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== History of decompression research and development ==
== History of decompression research and development ==

The first recorded experimental work related to decompression was conducted by [[Robert Boyle]], who subjected experimental animals to reduced ambient pressure by use of a primitive vacuum pump. In the earlies experiments the subjects died from asphyxiation, but in later experiments signs of what was later to become known as decompression sickness were observed.
Later, when technological advances allowed the use of pressurisation of mines and caissons to exclude water ingress, miners were observed to present symptoms of what would become known as caisson disease, the bends, and decmpression sickness.

Once it was recognised that the symptoms were caused by gas bubbles, and that recompression could relieve the symptoms, further work showed that it was possible to avoid symptoms by slow decompression, and subsequently various theoretical models have been derived to predict safe decompression profiles and treatment of decompression sickness.

=== Timeline ===
[[File:An Experiment on a Bird in an Air Pump by Joseph Wright of Derby, 1768.jpg|thumb|This painting, ''[[An Experiment on a Bird in the Air Pump]]'' by [[Joseph Wright of Derby]], 1768, depicts an experiment performed by [[Robert Boyle]] in 1660.]]
* 1660 – [[Sir Robert Boyle]] conducted an experiment on a bird in an air pump. This predates actual intentional investigations into decompression, but the experiment was effectively a rapid decompression and caused the death of the bird by asphyxiation.
* 1670 – [[Sir Robert Boyle]] performed an experiment with a [[Viperidae|viper]] in a [[vacuum]]. A bubble was observed in its eye and it displayed signs of extreme discomfort. This was the first recorded description of decompression sickness.<ref name="acott">{{cite journal |last=Acott |first=C. |title=A brief history of diving and decompression illness |journal=South Pacific Underwater Medicine Society Journal |volume=29 |issue=2 |year=1999 |issn=0813-1988 |oclc=16986801 |url=http://archive.rubicon-foundation.org/6004 |accessdate=2012-01-10 |ref=harv }}</ref>
* 1841 – [[Jacques Triger]] documented the first cases of decompression sickness in humans when two miners involved in pressurised [[Caisson (engineering)|caisson]] work developed symptoms.<ref name="acott" />
* 1847 – The effectiveness of recompression for treatment of DCS in caisson workers was described by Pol and Watelle<ref name="acott" /><ref name="Hill1912" />
* 1857 – Hoppe-Seyler repeated Boyle's experiments and suggested that sudden death in compressed air workers was caused by bubble formation, and recommended recompression therapy.<ref name="Huggins 1992 1-8">{{harvnb|Huggins|1992|loc=chpt. 1 page 8}}</ref>
* 1868 – [[Alfred Le Roy de Méricourt]] – Decompression sickness described as a sponge divers occupational illness<ref name="Hill1912" />
* 1873 – Dr. Andrew Smith first used the terms "caisson disease" and "compressed air illness", describing 110 cases of decompression sickness as the physician in charge during construction of the [[Brooklyn Bridge]].<ref name="Huggins 1992 1-8" /><ref name="Eads">{{cite journal |last=Butler |first=WP |title=Caisson disease during the construction of the Eads and Brooklyn Bridges: A review |journal=Undersea and Hyperbaric Medicine |volume=31 |issue=4 |pages=445–59 |year=2004 |pmid=15686275 |url=http://archive.rubicon-foundation.org/4028 |accessdate=2012-01-10 |ref=harv}}</ref> The nickname "the bends" was used after workers emerging from pressurized construction on the Brooklyn Bridge adopted a posture similar to fashionable ladies of the period "the Grecian Bend".<ref name="acott" />
* 1878 – [[Paul Bert]] determined that decompression sickness is caused by nitrogen gas bubbles which were released from tissues and blood during or after decompression, and showed the advantages of breathing oxygen after developing decompression sickness.<ref name="Bert">{{cite journal |last=Bert |first=P. |title=Barometric Pressure: researches in experimental physiology |journal=Translated by: Hitchcock MA and Hitchcock FA. College Book Company; 1943 |date= originally published 1878 |ref=harv }}</ref>
* 1897 – N. Zuntz proposed a perfusion based tissue model.<ref>Zuntz, N. (1897); ''Zur Pathogenese und Therapie der durch rasche Luftdruck-änderungen erzeugten Krankheiten'', Fortschr, d. Med. 15, 532–639</ref>
* 1906 – V. Schrotter suggested a uniform decompression of 20 minutes per atmosphere. J.S. Haldane was commissioned by the British Admiralty to study decompression sickness.<ref name="Huggins 1992 1-8" />
* 1908 – [[John Scott Haldane]] – the first recognised decompression table was prepared for the British Admiralty.<ref name="Haldane1908">{{cite journal |last1=Boycott |first1=AE |last2=Damant |first2=GCC |last3=Haldane |first3=John Scott |title=Prevention of compressed air illness |journal=Journal of Hygiene |volume=8 |pages= 342–443 |year=1908 |url=http://archive.rubicon-foundation.org/7489 |doi=10.1017/S0022172400003399 |pmid=20474365 |issue=3 |pmc=2167126 |accessdate=30 May 2010 |ref=harv}}</ref> This table was based on experiments performed on goats using an end point of symptomatic DCS.<ref name="Boycott">{{cite journal |last=Boycott |first=A. E. |coauthors=G. C. C. Damant, J. S. Haldane. |title=The Prevention of Compressed-air Illness |journal=J. Hygiene |volume=8 |pages=342–443 |year=1908 |url=http://archive.rubicon-foundation.org/7489 |accessdate=2008-08-06 |doi=10.1017/S0022172400003399 |pmid=20474365 |pmc=2167126 |issue=3 |ref=harv}}</ref><ref name="acott" />
* 1912 – Chief Gunner George D. Stillson of the [[United States Navy]] created a program to test and refine Haldane's tables.<ref>{{cite journal |author=Stillson, GD |title=Report in Deep Diving Tests |journal=US Bureau of Construction and Repair, Navy Department. Technical Report |volume= |year=1915 |url=http://archive.rubicon-foundation.org/6527 |accessdate=2008-08-06 |ref=harv }}</ref> This program ultimately led to the first publication of the [[United States Navy Diving Manual]] and the establishment of a Navy Diving School in Newport, Rhode Island. Diver training programs were later cut at the end of [[World War I]].
* 1912 – [[Leonard Erskine Hill]] – continuous uniform decompression<ref name="acott" /><ref name="Hill1912">{{cite book |author=Hill, L |publisher=London E. Arnold |year=1912 |title=Caisson sickness, and the physiology of work in compressed air |url=http://books.google.com/?id=FTC0AAAAIAAJ&dq=Leonard+Erskine+Hill&printsec=frontcover |accessdate=2011-10-31 }}</ref>
* 1927 – Naval School, Diving and Salvage was re-established at the Washington Navy Yard. At this time the United States moved their [[United States Navy Experimental Diving Unit|Navy Experimental Diving Unit]] (NEDU) to the same naval yard. In the following years, the Experimental Diving Unit developed the US Navy Air Decompression Tables which became the accepted world standard for diving with compressed air.<ref>{{cite web |url=http://www.history.navy.mil/faqs/faq100-1.htm |title=Diving in the U.S. Navy: A Brief History |author=US Navy |accessdate=2008-08-06 }}</ref>
* 1930's – Hawkins, Schilling and Hansen conduct extensive experimental dives to determine allowable supersturation ratios for different tissue compartments for Haldanean model<ref name="Huggins 1992 3-2">{{harvnb|Huggins|1992|loc=chpt. 3 page 2}}</ref>
* 1935 – [[Albert R. Behnke]] ''et al.'' experimented with oxygen for recompression therapy.<ref name="acott" />
* 1937 – US Navy 1937 tables published (Yarborough)<ref name="Huggins 1992 3-2" />
* 1941 – Altitude DCS is treated with hyperbaric oxygen for the first time.<ref name="pmid889546">{{cite journal |author=Davis Jefferson C, Sheffield Paul J, Schuknecht L, Heimbach RD, Dunn JM, Douglas G, Anderson GK |title=Altitude decompression sickness: hyperbaric therapy results in 145 cases |journal=Aviation, Space, and Environmental Medicine |volume=48 |issue=8 |pages=722–30 |year=1977 |month=August |pmid=889546 |ref=harv }}</ref>
* 1956 – US Navy Decompression Tables (1956) published
* 1960 – FC Golding ''et al.'' split the classification of DCS into Type 1 and 2.<ref name="pmid13850667">{{cite journal |last1=Golding |first1=F Campbell |last2=Griffiths |first2=P |last3=Hempleman |first3=HV |last4=Paton |first4=WDM |last5=Walder |first5=DN |title=Decompression sickness during construction of the Dartford Tunnel |journal=British Journal of Industrial Medicine |volume=17 |issue=3 |pages=167–80 |year=1960 |month=July |pmid=13850667 |pmc=1038052 |ref=harv}}</ref>
* 1965 – LeMessurier and Hills paper on ''A thermodynamic approach arising from a study on Torres Strait diving techniques'' which suggests that decompression by conventional models results in bubble formation which is then eliminated by re-dissolving at the decompression stops, which is slower than elimination while still in solution, thus indicating the importance of minimising bubble phase for efficient gas elimination.<ref name="LeMessurier and Hills" /><ref name="RRR6176">{{cite journal |author=Hills, BA |title=A fundamental approach to the prevention of decompression sickness |journal=[[South Pacific Underwater Medicine Society]] Journal |year=1978 |volume=8 |issue=2 |url=http://archive.rubicon-foundation.org/6176 |accessdate=2012-01-10 |ref=harv}}</ref>
* 1965 – French Navy GERS (Groupe d'Etudes et Recherches Sous-marines) 1965 table
* 1965 – Goodman and Workman – Introduction of recompression tables utilizing oxygen to accelerate elimination of inert gas<ref name="How">How, J., West, D. and Edmonds, C. (1976); ''Decompression sickness and diving'', Singapore Medical Journal, Vol. 17, No. 2, June 1976.</ref><ref name="RRR3342">{{cite journal |author=Goodman, MW; Workman, RD |title=Minimal-recompression, oxygen-breathing approach to treatment of decompression sickness in divers and aviators |journal=[[United States Navy Experimental Diving Unit]] Technical Report |volume=NEDU-RR-5-65 |year=1965 |url=http://archive.rubicon-foundation.org/3342 |accessdate=2012-01-10 |ref=harv}}</ref>
* 1972 – Royal Navy Physiological Laboratory (RNPL) tables based on Hempleman's tissue slab diffusion model.<ref name="Huggins 1992 4-3">{{harvnb|Huggins|1992|loc=chpt. 4 page 3}}</ref>
* 1973 – Isobaric counterdiffusion first described by Graves, Idicula, Lambertsen, and Quinn in subjects who breathed one inert gas mixture while being surrounded by another.<ref>Graves, DJ; Idicula, J; Lambertsen, Christian J; Quinn, JA (February 1973). "Bubble formation in physical and biological systems: a manifestation of counterdiffusion in composite media". ''Science'' 179 (4073): 582–584. {{doi|10.1126/science.179.4073.582}}. PMID 4686464. http://www.sciencemag.org/cgi/pmidlookup?view=long&pmid=4686464. Retrieved 10 January 2010.</ref><ref>Graves, DJ; Idicula, J; Lambertsen, Christian J; Quinn, JA (March 1973). "Bubble formation resulting from counterdiffusion supersaturation: a possible explanation for isobaric inert gas 'urticaria' and vertigo". Physics in medicine and biology 18 (2): 256–264. {{doi|10.1088/0031-9155/18/2/009}}. PMID 4805115. http://stacks.iop.org/0031-9155/18/256. Retrieved 10 January 2010.</ref>
* 1973 – French civilian ''Tables du Ministère du Travail 1974'' (MT74)
* 1976 – The sensitivity of decompression testing increased by the use of ultrasonic methods which can detect mobile venous bubbles before symptoms of DCS emerge.<ref name="pmid1249001">{{cite journal |author=Spencer MP |title=Decompression limits for compressed air determined by ultrasonically detected blood bubbles |journal=[[Journal of Applied Physiology]] |volume=40 |issue=2 |pages=229–35 |year=1976 |month=February |pmid=1249001 |doi= |url=http://jap.physiology.org/cgi/pmidlookup?view=long&pmid=1249001 |accessdate=2012-01-10 |ref=harv}}</ref>
* 1981 – Huggins model and tables using Spencer's formula for no-decompression limits.<ref name="Huggins 1992 4-11">{{harvnb|Huggins|1992|loc=chpt. 4 page 11}}</ref>
* 1982 – Paul K Weathersby, Louis D Homer and Edward T Flynn introduce [[survival analysis]] into the study of decompression sickness.<ref name="pmid6490468">{{cite journal |last1=Weathersby |first1=Paul K |last2=Homer |first2=Louis D |last3=Flynn |first3=Edward T |title=On the likelihood of decompression sickness |journal=Journal of Applied Physiology |volume=57 |issue=3 |pages=815–25 |year=1984 |month=September |pmid=6490468 |url=http://jap.physiology.org/cgi/pmidlookup?view=long&pmid=6490468 |accessdate=2009-04-27 |ref=harv}}</ref>
* 1983/4 – [[Albert A. Bühlmann]] publishes ''Decompression–Decompression sickness''.<ref name="Buhlmann 1984" /> Bühlmann recognized the problems associated with altitude diving, and proposed a method which calculated maximum nitrogen loading in the tissues at a particular ambient pressure.
* 1984 – DCIEM (Defence and Civil Institution of Environmental Medicine, Canada) release No-Decompression and Decompression Tables based on Kidd/Stubbs serial compartment model and extensive ultrasonic testing.<ref name="Huggins 1992 4-6">{{harvnb|Huggins|1992|loc=chpt. 4 page 6}}</ref>
* 1984 – [[Edward D. Thalmann]] publishes USN E-L algorithm and tables for constant PO<sub>2</sub> Nitrox closed circuit rebreather applications
* 1985 – Thalmann extends use of E-L model for constant PO<sub>2</sub> Heliox CCR.
* 1985 – Bassett tables (based on USN Tables)<ref name="Huggins 1992 4-10">{{harvnb|Huggins|1992|loc=chpt. 4 page 10}}</ref>
* 1986 – Swiss Sport Diving Tables based on Bühlmann model<ref name="Huggins 1992 4-11" />
* 1986 – D. E. Yount and D. C. Hoffman propose a bubble model.
* 1988 – BSAC'88 tables<ref name="Huggins 1992 4-4">{{harvnb|Huggins|1992|loc=chpt. 4 page 4}}</ref>
* 1990 – DCIEM sport diving tables released.
* 1990 – French Navy – ''Marine Nationale 90'' (MN90) decompression tables
* 1991 – D.E. Yount describes Varied Permeability Model
* 1992 – French civilian Tables du Ministère du Travail 1992 (MT92)
* 1999 – NAUI Trimix and Nitrox tables based on RGBM model
* 2001 – NAUI recreational air tables based on RGBM model
* 2007 – Gerth & Doolette publish VVal 18 and VVal 18M parameter sets for tables and programmes based on the Thalmann E-L algorithm, and produce an internally compatible set of decompression tables for open circuit and CCR on air and Nitrox, including in water air/oxygen decompression and surface decompression on oxygen.
* 2008 – US Navy Diving Manual Revision 6 includes a version of the 2007 tables by Gerth & Doolette.

=== Haldanean (perfusion limited, dissolved phase) models ===
Early decompression theory generally assumed that inert gas bubble formation in the tissues could be avoided during decompression, and the aim of the decompression tables and algorithms was to prevent bubble formation, while minimising decompression time. Most dissolved phase models are perfusion limited, and differ mainly by the number of compartments, range of half times, and supersaturation tolerances assumed. These models are commonly referred to as Haldanean.

==== Haldane's theory and tables ====
[[John Scott Haldane]] was commissioned by the Royal Navy to develop a safe decompression procedure. The current method was a slow linear decompression, and Haldane was concerned that this was ineffective due to additional nitrogen buildup in the slow early stages of the ascent.<ref name="Huggins 1992 2-1">{{harvnb|Huggins|1992|loc=chpt. 2 page 1}}</ref>

===== Theory =====
Haldane's hypothesis was that a diver could ascend immediately to a depth where the supersaturation reaches but does not exceed the critical supersaturation level, at which depth the pressure gradient for off-gassing is maximised and the decompression is most efficient.
The diver would remain at this depth until saturation had reduced sufficiently for him to ascend another 10 feet, to the new depth of critical supersaturation, where the process would be repeated until it was safe for the diver to reach the surface. Haldane assumed a constant critical ratio of dissolved nitrogen pressure to ambient pressure which was invariant with depth.<ref name="Huggins 1992 2-1" />

===== Experimental work =====
Large number of decompression experiments were performed using goats, which were compressed for three hours to assumed saturation, rapidly decompressed to surface pressure, and examined for symptoms of decompression sickness. Goats which had been compressed to 2.25 bar absolute or less showed no signs of DCS after rapid decompression to the surface. Goats compressed to 6 bar and rapidly decompressed to 2.6 bar (pressure ratio 2.3 to 1) also showed no signs of DCS. Haldane and his co-workers concluded that a decompression from saturation with a pressure ratio of 2 to 1 was unlikely to produce symptoms.<ref name="Huggins 1992 2-1-2">{{harvnb|Huggins|1992|loc=chpt. 2 pages 1–2}}</ref>

===== Haldane's model =====
The decompression model formulated from these findings made the following assumptions.
* Living tissues become saturated at different rates in different parts of the body. Saturation time varies from a few minutes to several hours
* The rate of saturation follows a logarithmic curve, and is approximately complete in 3 hours in goats, and 5 hours in humans.
* The desaturation process follows the same pressure/time function as saturation (symmetrical), provided no bubbles have formed
* The slow tissues are most important in avoiding bubble formation
* A pressure ratio of 2 to 1 during decompression will not produce decompression symptoms
* A supersaturation of dissolved Nitrogen that exceeds twice ambient atmospheric pressure is unsafe
* Efficient decompression from high pressures should start by rapidly halving the absolute pressure, followed by a slower ascent to ensure that the partial pressure in the tissues does not at any stage exceed about twice the ambient pressure.
* The different tissues were designated as tissue groups with different half times, and saturation was assumed after four half times (93.75%)
* Five tissue compartments were chosen, with half times of 5, 10, 20, 40 and 75 minutes.<ref name="Huggins 1992 2-2-3">{{harvnb|Huggins|1992|loc=chpt. 2 pages 2–3}}</ref>
* Depth intervals of 10&nbsp;ft were chosen for decompression stops.

===== Decompression tables =====
This model was used to compute a set of tables.
The method comprises choosing a depth and time exposure, and calculation the nitrogen partial pressure in each of the tissue compartments at the end of that exposure.
* The depth of the first stop is found from the tissue compartment with the highest partial pressure, and the depth of first decompression stop is the standard stop depth where this partial pressure is nearest without exceeding the critical pressure ratio.
* The time at each stop is the time required to reduce partial pressure in all compartments to a level safe for the next stop, 10&nbsp;ft shallower.
* The controlling compartment for the first stop is usually the fastest tissue, but this generally changes during the ascent, and slower tissues usually control the shallower stop times. The longer the bottom time and closer to saturation of the slower tissues, the slower the tissue controlling the final stops will be.

Chamber tests and open water dives with two divers were made in 1906. The divers were successfully decompressed from each exposure.
The tables were adopted by the Royal Navy in 1908.
The Haldane tables of 1906 are considered to be the first true set of decompression tables, and the basic concept of parallel tissue compartments with half times and critical supersaturation limits are still in use in several later decompression models, algorithms, tables and decompression computers.<ref name="Huggins 1992 2-3-6">{{harvnb|Huggins|1992|loc=chpt. 2 pages 3–6}}</ref>

==== U.S. Navy decompression tables ====
US Navy decompression tables have gone through a lot of development over the years. They have mostly been based on parallel multi-compartment exponential models. The number of compartments has varied, and the allowable supersaturation in the various compartments during ascent has undergone major development based on experimental work and records of decompression sickness incidents.

===== C&R tables (1915) =====
The first decompression tables produced for the U.S.Navy were developed by the Bureau of Construction and Repair in 1915 and were consequently known as the C&R tables.
They were derived from a Haldanean model, with oxygen decompression to depths up to 300fsw on air, and were successfully used to depths of slightly over 300fsw<ref name="Huggins 1992 3-1">{{harvnb|Huggins|1992|loc=chpt. 3 page 1}}</ref>

===== Hawkins Schilling and Hansen (1930s) =====
Submarine escape training led US Navy personnel to believe that Haldane's allowable supersaturation ratios for fast tissues were unnecessarily conservative, as calculated values indicated that supersaturation in trainees exceeded Haldane's limits, but they did not develop DCS.

A large number (2143) of experimental dives were conducted over 3 years to derive allowable supersaturation ratios for a Haldanian 5 compartment model with compartment half-times of 5, 10, 20, 40 and 70 minutes. Values for critical supersaturation derived from this experimental work were different for each tissue compartment. Values for slow tissues (75 and 40 minute) were close to Haldane's findings, but considerably higher values were found for the fast tissues. These values were so high that the researchers concluded that the 5 and 10 minute tissues were not relevant to the development of DCS. Based on these conclusions, a set of tables was computed which omitted the 5 and 10 minute tissues.<ref name="Huggins 1992 3-2" />

===== Yarborough (1937 tables) =====
Yarborough's 1937 tables were based on a Haldanean 3 compartment model with compartment half-times of 20, 40 and 70 minutes. Ascent rate was chosen to be 25&nbsp;ft per minute, which was a convenient rate to pull up a diver in standard dress.<ref name="Huggins 1992 3-2" />

===== 1956 tables =====
Van der Aue worked on procedures for surface decompression and oxygen use in the early 1950s and during his research found problems with the 1937 tables for long dive times. He also found that the fast tissues which had been dropped in the 1930s would control decompression in some cases, so he re-introduced the fast compartments to the model, and added an extra slower compartment to better model long-duration dives.<ref name="Huggins 1992 3-3">{{harvnb|Huggins|1992|loc=chpt. 3 page 3}}</ref>

Assumptions of the 1956 model:<ref name="Huggins 1992 3-3" />
* Six parallel tissue compartments with exponential uptake and elimination of gas with compartment half times of 5, 10, 20, 40, 80 and 120 minutes.
* Symmetrical uptake and elimination half times (same half time for each compartment for uptake and elimination)
* Supersaturation ratios decrease linearly with increased ambient pressure, (M-values) and are different for each compartment.
* Each tissue compartment is assumed to fully saturate/desaturate in 6 half times. This means desaturation of the slowest (120 min) compartment takes 12 hours – hence the 12-hour surface interval before a dive is not considered repetitive with these tables.

Ascent rate was chosen at 60 fsw/min as a compromise between the practical requirements for military scuba and surface supplied diving operations.<ref name="Huggins 1992 3-9">{{harvnb|Huggins|1992|loc=chpt. 3 page 9}}</ref>

Repetitive diving was accommodated in the tables using the slowest compartment to control surface off-gassing.<ref name="Huggins 1992 3-12">{{harvnb|Huggins|1992|loc=chpt. 3 page 12}}</ref>

A minimum surface interval of 10 minutes was found necessary to ensure that the 120-minute compartment would have controlling effect for repetitive dives.<ref name="Huggins 1992 3-13">{{harvnb|Huggins|1992|loc=chpt. 3 page 13}}</ref>

===== U.S.Navy exceptional exposure tables =====
The US Navy 1956 tables were soon found to be problematic for dives deeper than 100fsw for longer than 2 to 4 hours.

US Navy exceptional exposure tables use an 8 compartment Haldanean model developed by Workman, with half times of 5, 10, 20, 40, 80, 120, 160 and 240 minutes, and are not compatible with the rest of the US Navy Air tables for repetitive diving, although for convenience they have been appended to the standard US Navy Air tables.<ref name="Huggins 1992 4-1-2">{{harvnb|Huggins|1992|loc=chpt. 4 pages 1–2}}</ref> The tables warn that no repetitive diving is permitted following an exceptional exposure dive, and although the 240 minute tissue would only desaturate completely in 24 hours, there is no restriction to assuming an unsaturated diver after 12 hours.<ref name="usnR5">{{cite book |title=US Navy Diving Manual, 5th revision |year= |publisher=US Naval Sea Systems Command |location=United States |url= |accessdate=|author=US Navy }}</ref><!--Ch9pp34,56-->

==== Reformatting of the U.S. Navy tables by recreational diving community ====
Some of the earliest modifications to the U.S. Navy tables involved changes to their layout by the recreational diving community.
These include:<ref name="Huggins 1992 4-2">{{harvnb|Huggins|1992|loc=chpt. 4 page 2}}</ref>
* Nu-Way repetitive dive tables
* Dacor "No calculation dive tables"

==== Modified U.S.Navy 1956 tables ====
Decompression theory is not an exact science. Decompression models approximate a physiological process that is incompletely understood, and rather complex, by simple mathematical models, in the hope of producing a useful procedure with acceptably low risk of injury to the user. New information allows theories and models to be modified to provide more reliable results, and the availability of faster and more powerful computer processors at low cost has made more exhaustive numerical methods more practicable, and the computation of relatively far more complex models is now quite possible, even in real time.

Several factors have encouraged researchers to modify existing tables and develop new models:
* Doppler bubble detection allows models to use bubble formation as an endpoint rather than symptomatic DCS.
* The use of safety stops has been shown by Dr Andrew Pilmanis of the Catalina Marine Science Centre to greatly reduce bubble formation in divers.
* Many decompression models use a slower ascent rate than the 60fpm (18m/min) of the 1956 US Navy tables (The 2008 US Navy tables have reduced ascent rate to 30fpm (9m/min)).<ref name="usn">{{harvnb|US Navy Diving Manual Revision 6}}</ref>
* Multiple repetitive dives. The US Navy tables were designed for a single repetitive dive, and there were concerns about the safety of extending their use to multiple repetitive dives.As an attempt to address this issue, some tables were modified to reduce the allowable bottom time for repetitive dives.
* Longer nitrogen retention. Addition of longer half-time compartments allows the accumulation of residual nitrogen over longer periods to be accounted for.

===== Jeppesen tables =====
Jeppesen made the simplest modification to the U.S. Navy tables by drawing a new line to reduce no-stop limits on an otherwise unchanged table. Divers were recommended to remain within the modified no-stop limit. If one of the new time limits was not listed on the U.S. Navy table, the next shorter table entry was to be selected.<ref name="Huggins 1992 4-9">{{harvnb|Huggins|1992|loc=chpt. 4 page 9}}</ref>

===== Bassett tables =====
These tables were based on the 1956 US Navy tables and the no-decompression limits recommended by Bruce Bassett.<ref name="Huggins 1992 4-10" />

Changes were also made to the table rules and decompression requirements:
* Ascent rate of 10m per minute.
* A safety stop of 3 to 5 minutes at 3 to 5 metres is recommended where possible for all dives deeper than 9msw.
* Total dive time is used to calculate repetitive group.

===== NAUI tables =====
The first NAUI tables were based on unmodified US Navy 1956 tables and issued in the early 1980s.{{citation needed|date=April 2012}}
The next version was a NAUI modification of the US Navy 1956 tables using the following modifications,<ref name="Huggins 1992 4-10" /> and released a few years later.
* No decompression limits have been reduced. In most cases this results in the repetitive group shifting one letter down, but for 50fsw it shifted 2 letters, and for 40fsw, by three letters.
* A precautionary decompression stop (safety stop) of 3 minutes at 15fsw is recommended after all dives, but the time spent at the safety stop is not included in the time used to calculate repetitive group.
* A surface interval of at least one hour between repetitive dives is recommended.
* Repetitive dive depths are limited to 100fsw
* A repetitive dive is defined as occurring within 24 hours of the previous dive (this allows for the slowest tissues to equilibriate with atmospheric partial pressures)
* All required decompression is done at a stop depth of 15fsw

NAUI adapted the 1995 DCIEM Sports Table for use in all NAUI courses and these were used until they were replaced by RGBM based tables in 2002.<ref name="powell2008-213">{{harvnb|Powell|2008|loc="Other decompression models"; page 213 }}</ref> (The NAUI recreational air tables based on RGBM model are copyrighted 2001)<ref>{{cite web|url=http://www.divetable.de/dekotg_e.htm |title=Decompression Diving |publisher=Divetable.de |date= |accessdate=2012-07-17}}</ref>

NAUI RGBM Trimix and Nitrox tables copyrighted 1999 have also been released.<ref>Bruce R. Wienke,
and Timothy R. O'Leary (2001), ''Full Up Phase Model Decompression Tables'', Advanced Diver Magazine, Issue 5, 2001
Advanced diver magazine, http://www.advanceddivermagazine.com/articles/rgbmphase/rgbmphase.html</ref>

===== Pandora tables =====
These tables were designed for use on the excavation of the wreck of the Pandora<ref name="Huggins 1992 4-10" />

* Table values at 30 fsw and deeper were shortened by 1 to 4 minutes, putting divers into higher repetitive groups sooner.
* Repetitive group selection tables for repetitive dives were modified. The first repetitive dive uses the same repetitive group selection as the U.S. Navy tables but subsequent dives use more conservative tables which place the diver in a higher repetitive group than the Navy tables would for the same profile. This tendency is continued for the third and fourth repetitive dives.
* Safety stops at 3 msw (10 fsw) are required for repetitive dives; 3 minutes is required after the second dive, 6 minutes after the third and 9 minutes after the fourth dive.
* Maximum ascent rate was specified as 10 msw/min. (35 fsw/min.).

===== Huggins model and tables =====
In 1981 Karl Huggins modified the US Navy 6 compartment model using M values derived to follow the Spencer no-decompression limits. The tables are exclusively for no-decompression diving and are presented in the same format as the US Navy tables.

A major difference from the US Navy tables is that the repetitive group designators represent nitrogen levels in all tissues, unlike the USN table which represent only the 120 minute compartment. The Huggins repetitive group indicates a percentage of the M<sub>0</sub> for the most saturated tissue, and this is intended to make the tables more applicable to multilevel diving procedures.

The Huggins tables have not been officially tested, but are more conservative than the 1956 US Navy tables. They have been calculated from limits which would theoretically produce venous bubbles 10 to 20% of the time.<ref name="Huggins 1992 4-12">{{harvnb|Huggins|1992|loc=chpt. 4 page 12}}</ref>

===== PADI Recreational Dive Planner =====
The PADI tables known as the PADI Recreational Dive Planner (RDP)were developed by Raymond Rogers and tested by DSAT (Diving Science And Technology, an affiliate of PADI Inc.). The M values were derived from Spencer's no-stop limits and the repetitive group designators were based on a 60 minute tissue compartment. This combination resulted in more conservative first dives, but less conservative repetitive dives.

The RDP tables were developed for no-stop diving, but recommend a safety stop at 15fsw for 3 minutes. Emergency decompression for dives which inadvertently exceed the no-stop limit is specified.

The RDP tables are available in two formats:
* A regular table
* "The Wheel", Which is a circular slide-rule type calculator, and allows depths to be read to 5fsw inervals, and times to the nearest minute.
The RDP was tested for single day multi-level dives and multi-day dives with multiple dives per day. There were no incidences of symptomatic DCS during testing.<ref name="Huggins 1992 4-12-13">{{harvnb|Huggins|1992|loc=chpt. 4 pages 12–13}}</ref>

==== Bühlmann tables ====
Professor A.A. Bühlmann of the Laboratory of Hyperbaric medicine of the Medical Clinic of the University of Zurich developed the Swiss tables, more often referred to as Bühlmann tables, in the early 1960s. The model is Haldanian, with 16 tissue compartments with half times from 2.65 minutes to 635 minutes, each with linearly varying supersaturation limits depending on the tissue and the ambient pressure, and is based on absolute pressures, which simplifies application to altitude diving.

The full set of Swiss Tables consists of tables for four altitude ranges: 0 to 700m, 701 to 1500m, 1501 to 2500m and 2501 to 3500m. Ascent rate was chosen as 10m per minute

No stop limits and decompression schedules tend to be more conservative than the US Navy air tables.

The Swiss tables use the 80 minute tissue compartment for control of repetitive dive calculations, which tends to be less conservative than the US Navy tables for this application.<ref name="Huggins 1992 4-2-3">{{harvnb|Huggins|1992|loc=chpt. 4 pages 2–3}}</ref>

==== Modified Bühlmann tables ====

===== Swiss sport diving tables =====
In 1986 the Bühlmann model was used to generate dive tables for recreational divers. One set was for altitudes from 0 to 700m above sea level (0 to 2300&nbsp;ft.) and other for altitudes from 701 to 2500m (2301 to 8200&nbsp;ft.). The repetitive group designators are based on the 80-minute compartment.<ref name="Huggins 1992 4-11" />

===== Bühlmann/Hahn tables (German) =====
The German tables were developed by Dr. Max Hahn using a derivative of the Bühlmann ZH-L<sub>16</sub> model using half-times ranging from 2.65 to 635 minutes. Three sets were published for altitude ranges 0-25Om, 201-70Om, and 701-1,200m. The repetitive group designators are based on the 80-minute compartment.

Safety factors were added to the depths on the table to take into account depth gauge errors. The depth used for calculations was 2.4% greater than the actual depth for the two lower altitude tables, and 3% + 1 msw greater than actual depth on the highest altitude table.<ref name="Huggins 1992 4-11" />

==== French Navy – Marine Nationale 90 (MN90) decompression tables ====
The mathematical model used for the development of the MN 90 tables is Haldanian, and was also used for the GERS (Groupe d'Etudes et Recherches Sous-marines) 1965 table.<ref name="MN90">Jean-Noël Trucco, avec le concours de Jef Biard, Jean-Yves Redureau et Yvon Fauvel, (1999): Table Marine National 90 (MN90), Version du 03/05/1999, F.F.E.S.S.M. Comité interrégional Bretagne & Pays de la Loire; Commission Technique Régionale. (in French) http://www.acb-plongee.com/site/formation/pdf/theorie/tables_mn90.pdf</ref>

Haldane's assumptions about the limiting factors for ascent are:
* gas exchange in decompression is symmetrical with compression
* the role of bubbles in the modification of blood-tissue exchange is neglected,
* normal decompression does not produce bubbles: DCS occurs when bubbles appear,
* bubbles appear in a compartment where the ratio of the dissolved gas pressure and ambient hydrostatic pressure reaches a critical value, characterizing the maximum tolerable pressure compartment.

Specific assumptions and conditions for use of the MN90 model and tables are as follows:
* For Scuba dives using air as the breathing gas at sea level, with the diver initially saturated at atmospheric pressure
* 12 parallel tissue compartments with half times from 5 to 120 minutes, each with its own critical ratio
* The ascent rate used is 15 to 17 metres per minute to the first stop, which is the same as used in the GERS 1965 tables. From the first stop to the surface this is reduced to 6&nbsp;m/min
* The reference population with respect to physiology is based on 1095 medically fit divers from the French Navy in 1988:
** weight 74&nbsp;kg plus or minus 8&nbsp;kg,
** height 175.9 plus or minus 5.7&nbsp;cm,
** age 32.3 plus or minus 6.1 years.
* Only the 120 minute tissue is used for calculation of residual nitrogen for repetitive dives. Letter groups are used to indicate the residual gas content of the 120 minute tissue. Letter groups are modified according to surface interval. A residual nitrogen time is found from the repetitive group and the repetitive dive depth which is to be added to the planned bottom time.
* Decompression stops are at 3m intervals
* The tables have been validated by experimental dives and modified where necessary.
* The maximum permitted depth for use of air is 60 m. The data for the decompression depths of 62 m and 65m are included in the table in case of accidentally exceeding the depth limit of 60 m.
* Only one repetitive dive is allowed as there is no validation data for multiple repetitive dives
* Altitude corrections are available
* The tables can be used for Nitrox by calculating equivalent air depth
* Oxygen may be used to accelerate decompression in-water at depths not exceeding 6m
* An unusual feature of these tables is a table for reduction of residual nitrogen by breathing pure oxygen on the surface between dives.

=== Non-Haldanean dissolved phase models ===

==== Royal Navy Physiological Laboratory model ====
In the early 1950s Hempleman developed a diffusion limited model for gas transfer from the capillaries into the tissues (Haldanian model is perfusion model). The basis for this model is radial diffusion from a capillary into the surrounding tissue, but by assuming closely packed capillaries in a plane the model was developed into a "tissue slab" equivalent to one dimensional linear bulk diffusion in two directions into the tissues from a central surface.

The 1972 RNPL tables were based on a modified Hempleman tissue slab model, and are more conservative than the US Navy tables.<ref name="Huggins 1992 4-4" />

A version of the RNPL tables were used by the British Sub Aqua Club until the production of the BSAC'88 tables in 1988.

==== DCIEM model and tables ====
In the mid 1960's, the Canadian Defence and Civil Institute of Environmental Medicine developed the Kidd/Stubbs serial decompression model. This differs from Haldanian models which are parallel models, and assume that all compartments are exposed to ambient partial pressures and no gas interchange occurs between compartments. A serial model assumes that the diffusion takes place through a series of compartments, and only one is exposed to the ambient partial pressures, and is in effect a compartmentalised version of the Hempelman bulk diffusion slab model.<ref name="Huggins 1992 4-6" />

The Kidd/Stubbs model has four serial compartments,<ref name="Nishi 1984">{{cite journal |author=Nishi, Ronald, and Lauchner, G. |title=Development of the DCIEM 1983 Decompression Model for Compressed Air Diving |journal=Defence and Civil Institute of Environmental Medicine Technical Report |volume=DCIEM-84-R-44 |year=1984 |url=http://archive.rubicon-foundation.org/4282 |accessdate=2012-01-13 |ref=harv}}</ref> each with a half time of approximately 21 minutes. Allowable surfacing supersaturation ratios for the initial two compartments are taken as 1.92 and 1.73, while the gas concentration in the last two compartments is not considered in the computation.

DCIEM has continuously evaluated and modified the model over the years. A revised set of tables was released in 1984, based on thousands of Doppler evaluated dives.<ref name="Huggins 1992 4-6" />
The DCIEM 1983 decompression model is a decompression calculation model rather than a physiological model.<ref name="Nishi 1984" /><!--p17--> Modifications were made to the model to get it to fit observed data, as the original model had several observed shortcomings, while retaining the basic model structure so that it could be applied to existing hardware with minimal modifications.

=== Mixed phase models (dissolved and bubble phases) ===

==== Tables du Ministère du Travail ====

===== Tables du Ministère du Travail 1974 (MT74) =====
The first French official (civilian) air decompression tables were published in 1974 by the ''Ministère du Travail''<ref name="Imbert 2004" /><ref>Mesures particulières de protection applicables aux scaphandriers. Fascicule Spécial no 74-48 bis. Bulletin Officiel du Ministère du travail. Imprimerie du Journal Officiel, 26 rue Desaix, 75732 Paris cedex 15.</ref>

===== Tables du Ministère du Travail 1992 (MT92) =====
In 1982, the French government funded a research project for the evaluation of the MT74 tables using computer analysis of the dive report database, which indicated that the MT74 tables had limitations for severe exposures.<ref>Imbert JP, Bontoux M. Safety analysis of French 1974 air decompression tables. Proceedings of the Undersea Medical Society Workshop on Decompression in surface-based diving. Tokyo, Japan, September 12th, 1986.</ref> The government then supported a second project to develop and validate new tables.<ref>Imbert JP, Bontoux M. A method for introducing new decompression procedures. Proceedings of the Undersea Medical Society Workshop on validation of decompression schedules. Bethesda, Maryland, 13–14 February 1987.</ref> A complete set of air tables, with options of pure oxygen breathing at 6m (surface supplied), at 12 m (wet bell), surface decompression, split level diving, repetitive diving, etc. was developed in 1983. This early model already implemented the concept of continuous compartment half-times. For the safe ascent criteria, the Arterial Bubble model was not derived mathematically, but an approximation was defined empirically by fitting mathematical expressions to selected exposures from the Comex database. At the time, the best fit was obtained by the expression now called AB Model-1, which was used to compute a set of decompression tables that was evaluated offshore on selected Comex worksites. In 1986, after some minor adjustments, the tables were included in the Comex diving manuals and used as standard procedures. In 1992, the tables were included in the new French diving regulations under the name of Tables du Ministère du Travail 1992 or MT92 tables<ref>Travaux en Milieu Hyperbare. Mesures particulières de prévention. Fascicule no 1636. Imprimerie du Journal Officiel, 26 rue Desaix, 75732 Paris cedex 15. ISBN 2-11-073322-5.</ref>

===== The arterial bubble decompression model =====
The arterial bubble assumption is that the filtering capacity of the lung has a threshold radius of the size of a red blood cell and that sufficiently small decompression bubbles can pass to the arterial side, especially during the initial phase of ascent. Later in the ascent, bubbles grow to a larger size and remain trapped in the lung. This may explain why conventional Doppler measurements have not detected any bubbles in the arterial circulation.<ref name="Imbert 2004">JP Imbert, D Paris, J Hugon, Divetech, France. 2004; The Arterial Bubble Model for Decompression Tables Calculations, EUBS 2004, http://gtuem.praesentiert-ihnen.de/tools/literaturdb/project2/pdf/Imbert%20JP.%20-%20EUBS%202004.pdf</ref>

The arterial bubble assumption can introduce variability in the decompression outcome through the lung function. The first variable is individual susceptibility. The filtering capacity of the lung may be assumed to vary between individuals, and for a given individual, from day to day, and may account for the inter-personal and intra-persona variability which have been observed in DCS susceptibility. Basically, a
good diver is a good bubble filter. This is a justification for divers who seek top physical fitness for severe decompression exposures.

The second variable is related to dive conditions and speculates an influence of CO<sub>2</sub> on the lung filter. Raised levels of CO<sub>2</sub> could decrease the lungs' filtration capacity and allow bubbles to pass to the arterial side of the circulation. Thus diving situations associated with CO<sub>2</sub> retention and hypercapnia would be associated with a higher risk of Type II DCS. This could explain why the following situations, which are all related to high levels of CO<sub>2</sub>, have been identified as contributing factors to DCS:<ref name="Imbert 2004" />
* anxiety and stress,
* exhaustion or hyperventilation due to intense activity,
* cold,
* high work of breathimg.

The arterial bubble assumption is also consistent with accidental production of arterial bubbles. One scenario considers a shunt at the heart or lung level that passes bubbles from the venous to the arterial side. A PFO is thought to only open in certain conditions.<ref>Balestra C, P Germonpre, and A Marroni. Intrathoracic pressure changes after Valsalva strain and other maneuvers: implication for divers with patent foramen ovale. Undersea hyperb. Med, 1998. 25(3): page 171-4.</ref><ref>Germonpre P et al; Patent foramen ovale and decompression sickness in sport divers. J. Appl. Physiol, 1988, 84(5): p1622-6.</ref> A PFO conveniently explains neurological accidents after recreational air diving without any procedure violation, but it does not explain vestibular hits in deep diving. Vestibular symptoms can appear very early in the decompression, long before the massive bubble production required to overload the system.

A second scenario considers pressure increases during decompression that reduce bubble diameters. This can allow bubbles trapped in the lung during a normal decompression to suddenly pass through the capillaries and become responsible for Type II DCS symptoms. This could explain the difference in outcomes of in-water decompression versus surface decompression.<ref>Imbert JP. Decompression tables versus decompression procedures: an analysis of decompression sickness using diving data-bases. Proceedings of the XVIIth annual meeting of Diving and Hyperbaric Medicine, Heraklion, Crete, Greece, 20 September-3 October 1991.</ref> Data collected in the North Sea have shown that if the overall incidence rate of the two diving methods is about the same, that surface decompression tends to produce ten times more type II DCS than in-water decompression. It is assumed that when the diver ascends to the surface, bubbles are produced that are trapped by the lung capillaries, and on recompression of the diver in the deck chamber, these bubbles are reduced in diameter and pass to the arterial side, later causing neurological symptoms. The same scenario was proposed for type II DCS recorded after sawtooth diving profiles or multiple repetitive dives.

The arterial bubble assumption also provides an explanation for the criticality of the initial ascent phase. Bubbles associated with symptoms are not necessarily generated on site. There is an growth process at the beginning of the ascent that may last for several cycles until the bubbles have reached a critical size, when they are either filtered in the lung or stopped at the tissue level. It is postulated that the production of a shower of small arterial bubbles during the first minutes of the initial ascent is a precursor for DCS symptoms.

An attempt was made to turn this scenario into a decompression model.

'''The arterial bubble model assumptions'''<ref name="Imbert 2004" />
# A Diver breathes a compressed gas mixture that contains inert gas which dissolves in the various tissues during the pressure exposure. When the ascent is initiated, the inert gas is off-loaded as soon as a suitable gradient is created.
# Bubbles are normally produced in the vascular bed and transported by the venous system to heart, then to the lungs.
# The lungs work as a filter and trap the bubbles in the capillaries which have a smaller diameter. Gas transfer into the alveoli eliminates the bubbles.
# The critical issue is the filtering capacity of the lung system. Small bubbles may pass through the lungs into the systemic circulation.
# At the level of the aortic arch, the distribution of blood likely to carry bubbles to neurological tissue such as the brain or the spinal cord.
# The brain is a fast tissue and might be in supersaturated state in the early phase of decompression. It acts as a gas reservoir and feeds any local bubble which will grow. The bubble may just proceed through the capillaries to the venous side for another cycle, but may be trapped and will then grow in place, causing local restriction of the blood supply and finally ischemia. This may develop into central neurological symptoms.
# Similarly, arterial bubbles may reach the spinal cord and grow on site from local gas and produce spinal neurological symptoms.
# Much later in the decompression, bubbles may reach a significant size and exert a local deformation, particularly in stiffer tissues such as tendons and ligaments, that excites nerve terminations and produces pain.

'''Derivation of the Arterial Bubble Model'''

A model based on the Arterial Bubble assumption (Arterial Bubble model version 2, or AB Model 2) was developed for the calculation of decompression tables.
This gas phase model uses an equation which can be compared to a classic "M-value" associated to a corrective factor that reduces the permitted gradient for small values of the compartment time constant.

The consequence is the introduction of deeper stops than a classic dissolved phase decompression model.

The rationalization of the arterial bubble assumption considers two situations:<ref name="Imbert 2006" />
* In the initial phase of decompression, the critical event is assumed to be the arrival of an arterial bubble in a de-saturating neurological tissue. The bubble exchanges gas with the surrounding tissue and the blood. If the bubble does not exceed a critical radius, it will eventually leave the site without growing, otherwise it will block the blood circulation and cause ischemia. The critical parameter is bubble radius. This criterion is used to prevent type II neurological symptoms. The strategy for a safe rate of ascent at this stage is to balance gas exchange.
* In the later phase of decompression, the critical event is assumed to be the presence of a large bubble that has taken up a large quantity of dissolved gas from the adjacent tissue in a joint. If the bubble reaches a critical volume, it will have a mechanical effect on the nerve endings causing pain in a tendon. The bubble volume is the critical parameter. This criterion is used to prevent type I pain-only symptoms. The strategy for a safe ascent at this stage is to prevent any gas phase from growing beyond a critical volume.

The critical volume concept was developed by Hennessy and Hempleman who formulated a simple mathematical condition linking the dissolved gas and the safe ascent pressure:
: P<sub>tissue</sub> ≤ a×P<sub>ambient</sub> + b
Where P<sub>tissue</sub> represents the dissolved gas tension, P<sub>ambient</sub>, the ambient pressure and a and b two coefficients. This linear relationship between dissolved gas and ambient pressure has the same mathematical form as an M value, which suggests that all the Haldanean models using M-values (including the US Navy tables previous to those based on the E-L model, the Bühlmann tables and all the French Navy tables), may be considered expressions of the critical volume criterion, though their authors may have argued for other interpretations.<ref name="Imbert 2006" />

==== U.S.Navy E-L algorithm and the 2008 tables ====
{{further|Thalmann algorithm}}
[[File:Linear-Exponential tussue tensions.png|thumb|300px|Response of a tissue compartment to a step increase and decrease in pressure showing Exponential-Exponential and two possibilities for Linear-Exponential uptake and washout]]
The use of simple symmetrical exponential gas kinetics models has shown up the need for a model that would give slower tissue washout.<ref name="Parker 1992-1">{{harvnb|Parker|1992|p=1}}</ref> In the early 1980s the US Navy Experimental Diving Unit developed an algorithm using a decompression model with exponential gas absorption as in the usual Haldanian model, but a slower linear release during ascent. The effect of adding linear kinetics to the exponential model is to lengthen the duration of risk accumulation for a given compartment time constant<ref name="Parker 1992-1" />

The model was originally developed for programming decompression computers for constant oxygen partial pressure closed circuit rebreathers.<ref name="Thalmann 1984 abstract">{{harvnb|Thalmann|1984|loc=abstract }}</ref><ref name="Huggings 4-13">{{harvnb|Huggins|1992|loc=chpt. 4 page 13}}</ref> Initial experimental diving using an exponential-exponential algorithm resulted in an unacceptable incidence of DCS, so a change was made to a model using the linear release model, with a reduction in DCS incidence.
The same principles were applied to developing an algorithm and tables for a constant oxygen partial pressure model for Heliox diving<ref name="Thalmann 1985-6">{{harvnb|Thalmann|1985|p=6}}</ref>

The linear component is active when the tissue pressure exceeds ambient pressure by a given amount specific to the tissue compartment. When the tissue pressure drops below this cross-over criterion the tissue is modelled by exponential kinetics. During gas uptake tissue pressure never exceeds ambient, so it is always modelled by exponential kinetics. This results in a model with the desired asymmetrical characteristics of slower washout than uptake.<ref name="Parker 1992-3">{{harvnb|Parker|1992|p=3}}</ref>
The linear/exponential transition is smooth. Choice of cross-over pressure determines the slope of the linear region as equal to the slope of the exponential region at the cross-over point.

During the development of these algorithms and tables, it was recognized that a successful algorithm could be used to replace the existing collection of incompatible tables for various air and Nitrox diving modes currently in the U.S. Navy Diving Manual with a set of mutually compatible decompression tables based on a single model, which was proposed by Gerth and Doolette in 2007.{{sfn|Gerth|Doolette|2007|p=1}} This has been done in Revision 6 of the US Navy Diving Manual published in 2008, though some changes were made.

An independent implementation of the EL-Real Time Algotithm was developed by Cochran Consulting, Inc. for the diver-carried Navy Dive Computer
under the guidance of E. D. Thalmann.{{sfn|Gerth|Doolette|2007|p=2}}

===== Physiological interpretation =====
Computer testing of a theoretical bubble growth model reported by Ball, Himm, Homer and Thalmann produced results which led to the interpretation of the three compertments used in the probabilistic LE model, with fast (1.5min), intermediate (51 min) and slow (488min) time constants, of which only the intermediate compartment uses the linear kinetics modification during decompression, as possibly not representing distinct anatomically identifiable tissues, but three different kinetic processes which relate to different elements of DCS risk.{{sfn|Ball|1995|p=272}}

They conclude that bubble evolution may not be sufficient to explain all aspects of DCS risk, and the relationship between gas phase dynamics and tissue injury requires further investigation.{{sfn|Ball|1995|p=273}}

==== BSAC'88 Tables ====
The BSAC '88 Tables are published in the form of a booklet of four table sets giving no calculation repetitive diving solutions from sea level to 3000 metres altitude.

These tables were developed by Tom Hennessy to replace the RNPL/BSAC tables, when the Club wanted a set of tables which could approach the versatility of a dive computer.<ref name="Lippmann1990 BSAC88">{{harvnb|Lippmann|1990|pp=325–328}}</ref>

Very little information on the theoretical model and algorithm for the BSAC 1988 tables appears to be available.
What is known, is that the tables were developed specifically for recreational diving for the British Sub-Aqua Club by Dr Tom Hennessy and were released in 1988.<ref>{{cite web|url=http://www.bsac.com/shop.asp?section=1362&sectionTitle=Decompression+Tables&itemid=1677 |title=BSAC 88 Decompression Tables – British Sub-Aqua Club |publisher=Bsac.com |date= |accessdate=2012-07-17}}</ref>

Also in 1988, a chapter titled ''Modelling Human Exposure to Altered Pressure Environments'', by T.R. Hennessy was published in ''Environmental Ergonomics'',<ref>Hennessy T.R. 1988; Modelling human exposure to altered pressure environments. In: ''Environmental Ergonomics'' pp. 316 to 331, (eds Mekjavik, IB, Banister, EW, Morrison, JB,). London: Taylor & Francis</ref> discussing the shortcomings of several decompression models and the associated experimental validation procedures.
In this work Hennessy proposes an alternative combined perfusion/diffusion model. The number of compartments discussed ranges fron 4 in model "A", (perfusion limited aqueous tissue, perfusion limited lipid tissue, diffusion limited aqueous tissue and diffusion limited lipid tissue) to 2 in model "B" (where the assumption is made that if there is intravascular undissolved gas (bubbles), the perfusion limited comparments would become diffusion limited).

Hennessy concludes that if the undissolved and dissolved gas content of a tissue cannot be independently measured either directly or indirectly then the safe maximum limits relative to the ambient pressure cannot be accurately determined through decompression trials and it will not be possible to systematically develop a comprehensive biophysical model for gas exchange.
He proposes a best fit double compartment model for dissolved gas and a single compartment model for undissolved gas as these are the simplest models consistent with available data.

The parameters used in the design of these tables include:<ref name="Lippmann1990 BSAC88" />

* Bubbles are assumed to form after every decompression.
* These bubbles affect gas uptake and release on repetitive dives, resulting in a faster saturation on repetitive dives due to a combination of redissolved nitrogen from the bubbles, residual dissolved nitrogen, plus the nitrogen uptake due to the repeated exposure.
* Bubbles do not redissolve immediately on recompression, and rates of gas uptake will alter from initial dive to repetitive dives, so repetitive dives must be handled differently in the mathematical model to predict safe decompression.
* Rates of gas elimination are considered to be assymetrical to uptake, and the model becomes more conservative as the number of dives, depth and duration increases.
* The BSAC'88 Tables use a series of seven tables, labelled A to G, to take into account the variation in ingassing and outgassing rates assumed for sequential dives.
* Depth increments of 3m are used.
* In a significant departure from conventional practice, the tables are not based on a bottom time defined as time of leaving the surface to time leaving the bottom, but on time to reach a depth of 6m during the ascent.
* Ascent rate to 6m is restricted to a maximum of 15m per minute.
* Ascent from 6m to the surface must take 1 minute.
* Decompression stops are done at 9m and 6m, and at the surface, as surface interval is considered a decompression period.
* No stops are scheduled at 3m, as it are considered too difficult to maintain a consistent depth in waves.

The initial dive uses table A, and the diver is allocated a Surfacing Code based on depth and time of the dive. After a surface interval of at least 15 minutes the diver can select a new Current Tissue Code which models the residual nitrogen load, and uses this code to select the repetitive dive table.<ref name="Lippmann1990 BSAC88" />

The BSAC'88 tables are presented in a format which does not require any calculation by the user.

==== Varying Permeability Model ====
{{main|Varying Permeability Model}}

This decompression model was developed by D.E. Yount and others at the University of Hawaii to model laboratory observations of bubble formation and growth in both inanimate and in vivo systems exposed to pressure variations. It presumes that microscopic bubble nuclei always exist in aqueous media, including living tissues. These bubble nuclei are spherical gas phases that are small enough to remain in suspension yet strong enough to resist collapse, their stability being provided by elastic surface layer consisting of surface-active molecules with variable gas permeability.{{sfn|Yount|1991|p=}} These skins resist the effect of surface tension, as surface tension tends to collapse a small bubble by raising internal pressure above ambient so that the partial pressure gradient favours diffusion out of the bubble in inverse proportion to the radius of the surface.

Any nuclei larger than a specific "critical" size, (more physics needed here) <!--which is related to the maximum dive depth (exposure pressure),--> will grow during decompression.{{citation needed|date=January 2012}} The VPM aims to limit the cumulative volume of these growing bubbles during and after decompression to a tolerable level by limiting the pressure difference between the gas in the bubbles and the ambient pressure. In effect this is equivalent to limiting the supersaturation, but instead of using an arbitrary linear fit to experimental data, the physics of bubble growth is used to model the acceptable supersaturation for any given pressure exposure history.

Growth in size and number of gas bubbles is computed based on factors representing pressure balances in the bubbles, physical properties of the "skins" and the surrounding environment. If the total volume of gas in the bubbles is predicted to be less than a "critical volume", then the diver is assumed to be within the safe limits of the model.

The bubble model is superposed on a multiple parallel tissue compartment model. Ingassing is assumed to follow the classic Haldanean model.

===== Bubble population distribution =====
Bubble size vs number has an [[exponential distribution]]{{sfn|Yount|1991|p=136}}

===== Bubble nucleation =====
Gas bubbles with a radius greater than 1 micron should float to the surface of a standing liquid, whereas smaller ones should dissolve rapidly due to surface tension. The Tiny Bubble Group has been able to resolve this apparent paradox by developing and experimentally verifying a new model for stable gas nuclei.{{sfn|Yount|1991|p=130}}

According to the varying-permeability model, gas bubble nuclei are simply stable microbubbles. The stability of these microbubbles is due to
elastic skins or membranes consisting of surface-active molecules. These skins are normally permeable to gas, and collapse is prevented by their compression strength. These skins can become stiff and effectively impermeable to gas when they are subjected to large compressions, typically exceeding 8 atm, at which stage the pressure inside increases during further compression as predicted by Boyle's law.

Essentially, there are three parameters in the VP model:
the compression strength of the skin; the initial radius; and the onset pressure for impermeability.

===== Ordering hypothesis =====
The ordering hypothesis states that nuclei are neither created nor destroyed by the pressure schedule, and initial ordering according to size is preserved.

It follows from the ordering hypothesis that each bubble count is determined by the properties and behavior of that one "critical" nucleus which is right at the bubble-formation threshold.
All nuclei that are larger than the critical nucleus will form bubbles, and all nuclei that are smaller will not.
Furthermore, a family of pressure schedules which yields the same bubble count N is characterized by
the same critical nucleus and hence by the same critical radius, the same crumbling compression, and the same onset of impermeability.{{sfn|Yount|1991|p=132}}

===== Development of decompression model =====
The original assumption was that bubble number is directly proportional to decompression stress. This approach worked well for long exposures, but not when the exposure time varied considerably.

A better model was obtained by allowing more bubbles to form on the shorter dives than on the longer dives.
The constant bubble number assumption was replaced by a "dynamic-critical-volume hypothesis". As in earlier applications of the
critical-volume criterion,<ref name="Hennessy and Hempleman 1977">Hennessy, T. R. and H. V. Hempleman. 1977. ''An examination of the critical released gas volume concept in decompression sickness''. Proceedings of the Royal Society of London. Series B, 197: 299–313.</ref> it was assumed that whenever the total volume of gas phase accumulated exceeds a critical value, signs or symptoms of DCS will appear. In the special case of long exposures the two models are equivalent.{{sfn|Yount|1991|p=138}}

The "dynamic" aspect of this hypothesis is that gas is continuously entering and leaving the gas phase.<ref name="Yount and Hoffman 1986">Yount, D. E. and D. C. Hoffman. 1986. ''On the use of a bubble formation model to calculate diving tables''. Aviation, Space, and Environmental Medicine, 57: 149–156.</ref>

The accumulated volume is calculated as a function of time by integrating over the product of the bubble number and the degree of supersaturation, and subtracting the free gas that is being dissipated continuously by the lung.{{sfn|Yount|1991|p=137}}

Gas uptake and elimination are assumed to be exponential, as in conventional Haldanean models, and the tissue half-times used range from 1 to 720 min.<ref name="Yount and Hoffman 1986" />

As a first approximation only the inert gasses are taken into account. For oxygen partial pressures above 2.4 bar, the quantity of oxygen dissolyed in the arterial blood exceeds the amount that the body can use, and the hemoglobin is saturated with oxygen in both the veins and the arteries. If more oxygen is added, the partial pressure of oxygen in the venous blood rises.<ref name="Yount and Lally 1980">Yount, D. E. and D. A. Lally. 1980. ''On the use of oxygen to facilitate decompression''. Aviation, Space, and Environmental Medicine, 51: 544–550.</ref>

===== Comparison of VPM profiles with other models =====
Comparisons of VPM profiles with USN decompression schedules for extreme exposure dives consistently produce similar total ascent times, but significantly deeper first decompression stops.{{sfn|Yount|1991|p=138}}

==== Reduced Gradient Bubble Model ====
{{main|Reduced Gradient Bubble Model}}
The RGBM developed by Dr Bruce Wienke at Los Alamos National Laboratory is a hybrid model which modifies a Haldanian model with factors to take some account of bubble mechanics to model gas phase production during decompression. The bubble factor modifies the M-values of the Haldanian model, making it more conservative.

Features of the modifying factor ξ include:<ref name="Huggins 1992 4-14">{{harvnb|Huggins|1992|loc=chpt. 4 page 14}}</ref>

* ξ starts on the first dive of a repetitive series with the maximum value of one, so it will make the model more conservative or unchanged.
* ξ decreases for repetitive dives.
* ξ decreases as exposure time increases.
* ξ increases with increased surface interval.
* ξ modifies fast compartments more than slow compartments.
* ξ decreases with the depth of a dive segment
* ξ has more effect on repetitive dives which are deeper than previous dives in the series.
The effect is to reduce no-stop dive time or increase decompression requirements for repetitive dive in the following categories:
* Following a short surface interval.
* Following a long dive.
* Following a deep dive.
* Which are deeper than previous dives.

The model has been used to some extent in some Suunto dive computers,<ref>''Suunto Reduced Gradient Bubble Model'', suunto_brochure.qxd 24.7.2003 11:53 Sivu 2, http://www.suunto.com/za/Sports/Diving/Diving-Academy/suunto-rgbm</ref> and in the HydroSpace Explorer computer, where it is a user selected option<ref name="HSE Manual">''HS Explorer Dive Computer Owner's Manual'',2003, HydroSpace Engineering, Inc. St. Augustine, FL, http://hs-eng.com</ref> for computation formula, with a choice of additional conservatism factors.

The complete RGBM treats coupled perfusion-diffusion transport as a two stage process, with perfusion providing as a boundary condition for gas penetration of the tissues by diffusion. Either process can dominate the exchange depending on time and rate ceofficents.

Simplified implementations which require less computational power are available for use in personal decompression computers. These are dominated by perfusion. The inherent biological unsaturation of tissues is considered in the calculations.<ref name="Wienke 2002 10" />

The model assumes that bubble nuclei are always present in a specific size distribution, and that a certain number are induced to grow by compression and decompression. An iterative computation is used to model ascent to limit the combined volume of the gas phase. Gas mixtures of helium, nitrogen, and oxygen contain bubble distributions of different sizes, but the same phase volume limit is used.<ref name="Wienke 2002 11">{{harvnb|Wienke|2002|p=11}}</ref>

The model postulates bubble nuclei with aqueous and/or lipid skin structure, in a number and size distribution quantified by an equation-of-state. Like the VPM, RGBM assumes the size distribution is exponentially decreasing in size. Unlike the varying permeability model, bubble seeds are assumed permeable to gas transfer across skin boundaries under all pressures.

The size of nuclei which will grow during decompression is inversely proportional to the supersaturation gradient.

At higher pressures, skin tension of the bubble nuclei reduces gas diffusion to a slower rate. The model assumes that bubble skins are stabilized by surfactants over calculable times scales, which results in variable persistence of the bubble nuclei in the tissues.<ref name="Wienke 2002 11" />

=== Modifications to models and algorithms for diluent gases other than nitrogen ===
Decompression models and algorithms developed for binary mixtures of nitrogen and oxygen can not be used for gases containing significant amounts of other diluent gases without modification to take into account the different solubilities and diffusion constants of the alternative or added diluents. It is also highly desirable to test any such modifications, to make sure the schedules produced by them are acceptably safe.

==== Alternative diluent gases ====
* Helium is by far the most important of the alternative diluents used to date.
* Hydrogen
* Neon
* Combinations of these gases, particularly the trinary mixtures of helium, nitrogen and oxygen known generically as [[Trimix (breathing gas)|Trimix]].

==== Decompression models which have been adapted to include alternative and multiple diluents ====
* Bühlmann algorithm
* VPM algorithm<ref>{{cite web|url=http://www.hhssoftware.com/v-planner/ |title=V-Planner VPM & VPM-B & VPMB & VPM-B/E dive decompression software |publisher=Hhssoftware.com |date= |accessdate=2012-07-17}}</ref>
* RGBM algorithm<ref name="HSE Manual" />

=== Commercial diving tables ===
To a large extent commercial offshore diving uses Heliox tables that have been developed by the major commercial diving enterprises such as [[Compagnie maritime d'expertises|Comex]], [[Oceaneering International]] (OI) Alpha tables, American Oilfield Diving (AOD) Company gas tables, though modifications of the US Navy Partial pressure tables are also used.<ref name="Beyerstein 2006">{{cite web|title=Commercial Diving: Surface-Mixed Gas, Sur-D-O2, Bell Bounce, Saturation |last1=Beyerstein |first1=Gary |location=New Orleans, La |url=http://archive.rubicon-foundation.org/4661 |year=2006|accessdate=2012-05-07|ref=harv}}</ref> In 2006 the unmodified US Navy tables (Revision 5) were considered to result in an unacceptably high rate of decompression sickness for commercial applications.<ref name="Beyerstein 2006" />

"Cx70" heliox tables were developed and used by Comex between 1970 and 1982. The tables were available in two versions. One was designed for surface-supplied diving and limited to 75 m. The diver breathed heliox as the bottom mix and 100% oxygen at the 6 m stop. The other was designed for closed bell bounce diving and allowed for exposures up to 120 minutes, and depths to 120 m. The diver breathed heliox in the water and in the bell, air after transfer into the deck decompression chamber, and finally oxygen on built in breathing system (BIBS) from 12 m to the surface. These tables produced a relatively high incidence of decompression sickness.<ref name="Imbert 2006" />

The French ''Tables du Ministère du Travail 1974'' (MT74) and ''Tables du Ministère du Travail 1992'' (MT92) were developed specifically for commercial diving.

Norwegian Diving and Treatment Tables, ISBN: 82-992411-0-3, referenced in. NORSOK Standard U100 2.24 for manned underwater operations, are available in Norwegian, Danish and English text and are approved for commercial diving.<ref name="NORSOK U100">NORSOK STANDARD U-100, Edition 3, April 2009, Manned underwater operations. Standards Norway, Lysaker. http://www.standard.no/PageFiles/13273/u100e3.pdf, retrieved 9 March 2012</ref>


== See also ==
== See also ==

Revision as of 14:05, 14 March 2013

Divers decompressing in the water at the end of a dive

Decompression in the context of diving derives from the reduction in ambient pressure experienced by the diver during the ascent at the end of a dive or hyperbaric exposure and refers to both the reduction in pressure and the process of allowing dissolved inert gases to be eliminated from the tissues during this reduction in pressure.

When a diver descends in the water column the ambient pressure rises. Breathing gas is supplied at the same pressure as the surrounding water, and some of this gas dissolves into the diver's blood and other fluids. Inert gas continues to be taken up until the gas dissolved in the diver is in a state of equilibrium with the breathing gas in the diver's lungs, (see: "Saturation diving"), or the diver moves up in the water column and reduces the ambient pressure of the breathing gas until the inert gases dissolved in the tissues are at a higher concentration than the equilibrium state, and start diffusing out again.

In a manner similar to the fizzing of a carbonated beverage when opened, dissolved inert gases such as nitrogen or helium can form bubbles in the blood and tissues of the diver if the partial pressures of the dissolved gases in the diver gets too high when compared to the ambient pressure. These bubbles and products of injury caused by the bubbles, can cause damage to tissues known as decompression sickness or the bends. The immediate goal of controlled decompression is to avoid development of symptoms of bubble formation in the tissues of the diver, and the long term goal is to also avoid complications due to sub-clinical decompression injury.

The symptoms of decompression sickness are known to be caused by damage resulting from the formation and growth of bubbles of inert gas within the tissues and by blockage of arterial blood supply to tissues by gas bubbles and other emboli consequential to bubble formation and tissue damage.

The precise mechanisms of bubble formation and the damage they cause has been the subject of medical research for a considerable time and several hypotheses have been advanced and tested. Tables and algorithms for predicting the outcome of decompression schedules for specified hyperbaric exposures have been proposed, tested, and used, and usually found to be of some use but not entirely reliable. Decompression remains a procedure with some risk, but this has been reduced and is generally considered to be acceptable for dives within the well tested range of commercial, military and recreational diving.

During effective decompression, the asymptomatic venous microbubbles present after most dives are eliminated from the diver's body through the lungs. If they are not given enough time, or more bubbles are created than can be eliminated safely, the bubbles grow in size and number causing the symptoms and injuries of decompression sickness.[1]

Decompression may be continuous or staged, where the ascent is interrupted by stops at regular depth intervals, but the entire ascent is part of the decompression, and ascent rate can be critical to harmless elimination of inert gas. What is commonly known as no-decompression diving, or more accurately no-stop decompression, relies on limiting ascent rate for avoidance of excessive bubble formation.

When diving with nitrogen-based breathing gases, decompression stops are typically carried out in the 3 to 20 metres (10 to 70 ft) depth range. With helium-based breathing gases the stop depths may start deeper.

The period at surface pressure immediately after dives is also an important part of decompression and can be thought of as the last decompression stop of a dive. It typically takes up to 24 hours for the body to return to its normal atmospheric levels of inert gas saturation after a dive.[2] When time is spent on the surface between dives this is known as the "surface interval" and is considered when calculating decompression requirements of the subsequent dive.

Divers breathing gas at high pressure may need to do decompression stops, but a diver who only breathes gas at atmospheric pressure when free-diving, does not usually need to do decompression stops. However, it is possible to get taravana, thought to be a form of decompression sickness, from repetitive deep free-diving with short surface intervals.[3]

Divers who use a snorkel to free-dive near the surface or use an atmospheric diving suit will not need to decompress.

Decompression theory

Physics and physiology of decompression

Decompression involves a complex interaction of gas solubility, partial pressures and concentration gradients, bulk transport and bubble mechanics in living tissues.

This section provides an introductory discussion of some of the factors influencing inert gas uptake and elimination in living tissues.

Solubility

Solubility is the property of a gas, liquid or solid substance (the solute) to be held homogeneously dispersed as molecules or ions in a liquid or solid medium (the solvent).

In decompression theory the solubility of gases in liquids is of primary importance.

Solubility of gases in liquids is influenced by three main factors:

The presence of other solutes in the solvent can also influence solubility.

Solubility of gases at 37°C[4]
Gas Molecular weight Water solubility Lipid solubility Water/lipid solubility ratio
Hydrogen 2 0.016 0.048 3.1
Helium 4 0.0085 0.015 1.7
Neon 20 0.0097 0.019 2.07
Nitrogen 28 0.013 0.067 5.2
Oxygen 32 0.024 0.12 5.0
Carbon dioxide 44 0.56 0.876 1.6

Diffusion

Diffusion is the movement of molecules or ions in a medium when there is no gross mass flow of the medium, and can occur in gases, liquids or solids, or any combination.

Diffusion is driven by the kinetic energy of the diffusing molecules – it is faster in gases and slower in solids when compared with liquids due to the variation in distance between collisions, and diffusion is faster when the temperature is higher as the average energy of the molecules is greater. Diffusion is also faster in smaller, lighter molecules of which helium is the extreme example. Diffusivity of helium is 2.65 times faster than nitrogen.[5]

In decompression theory the diffusion of gases, particularly when dissolved in liquids, is of primary importance.

Partial pressure gradient

Also known as concentration gradient, this can be used as a model for the driving mechanism of diffusion. The partial pressure gradient is the variation of partial pressure (or more accurately, the concentration) of the solute (dissolved gas) from one point to another in the solvent. The solute molecules will randomly collide with the other molecules present, and tend over time to spread out until the distribution is statistically uniform. This has the effect that molecules will diffuse from regions of higher concentration (partial pressure) to regions of lower concentration, and the rate of diffusion is proportional to the rate of change of the concentration.

Molecules of solute will also tend to aggregate in areas of greater solubility in a non-homogeneous solvent medium.

Inert gas uptake (Ingassing)

In this context, inert gas refers to a gas which is not metabolically active. Atmospheric nitrogen (N2) is the most common example, and helium (He) is the other inert gas commonly used in breathing mixtures for divers.

Atmospheric nitrogen has a partial pressure of approximately 0.78bar at sea level. Air in the alveoli of the lungs is diluted by saturated water vapour (H2O) and carbon dioxide (CO2), a metabolic product given off by the blood, and contains less oxygen (O2) than atmospheric air as some of it is taken up by the blood for metabolic use. The resulting partial pressure of nitrogen is about 0,758bar.[6]

At atmospheric pressure the body tissues are therefore normally saturated with nitrogen at 0.758bar (569mmHg). At increased ambient pressures due to depth or habitat pressurisation, a diver's lungs are filled with breathing gas at the increased pressure, and the partial pressures of the constituent gases will be increased proportionately.

For example: At 10 meters sea water (msw) the partial pressure of nitrogen in air will be 1.58 bar.

The inert gases from the breathing gas in the lungs diffuse into blood in the alveolar capillaries ("move down the pressure gradient") and are distributed around the body by the systemic circulation in the process known as perfusion.

Perfusion

Perfusion is the mass flow of blood through the tissues. Dissolved materials are transported in the blood much faster than they would be distributed by diffusion alone (order of minutes compared to hours).

The dissolved gas in the alveolar blood is transported to the body tissues by the blood circulation. There it diffuses through the cell walls and into the tissues, where it may eventually reach equilibrium. The greater the blood supply to a tissue, the faster it will reach equilibrium with gas at the new partial pressure.

Saturation and supersaturation

If the supply of gas to a solvent is unlimited, the gas will diffuse into the solvent until there is so much dissolved that equilibrium is reached and the amount diffusing back out is equal to the amount diffusing in. This is called saturation.

If the external partial pressure of the gas (in the lungs) is then reduced, more gas will diffuse out than in. This is a condition known as supersaturation. The gas will not necessarily form bubbles in the solvent at this stage.

Tissue compartments

Most decompression models work with slow and fast tissue compartments. These are imaginary tissues which are designated as fast and slow to describe the rate of saturation. Real tissues will also take more or less time to saturate, but the models do not need to use actual tissue values to produce a useful result. Models with from one to 16 tissue compartments[7] have been used to generate decompression tables.

For example: Tissues with a high lipid content can take up a larger amount of nitrogen, but often have a poor blood supply. These will take longer to reach equilibrium, and are described as slow, than tissues with a good blood supply and less capacity for dissolved gas, which are described as fast.
Tissue half times

Half time of a tissue is the time it takes for the tissue to take up or release 50% of the difference in dissolved gas capacity at a changed partial pressure. For each consecutive half time the tissue will take up or release half again of the cumulative difference in the sequence ½, ¾, 7/8, 15/16, 31/32, 63/64 etc. The number of half times chosen to assume full saturation depends on the decompression model, and typically ranges from 4 (93.75%) to 6 (98.44%).

For example: A 5 minute tissue will be 50% saturated in 5 minutes, 75% in 10 minutes, 87.5% in 15 minutes and for practical purposes, saturated in about 30 minutes (98.44% saturated at 6 half times)

Tissue compartment half times range from 1 minute to 720 minutes[8] or more in current decompression models.

A specific tissue comparment will have different half times for gases with different solubilities and diffusion rates. This model may not adequately describe the dynamics of outgassing if it includes gas phase bubbles.

Outgassing of tissues

Gas remains in the tissues until the partial pressure of that gas in the lungs is reduced sufficiently to cause a concentration gradient with the blood at a lower concentration then the relevant tissues. A lowered partial pressure in the lungs will result in more gas diffusing out of the blood into the lung gas and less from the lung gas into the blood. A similar situation occurs between the blood and each tissue. As the concentration in the blood drops below the concentration in the adjacent tissue, the gas will diffuse out of the tissue into the blood, and will then be transported back to the lungs where it will diffuse into the lung gas and then eliminated by exhalation.

If the ambient pressure reduction is limited, this desaturation will take place in the dissolved phase, but if the ambient pressure is lowered sufficiently, bubbles may form and grow, both in blood and other supersaturated tissues.

When the gas in a tissue is at a concentration where more diffuses out than in it is called supersaturated, though some authorities define supersturation in this context as when the partial pressure of inert gas dissolved in a tissue exceeds the total ambient pressure on the tissue,[9] and there is a treoretical possibility of bubble formation.

Inherent unsaturation

There is a metabolic reduction of total gas pressure in the tissues.[10]

The sum of partial pressures of the gas that the diver breathes must necessarily balance with the sum of partial pressures in the lung gas. In the alveoli the gas has been humidified by a partial pressure of approximately 63 mbar (47 mmHg) and has gained about 55 mbar (41 mmHg) carbon dioxide from the venous blood. Oxygen has also diffused into the arterial blood, reducing the partial pressure of oxygen in the alveoli by about 67 mbar(50 mmHg) As the total pressure in the alveoli must balance with the ambient pressure, this dilution results in an effective partial pressure of nitrogen of about 758 mb (569 mmHg) in air at normal atmospheric pressure.

At a steady state, when the tissues have been saturated by the inert gases of the breathing mixture, metabolic processes reduce the partial pressure of the less soluble oxygen and replace it with carbon dioxide, which is considerably more soluble in water. In the cells of a typical tissue, the partial pressure of oxygen will drop to around 13 mbar (10 mmHg), while the partial pressure of carbon dioxide will be about 65 mbar (49 mmHg). The sum of these partial pressures (water, oxygen, carbon dioxide and nitrogen) comes to roughly 900 mbar (675 mmHg), which is some 113 mbar (85 mmHg) less than the total pressure of the respiratory gas. This is a significant saturation deficit, and it provides a buffer against supersaturation and a driving force for dissolving bubbles.[10]

Experiments suggest that the degree of unsaturation increases linearly with pressure for a breathing mixture of fixed composition, and decreases linearily with fraction of inert gas in the breathing mixture.[11] As a consequence, the conditions for maximising the degree of unsaturation are a breathing gas with the lowest possible fraction of inert gas – i.e. pure oxygen, at the maximum permissible partial pressure.

This saturation deficit is also referred to as the "Oxygen window".[12] or partial pressure vacancy.[13]

Inert gas elimination (Outgassing)

For optimised decompression the driving force for tissue desaturation should be kept at a maximum, provided that this does not cause symptomatic tissue injury due to bubble formation and growth (symptomatic decompression sickness), or produce a condition where diffusion is retarded for any reason.

There are two fundamentally different ways this has been approached. The first is based on an assumption that there is a level of supersaturation which does not produce symptomatic bubble formation and is based on empirical observations of the maximum decompression rate which does not result in an unacceptable rate of symptoms. This approach seeks to maximise the concentration gradient providing there are no symptoms. The second assumes that bubbles will form at any level of supersaturation where the total gas tension in the tissue is greater than the ambient pressure and that gas in bubbles is eliminated more slowly than dissolved gas. These philosophies result in differing characteristics of the decompression profiles derived for the two models: The critical supersaturation approach gives relatively rapid initial ascents, which maximise the concentration gradient, and long shallow stops, while the bubble models require slower ascents, with deeper first stops, but may have shorter shallow stops.

The critical supersaturation approach
Critical ratio model

J.S. Haldane originally used a pressure ratio of 2 to 1 for decompression on the principle that the saturation of the body should at no time be allowed to exceed about double the air pressure.[14] This principle was applied as a pressure ratio of total ambient pressure and did not take into account the partial pressures of the component gases of the breathing air. His experimental work on goats and observations of human divers appeared to support this assumption. However, in time, this was found to be inconsistent with incidence of decompression sickness and changes were made to the initial assumptions. This was later changed to a 1.58:1 ratio of nitrogen partial pressures.

Critical difference models

Further research by people such as Robert Workman suggested that the criterion was not the ratio of pressures, but the actual pressure differentials. Applied to Haldane's work, this would suggest that the limit is not determined by the 1.58:1 ratio but rather by the difference of 0.58 atmospheres between tissue pressure and ambient pressure. Most tables today, including the Bühlmann tables, are based on the critical difference model.[15]

M-values

At a given ambient pressure, the M-value is the maximum value of absolute inert gas pressure that a tissue compartment can take without presenting symptoms of decompression sickness. M-values are limits for the tolerated gradient between inert gas pressure and ambient pressure in each compartment. Alternative terminology for M-values include "supersaturation limits", "limits for tolerated overpressure", and "critical tensions".[16][17]

Gradient factors

Gradient factors are a way of modifying the M-value to a more conservative value for use in a decompression algorithm. The gradient factor is a percentage of the M-value chosen by the algorithm designer, and varies linearly between the maximum depth and the surface. They are expressed as a two number designation, where the first number is the percentage of the deep M-value, and the second is a percentage of the shallow M-value.[18]

For example: A 30/85 gradient factor would limit the allowed supersaturation at depth to 30% of the designer's maximum, and to 85% at the surface.

In effect the user is selecting a lower maximum supersaturation than the designer considered appropriate. Use of gradient factors will increase decompression time, particularly in the depth zone where the M-value is reduced the most. Gradient factors may be used to force deeper stops in a model which would otherwise tend to produce relatively shallow stops, by using a gradient factor with a small first number.

Gradient factors produce an M-value which is linearly variable in proportion to ambient pressure.

The critical volume approach

The critical-volume criterion assumes that whenever the total volume of gas phase accumulated in the tissues exceeds a critical value, signs or symptoms of DCS will appear. This assumption is supported by doppler bubble detection surveys. The consequences of this approach depend strongly on the bubble formation and growth model used, primarily whether bubble formation is practicably avoidable during decompression.

This approach is used in decompression models that assume that during practical decompression profiles, there will be growth of stable microscopic bubble nuclei which always exist in aqueous media, including living tissues.

Efficient decompression will minimise the total ascent time while limiting the total accumulation of bubbles to an acceptable non-symptomatic critical value. The physics and physiology of bubble growth and elimination indicate that it is more efficient to eliminate bubbles while they are very small. Models which include bubble phase have produced decompression profiles with slower ascents and deeper initial decompression stops as a way of curtailing bubble growth and facilitating early elimination, in comparison with the models which consider only dissolved phase gas.

The no-supersaturation approach

According to the thermodynamic model of LeMessurier and Hills,[19] this condition of optimum driving force for outgassing is satisfied when the ambient pressure is just sufficient to prevent phase separation (bubble formation).

The fundamental difference of this approach is equating absolute ambient pressure with the total of the partial gas tensions in the tissue for each gas after decompression as the limiting point beyond which bubble formation is expected.

The model assumes that the natural unsaturation in the tissues due to metabolic reduction in oxygen partial pressure provides the buffer against bubble formation, and that the tissue may be safely decompressed provided that the reduction in ambient pressure does not exceed this unsaturation value. Clearly any method which increases the unsaturation would allow faster decompression, as the concentration gradient would be greater without risk of bubble formation.

The natural unsaturation increases with depth, so a larger ambient pressure differential is possible at greater depth, and reduces as the diver surfaces. This model leads to slower ascent rates and deeper first stops, but shorter shallow stops, as there is less bubble phase gas to be eliminated.

Bubble formation, growth and elimination

Bubble mechanics

Equilibrium of forces on the surface is required for a bubble to exist. These are:

  • Ambient pressure, exerted on the outside of the surface, acting inwards
  • Pressure due to tissue distortion, also on the outside and acting inwards
  • Surface tension of the liquid at the interface between the bubble and the surroundings. This is along the surface of the bubble, so the resultant acts towards the centre of curvature. This will tend to squeeze the bubble, and is more severe for small bubbles as it is an inverse function of the radius.
  • The resulting forces must be balanced by the pressure on the inside of the bubble. This is the sum of the partial pressures of the gases inside due to the net diffusion of gas to and from the bubble.
  • The force balance in the bubble may be modified by a layer of surface active molecules which can stabilise a microbubble at a size where surface tension on a a clean bubble would cause it to collapse rapidly.[20]
  • This surface layer may vary in permeability, so that if the bubble is compressed it may become impermeable to diffusion at sufficient compression.[20]

If the solvent outside the bubble is saturated or unsaturated, the partial pressure will be less than in the bubble, and the surface tension will be increasing the internal pressure in direct proportion to surface curvature, providing a pressure gradient to increase diffusion out of the bubble, effectively "squeezing the gas out of the bubble", and the smaller the bubble the faster it will get squeezed out. A gas bubble can only grow at constant pressure if the surrounding solvent is sufficiently supersaturated to overcome the surface tension or if the surface layer provides sufficient reaction to overcome surface tension.[20]

Clean bubbles that are sufficiently small will collapse due to surface tension if the supersaturation is low. Bubbles with semipermeable surfaces will either stabilise at a specific radius depending on the pressure, the composition of the surface layer, and the supersaturation, or continue to grow indefinitely, if larger than the critical radius.[21]

Bubble nucleation

Bubble formation occurs in the blood or other tissues, possibly in crevices in macromolecules.[22]

A solvent can carry a supersaturated load of gas in solution. Whether it will come out of solution in the bulk of the solvent to form bubbles will depend on a number of factors. Something which reduces surface tension, or adsorbs gas molecules, or locally reduces solubility of the gas, or causes a local reduction in static pressure in a fluid may result in a bubble nucleation or growth. This may include velocity changes and turbulence in fluids and local tensile loads in solids and semi-solids. Lipids and other hydrophobic surfaces may reduce surface tension (blood vessel walls may have this effect). Dehydration may reduce gas solubility in a tissue due to higher concentration of other solutes, and less solvent to hold the gas.

Another theory presumes that microscopic bubble nuclei always exist in aqueous media, including living tissues. These bubble nuclei are spherical gas phases that are small enough to remain in suspension yet strong enough to resist collapse, their stability being provided by an elastic surface layer consisting of surface-active molecules which resists the effect of surface tension.[23]

Bubble growth

Once a micro-bubble forms it may continue to grow if the tissues are still supersaturated. As the bubble grows it may distort the surrounding tissue and cause damage to cells and pressure on nerves resulting in pain, or may block a blood vessel, cutting off blood flow and causing hypoxia in the tissues normally perfused by the vessel.

If a bubble or an object exists which collects gas molecules this may reach a size where the internal pressure exceeds the combined surface tension and external pressure and the bubble will grow.

If the solvent is sufficiently supersaturated, the diffusion of gas into the bubble will exceed the rate at which it diffuses back into solution. If this excess pressure is greater than the pressure due to surface tension the bubble will grow. When a bubble grows, the surface tension decreases, and the interior pressure drops, allowing gas to diffuse in faster, and diffuse out slower, so the bubble grows or shrinks in a positive feedback situation. The growth rate is reduced as the bubble grows by the fact that the surface area increases as the square of the radius, while the volume increases as the cube of the radius. If the external pressure is reduced (due to reduced hydrostatic pressure during ascent, for example) the bubble will also grow.

The Variable Permeability Model ordering hypothesis states that nuclei are neither created nor totally eliminated during the pressure cycle, and the initial ordering according to size is preserved. therefore each bubble count is determined by the properties and behavior of a nominal "critical" nucleus which is at the threshold of bubble-formation – all larger nuclei will form bubbles, and all smaller nuclei will not.[20]

Bubble distribution

Decompression bubbles appear to form mostly in the systemic capillaries where the gas concentration is highest, often those feeding the veins draining the active limbs. They do not generally form in the arteries, as arterial blood has recently had the opportunity to release excess gas into the lungs. The bubbles carried back to the heart in the veins may be transferred to the systemic circulation via a patent foramen ovale in divers with this septal defect, after which there is a risk of occlusion of capillaries in whichever part of the body they end up in.

Bubbles are also known to form within other tissues, where they may cause damage leading to symptoms of decompression sickness. This damage is likely to be caused by mechanical deformation and stresses on the cells rather than local hypoxia, which is the assumed mechanism in the case of gas embolism of the capillaries.

Bubble elimination

Bubbles which are carried back to the heart in the veins will normally find their way to the right side of the heart, and from there they will normally enter the pulmonary circulation and eventually pass through or be trapped in the capillaries of the lungs, which are around the alveoli and very near to the respiratory gas, where the gas will diffuse from the bubbles though the capillary and alveolar walls into the gas in the lung. If the number of lung capillaries blocked by these bubbles is relatively small, the diver will not display symptoms, and no tissue will be damaged (lung tissues are adequately oxygenated by diffusion).

The bubbles which are small enough to pass through the lung capillaries may be small enough to be dissolved due to a combination of surface tension and diffusion to a lowered concentration in the surrounding blood, though the Varying Permeability Model nucleation theory implies that most bubbles passing through the pulmonary circulation will lose enough gas to pass through the capillaries and return to the systemic circulation as recycled but stable nuclei.[24]

Bubbles which form within the tissues must be eliminated in situ by diffusion, which implies a suitable concentration gradient.

Isobaric counterdiffusion (ICD)

Isobaric counterdiffusion is the diffusion of gases in opposite directions caused by a change in the composition of the external ambient gas or breathing gas without change in the ambient pressure. During decompression after a dive this can occur when a change is made to the breathing gas, or when the diver moves into a gas filled environment which differs from the breathing gas.

While not strictly speaking a phenomenon of decompression, it is a complication that can occur during decompression, and that can result in the formation or growth of bubbles without changes in the environmental pressure. Two forms of this phenomenon have been described by Lambertsen:[25][26]

Superficial ICD

Superficial ICD (also known as Steady State Isobaric Counterdiffusion[27]) occurs when the inert gas breathed by the diver diffuses more slowly into the body than the inert gas surrounding the body.[25][26][27]

An example of this would be breathing air in an heliox environment. The helium in the heliox diffuses into the skin quickly, while the nitrogen diffuses more slowly from the capillaries to the skin and out of the body. The resulting effect generates supersaturation in certain sites of the superficial tissues and the formation of inert gas bubbles.

Deep Tissue ICD

Deep Tissue ICD (also known as Transient Isobaric Counterdiffusion[27]) occurs when different inert gases are breathed by the diver in sequence.[25][26] The rapidly diffusing gas is transported into the tissue faster than the slower diffusing gas is transported out of the tissue.

This can occur as divers switch from a nitrogen mixture to a helium mixture (diffusivity of helium is 2.65 times faster than nitrogen), or when saturation divers breathing hydreliox switch to a heliox mixture.[citation needed]

There is another effect which can manifest as a result of the disparity in solubility between inert breathing gas diluents, which occurs in isobaric gas switches near the decompression ceiling between a low solubility gas (typically helium, and a higher solubility gas, typically nitrogen)

An inner ear decompression model by Doolette and Mitchell[28] suggests that a transient increase in gas tension after a switch from helium to nitrogen in breathing gas may result from the difference in gas transfer between compartments. If the transport of nitrogen into the vascular compartment by perfusion exceeds removal of helium by perfusion, while transfer of helium into the vascular compartment by diffusion from the perilymph and endolymph exceeds the counterdiffusion of nitrogen, this may result in a temporary increase in total gas tension, as the input of nitrogen exceeds the removal of helium, which can result in bubble formation and growth. This model suggests that diffusion of gases from the middle ear across the round window is negligible. The model is not necessarily applicable to all tissue types.

ICD Prevention

Lambertsen made suggestions to help avoid ICD while diving:[25][26]

  • If the diver is surrounded by or saturated with nitrogen, they should not breathe helium rich gases.
  • Gas switches that involve going from helium rich mixtures to nitrogen rich mixtures would be acceptable, but changes from nitrogen to helium should include recompression.

However Doolette and Mitchell's more recent study of Inner Ear Decompression Sickness (IEDCS) shows that the inner ear may not be well-modelled by common (e.g. Bühlmann) algorithms. Doolette and Mitchell propose that a switch from a helium-rich mix to a nitrogen-rich mix, as is common in technical diving when switching from trimix to nitrox on ascent, may cause a transient supersaturation of inert gas within the inner ear and result in IEDCS. They suggest that:[28]

  • Breathing-gas switches from helium-rich to nitrogen-rich mixtures should be carefully scheduled either deep (with due consideration to nitrogen narcosis) or shallow to avoid the period of maximum supersaturation resulting from the decompression. Switches should also be made during breathing of the largest inspired oxygen partial pressure that can be safely tolerated with due consideration to oxygen toxicity.

A similar hypothesis to explain the incidence of IEDCS when switching from trimix to nitrox was proposed by Steve Burton, who considered the effect of the much greater solubility of nitrogen than helium in producing transient increases in total inert gas pressure, which could lead to DCS under isobaric conditions.[29]

Burton argues that effect of switching to Nitrox from Trimix with a large increase of nitrogen fraction at constant pressure has the effect of increasing the overall gas loading within particularly the faster tissues, since the loss of helium is more than compensated by the increase in nitrogen. This could cause immediate bubble formation and growth in the fast tissues. A simple rule for avoidance of ICD when gas switching at a decompression ceiling is suggested:

  • Any increase in gas fraction of nitrogen in the decompression gas should be limited to 1/5 of the decrease in gas fraction of helium.[29]

This rule has been found to successfully avoid ICD on hundreds of deep trimix dives.[29]

Doppler ultrasonic bubble detection

Doppler bubble detection equipment uses ultrasonic signals reflected from bubble surfaces to identify and quantify gas bubbles present in venous blood. This method was used by Dr Merrill Spencer of the Institute of Applied Physiology and Medicine in Seattle, who published a report in 1976 recommending that the then current no-decompression limits be reduced on the basis that large counts of venous gas bubbles were detected in divers exposed to the US Navy no-decompression limits. These non-symptomatic bubbles have become known as "silent bubbles", and are thought to be nitrogen bubbles released from solution during ascent.[30]

Decompression sickness and injuries

Problems due to vascular decompression bubbles

Bubbles may be trapped in the lung capillaries, temporarily blocking them. If this is severe, the symptom called "chokes" may occur.[31]

If the diver has a patent foramen ovale (or a shunt in the pulmonary circulation), bubbles may pass through it and bypass the pulmonary circulation to enter the arterial blood. If these bubbles are not absorbed in the arterial plasma and lodge in systemic capillaries they will block the flow of oxygenated blood to the tissues supplied by those capillaries, and those tissues will be starved of oxygen. Moon and Kisslo concluded that "the evidence suggests that the risk of serious neurological DCI or early onset DCI is increased in divers with a resting right-to-left shunt through a PFO. There is, at present, no evidence that PFO is related to mild or late onset bends."[32]

Extravascular bubbles

Bubbles form within other tissues as well as the blood vessels.[31] Inert gas can diffuse into bubble nuclei between tissues. In this case, the bubbles can distort and permanently damage the tissue. As they grow, the bubbles may also compress nerves as they grow causing pain.

Extravascular bubbles usually form in slow tissues such as joints, tendons and muscle sheaths. Direct expansion causes tissue damage, with the release of histamines and their associated affects. Biochemical damage may be as important as, or more important than mechanical effects.[31]

Factors influencing uptake and elimination of dissolved gases and decompression risk

The exchange of dissolved gases between the blood and tissues is controlled by perfusion and to a lesser extent by diffusion, particularly in heterogenous tissues. The distribution of blood flow to the tissues is variable and subject to a variety of influences. When the flow is locally high, that area is dominated by perfusion, and by diffusion when the flow is low. The distribution of flow is controlled by the mean arterial pressure and the local vascular resistance, and the arterial pressure depends on cardiac output and the total vascular resistance. Basic vascular resistance is controlled by the sympathetic nervous system, and metabolites, temperature, and local and systemic hormones have secondary and often localised effects, which can vary considerably with circumstances. Peripheral vasoconstriction in cold water decreases heat loss without increasing oxygen consumption until shivering begins, at which point oxygen consumption will rise, though the vasoconstriction can persist.[31]

Breathing gas composition

The composition of the breathing gas during pressure exposure and decompression is the most significant factor in inert gas uptake and elimination for a given pressure exposure profile, for two main reasons:

Gas fraction and partial pressure of the component inert gas

Breathing gas mixtures for diving will typically have a different gas fraction of nitrogen to that of air. The partial pressure of each component gas will differ to that of nitrogen in air at any given depth, and uptake and elimination of each inert gas component is proportional to the actual partial pressure over time. The two foremost reasons for use of mixed breathing gases are the reduction of nitrogen partial pressure by dilution with oxygen, to make Nitrox mixtures, primarily to reduce the rate of nitrogen uptake during pressure exposure, and the substitution of helium (and occasionally other gases) for the nitrogen to reduce the narcotic effects under high partial pressure exposure. Depending on the proportions of helium and nitrogen, these gases are called Heliox, if there is no nitrogen, or Trimix, if there is nitrogen and helium along with the essential oxygen.

Solubility characteristics of the inert gases in the mixture

The inert gases used as substitutes for nitrogen have different solubility and diffusion characteristics in living tissues to the nitrogen they replace. For example, the most common inert gas diluent substitute for nitrogen is helium, which is significantly less soluble[33] in living tissue, but also diffuses faster[34] due to the relatively small size and mass of the He atom in comparison with the N2 molecule.

Body temperature and exercise

Blood flow to skin and fat are affected by skin and core temperature, and resting muscle perfusion is controlled by the temperature of the muscle itself. During exercise increased flow to the working muscles is often balanced by reduced flow to other tissues, such as kidneys spleen and liver.

Blood flow to the muscles is lower in cold water, but exercise keeps the muscle warm and flow elevated even when the skin is chilled. Blood flow to fat normally increases during exercise, but this is inhibited by immersion in cold water. Adaptation to cold reduces the extreme vasoconstiction which usually occurs with cold water immersion.

Variations in perfusion distribution do not necessarily affect respiratory inert gas exchange, though some gas may be locally trapped by changes in perfusion. Rest in a cold environment will reduce inert gas exchange from skin, fat and muscle, whereas exercise will increase gas exchange. Exercise during decompression can reduce decompression time and risk, providing bubbles are not present, but can increase risk if bubbles are present.

Inert gas exchange is least favourable for the diver who is warm and exercises at depth during the ingassing phase, and rests and is cold during decompression.[31]

Other factors

Other factors which can affect decompression risk include oxygen concentration, carbon dioxide levels, body position, vasodilators and constrictors, positive or negative pressure breathing.[31] and dehydration (blood volume).[35]

Personal factors

Individual susceptibility to decompression sickness has components which can be attributed to a specific cause, and components which appear to be random. The random component makes successive decompressions a poor test of susceptibility.[31] Obesity and high serum lipid levels have been implicated as risk factors, and risk seems to increase with age. Other factors, such as gender and previous injury provide inconsistent results.

A more recent study has shown that older subjects tended to bubble more than younger subjects for reasons not yet known. No trends between weight, body fat, or gender and bubbles were identified, and the question of why some people are more likely to form bubbles than others remains unclear.[36]

Decompression models

A fundamental problem in the design of decompression tables is that the rules that govern a single dive and ascent do not apply when some tissue bubbles already exist, as these will delay inert gas elimination and equivalent decompression may result in decompression sickness.[37]

One attempt at a solution was the development of multi-tissue models, which assumed that different parts of the body absorbed gas at different rates. Each tissue, or compartment, has a different half-life. Fast tissues absorb gas relatively quickly, but will release it quickly during ascent. A fast tissue may become saturated in the course of a normal sports dive, while a slow tissue may hardly have absorbed any gas. By calculating the levels in each compartment separately, researchers are able to construct better tables. In addition, each compartment may be able to tolerate more or less supersaturation than others. The final form is a complicated model, but one that allows for the construction of tables suited to a wide variety of diving. A typical dive computer has a 8–12 tissue model, with half times varying from 5 minutes to 400 minutes.[citation needed] The Bühlmann tables have 16 tissues, with half times varying from 4 minutes to 640 minutes.[7]

The ideal decompression profile creates the greatest possible gradient for inert gas elimination from a tissue without causing bubbles to form,[38] but it is not certain whether this is practically possible: some of the decompression models assume that stable bubble micronuclei always exist.[23] However, the dissolved phase decompression models are based on the assumption that bubble formation can be avoided. The bubble models make the assumption that there will be bubbles, but there is a tolerable total gas phase volume[23] or a tolerable gas bubble size,[39] and limit the maximum gradient to take these tolerances into account. A number of empirical modifications to dissolved phase models have been made since the identification of venous bubbles by doppler measurement in asymptomatic divers soon after surfacing.

Repetitive diving, multiple ascents within a single dive, and surface decompression procedures are significant risk factors for DCS.[38]

Validation of models

It is important that any theory be validated by carefully controlled testing procedures. As testing procedures and equipment become more sophisticated, researchers learn more about the effects of decompression on the body. Initial research focused on producing dives that were free of recognizable symptoms decompression sickness (DCS). With the later use of Doppler ultrasound testing, it was realized that bubbles were forming within the body even on dives where no DCI signs or symptoms were encountered. This phenomenon has become known as "silent bubbles". The US Navy 1956 tables were based on limits determined by external DCS signs and symptoms. Later researchers were able to improve on this work by adjusting the limitations based on Doppler testing. However the US Navy CCR tables based on the Thalmann algorithm also used only recognisable DCS symptoms as the test criteria.[40][41]

Since the testing procedures are lengthy and costly, it is common practice for researchers to make initial validations of new models based on experimental results from earlier trials. This has some implications when comparing models.

Residual inert gas

Gas bubble formation has been experimentally shown to significantly inhibit inert gas elimination.[6][42]

A considerable amount of inert gas will remain in the tissues after a diver has surfaced. This residual gas may be dissolved or in sub-clinical bubble form, and will continue to outgas while the diver remains at the surface. If a repetitive dive is made, the tissues are preloaded with this residual gas which will make them saturate faster.

In repetitive diving, the slower tissues can accumulate gas day after day. This can be a problem for multi-day multi-dive situations. Multiple decompressions per day over multiple days can increase the risk of decompression sickness because of the build up of asymptomatic bubbles, which reduce the rate of off-gassing and are not accounted for in most decompression algorithms.[43] Consequently, some diver training organisations make extra recommendations such as taking "the seventh day off".[44]

Deterministic models

Deterministic decompression models are a rule based approach to calculating decompression.[45] These models work from the idea that "excessive" supersaturation in various tissues is "unsafe" (resulting in decompression sickness). The models usually contain multiple depth and tissue dependent rules based on mathematical models of idealised tissue compartments. There is no objective mathematical way of evaluating the rules or overall risk other than comparison with empirical test results. The models are compared with experimental results and reports from the field, and rules are revised by qualitative judgment and curve fitting so that the revised model more closely predicts observed reality, and then further observations are made to assess the reliability of the model in extrapolations into previously untested ranges. The usefulness of the model is judged on its accuracy and reliability in predicting the onset of symptomatic decompression sickness and asymptomatic venous bubbles during ascent.

It may be reasonably assumed that in reality, both perfusion transport by blood circulation, and diffusion transport in tissues where there is little or no blood flow occur. The problem with attempts to simultaneously model perfusion and diffusion is that there are large numbers of variables due to interactions between all of the tissue compartments and the problem becomes intractable.

A way of simplifying the modelling of gas transfer into and out of tissues is to make assumptions about the limiting mechanism of dissolved gas transport to the tissues which control decompression. Assuming that either perfusion or diffusion has a dominant influence, and the other can be disregarded, can greatly reduce the number of variables.

Perfusion limited tissues and parallel tissue models

The assumption that perfusion is the limiting mechanism leads to a model comprising a group of tissues with varied rates of perfusion, but supplied by blood of approximately equivalent gas concentration. It is also assumed that there is no gas transfer between tissue compartments by diffusion. This results in a parallel set of independent tissues, each with its own rate of ingassing and outgassing dependent on the rate of blood flowing through the tissue. Gas uptake for each tissue is generally modelled as an exponential function, with a fixed compartment half-time, and gas elimination may also be modelled by an exponential function, with the same or a longer half time, or as a more complex function, as in the exponential-linear elimination model.

Critical ratio hypothesis

This hypothesis predicts that the development of bubbles will occur in a tissue when the ratio of dissolved gas partial pressure to ambient pressure exceeds a particular ratio for a given tissue. The ratio may be the same for all tissue compartments or it may vary, and each compartment is allocated a specific critical supersaturation ratio, based on experimental observations.

= John Scott Haldane =

Haldane introduced the concept of half times to model the uptake and release of nitrogen into the blood. He suggested 5 tissue compartments with half times of 5, 10, 20, 40 and 75 minutes.

In this early hypothesis (Haldane 1908)[14] it was predicted that if the ascent rate does not allow the inert gas partial pressure in each of the hypothetical tissues to exceed the environmental pressure by more than 2:1 bubbles will not form.

Basically this meant that one could ascend from 30 m (4 bar) to 10 m (2 bar), or from 10 m (2 bar) to the surface when saturated, without a decompression problem.

To ensure this a number of decompression stops were incorporated into the ascent schedules.

The ascent rate and the fastest tissue in the model determine the time and depth of the first stop. Thereafter the slower tissues determine when it is safe to ascend further.

This 2:1 ratio was found to be too conservative for fast tissues (short dives) and not conservative enough for slow tissues (long dives). The ratio also seemed to vary with depth.

The ascent rates used on older tables were 18 m/min, but newer tables use 9 m/min.

Critical difference hypothesis
= Robert D. Workman =

Haldane's approach to decompression modeling was used from 1908 to the 1960s with minor modifications, primarily changes to the number of compartments and half times used. The 1937 US Navy tables were based on research by O. D. Yarborough and used 3 compartments. The 5 and 10 min compartments were dropped. In the 1950s the tables were revised and the 5 and 10 minute compartments restored, and a 120 minute compartment added.

In the 1960s Robert D. Workman of the U.S. Navy Experimental Diving Unit (NEDU) undertook a review of the basis of the model and subsequent research performed by the US Navy. Tables based on Haldane's work and subsequent refinements were observed to still be inadequate for longer and deeper dives.

Workman revised Haldane's model to allow each tissue compartment to tolerate a different amount of supersaturation which varies with depth. He introduced the term "M-value" to indicate the maximum amount of supersaturation each compartment could tolerate at a given depth and added three additional compartments with 160, 200 and 240 minute half times.

Workman presented his findings as an equation which could be used to calculate the results for any depth and stated that a linear projection of M-values would be useful for computer programming.

= Albert A. Bühlmann =

A large part of Bühlmann's research was to determine the longest half time compartments for Nitrogen and Helium, and he increased the number of compartments to 16. He investigated the implications of decompression after diving at altitude and published decompression tables that could be used at a range of altitudes. Bühlmann used a method for decompression calculation similar to that proposed by Workman, which included M-values expressing a linear relationship between maximum inert gas pressure in the tissue compartments and ambient pressure, but based on absolute pressure, which made them more easily adapted for altitude diving.

Bühlmann's algorithm was used to generate the standard decompression tables for a number of sports diving associations, and are used in several personal decompression computers, sometimes in a modified form.

Thermodynamic model and deep stops
= Torres Strait pearl divers =

B.A. Hills and D.H. LeMessurier studied the empirical decompression practices of Okinawan pearl divers in the Torres Strait and observed that they made deeper stops but reduced the total decompression time compared with the generally used tables of the time. Their analysis strongly suggested that bubble presence limits gas elimination rates, and emphasised the importance of inherent unsaturation of tissues due to metabolic processing of oxygen.[19]

= Pyle stops =

A "Pyle stop" is an additional brief deep-water stop, which is increasingly used in deep diving (named after Richard Pyle, an early advocate of deep stops).[46] Typically, a Pyle stop is 2 minutes long and at the depth where the pressure change halves on an ascent between the bottom and the first conventional decompression stop.

For example, a diver ascends from a maximum depth of 60 metres (200 ft), where the ambient pressure is 7 bars (100 psi), to a decompression stop at 20 metres (66 ft), where the pressure is 3 bars (40 psi). The Pyle stop would take place at the halfway pressure, which is 5 bars (70 psi) corresponding to a depth of 40 metres (130 ft).[47][48]

Pyle found that on dives where he stopped periodically to vent the swim-bladders of his fish specimens, he felt better after the dive, and based the deep stop procedure on the depths and duration of these pauses. The hypothesis is that these stops provide an opportunity to eliminate gas while still dissolved, or at least while the bubbles are still small enough to be easily eliminated, and the result is that there will be considerably fewer or smaller venous bubbles to eliminate at the shallower stops as predicted by the thermodynamic model of Hills.

Diffusion limited tissues and the "Tissue slab", and series models
Derivation of the one-dimensional tissue slab model from a uniform tissue perfused by parallel capillaries

The assumption that diffusion is the limiting mechanism of dissolved gas transport in the tissues results in a rather different tissue compartment model. In this case a series of compartments has been postulated, with perfusion transport into one compartment, and diffusion between the compartments, which for simplicity are arranged in series, so that for the generalised compartment, diffusion is to and from only the two adjacent compartments on opposite sides, and the limit cases are the first compartment where the gas is supplied and removed via perfusion, and the end of the line, where there is only one neighbouring compartment.

The simplest series model is a single compartment, and this can be further reduced to a one dimensional "tissue slab" model.

Bubble models

Bubble decompression models are a rule based approach to calculating decompression based on the idea that microscopic bubble nuclei always exist in water and tissues that contain water and that by predicting and controlling the bubble growth, one can avoid decompression sickness. Most of the bubble models assume that bubbles will form during decompression, and that mixed phase gas elimination occurs.

Decompression models that assume mixed phase gas elimination include:

  • The arterial bubble decompression model of the French Tables du Ministère du Travail 1992
  • The U.S.Navy Exponential-Linear (Thalmann) algorithm used for the 2008 US Navy air decompression tables (among others)
  • Hennessy's combined perfusion/diffusion model of the BSAC'88 tables
  • The Varying Permeability Model (VPM) developed by D.E. Yount and others at the University of Hawaii
  • The Reduced Gradient Bubble Model (RGBM) developed by Bruce Wienke at Los Alamos National Laboratory

Probabilistic models

Probabilistic decompression models are designed to calculate the risk (or probability) of decompression sickness (DCS) occurring on a given decompression profile.[45] These models can vary the decompression stop depths and times to arrive at a final decompression schedule that assumes a specified probability of DCS occurring. The model does this while minimizing the total decompression time. This process can also work in reverse allowing one to calculate the probability of DCS for any decompression schedule.

Decompression practice

History of decompression research and development

See also

References

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  2. ^ BSAC '88 Decompression Tables Levels 1 to 4
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  40. ^ Thalmann 1984, p. 24
  41. ^ Thalmann 1985, p. 5
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  43. ^ Lang, Michael A; Vann, Richard D (1991). Proceedings of the AAUS Repetitive Diving Workshop. Duke University, Durham, NC: American Academy of Underwater Sciences. p. 339. Retrieved 31 October 2011.{{cite book}}: CS1 maint: multiple names: authors list (link)
  44. ^ Cole, Bob (2008). "Diver Behaviour – Micro-bubble Control". SAA Buhlmann Deep Stop System Handbook. Sub-Aqua Association. pp. 4–2. ISBN 0-9532904-8-4. The SAA recommends that you to [sic] take at least the seventh day off to allow your body to off-gas and return to some level of normality
  45. ^ a b Doolette David J (2005). "Development and testing of deterministic and probabilistic decompression models". South Pacific Underwater Medicine Society Journal. 35 (1). Retrieved 10 January 2012. {{cite journal}}: Invalid |ref=harv (help)
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Sources

Further reading

  1. Powell, Mark (2008). Deco for Divers. Southend-on-Sea: Aquapress. ISBN 1-905492-07-3.
  2. Hills. B. (1966); A thermodynamic and kinetic approach to decompression sickness. Thesis
  3. Gribble, M. de G. (1960); A comparison of the High-Altitude and High-Pressure syndromes of decompression sickness, Brit. J. industr. Med., 1960, 17, 181.
  4. Lippmann, John; Mitchell, Simon (2005). Deeper into Diving (2nd ed.). Melbourne, Australia: J L Publications. ISBN 0-9752290-1-X. Section 2 chapters 13–24 pages 181–350