. However, much of the decompression
time is deeper than the USN depths. Presumably, a diver would evolve fewer
bubbles using a VPM schedule than on the Navy table. This is not very stringent
once you consider the risky (O2 & bends) nature of the old USN exceptional
exposure tables. Yount and Hoffman might better have forced the times to look
like Buhlmann's for conservatism. The parameters in the open source code produce
Bühlmann-like
no-stop times, and total decompression times between the old USN tables and the
Bühlmann tables.

### Reference

- The appendix of: D.E. Yount, D.C. Hoffman,
*On the Use of a Bubble
Formation Model to Calculate Diving Tables*. Aviation, Space, and
Environmental Medicine, February, 1986.