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{{main|Physiology of decompression}}
[[File:Tissue half times (1).svg|thumb|upright=1.5|alt=Graph showing dissolved gas concentration change over time for a step pressure increment in an initially saturated solvent]]
The evidence that decompression sickness is caused by bubble formation and growth within the body tissues resulting from supersaturated dissolved gas is strong, but research results also suggest that the quantity of those bubbles alone is not enough to predict whether someone will experience symptoms of DCS.<ref name="Fogarty 2025" />
[[Breathing gas|Gas]] is breathed at ambient pressure, and some of this gas dissolves into the blood and other fluids. Inert gas continues to be taken up until the gas dissolved in the tissues is in a state of equilibrium with the gas in the [[lungs]] (see [[saturation diving]]), or the ambient pressure is reduced until the inert gases dissolved in the tissues are at a higher concentration than the equilibrium state, and start diffusing out again.<ref name="USNDM R6 3-9.3" />
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If the concentration of the inert gas in the breathing gas is reduced below that of any of the tissues, there will be a tendency for gas to return from the tissues to the breathing gas. This is known as [[outgassing]], and occurs during decompression, when the reduction in ambient pressure or a change of breathing gas reduces the partial pressure of the inert gas in the lungs.<ref name="USNDM R6 3-9.3" />
The combined concentrations of gases in any given tissue will depend on the history of pressure and gas composition. Under equilibrium conditions, the total concentration of dissolved gases will be less than the ambient pressure, as oxygen is metabolised in the tissues, and the carbon dioxide produced is much more soluble. However, during a reduction in ambient pressure, the rate of pressure reduction may exceed the rate at which gas can be eliminated by diffusion and perfusion, and if the concentration gets too high, it may reach a stage where bubble formation can occur in the supersaturated tissues. When the pressure of gases in a bubble
The actual rates of diffusion and perfusion
Decompression involves a complex interaction of gas solubility, partial pressures and concentration gradients, diffusion, bulk transport and bubble mechanics in living tissues.<ref name="Wienke" />
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The function of decompression models has changed with the availability of Doppler ultrasonic bubble detectors, and is no longer merely to limit symptomatic occurrence of decompression sickness, but also to limit asymptomatic post-dive venous gas bubbles.<ref name="Papadopoulou 2013" /> 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.<ref name="Huggins 1981"/>
===Efficiency and safety===
Two criteria that have been used in comparing decompression schedules are efficiency and safety, where decompression efficiency is defined as the ability of a schedule to provide acceptable safety from decompression sickness in the shortest time spent decompressing, and decompression safety, or converely, risk, is measured by the probability of decompression sickness incurred by following a given schedule for a given dive profile. Since it is impracticable to eliminate all risk using current knowledge of the effects of several variables, risk is estimated by statistical analysis of the recorded outcomes of exposure and decompression profiles, and an acceptable risk is stipulated, which may vary depending on the circumstances of the application.<ref name="Edel 1980" />
=== Tissue compartments ===
One attempt at a solution was the development of multi-tissue models, which assumed that different parts of the body absorbed and eliminated gas at different rates. These are hypothetical tissues which are designated as fast and slow to describe the rate of saturation. Each tissue, or compartment, has a different half-life. 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<ref name="Buhlmann 1984" /> have been used to generate decompression tables, and [[dive computer]]s have used up to 20 compartments.<ref name="Validation workshop" />
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, compared to tissues with a good blood supply and less capacity for dissolved gas, which are described as fast.<ref name="DAN intro to DCS" />
Fast tissues absorb gas relatively quickly, but will generally release it quickly during ascent. A fast tissue may become saturated in the course of a normal recreational dive, while a slow tissue may have absorbed only a small part of its potential gas capacity. By calculating the levels in each compartment separately, researchers are able to construct more effective algorithms. 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 algorithms and tables suited to a wide variety of diving.<ref name="DAN intro to DCS" /> A typical dive computer has an 8–12 tissue model, with half times varying from 5 minutes to 400 minutes.<ref name="Validation workshop" /> The [[Bühlmann tables]] use an algorithm with 16 tissues, with half times varying from 4 minutes to 640 minutes.<ref name="Buhlmann 1984" />
Tissues may be assumed to be in series, where dissolved gas must diffuse through one tissue to reach the next, which has different solubility properties, in parallel, where diffusion into and out of each tissue is considered to be independent of the others, and as combinations of series and parallel tissues, which becomes computationally complex.<ref name="Goldman 2007" />
===Ingassing model===
<!-- target for redirect [[Ingassing]] -->
The 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.<ref name="Bookspan"/> Tissue compartment half times range from 1 minute to at least 720 minutes.{{sfn|Yount|1991|p=137}} A specific tissue compartment will have different half times for gases with different solubilities and diffusion rates. Ingassing is generally modeled as following a simple inverse exponential equation where saturation is assumed after approximately four (93.75%) to six (98.44%) half-times depending on the decompression model.<ref name="Huggins 1992 Chapter 2"/><ref name=logodiving /><ref name="Maiken" /> There is normally no phase change during ingassing after the gases are dissolved in the blood of the pulmonary circulation in the lungs. They remain in solution in whichever tissues they reach by perfusion and diffusion, so the model is fairly robust. The exception is for [[isobaric counterdiffusion]] which can induce bubble growth and posssibly bubble formation when a gas of different solubility is introduced to the breathing mixture.{{sfn|Hamilton|Thalmann|2003|pp=477–478}}<ref name="Lambertson 1989" />
This model may not adequately describe the dynamics of outgassing if gas phase bubbles are present.<ref name="Wienke 1990" /><ref name="Yount 1990" />
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==== The critical supersaturation approach ====
<!-- target for redirect [[M-value (decompression)]] -->
[[John Scott Haldane|J.S. Haldane]] originally used a ''critical 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.<ref name="Haldane1908" /> 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.<ref name="Huggins 1992 3-2" />
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=== Bounce dives ===
A bounce dive is any dive where the exposure to pressure is not long enough for all the tissues to reach equilibrium with the inert gases in the breathing gas.
=== Saturation dives===
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=== Decompression obligation ===
A decompression obligation is the presence in the tissues of sufficient dissolved gas that the risk of symptomatic decompression sickness is unacceptable if a direct ascent to surface pressure is made at the prescribed ascent rate for the decompression model in use. A diver with a decompression ceiling can be said to have a decompression obligation, meaning that time must be spent outgassing during the ascent additional to the time spent ascending at the appropriate ascent rate. This time is nominally and most efficiently spent at decompression stops, though outgassing will occur at any depth where the arterial blood and lung gas have a lower partial pressure of the inert gas than the limiting tissue. When a decompression obligation exists, there will be a theoretical safe minimum depth known as the [[decompression ceiling]]. {{visible anchor|Obligatory decompression stops}} will be indicated at a depth at or below the current ceiling.<ref name="Doolette et al 2015" />
=== Time to surface ===
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A large part of [[Albert A. 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.<ref name="Huggins 1992 Chapter 4"/> Bühlmann's algorithm was used to generate the standard decompression tables for a number of sports diving associations, and is used in several personal decompression computers, sometimes in a modified form.<ref name="Huggins 1992 Chapter 4"/>
[[Brian Andrew Hills|B.A. Hills]] and [[David Hugh LeMessurier|D.H. LeMessurier]] studied the empirical decompression practices of [[Okinawa Prefecture|Okinawa]]n [[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 emphasized the importance of inherent unsaturation of tissues due to metabolic processing of oxygen. This became known as the thermodynamic model.<ref name="LeMessurier and Hills" /> More recently, recreational technical divers developed decompression procedures using deeper stops than required by the decompression tables in use. These led to the RGBM and VPM bubble models.<ref name="BMC2004" /> A deep stop was originally an extra stop introduced by divers during ascent, at a greater depth than the deepest stop required by their computer algorithm. There are also computer algorithms that are claimed to use deep stops, but these algorithms and the practice of deep stops have not been adequately validated.<ref name="Denoble" />
A "[[Pyle stop (Decompression)|Pyle stop]]" is a deep stop named after [[Richard Pyle]], an early advocate of deep stops,<ref name="DecoWeenie" /> at the depths halfway between the bottom and the first conventional decompression stop, and halfway between the previous Pyle stop and the deepest conventional stop, provided the conventional stop is more than 9 m shallower. A Pyle stop is about 2 minutes long. The additional ascent time required for Pyle stops is included in the dive profile before finalising the decompression schedule.<ref name="Pyle1997" /> Pyle found that on dives where he stopped periodically to vent the [[swim-bladder]]s of his fish specimens, he felt better after the dive, and based the deep stop procedure on the depths and duration of these pauses.<ref name="Denoble" /> 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.<ref name="Wienke 2002" />
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==== Diffusion limited tissues and the "Tissue slab", and series models ====
<!-- target for redirect from [[Tissue slab diffusion model]], and [[Tissue slab decompression model]] -->
[[File:Ttissue slab model development.svg|thumb|upright=1.4|alt= |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.<ref name="Huggins 1992 Chapter 4"/> The simplest series model is a single compartment, and this can be further reduced to a one-dimensional "tissue slab" model.<ref name="Huggins 1992 Chapter 4"/>
==== Bubble models ====
<!--target for redirect [[Bubble decompression model]]-->
[[
Decompression models that assume mixed phase gas elimination include:
* The arterial bubble decompression model of the French ''Tables du Ministère du Travail''<ref name="Lang and Angelini 2009" /> 1992<ref name="Imbert 2004" />
* The U.S. Navy Exponential-Linear (Thalmann) algorithm used for the 2008 US Navy air decompression tables (among others)<ref name="Huggins 1992 Chapter 4"/>
* Hennessy's combined perfusion/diffusion model of the BSAC'88 tables
* The Varying Permeability Model (VPM) developed by D.E. Yount and
* The Reduced Gradient Bubble Model (RGBM) developed by Bruce Wienke in 1990 at Los Alamos National Laboratory<ref name="Wienke 2002" />
*Michael Gernhardt proposed the Tissue Bubble Dynamics Model (1991)
*Wayne Gerth and Richard Vann (1997) published the Probabilistic Gas and Bubble Dynamics Model.<ref name="Lang and Angelini 2009" />
* Lewis and Crow introduced their Gas Formation Model (GFM) in 2008.<ref name="Lang and Angelini 2009" />
* The Copernicus model of Gutvik and Brubakk (2009)<ref name="Lang and Angelini 2009" />
The most widely implemented model in dive computers is a simplified modification of the RGBM.<ref name="Lang and Angelini 2009" />
The models of Yount and Hoffman, and Wienke, assume that bubble formation is due to supersaturation, while Gernhardt, Gerth and Vann, and Gutvik and Brubakk assume pre-existing microscopic bubble nuclei, which grow when concentration of gases in the tissues is high enough. These models are more mathematically complex, and as of 2009 were unsuitable for real-time computation by dive computer.<ref name="Lang and Angelini 2009" />
====Goldman Interconnected Compartment Model====
<!--target for redirect from [[Goldman Interconnected Compartment Model]] -->
[[File:Interconnected 3 compartment models.svg|thumb|upright=1.4|alt= |Interconnected 3 compartment models, as used in the Goldman models]]
In contrast to the independent parallel compartments of the Haldanean models, in which all compartments are considered risk bearing, the Goldman model posits a relatively well perfused "active" or "risk-bearing" compartment in series with adjacent relatively poorly perfused "reservoir" or "buffer" compartments, which are not considered potential sites for bubble formation, but affect the probability of bubble formation in the active compartment by diffusive inert gas exchange with the active compartment.<ref name="Goldman 2007" /><ref name="Goldman 2010" /> During compression, gas diffuses into the active compartment and through it into the buffer compartments, increasing the total amount of dissolved gas passing through the active compartment. During decompression, this buffered gas must pass through the active compartment again before it can be eliminated. If the gas loading of the buffer compartments is small, the added gas diffusion through the active compartment is slow.<ref name="Goldman 2010" /> The interconnected models predict a reduction in gas washout rate with time during decompression compared with the rate predicted for the independent parallel compartment model used for comparison.<ref name="Goldman 2007" />
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=== Probabilistic models ===
<!--target for redirect [[Probabilistic decompression model]]-->
[[Probability theory|Probabilistic]] decompression models are designed to calculate the [[risk]] (or probability) of [[decompression sickness]] (DCS) occurring on a given decompression profile.<ref name="Howle et al 2017" /><ref name="RRR9570" /> Statistical analysis is well suited to compressed air work in tunneling operations due to the large number of subjects undergoing similar exposures at the same ambient pressure and temperature, with similar workloads and exposure times, with the same decompression schedule.<ref name="Vann and Dunford 2013" /> Large numbers of decompressions under similar circumstances have shown that it is not reasonably practicable to eliminate all risk of DCS, so it is necessary to set an acceptable risk, based on the other factors relevant to the application. For example, easy access to effective treatment in the form of hyperbaric oxygen treatment on site, or greater advantage to getting the diver out of the water sooner, may make a higher incidence acceptable, while interfering with work schedule, adverse effects on worker morale or a high expectation of litigation would shift acceptable incidence rate downward. Efficiency is also a factor, as decompression of employees occurs during working hours.<ref name="Vann and Dunford 2013" />
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=== Validation of models ===
<!--target for redirect [[Validation of decompression 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 of 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 presence of venous gas emboli is considered a low specificity predictor of decompression sickness, but their absence is recognised to be a sensitive indicator of low risk decompression, therefore the quantitative detection of VGE is thought to be useful as an indicator of decompression stress when comparing decompression strategies, or assessing the efficiency of procedures.<ref name="Hugon et al 2018" />
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Gas switching during decompression on open circuit is done primarily to increase the partial pressure of oxygen to increase the [[oxygen window]] effect, while keeping below [[Oxygen toxicity|acute toxicity]] levels. It is well established both in theory and practice, that a higher oxygen partial pressure facilitates a more rapid and effective elimination of inert gas, both in the dissolved state and as bubbles.
In closed circuit rebreather diving the oxygen partial pressure throughout the dive is maintained at a relatively high but tolerable level to reduce the ongassing as well as to accelerate offgassing of the diluent gas. Changes from helium-based diluents to nitrogen during ascent are desirable for reducing the use of expensive helium, but have other implications. It is unlikely that changes to nitrogen based decompression gas will accelerate decompression in typical technical bounce dive profiles, but there is some evidence that decompressing on helium-oxygen mixtures is more likely to result in neurological DCS, while nitrogen based decompression is more likely to produce other
==== Altitude exposure, altitude diving and flying after diving ====
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* Early decompression stress biomarkers
* The effects of normobaric oxygen on blood and in DCI first aid
{{expand section|<ref name="Fogarty 2025" /> |date=May 2025}}
===Practical effectiveness of models===
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The practical efficacy of gas switches from helium-based diluent to nitrox for accelerating decompression has not been demonstrated convincingly. These switches increase risk of inner ear decompression sickness due to counterdiffusion effects.<ref name="Mitchell 2016" />
Besides the basic dive profile and gas mixes, and the residual gas load from previous dives, three groups of factors are considered likely to have significant influence on decompression stress, the evolution of bubbles in the diver, and development of symptoms. These are exercise, before, during and after the dive, Thermal status, during and after the dive, including the effects on perfusion distribution and changes during the dive, and the set of factors grouped under the label "predisposition", such as the state of hydration, physical fitness, age, biological health, and other characteristics which could affect the uptake and release of gases in the diver. Currently these factors cannot be used to make reproducible predictions about decompression risk, and some cannot be numerically evaluated in real time.<ref name="Fogarty 2025" />
{{expand section|from<ref name="Blömeke 2024" >{{cite magazine |url=https://indepthmag.com/thalmann-algorithm/ |title=Dial In Your DCS Risk with the Thalmann Algorithm |work=InDepth |first=Tim |last=Blömeke |date=3 April 2024 }}</ref> |date=April 2024}}▼
▲{{expand section|from<ref name="Blömeke 2024" >{{cite magazine |url=https://indepthmag.com/thalmann-algorithm/ |title=Dial In Your DCS Risk with the Thalmann Algorithm |
== Teaching of decompression theory ==
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<ref name="About DAN research" >{{cite web |url=https://www.daneurope.org/about-dan-research |title=About DAN Research |last=<!-- not specfied --> |website=daneurope.org |publisher=DAN Europe |access-date=13 February 2016 |archive-date=22 February 2016 |archive-url=https://web.archive.org/web/20160222095529/http://www.daneurope.org/about-dan-research |url-status=dead }}</ref>
<ref name="Angelini et al 2022" >{{cite journal
<ref name="Anttila" >{{cite web |url=http://www.diverite.com/education/rebreather/tips/gradient%20factors/ |title=Gradient Factors |last=Anttila |first=Matti |access-date=2 May 2012 |archive-date=26 December 2011 |archive-url=https://web.archive.org/web/20111226064146/http://www.diverite.com/education/rebreather/tips/gradient%20factors/ |url-status=dead }}</ref>
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|url=https://www.diversalertnetwork.org/default.aspx?a=news&id=514 }}</ref>
<ref name="Bookspan" >{{cite web |url=http://www.diversalertnetwork.org/medical/articles/Are_Tissue_Halftimes_Real |title=Are Tissue Halftimes Real? |last=Bookspan |first=Jolie |date=June 2005 |work=DAN Mediucal articles |publisher=Divers Alert Network |access-date=8 March 2016 |archive-date=12 October 2015 |archive-url=https://web.archive.org/web/20151012235042/https://www.diversalertnetwork.org/medical/articles/Are_Tissue_Halftimes_Real |url-status=live }}</ref>
<ref name="Bookspan 2003" >{{Cite journal |last1=Bookspan |first1=J. |title=Detection of endogenous gas phase formation in humans at altitude |journal=Medicine & Science in Sports & Exercise |volume=35 |issue=5 |date=May 2003 |page=S164 |url=http://scuba-doc.com/bubbalt.html |access-date=7 May 2012 |doi=10.1097/00005768-200305001-00901 |doi-access=free |archive-date=19 November 2011 |archive-url=https://web.archive.org/web/20111119000233/http://scuba-doc.com/bubbalt.html |url-status=live }}</ref>
<ref name=Brubakk >{{cite book |title=Bennett and Elliott's physiology and medicine of diving
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|isbn=978-0-387-13308-9 |author-link=Albert A. Bühlmann }}</ref>
<ref name="burton2004">{{cite web |last=Burton |first=Steve |title=Isobaric Counter Diffusion |publisher=ScubaEngineer |date=December 2004 |url=http://www.scubaengineer.com/isobaric_counter_diffusion.htm |access-date=3 February 2011 |archive-date=10 March 2009 |archive-url=https://web.archive.org/web/20090310021040/http://www.scubaengineer.com/isobaric_counter_diffusion.htm |url-status=live }}</ref>
<ref name="Campbell 1997" >{{cite web |url=http://www.scuba-doc.com/dcsprbs.html#DCS:Definition |title=Decompression Illness in Sports Divers: Part I |last=Campbell |first=Ernest S. |year=1997 |work=Medscape Orthopaedics & Sports Medicine eJournal, 1(5) |publisher=Medscape Portals, Inc. |access-date=14 March 2016| ___location=Orange Beach, Ala. |archive-url=https://web.archive.org/web/20100129115052/http://www.scuba-doc.com/dcsprbs.html#DCS:Definition |archive-date=29 January 2010 }}</ref>
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<ref name="CMAS-ISA Tx Manual">{{cite book |last1=Beresford |first1=M. |last2=Southwood |first2=P. |title=CMAS-ISA Normoxic Trimix Manual |edition=4th |year=2006 |publisher=CMAS Instructors South Africa |___location=Pretoria, South Africa }}</ref>
<ref name="DAN data uploads">{{cite web |url=https://www.daneurope.org/send-your-dive-profile |title=Send your Dive Profile |last=<!-- not specified --> |website=daneurope.org |publisher=DAN Europe |access-date=13 February 2016 |archive-date=8 April 2016 |archive-url=https://web.archive.org/web/20160408170051/http://www.daneurope.org/send-your-dive-profile |url-status=live }}</ref>
<ref name="DAN intro to DCS" >{{cite web |url=https://dan.org/health-medicine/health-resource/dive-medical-reference-books/decompression-sickness/introduction/ |title=Chapter 1: Introduction to Decompression Sickness |website=dan.org |access-date=31 August 2025 }}</ref>
<ref name="DAN projects">{{cite web |url=https://www.daneurope.org/our-projects |title=Our Projects |last=<!-- not specified --> |work=DAN Europe website |access-date=13 February 2016 |archive-date=11 April 2016 |archive-url=https://web.archive.org/web/20160411164440/https://www.daneurope.org/our-projects |url-status=dead }}</ref>
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<ref name="DecoWeenie">{{cite web |url=http://www.decoweenie.com/DecoWeenie%20Manual%2039.pdf |title=Decoweenie Manual |publisher=decoweenie.com |access-date=26 September 2008 |archive-url=https://web.archive.org/web/20080906142904/http://www.decoweenie.com/DecoWeenie%20Manual%2039.pdf |archive-date=6 September 2008 }}</ref>
<ref name="Deep stops">{{cite web |url=http://wrobell.it-zone.org/decotengu/_downloads/deepstops.pdf
<ref name="Denoble">{{cite web |url=http://www.alertdiver.com/?articleNo=255 |title=Deep stops |last=Denoble |first=Petar |date=Winter 2010 |work=Alert Diver |publisher=Diver Alert Network |access-date=3 August 2015 |archive-date=4 October 2015 |archive-url=https://web.archive.org/web/20151004074855/http://www.alertdiver.com/?articleNo=255 |url-status=live }}</ref>
<ref name="Doboszynski 2012" >{{cite journal |title=Oxygen-driven decompression after air, nitrox, heliox and trimix saturation exposures |last1=Doboszynski |first1=T |last2=Sicko |first2=Z |last3=Kot |first3=J |year=2012 |journal=Journal of the Undersea and Hyperbaric Medical Society |publisher=Undersea and Hyperbaric Medicine, Inc. }}</ref>
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<ref name="Doolette & Mitchell 2003" >{{cite journal |last1=Doolette |first1=David J. |last2=Mitchell |first2=Simon J. |title=Biophysical basis for inner ear decompression sickness |journal=Journal of Applied Physiology |volume=94 |issue=6 |pages=2145–50 |date=June 2003 |pmid=12562679 |doi=10.1152/japplphysiol.01090.2002 }}</ref>
<ref name="Doolette and Mitchell 2013" >{{cite journal |last1=Doolette
<ref name="Doolette et al 2015" >{{cite report |url=https://apps.dtic.mil/sti/tr/pdf/AD1000575.pdf |publisher=Navy Experimental Diving Unit |___location=Panama City, FL |work=TA 13-04, NEDU TR 15-04 |date=May 2015 |title=Decompression from He-N<sub>2</sub>-O<sub>2</sub> (Trimix) Bounce Dives is not more efficient than from He-O<sub>2</sub> (Heliox) Bounce Dives |first1=David J. |last1=Doolette |first2=Keith A. |last2=Gault |first3=Wayne A. |last3=Gerth }}</ref>
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<ref name="Eckenhoff 1986" >{{cite journal |title=Direct ascent from shallow air saturation exposures |journal=Undersea Biomedical Research |volume=13 |issue=3 |pages=305–16 |last1=Eckenhoff |first1=R.G. |last2=Osborne |first2=S.F. |last3=Parker |first3=J.W. |last4=Bondi |first4=K.R. |year=1986 |publisher=Undersea and Hyperbaric Medical Society, Inc. |pmid= 3535200 }}</ref>
<ref name="Edel 1980" >{{cite report |url=https://diving-rov-specialists.com/index_htm_files/scient-b_73-analysis-deco-tables-calculated-by-non-u_s.pdf |title=Analysis of Decompression Tables Calculated by non-U.S. Navy Methods |via=diving-rov-specialists.com |first=Peter O. |last=Edel |date= 31 March 1980 |publisher=Sea-Space Research Company Inc. |___location=Harvey, Louisiana }}</ref>
<ref name="EOW" >{{cite journal |title=The Extended Oxygen Window Concept for Programming Saturation Decompressions Using Air and Nitrox |last1=Kot |first1=Jacek |first2=Zdzislaw |last2=Sicko |first3=Tadeusz |last3=Doboszynski |year=2015 |journal=PLOS ONE |doi=10.1371/journal.pone.0130835 |pages=1–20 |pmid=26111113 |pmc=4482426 |volume=10 |issue = 6 |bibcode=2015PLoSO..1030835K |doi-access=free }}</ref>
<ref name="FAA" >{{cite web |url=http://www.faa.gov/pilots/safety/pilotsafetybrochures/media/dcs.pdf |publisher=[[Federal Aviation Administration]] |title=Altitude-induced Decompression Sickness |access-date=21 February 2012 |archive-date=3 February 2012 |archive-url=https://web.archive.org/web/20120203141302/http://www.faa.gov/pilots/safety/pilotsafetybrochures/media/dcs.pdf |url-status=live }}</ref>
<ref name="Flook 2004" >{{cite book |last=Flook |first=Valerie |title=Excursion tables in saturation diving - decompression implications of current UK practice
<ref name="Fogarty 2025" >{{cite web |url=https://indepthmag.com/d-word-dilemmas-the-push-for-personalized-decompression-modeling/ |title=Deco Dilemmas: The Push for Personalized Decompression Modeling |date=30 April 2025 |work=InDEPTH |first=Reilly |last=Fogarty |access-date=20 May 2025 }}</ref>
▲<ref name="Flook 2004" >{{cite book |last=Flook |first=Valerie |title=Excursion tables in saturation diving - decompression implications of current UK practice RESEARCH REPORT 244 |url=http://www.hse.gov.uk/research/rrpdf/rr244.pdf |access-date=27 November 2013 |year=2004 |publisher=Prepared by Unimed Scientific Limited for the Health and Safety Executive |___location=Aberdeen, U.K. |isbn=0-7176-2869-8 }}</ref>
<ref name=gernhardt >{{cite journal |last=Gernhardt |first=M.L. |title=Biomedical and Operational Considerations for Surface-Supplied Mixed-Gas Diving to 300 FSW. |editor1-last=Lang |editor1-first=M.A. |editor2-last=Smith |editor2-first=N.E. |journal=Proceedings of Advanced Scientific Diving Workshop |publisher=Smithsonian Institution |place=Washington, DC |year=2006 }}</ref>
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<ref name="Gurr 2019" >{{cite web |url=https://gue.com/blog/create-more-efficient-decompressions-using-gradient-factors/ |title=Variable Gradient Model: An Approach To Create More Efficient Decompressions |date=2 July 2019 |last=Gurr |first=Kevin |website=In Depth |access-date=11 February 2021 }}</ref>
<ref name="Goldman" >{{cite journal |url=http://moderndecompression.com/wp-content/uploads/2012/12/ARTICLE-TEXT-AND-FIGS.pdf |title=To stop or not to stop and why? |last1=Goldman |first1=Saul |last2=Goldman |first2=Ethel |publisher=DAN South Africa |journal=Alert Diver |issn=2071-7628 |volume=6 |issue=2 |pages=34–37 |year=2014 |access-date=10 September 2014 |archive-date=11 September 2014 |archive-url=https://web.archive.org/web/20140911001728/http://moderndecompression.com/wp-content/uploads/2012/12/ARTICLE-TEXT-AND-FIGS.pdf |url-status=live }}</ref>
<ref name="Goldman 2007" >{{cite journal |last=Goldman |first=Saul |date=19 April 2007 |title=A new class of biophysical models for predicting the probability of decompression sickness in scuba diving |journal=Journal of Applied Physiology |volume=103 |issue=2 |pages=484–493 |doi=10.1152/japplphysiol.00315.2006 |pmid=17446410 }}</ref>
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<ref name="Goldman 2010" >{{cite journal |last1=Goldman |first1=Saul |last2=Goldman |first2=Ethel |year=2010 |title=Coming soon to a Dive Computer near you |journal=Alert Diver (European Edition) |publisher=DAN Europe |___location=Roseto degli Abruzzi, Italy |issue=4th quarter, 2010 |pages=4–8 |url=http://moderndecompression.com/wp-content/uploads/2012/01/published-article-comprss-1.pdf }}</ref>
<ref name="Goldman 2013" >{{cite web |url=http://moderndecompression.com/?p=294 |title=How SAUL relates to the PADI dive tables |last=Goldman |first=Saul |date=23 September 2013 |work=Modern decompression |access-date=10 September 2014 |archive-date=3 April 2015 |archive-url=https://web.archive.org/web/20150403222353/http://moderndecompression.com/?p=294 |url-status=live }}</ref>
<ref name="Gorman" >{{cite web |title=Decompression theory
<ref name="Gorman1988" >{{cite journal |last1=Gorman |first1=Desmond F. |last2=Pearce |first2=A. |last3=Webb |first3=R.K. |title=Dysbaric illness treated at the Royal Adelaide Hospital 1987, a factorial analysis |journal=South Pacific Underwater Medicine Society Journal |year=1988 |volume=18 |issue=3 |pages=95–101 }}</ref>
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<!--<ref name="Imbert 2006">{{cite journal |last=Imbert |first=Jean Pierre |title=Commercial Diving: 90m Operational Aspects |journal=Advanced Scientific Diving Workshop |publisher=Smithsonian Institution |editor=Lang |editor2=Smith |date=February 2006 |url=http://www.plongeesout.com/articles%20publication/decompression/imbert/imbert%2090m.pdf |access-date=30 June 2012 }}</ref>-->
<ref name="Imbert 2004">{{cite conference |first1=J.P. |last1=Imbert |first2=D. |last2=Paris |first3=J. |last3=Hugon |publisher=Divetech |___location=France |date=2004 |title=The Arterial Bubble Model for Decompression Tables Calculations |conference=EUBS 2004 |url=http://gtuem.praesentiert-ihnen.de/tools/literaturdb/project2/pdf/Imbert%20JP.%20-%20EUBS%202004.pdf |access-date=14 March 2013 |archive-date=4 May 2018 |archive-url=https://web.archive.org/web/20180504155219/http://gtuem.praesentiert-ihnen.de/tools/literaturdb/project2/pdf/Imbert%20JP.%20-%20EUBS%202004.pdf |url-status=dead }}</ref>
<ref name="IMCAD022">{{cite book |last=Staff |editor=Paul Williams |title=The Diving Supervisor's Manual |url=http://www.imca-int.com/diving |edition=IMCA D 022 May 2000, incorporating the May 2002 erratum |year=2002 |publisher=International Marine Contractors' Association |___location=London |isbn=978-1-903513-00-2 |archive-date=12 August 2001 |access-date=14 March 2016 |archive-url=https://web.archive.org/web/20010812220108/http://www.imca-int.com/diving/ |url-status=live }}</ref>
<ref name="Kasture" >{{cite book |last=Kasture |first=A.V.
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<ref name="Lambertson 1989" >{{cite conference |last1=Lambertson |first1=Christian J. |year=1989 |title=Relations of isobaric gas counterdiffusion and decompression gas lesion diseases |editor1-last=Vann |editor1-first=R.D. |work=The Physiological Basis of Decompression. 38th Undersea and Hyperbaric Medical Society Workshop UHMS Publication Number 75(Phys)6-1-89. }}</ref>
<ref name="Lang and Angelini 2009" >{{cite book |editor1-last=Lang |editor1-first=M.A. |editor2-last=Brubakk |editor2-first=A.O. |date=2009 |url=http://www.sil.si.edu/smithsoniancontributions/proceedings/SC_RecordSingle.cfm?title=33 |title=The Future of Diving: 100 Years of Haldane and Beyond |publisher=Smithsonian Institution Scholarly Press |___location=Washington DC |chapter=The Future of Dive Computers |pages=91–100|first=Michael D. |last1=Lang |first2=Sergio |last2=Angelini |isbn=978-0-9788460-5-3 }}</ref>
<ref name="LeMessurier and Hills" >{{cite journal |last1=LeMessurier |first1=H. |last2=Hills |first2=B.A. |year=1965 |title=Decompression Sickness. A thermodynamic approach arising from a study on Torres Strait diving techniques |journal=Hvalradets Skrifter |volume=48 |pages=54–84 }}</ref>
<ref name=logodiving >{{cite web |url=
<ref name="Maiken" >{{cite web |url=http://www.decompression.org/maiken/Bubble_Decompression_Strategies.htm |title=Part I: background and theory. Bubble physics |last=Maiken |first=Eric |year=1995 |work=Bubble Decompression Strategies |access-date=11 March 2016 |archive-date=12 April 2016 |archive-url=https://web.archive.org/web/20160412210256/http://www.decompression.org/maiken/Bubble_Decompression_Strategies.htm |url-status=live }}</ref>
<ref name="Masurel et al 1987" >{{cite report |title=Hydrogen dive and decompression. |last1=Masurel |first1=G. |last2=Gutierrez |first2=N. |last3=Giacomoni |first3=L. |year=1987|work=Abstract of the Undersea and Hyperbaric Medical Society, Inc. Annual Scientific Meeting held May 26–30, 1987. The Hyatt Regency Hotel, Baltimore, Maryland |publisher=Undersea and Hyperbaric Medical Society, Inc. }}</ref>
<ref name="Medscape" >{{cite web
<ref name="Mitchell 2016" >{{cite conference |url=https://www.omao.noaa.gov/sites/default/files/documents/Rebreathers%20and%20Scientific%20Diving%20Proceedings%202016.pdf |title=Decompression Science: Critical Gas Exchange |first1=Simon J. |last1=Mitchell |editor1-last=Pollock |editor1-first=NW |editor2-last=Sellers |editor2-first=SH |editor3-last=Godfrey |editor3-first=JM |work=Rebreathers and Scientific Diving. Proceedings of NPS/NOAA/DAN/AAUS June 16–19, 2015 Workshop |___location=Wrigley Marine Science Center, Catalina Island, CA |year=2016 |pages=163–174 |access-date=23 November 2019 |archive-date=11 August 2023 |archive-url=https://web.archive.org/web/20230811200013/https://www.omao.noaa.gov/sites/default/files/documents/Rebreathers%20and%20Scientific%20Diving%20Proceedings%202016.pdf |url-status=live }}</ref>
<ref name="Mitchell 2020" >{{cite web |title=What is optimal decompression?<!-- Dr Simon Mitchell - Wats is optimal decompression? --> |url=https://www.youtube.com/watch?v=nIO9qI5XODw |via=YouTube |publisher=#NurkowiePomagajmySobie |date=16 May 2020 |last=Mitchell |first=Simon |access-date=
<!-- <ref name="Mitchell 2021-1" >{{cite web |url=https://www.youtube.com/watch?v=dYIux8KbUKo |title=Deco theory with Prof. Simon Mitchell, part 1/3: Contributing factors to decompression stress |publisher=UTD Diving |date=23 March 2021 |first=Simon |last=Mitchell |via=YouTube }}</ref>
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<ref name="Mitchell 2021-2" >{{cite web |url=https://www.youtube.com/watch?v=AicUyu4WGA0 |title=Deco theory with Prof. Simon Mitchell, part 2/3: Gas density and CO<sub>2</sub> retention |publisher=UTD Diving |date=23 March 2021 |first=Simon |last=Mitchell |via=YouTube }}</ref>-->
<ref name="Mitchell 2021-3" >{{cite web |url=https://www.youtube.com/watch?v=28_wM9CXXQ8 |title=Deco theory with Prof. Simon Mitchell, part 3/3: Deep Stops, the good the bad and the how we changed |publisher=UTD Diving |date=23 March 2021 |first=Simon |last=Mitchell |via=YouTube |access-date=8 October 2021 |archive-date=8 October 2021 |archive-url=https://web.archive.org/web/20211008095041/https://www.youtube.com/watch?v=28_wM9CXXQ8 |url-status=live }}</ref>
<ref name="Moon1998" >{{cite journal |last1=Moon |first1=Richard E. |first2=Joseph |last2=Kisslo |title=PFO and decompression illness: An update |journal=South Pacific Underwater Medicine Society Journal |volume=28 |issue=3 |year=1998 |issn=0813-1988 |oclc=16986801 }}</ref>
<ref name="Mouret 2006" >{{cite journal |title=Obesity and diving |last=Mouret |first=G.M.L. |year=2006 |
<ref name="NOAA" >{{cite book |title=The NOAA Diving Manual: Diving for Science and Technology |chapter-url=https://books.google.com/books?id=dWI8e8rVbJ0C&q=helium+%28He%29+is+the+other+inert+gas+commonly+used+in+breathing+mixtures+for+divers |access-date=8 March 2016 |edition=illustrated |year=1992 |publisher=DIANE Publishing |isbn=978-1-56806-231-0 |pages=15.1 |chapter=15: Mixed gas and oxygen diving }}</ref>
<ref name="NORSOK U100" >{{cite book |last=Staff |title=NORSOK Standard U-100: Manned underwater operations |url=http://www.standard.no/en/sectors/energi-og-klima/Petroleum/NORSOK-Standard-Categories/U-Underwater-Op/U-100-Edition-2-July-2008/
<ref name="Papadopoulou 2013" >{{cite journal |last1=Papadopoulou |first1=Virginie |first2=Robert J. |last2=Eckersley |first3=Costantino |last3=Balestra |first4=Thodoris D. |last4=Karapantsios |first5=Meng-Xing |last5=Tang |year=2013 |title=A critical review of physiological bubble formation in hyperbaric decompression |journal=Advances in Colloid and Interface Science |volume=191-192 |publisher=Elsevier |issue=191–192 |pages=22–30 |doi=10.1016/j.cis.2013.02.002 |pmid=23523006 |hdl=10044/1/31585 |s2cid=34264173 |hdl-access=free }}</ref>
<ref name="Perdix manual" >{{cite
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<ref name="Scharlin et al 1998" >{{cite journal |last1=Scharlin |first1=P. |last2=Battino |first2=R. |last3=Silla |first3=E. |last4=Tuñón |first4=I. |last5=Pascual-Ahuir |first5=J.L. |year=1998 |title=Solubility of gases in water: Correlation between solubility and the number of water molecules in the first solvation shell |journal=Pure and Applied Chemistry |volume=70 |issue=10 |pages=1895–1904 |doi=10.1351/pac199870101895 |s2cid=96604119 |doi-access=free }}</ref>
<ref name="Shearwater" >{{cite web |url=https://shearwater.com/blogs/community/evolution-of-dive-planning |title=Evolution of Dive Planning |date=11 August 2020 |website=shearwater.com |access-date=24 April 2024 |archive-date=24 April 2024 |archive-url=https://web.archive.org/web/20240424173256/https://shearwater.com/blogs/community/evolution-of-dive-planning |url-status=live }}</ref>
<!--<ref name="Sport Diving">Sport Diving, British Sub Aqua Club, ISBN 0-09-163831-3, page 104</ref>-->
<ref name="Stephenson" >{{cite journal |last=Stephenson |first=Jeffrey |year=2016 |title=Pathophysiology, treatment and aeromedical retrieval of SCUBA – related DCI |journal=Journal of Military and Veterans' Health |publisher=Australasian Military Medicine Association |volume=17 |issue=3 |issn=1839-2733 |url=http://jmvh.org/article/pathophysiology-treatment-and-aeromedical-retrieval-of-scuba-related-dci/ |archive-date=23 December 2017 |access-date=8 March 2016 |archive-url=https://web.archive.org/web/20171223104343/http://jmvh.org/article/pathophysiology-treatment-and-aeromedical-retrieval-of-scuba-related-dci/ |url-status=live }}</ref>
<ref name="Thalmann 1984-24">{{harvnb|Thalmann|1984|p=24}}</ref>
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<ref name="Validation workshop" >{{cite report |editor1-last=Blogg |editor1-first=S.L. |editor2-first=M.A. |editor2-last=Lang |editor3-first=A. |editor3-last=Møllerløkken |year=2012 |title=Proceedings of the Validation of Dive Computers Workshop. |work=European Underwater and Baromedical Society Symposium, August 24, 2011. Gdansk. Trondheim: Norwegian University of Science and Technology }}</ref>
<ref name="Van Liew 1993" >{{cite journal |last1=Van Liew |
<ref name="Van Liew and Conkin 2007" >{{cite conference |last1=Van Liew |first1=H.D. |last2=Conkin |first2=J. |year=2007 |title=A start toward micronucleus-based decompression models: Altitude decompression |
<ref name="Vann 1984" >{{cite web |url=https://apps.dtic.mil/sti/pdfs/ADA151743.pdf |title=Decompression from Saturation Dives |last=Vann |first=R. D. |date=March 1984 |work=Proceedings of the 3rd annual Canadian Ocean Technology Congress |pages=175–186 |access-date=5 April 2016 |___location=Toronto, Canada |archive-date=18 March 2023 |archive-url=https://web.archive.org/web/20230318110044/https://apps.dtic.mil/sti/pdfs/ADA151743.pdf |url-status=live }}</ref>
<ref name="Vann 1989" >{{cite conference |title=The Physiological Basis of Decompression: An overview |editor-last=Vann |editor-first=Richard D. |last=Vann |first=Richard D. |year=1989 |work=Proceedings of the thirty-eighth undersea and hyperbaric medical society workshop |publisher=Undersea and Hyperbaric Medical Society |___location=Bethesda, Maryland |pages=1–10 }}</ref>
<ref name="Vann and Dunford 2013" >{{cite web |url=https://www.youtube.com/watch?v=TJ5smR8W26U |title=Evidence-Based Decompression |date=23 September 2013 |via=YouTube |last1=Vann |first1=Richard D. |last2=Dunford |first2=Richard |publisher=DAN TV |access-date=5 October 2021 |archive-date=5 October 2021 |archive-url=https://web.archive.org/web/20211005151225/https://www.youtube.com/watch?v=TJ5smR8W26U |url-status=live }}</ref>
<ref name="Vann et al 2004" >{{cite journal |last1=Vann |first1=R.D. |last2=Gerth |first2=W.A. |last3=Denoble |first3=P.J.
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<ref name="Vann et al 2009" >{{cite journal |journal=Aviat Space Environ Med |date=May 2009 |volume=80 |issue=5 |pages=466–71 |title=Resolution and severity in decompression illness |first1=Richard D. |last1=Vann |first2=Petar J. |last2=Denoble |first3=Laurens E. |last3=Howle |first4=Paul W. |last4=Weber |first5=John J. |last5=Freiberger |first6=Carl F. |last6=Pieper |pmid=19456008 |doi=10.3357/asem.2471.2009 }}</ref>
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<ref name="Wienke 1989" >{{cite journal |title=Tissue gas exchange models and decompression computations: a review |journal=Undersea Biomedical Research |volume=16 |issue=1 |pages=53–89 |last=Wienke |first=B.R. |year=1989 |publisher=Undersea and Hyperbaric Medical Society, Inc. |pmid=2648656 }}</ref>
<ref name="Wienke 1990" >{{cite report |url=http://www.si.edu/dive/pdfs/proceedings_safeascents.pdf |title=Phase dynamics and diving |year=1990 |pages=13–29 |last=Wienke |first=Bruce R. |editor1-first=Michael A. |editor1-last=Lang |editor2-first=Glen H. |editor2-last=Egstrom |work=Proceedings of the AAUS Biomechanics of Safe Ascents Workshop
<ref name="Wienke 2002" >{{harvnb|Wienke|2002}}</ref>
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<ref name="Workman 1957" >{{cite journal |last=Workman |first=Robert D. |title=Calculation of air saturation decompression tables |year=1957 |journal=Navy Experimental Diving Unit Technical Report |volume=NEDU-RR-11-57 }}</ref>
<ref name="Young 1982" >{{cite web |url=http://srdata.nist.gov/solubility/IUPAC/SDS-27-28/SDS-27-28-intro_12.pdf |title=The solubility of gases in liquids |last1=Young |first1=C.L. |last2=Battino |first2=R. |last3=Clever |first3=H.L. |year=1982 |access-date=9 February 2016 |archive-date=22 February 2016 |archive-url=https://web.archive.org/web/20160222043604/http://srdata.nist.gov/solubility/IUPAC/SDS-27-28/SDS-27-28-intro_12.pdf |url-status=live }}</ref>
<ref name="Yount 1990" >{{cite web |url=http://www.si.edu/dive/pdfs/proceedings_safeascents.pdf |title=The physics of bubble formation |last=Yount |first=David E. |editor1-first=Michael A. |editor1-last=Lang |editor2-first=Glen H. |editor2-last=Egstrom |work=Proceedings of the AAUS Biomechanics of Safe Ascents Workshop |year=1990 |publisher=American Academy of Underwater Science |___location=Costa Mesa CA. |pages=13–29 |access-date=8 March 2016 |archive-date=18 October 2013 |archive-url=https://web.archive.org/web/20131018183438/http://www.si.edu/dive/pdfs/proceedings_safeascents.pdf |url-status=live }}</ref>
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