Bühlmann decompression algorithm

The Bühlmann desaturation set of parameters is a pure Haldanian model (using Haldane's or Schreiner formula and M-Values) which models the way inert gases enter and leave the human body as the ambient pressure changes. Versions are used to create decompression tables and in personal dive computers to compute no-decompression limits and decompression schedules for dives in real-time, allowing divers to plan the depth and duration for dives and the required decompression stops.

The model (Haldane, 1908) assumes perfusion limited gas exchange and multiple parallel tissue compartments and uses an exponential formula for in-gassing and out-gassing, both of which are assumed to occur in the dissolved phase.

Multiple sets of parameters were developed by Swiss physician Dr. Albert A. Bühlmann, who did research into decompression theory at the Laboratory of Hyperbaric Physiology at the University Hospital in Zürich, Switzerland. The results of Bühlmann's research that began in 1959 were published in a 1983 German book whose English translation was entitled Decompression-Decompression Sickness. The book was regarded as the most complete public reference on decompression calculations and was used soon after in dive computer algorithms.

Principles

Building on the previous work of John Scott Haldane (The Haldane model, Royal Navy, 1908) and Robert Workman (M-Values, US-Navy, 1965) and working off funding from Shell Oil Company, Bühlmann designed studies to establish the longest half-times of nitrogen and helium in human tissues. These studies were confirmed by the Capshell experiments in the Mediterranean Sea in 1966.

The basic idea (Haldane, 1908) is to represent the human body by multiple tissues (compartments) of different saturation half-times and to calculate the partial pressure $P$ of the inert gases in each of the $n$ compartments (Haldane's equation):

$P=P_{0}+(P_{gas}-P_{0})\cdot (1-2^{-{\frac {t_{exp}}{t_{1/2}}}})$

with the initial partial pressure $P_{0}$, the partial pressure in the breathing gas $P_{gas}$ (minus the vapour pressure of water in the lung of about 60 mbar), the time of exposure $t_{exp}$ and the compartment-specific saturation half-time $t_{1/2}$.

When the gas pressure drops, the compartments start to off-gas.

Nitrogen (air, nitrox) set of parameters

To calculate the maximum tolerable pressure $P_{t.tol}i.g.$, the constants $a$ and $b$, which are derived from the saturation half-time as follows (ZH-L 16 A):

$a={\frac {2\,{\text{atm}}}{\sqrt[{3}]{t_{1/2}}}}$

$b=1.005-{\frac {1}{\sqrt[{2}]{t_{1/2}}}}$

are used to calculate M-Value ($P_{t.tol}i.g.$):

$P_{t.tol}i.g.={\frac {P_{amb.}}{b}}+a$ (Source : A.A. Bühlmann et al., Tauchmedizin, Springer, 2002, p. 117)

The $b$ values calculated do not precisely correspond to those used by Bühlmann for tissue compartments 4 (0.7825 instead of 0.7725) and 5 (0.8126 instead of 0.8125).

Versions B and C have manually modified the coefficient $a$.

Versions

Several versions of the Bühlmann set of parameters have been developed, both by Bühlmann and by later workers. The naming convention used to identify the set of parameters is a code starting ZH-L, from Zürich (ZH), Linear (L) followed by the number of different (a,b) couples (ZH-L 12 and ZH-L 16)) or the number of tissue compartments (ZH-L 6, ZH-L 8), and other unique identifiers. For example:

ZH-L 12 (1983)

• ZH-L 12: The set of parameters published in 1983 with "Twelve Pairs of Coefficients for Sixteen Half-Value Times"

ZH-L 16 (1986)

• ZH-L 16 or ZH-L 16 A (air, nitrox): The experimental set of parameters published in 1986.
• ZH-L 16 B (air, nitrox): The set of parameters modified for printed dive table production, using slightly more conservative “a” values for tissue compartments #6, 7, 8 and 13.
• ZH-L 16 C (air, nitrox): The set of parameters with more conservative “a” values for tissue compartments #5 to 15. For use in dive computers.
• ZH-L 16 (helium): The set of parameters for use with helium.
• ZH-L 16 ADT MB: set of parameters and specific algorithm used by Uwatec for their trimix-enabled computers. Modified in the middle compartments from the original ZHL-C, is adaptive to diver workload and includes Profile-Determined Intermediate Stops. Profile modification is by means of "MB Levels", personal option conservatism settings, which are not defined in the manual.

ZH-L 6 (1988)

• ZH-L 6 is an adaptation (Albert Bühlmann, Ernst B.Völlm and Markus Mock) of the ZH-L16 set of parameters, implemented in Aladin Pro computers (Uwatec, Beuchat), with 6 tissue compartments (half-time : 6 mn / 14 mn / 34 mn / 64 mn / 124 mn / 320 mn).

ZH-L 8 ADT (1992)

• ZH-L 8 ADT: A new approach with variable half-times and supersaturation tolerance depending on risk factors. The set of parameters and the algorithm are not public (Uwatec property, implemented in Aladin Air-X in 1992 and presented at BOOT in 1994). This algorithm may reduce the no-stop limit or require the diver to complete a compensatory decompression stop after an ascent rate violation, high work level during the dive, or low water temperature. This algorithm may also take into account the specific nature of repetitive dives.

• ZH-L 8 ADT MB: A version of the ZHL-8 ADT claimed to suppress MicroBubble formation.
• ZH-L 8 ADT MB PDIS: Profile-Determined Intermediate Stops.
• ZH-L 8 ADT MB PMG: Predictive Multi-Gas.

Ascent rates

Ascent rate is intrinsically a variable, and may be selected by the programmer or user for table generation or simulations, and measured as real-time input in dive computer applications.

The rate of ascent to the first stop is limited to 3 bar per minute for compartments 1 to 5, 2 bar per minute for compartments 6 and 7, and 1 bar per minute for compartments 8 to 16. Chamber decompression may be continuous, or if stops are preferred they may be done at intervals of 1 or 3 m.

Further reading

• Keller, Hannes; Bühlmann, Albert A (November 1965). "Deep diving and short decompression by breathing mixed gases". Journal of Applied Physiology. 20 (6): 1267–70. doi:10.1152/jappl.1965.20.6.1267.
• Bühlmann, Albert A (1992). Tauchmedizin: Barotrauma Gasembolie Dekompression Dekompressionskrankheit (in German). Berlin: Springer-Verlag. ISBN 3-540-55581-1.
• Bühlmann, Albert A (1995). Tauchmedizin (in German). Berlin: Springer-Verlag. ISBN 3-540-55581-1.

External links

Many articles on the Bühlmann tables are available on the web.

• Chapman, Paul (November 1999). "An Explanation of Professor A.A. Buehlmann's ZH-L16 Algorithm". New Jersey Scuba Diver. Archived from the original on 2010-02-15. Retrieved 20 January 2010. – Detailed background and worked examples
• Decompression Theory: Robert Workman and Prof A Bühlmann. An overview of the history of Bühlmann tables
• Stuart Morrison: DIY Decompression (2000). Works through the steps involved in using Bühlmann's ZH-L16 algorithm to write a decompression program.