Bühlmann decompression algorithm

The Bühlmann decompression algorithm is a mathematical model (algorithm) of the way in which inert gases enter and leave the human body as the ambient pressure changes.^[1] Versions are used to create Bühlmann decompression tables and in personal dive computers to compute no-decompression limits and decompression schedules for dives in real-time. These decompression tables allow divers to plan the depth and duration for dives and the required decompression stops.

The algorithm was 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.^[2][3] 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.^[1] The book was regarded as the most complete public reference on decompression calculations and was used soon after in dive computer algorithms.

The model 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 (without bubble formation).

Principles

Building on the previous work of John Scott Haldane and Robert Workman,^[4][5] and working off funding from Shell Oil Company,^[6] Bühlmann designed studies to establish the longest half-times of nitrogen and helium in human tissues.^[1] These studies were confirmed by the Capshell experiments in the Mediterranean sea in 1966.^[6][7]

Table of ZH-L16A Half-times with “a” and “b” values for nitrogen and helium.^[8]

Compartment	Half-time N2 (minutes)	N2 'a' value	N2 'b' value	Half-time He (minutes)	He 'a' value	He 'b' value
1	4	1.2599	0.5050	1.5	1.7435	0.1911
2	8	1.0000	0.6514	3.0	1.3838	0.4295
3	12.5	0.8618	0.7222	4.7	1.1925	0.5446
4	18.5	0.7562	0.7725	7.0	1.0465	0.6265
5	27	0.6667	0.8125	10.2	0.9226	0.6917
6	38.3	0.5933	0.8434	14.5	0.8211	0.7420
7	54.3	0.5282	0.8693	20.5	0.7309	0.7841
8	77	0.4701	0.8910	29.1	0.6506	0.8195
9	109	0.4187	0.9092	41.1	0.5794	0.8491
10	146	0.3798	0.9222	55.1	0.5256	0.8703
11	187	0.3497	0.9319	70.6	0.4840	0.8860
12	239	0.3223	0.9403	90.2	0.4460	0.8997
13	305	0.2971	0.9477	115.1	0.4112	0.9118
14	390	0.2737	0.9544	147.2	0.3788	0.9226
15	498	0.2523	0.9602	187.9	0.3492	0.9321
16	635	0.2327	0.9653	239.6	0.3220	0.9404

Versions

Several versions of the Bühlmann algorithm have been developed, both by Bühlmann and by later workers. The naming convention used to identify the algorithms is a code starting ZH-L, from Zürich (ZH), limits (L) followed by the number of tissue compartments, and other unique identifiers. For example:

• ZH-L16 or ZH-L16A: The original 16 compartment algorithm.
• ZH-L16B: The 16 compartment algorithm modified for dive table production, using slightly more conservative “a” values, mainly in the middle compartments.^[8]
• ZH-L16C:The 16 compartment algorithm with further modification to the middle and faster “a” values, intended for use in dive computers, where real-time depth and time tracking eliminated the inherent conservatism associated with square profiles.^[8]
• ZHL-8: A version using a reduced number of tissue compartments to reduce the computational load for personal dive computers.
• ZHL-8 ADT: 8-compartment adaptive model used by Uwatec. This model 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 is used in computers which can accurately monitor air consumption and instantaneous rate of air consumption to model work load (exertion) via changes in the rate of gas consumption, which allows plausible modelling of additional decompression obligation based on exertion at depth. It also monitors ambient temperature and selects the choice of risk tissue accordingly. This results in earlier and longer decompression requirements in colder water.^[9][10]
• ZHL-8 ADT MB: A version of the ZHL-8 ADT claimed to suppress microbubble formation.^[9]
• ZHL–8 ADT MB PDIS: Profile-Determined Intermediate Stops.^[11]
• ZHL-8 ADT MB PMG: Predictive Multi-Gas.
• ZHL-12

Tables

Max Hahn first used Bühlmann's algorithm to develop dive tables for the Swiss Underwater Sport Association. In 1987, the SAA Bühlmann System was developed by Bob Cole. This system used the dive tables and a set of rules so that people could dive safely and stay below their no-decompression limit.^[12] The tables are still used today and are very popular; many dive computers still use the ZHL-8 algorithm and many tables are based on the ZHL-16 algorithm or derivatives. These calculations also include considerations for repetitive and altitude diving.^{[1][13][14][15][16][17]}

References

1. Bühlmann, Albert A (1984). Decompression-Decompression Sickness. Berlin New York: Springer-Verlag. ISBN 0-387-13308-9.
2. Bühlmann, Albert A (1982). "[Experimental principles of risk-free decompression following hyperbaric exposure. 20 years of applied decompression research in Zurich]". Schweizerische Medizinische Wochenschrift (in German) 112 (2): 48–59. PMID 7071573.
3. Wendling, J; Nussberger, P; Schenk, B (1999). "Milestones of the deep diving research laboratory Zurich". South Pacific Underwater Medicine Society Journal 29 (2). ISSN 0813-1988. OCLC 16986801. Retrieved 2009-04-02.
4. Boycott, AE; Damant, GCC; Haldane, John Scott (1908). "Prevention of compressed air illness". Journal of Hygiene (Cambridge University Press) 8 (3): 342–443. doi:10.1017/S0022172400003399. PMC 2167126. PMID 20474365. Retrieved 2009-06-12.
5. Workman, Robert D (1957). "Calculation of air saturation decompression tables". Navy Experimental Diving Unit Technical Report. NEDU-RR-11-57. Retrieved 2009-06-12.
6. Völlm, Ernst B; Götte, Georg (1994). "Leading diving researcher dies unexpectedly: Albert A Bühlmann, 1923 - 1994". Pressure, newsletter of the Undersea and Hyperbaric Medical Society 23 (3): 1–3. ISSN 0889-0242.
7. Bühlmann, Albert A; Frei, P; Keller, Hannes (October 1967). "Saturation and desaturation with N2 and He at 4 atm". Journal of Applied Physiology 23 (4): 458–62. PMID 6053671. Retrieved 2009-06-13.
8. Chapman, Paul. "An explanation Professor A A Buhlmann’s ZH-L16 Algorithm" (PDF). Retrieved 12 March 2016.
9. Staff. "Smart microbubble management" (PDF). In Depth. Uwatec. Retrieved 12 March 2016.
10. Marroni, A; Cali Corleo, R; Balestra, C; Longobardi, P; Voellm, E; Pieri, M; Pepoli, R (2000). "Effects of the variation of Ascent Speed and Profile on the production of Circulating Venous Gas Emboli and the Incidence of DCI in Compressed Air Diving. Phase 1. Introduction of extra deep stops in the ascent profile without changing the original ascent rates. DSL Special Project 01/2000" (PDF). Divers Alert Network. Retrieved 12 March 2016.
11. Staff. "Diving with PDIS (Profile-Dependent Intermediate Stop)" (PDF). Dykkercentret website. Frederiksberg: Dykkercentret ApS. Retrieved 5 March 2016.
12. Powell, Mark (2008). Deco for Divers. Southend-on-Sea: Aquapress. p. 18. ISBN 1-905492-07-3.
13. Bühlmann, Albert A (1987). "Decompression after repeated dives". Undersea Biomedical Research 14 (1): 59–66. ISSN 0093-5387. OCLC 2068005. PMID 3810993. Retrieved 2008-04-25.
14. Böni, M; Schibli, R; Nussberger, P; Bühlmann, Albert A (1976). "Diving at diminished atmospheric pressure: air decompression tables for different altitudes". Undersea Biomedical Research 3 (3): 189–204. ISSN 0093-5387. OCLC 2068005. PMID 969023. Retrieved 2008-04-24.
15. Bühlmann, Albert A; Schibli, R; Gehring, H (March 1973). "[Experimental studies on decompression following diving in mountain lakes at reduced air pressure]". Schweizerische Medizinische Wochenschrift (in German) 103 (10): 378–83. PMID 4144210.
16. Bühlmann, Albert A (1989). "[Decompression problems in diving in mountain lakes]". Schweizerische Zeitschrift fur Sportmedizin (in French) 37 (2): 80–3; discussion 99–102. PMID 2799365.
17. Bühlmann, Albert A (1984). "[Decompression during lowered air pressure]". Schweizerische Medizinische Wochenschrift (in German) 114 (26): 942–7. PMID 6087447.

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. Retrieved 2008-04-25.
• 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. 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.