The supersaturation tolerance was explained in the previous article. To recap: It represents the limit at which bubbles form in a tissue that is supersaturated with inert gas (nitrogen or helium) compared to its surroundings, resulting in decompression sickness. It can be easily calculated using a linear function depending on the ambient pressure. Bühlmann, the Zurich diving researcher, formulated this relationship as follows:
where Ptol corresponds to the maximum tolerated inert gas pressure (e.g. nitrogen) in the tissue at the ambient pressure Pamb and the coefficients a and b are specifically assigned to a tissue.
The next figure illustrates the relationship in practical terms for diving: After a dive with compressed air to 40 m (5 bar ambient pressure), the inert gas pressure in a tissue (here as an example compartment 7 of the Buhlmann-Model) would be 2.43 bar. Bubbles would only form when the ambient pressure falls below 1.65 bar. In practical terms, this means that it is possible to ascend to a depth of 6.5 m (corresponding to 1.65 bar).
It is even easier if the above equation is solved according to Pamb. Then you get
In this way, the value from the figure, which was determined graphically there, can be calculated directly, whereby Pamb.tol corresponds to the tolerated ambient pressure for a specific inert gas pressure (p) in the tissue of a compartment.
Because the inert gas pressure (p) in the tissue is known for each compartment during a dive (by calculation from the saturation equation), this formula can be used at any time to determine the depth to which the respective compartment may ascend without bubble formation occurring.
For our example, the following results for compartment 7
(2.4300 bar - 0.5282 bar) x 0.8693 = 1.6532 bar, which corresponds to a depth of 6.5 m (as determined graphically).
The practical relevance is obvious: dive computers calculate this value continuously not only for one, but for all tissues of a model, whereby the ambient pressure is provided by the pressure sensor and the corresponding coefficients are taken from the associated decompression model. In this way, they inform the diver whether he can ascend directly or must use decompression stops.
It is to Bühlmann's great credit that, in addition to describing the saturation kinetics, he not only succeeded in determining the supersaturation tolerance of the tissues, but also published the complete model developed by him and Keller and made it fully available to the public (A.A. Bühlmann. Dekompression - Dekompressionskrankheit. Springer 1983), in contrast to other models (such as the RGBM - Reduced Gradient Bubble Model), which are proprietary and have never been published in full. It is still widely used today in the latest generation of dive computers (model ZH-L 16 C).
Since then, however, there have been no real innovations in this area. Although other models such as RGBM and VPM have been developed for modern dive computers, none of them outperform the Bühlmann model. Manufacturers who use the Bühlmann model in their dive computers therefore benefit from research work that is over 40 years old without ever having invested in developing or updating it. The princely margins are generously passed on to consumers, who are prepared to pay excessive prices for them.
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