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  • AutorenbildMichael Mutter

The little decompression theory I - Supersaturation tolerance

Every diving course teaches the saturation and desaturation of tissues with inert gases. Unfortunately, the concept of supersaturation tolerance is never discussed. However, an understanding of modern decompression theory is not possible without it. Trigger warning: This text contains college math.

Foto: Karin Aggeler

Depending on its blood flow, tissue at depth primarily absorb non-metabolizable gases, so-called inert gases such as nitrogen or, in the case of technical diving, helium, from the breathing gas more or less quickly or releases them again via the lungs when surfacing. This saturation or desaturation behavior can be easily calculated from the ambient pressure and the partial pressure of the breathed gas, taking into account a saturation half-life specific to each tissue. If ascending too quickly, at some point a limit is exceeded where inert gas bubble form in the tissue and trigger decompression sickness. This "some point" is called supersaturation tolerance and can be predicted quite easily.

The supersaturation tolerance of a tissue determines whether bubbles occur.


The desaturation of a tissue lags behind the drop in ambient pressure. This is why the ambient pressure falls below the inert gas pressure in a tissue when it surfacing. An overpressure develops in the tissue compared to the ambient pressure. This is called supersaturation. This always happens during ascent, but not in all tissues at the same time and to the same extent.

Figure 1 (Manual saturation © Michael Mutter). Saturation and desaturation of a tissue (gray) during a dive with air at 40 m. During ascent, the ambient pressure (black) falls below the N2 partial pressure in the tissue (gray). This results in an overpressure in the tissue compared to the ambient pressure. The tissue is supersaturated.


As early as the end of the 19th century, Paul Bert was able to prove in animal experiments that caisson workers died from gas bubbles after a rapid ascent from depths. John Scott Haldane, the father of modern decompression research, found that halving the ambient pressure in mammals after overpressure exposure (including experiments on himself and his 13-year-old son!) caused no problems.

It can be concluded that supersaturation is tolerated to a certain degree. This supersaturation tolerance basically means that the ambient pressure can be relieved to a certain extent without the formation of bubbles. If this tolerance is exceeded, bubbles form in the tissue.

An example will illustrate this: after a dive to 40 m (5 bar) with compressed air, a tissue is saturated, its nitrogen partial pressure is 3.9 bar. The diver now ascends to 20 m within a short time. In the meantime, the partial pressure in the tissue hardly decreases, but the ambient pressure does, dropping to 3 bar. Although the ambient pressure is lower than the partial pressure of nitrogen in the tissue, no bubbles form. The supersaturation tolerance was not exceeded.

The supersaturation tolerance can be easily predicted for each depth.


It thus follows that the maximum tolerated nitrogen pressure in the fabric corresponds to the sum of the prevailing ambient pressure plus a pressure surcharge.

This relationship can be easily expressed using the formula


Ptol = b*Pamb + a


where Ptol corresponds to the maximum tolerated inert gas pressure (e.g. nitrogen) in the tissue at the ambient pressure Pamb.

In other words, since the maximum tolerated inert gas pressure (Ptol) must be greater than the ambient pressure (Pamb) (otherwise we would not be able to surface without bubble formation), a value must be added to Pamb (a). This relationship is nothing else but a linear function (where the coefficient b is introduced to indicate the slope of the straight line).

Bühlmann, the Zurich decompression physiologist and diving physician, together with the diving pioneer Keller, adopted the observation made by Haldane (and Workman) that a linear relationship exists between supersaturation tolerance and ambient pressure, and formulated this relationship in a slightly modified form (A.A. Bühlmann. Dekompression - Dekompressionskrankheit. Springer 1983):

Don't let this confuse you. It is mathematically the same. Bühlmann and Keller have defined this in their model with specific coefficients for 16 different tissues (Modell ZHL16B):

The model exists in several variants under the abbreviations ZH-L 16 A, B and C, where ZH stands for Zurich, L for limits, 16 for the 16 tissue compartments and the letters for the adjustment of the coefficients a and b for theoretical considerations (A), the calculation of dive tables (B) and for decompression computers (C). The latter is widely used today in dive computers (ZH-L 16 C). The model can be used to calculate not only the saturation and desaturation of the tissues during a dive, but also the corresponding supersaturation tolerances.

A decompression model always includes 2 parts: the saturation kinetics and the supersaturation tolerance.

In this way, it is possible to predict whether you are still safe at a given inert gas pressure (e.g. nitrogen) in the tissue and a known diving depth. If the supersaturation is less than the supersaturation tolerance value, decompression sickness will not occur. Graphically, this looks like this:

Figure 2 (Manual saturation © Michael Mutter). Green: supersaturation tolerance. As long as the supersaturation does not exceed this, no decompression sickness occurs.

In the next figure, the results of this function are plotted for 2 tissues with different half-lives.

Figure 3 (Manual saturation © Michael Mutter). Max. tolerated inert gas pressures as a function of ambient pressure for tissues 1 and 16. Black vertical line = surface = 1 bar.

2 points stand out:

  1. The "faster" tissue (halftime 4 min., blue line) has the higher supersaturation tolerance. Its tolerated inert gas pressure at the surface (ambient pressure 1 bar) is 3.2 bar. For the "slower" (halftime 635 min.) tissue, the tolerated ambient pressure is 1.3 bar and is therefore only just above the ambient pressure at the surface.

  2. The supersaturation tolerance increases with increasing ambient pressure. For example, at 6 bar ambient pressure the difference to the tolerated inert gas pressure for compartment 1 (blue line) is 7.1 bar (6 + 7.1 = 13.1), but at 11 bar ambient pressure it is 12 bar (11 + 12 = 23).

From this, 2 rules can be derived:

1 The "faster" the tissue, the greater its supersaturation tolerance.
2. The greater the diving depth, the higher the supersaturation tolerance.


(Readers with mathematical flair will derive rules 1 and 2 directly from the table using the coefficients, as coefficient b increases steadily from the fastest to the slowest compartment and is in the denominator, so the gradient of the straight line increases from the fastest to the slowest compartment and coefficient a, on the other hand, decreases steadily).


Does this make sense and is it plausible? - You bet! The tolerated inert gas pressure must necessarily be higher than the ambient pressure. If this were not the case, we would not be able to ascend quickly to high altitudes without suffering decompression syndrome. Nature has even given us so much reserve that we can take the train to the Jungfraujoch without forming bubbles; something that evolution certainly did not intend. Nor did nature intend for airplanes without pressurized cabins to ascend to ever greater heights during the Second World War, something the pilots had to learn the hard way. In fact, decompression syndromes have been known in aviation ever since. Here too, the problem lies in the rapid drop in ambient pressure, similar to diving, and is the reason why pilots of very high-flying aircraft wear pressure suits. The same applies to astronauts. During a spacewalk, the ambient pressure is zero. This means that the astronaut's tissue is oversaturated in any case. By maintaining a minimum pressure, the spacesuit prevents the supersaturation tolerance from being exceeded. The following video demonstrates this problem during pilot training in the pressurized chamber.

Sudden pressure drop U2 pilot. Source: youtube

The next figure shows the supersaturation tolerance for compartments 1 and 16 for an air pressure of 670 hPa (=0.67 bar) on the Jungfraujoch (measured on 19.6.22). The brain (compartment 1) has a very high tolerance. The inert gas pressure on the Jungfraujoch should even be 2.6 bar without bubbles forming. Even in the slowest compartment, bubble formation is not to be expected if the visitor has previously spent a few days in Interlaken (air pressure 1008 hPa = 1.0 bar: Inert gas pressure in the tissue (1.0 bar - 0.063 bar) x 0.79 = 0.74 bar) and has not just come from a deep dive in Lake Thun...

Figure 4 (Manual saturation © Michael Mutter): Ambient pressure and tolerated inert gas pressure (2.6 bar comp. 1 and 0.9 bar comp. 16) on the Jungfraujoch at 670 hPa air pressure (=0.67 bar).

The vital organs have the highest supersaturation tolerance.

The fact that the "fastest" tissues have the greatest tolerance makes a lot of sense from a biological point of view, as they represent the vital organs. Nature has therefore endowed them with the greatest reserve.

This shows that knowledge of supersaturation tolerance is essential for understanding decompression physiology. I will explain what to do with it in diving practice in the next article.

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