VPM Background




Copyright 1994-2004 by Eric Maiken


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.


  1. 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.