Bühlmann decompression algorithm

The Bühlmann decompression model is a Haldanian 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 inverse exponential model 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 $P_{tol}$, 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 ($P_{tol}$):

$P_{tol}=(P-a)\cdot b$

The $b$ values calculated do not 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 $a$.

The modified values of $a$ and $b$ are shown in bold in the table below.

Helium (heliox) set of parameters

According to Graham's Law, the speed of diffusion (or effusion) of two gases under the same conditions of temperature and pressure is inversely proportional to the square root of their molar mass (28.0184 g/mol for $N_{2}$ and 4.0026 g/mol for $He$, i.e. ${\sqrt[{2}]{\frac {28.0184}{4.0026}}}=2.645$), which means that $He$ molecules diffuse 2.645 times faster than $N_{2}$ molecules.

Bühlmann took this into account and divided all the tissue compartment half-time for air (nitrogen) by 2.645 to obtain a helium-specific set of parameters with the longest compartment set at ${\frac {635}{2.645}}=240{\text{ min.}}$

The parameters of the M-Values (coefficients a and b) were determined specifically.

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.