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[[File:Leszek Czarnecki wyprawa na Atol Bikini 2006.JPG|thumb|Scuba diver decompressing at a planned stop during ascent from a dive]]
'''Decompression theory''' is the study and modelling of the transfer of the [[inert gas]] component of [[breathing gas]]es from the gas in the lungs to the tissues and back during exposure to variations in ambient pressure. In the case of underwater diving and compressed air work, this mostly involves ambient pressures greater than the local surface pressure,<ref name="USNDM R6 3-9.3" /> but astronauts, high altitude mountaineers, and travellers in aircraft which are not pressurised to sea level pressure,<ref name="Van Liew and Conkin 2007" /><ref name="FAA"
The term "decompression" derives from the reduction in [[ambient pressure]] experienced by the organism and refers to both the reduction in [[pressure]] and the process of allowing dissolved inert gases to be eliminated from the [[Tissue (biology)|tissue]]s during and after this reduction in pressure. The uptake of gas by the tissues is in the dissolved state, and elimination also requires the gas to be dissolved, however a sufficient reduction in ambient pressure may cause bubble formation in the tissues, which can lead to tissue damage and the symptoms known as decompression sickness, and also delays the elimination of the gas.<ref name="USNDM R6 3-9.3" />
Decompression modeling attempts to explain and predict the mechanism of gas elimination and bubble formation within the organism during and after changes in ambient pressure,<ref name="Gorman"
Efficient decompression requires the diver to ascend fast enough to establish as high a decompression gradient, in as many tissues, as safely possible, without provoking the development of symptomatic bubbles. This is facilitated by the highest acceptably safe oxygen partial pressure in the breathing gas, and avoiding gas changes that could cause counterdiffusion bubble formation or growth. The development of schedules that are both safe and efficient has been complicated by the large number of variables and uncertainties, including personal variation in response under varying environmental conditions and workload.
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[[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" />
The absorption of gases in liquids depends on the [[solubility]] of the specific gas in the specific liquid, the concentration of gas, customarily measured by [[partial pressure]], and temperature.<ref name="USNDM R6 3-9.3" /> In the study of decompression theory the behaviour of gases dissolved in the tissues is investigated and modeled for variations of pressure over time.<ref name="Huggins 1992 Chapter 1"
Once dissolved, distribution of the dissolved gas may be by [[diffusion]], where there is no bulk flow of the [[solvent]], or by [[perfusion]] where the solvent (blood) is circulated around the diver's body, where gas can diffuse to local regions of lower [[concentration]]. Given sufficient time at a specific partial pressure in the breathing gas, the concentration in the tissues will stabilise, or saturate, at a rate depending on the solubility, diffusion rate and perfusion.<ref name="USNDM R6 3-9.3" />
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=== Dissolved phase gas dynamics ===
[[Solubility]] of gases in liquids is influenced by the nature of the solvent liquid and the solute,<ref name="Young 1982"/> the [[Solubility#Factors affecting solubility|temperature]],<ref name="JW Hill" />
At atmospheric pressure the body [[Tissue (biology)|tissues]] are therefore normally saturated with nitrogen at 0.758 bar (569 mmHg). At increased ambient [[Hydrostatic pressure|pressures due to depth]] or [[Diving chamber|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.<ref name="Huggins 1992 Chapter 1" /> The inert gases from the breathing gas in the lungs diffuse into blood in the [[Blood-air barrier|alveolar capillaries]] and are distributed around the body by the [[systemic circulation]] in the process known as [[perfusion]].<ref name="Huggins 1992 Chapter 1" /> Dissolved materials are transported in the blood much faster than they would be distributed by diffusion alone.<ref name="Pittman" /> From the systemic capillaries the dissolved gases diffuse through the cell membranes 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.<ref name="Huggins 1992 Chapter 1" /><ref name="Pittman" /> This equilibrium is called [[Solubility|saturation]].<ref name="Huggins 1992 Chapter 1" /> Ingassing appears to follow a simple inverse exponential equation. The time it takes for a tissue to take up or release 50% of the difference in dissolved gas capacity at a changed partial pressure is called the half-time for that tissue and gas.<ref name="Huggins 1992 Chapter 2"
Gas remains dissolved 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 than the relevant tissues. 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 be 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.<ref name="Huggins 1992 Chapter 1" /> When the partial pressure of all gas dissolved in a tissue exceeds the total ambient pressure on the tissue it is supersaturated,<ref name="Huggins 1992 1-7"
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 and has gained carbon dioxide from the venous blood. Oxygen has also diffused into the arterial blood, reducing the partial pressure of oxygen in the alveoli. 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.<ref name="Hills 1978b"
The ___location of micronuclei or where bubbles initially form is not known.<ref name="Papadopoulou 2013" /> The incorporation of bubble formation and growth mechanisms in decompression models may make the models more biophysical and allow better extrapolation.<ref name="Papadopoulou 2013" /> Flow conditions and perfusion rates are dominant parameters in competition between tissue and circulation bubbles, and between multiple bubbles, for dissolved gas for bubble growth.<ref name="Papadopoulou 2013" />
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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.<ref name="Tikuisis 1993" /> 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.{{sfn|Yount|1991|p=}}
Once a micro-bubble forms it may continue to grow if the tissues are sufficiently 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.<ref name="Campbell 1997"
If a bubble or an object exists which collects gas molecules this collection of gas molecules may reach a size where the internal pressure exceeds the combined surface tension and external pressure and the bubble will grow.<ref name="Yount VPM" /> If the solvent is sufficiently supersaturated, the diffusion of gas into the bubble will exceed the rate at which it diffuses back into solution, and if this excess pressure is greater than the pressure due to surface tension the bubble will continue to 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 because 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, the bubble will also grow, and conversely, an increased external pressure will cause the bubble to shrink, but may not cause it to be eliminated entirely if a compression-resistant surface layer exists.<ref name="Yount VPM" />
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=== Isobaric counterdiffusion (ICD) ===
{{main|Isobaric counterdiffusion}}
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.<ref name="Lambertson 1989"
Superficial ICD (also known as Steady State Isobaric Counterdiffusion)<ref name="D'Aoust 1982"
Deep Tissue ICD (also known as Transient Isobaric Counterdiffusion)<ref name="D'Aoust 1982" /> occurs when different inert gases are breathed by the diver in sequence.{{sfn|Hamilton|Thalmann|2003|pp=477–478}} The rapidly diffusing gas is transported into the tissue faster than the slower diffusing gas is transported out of the tissue.<ref name="Lambertson 1989" /> This can occur as divers switch from a nitrogen mixture to a helium mixture or when saturation divers breathing hydreliox switch to a heliox mixture.<ref name="Lambertson 1989" /><ref name="Masurel et al 1987"
Doolette and Mitchell's 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.<ref name="Doolette & Mitchell 2003"
=== Causative role of oxygen ===
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Bubbles form within other tissues as well as the blood vessels.<ref name="Vann 1989" /> 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.<ref name="Stephenson" /><ref name="Medscape" />
[[Extravascular]] or autochthonous{{ref label|a|a}} 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.<ref name="Stephenson" /><ref name="Vann 1989" /><ref name="Kitano"
The exchange of dissolved gases between the blood and tissues is controlled by perfusion and to a lesser extent by diffusion, particularly in heterogeneous 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 overall heat loss without increasing oxygen consumption until shivering begins, at which point oxygen consumption will rise, though the vasoconstriction can persist.<ref name="Vann 1989" />
The composition of the breathing gas during pressure exposure and decompression is significant in inert gas uptake and elimination for a given pressure exposure profile. 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 from 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 [[Nitrogen narcosis|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 (breathing gas)|Trimix]], if there is nitrogen and helium along with the essential oxygen.<ref name=Brubakk />
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.<ref name="Vann 1989" /> Blood flow to the muscles is also 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 vasoconstriction which usually occurs with cold water immersion.<ref name="Vann 1989" /> 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.<ref name="Vann 1989" /> 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.<ref name="Vann 1989" />
Other factors which can affect decompression risk include oxygen concentration, carbon dioxide levels, body position, vasodilators and constrictors, positive or negative pressure breathing.<ref name="Vann 1989" /> and dehydration (blood volume).<ref name="Williams et al 2005" /> 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.<ref name="Vann 1989" /> Obesity and high serum lipid levels have been implicated by some studies as risk factors, and risk seems to increase with age.<ref name="Mouret 2006" /> Another study has also shown that older subjects tended to bubble more than younger subjects for reasons not yet known, but 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.<ref name="Bookspan 2003" />
== Decompression model concepts ==
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Two rather different concepts have been used for decompression modelling. The first assumes that dissolved gas is eliminated while in the dissolved phase, and that bubbles are not formed during asymptomatic decompression. The second, which is supported by experimental observation, assumes that bubbles are formed during most asymptomatic decompressions, and that gas elimination must consider both dissolved and bubble phases.<ref name="Yount VPM" />
Early decompression models tended to use the dissolved phase models, and adjusted them by more or less arbitrary factors to reduce the risk of symptomatic bubble formation. Dissolved phase models are of two main groups. Parallel compartment models, where several compartments with varying rates of gas absorption (half time), are considered to exist independently of each other, and the limiting condition is controlled by the compartment which shows the worst case for a specific exposure profile. These compartments represent conceptual tissues and are not intended to represent specific organic tissues, merely to represent the range of possibilities for the organic tissues. The second group uses serial compartments, where gas is assumed to diffuse through one compartment before it reaches the next.<ref name="Huggins 1992 Chapter 4"
More recent models attempt to model bubble dynamics, also by simplified models, to facilitate the computation of tables, and later to allow real time predictions during a dive. The models used to approximate bubble dynamics are varied, and range from those which are not much more complex that the dissolved phase models, to those which require considerably greater computational power.<ref name="Kuch"
None of the decompression models can be shown to be an accurate representation of the physiological processes, although interpretations of the mathematical models have been proposed which correspond with various hypotheses. They are all approximations which predict reality to a greater or lesser extent, and are acceptably reliable only within the bounds of calibration against collected experimental data.<ref name="Huggins 1992 Intro-2"
===Range of application===
The ideal decompression profile creates the greatest possible gradient for inert gas elimination from a tissue without causing bubbles to form,<ref name="Gorman1988"
Decompression models should ideally accurately predict risk over the full range of exposure from short dives within the no-stop limits, decompression bounce dives over the full range of practical applicability, including extreme exposure dives and repetitive dives, alternative breathing gases, including gas switches and constant PO<sub>2</sub>, variations in dive profile, and saturation dives. This is not generally the case, and most models are limited to a part of the possible range of depths and times. They are also limited to a specified range of breathing gases, and sometimes restricted to air.<ref name="Gorman2011"
A fundamental problem in the design of decompression tables is that the simplified 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.<ref name="Gorman2011" /> Repetitive diving, multiple ascents within a single dive, and surface decompression procedures are significant risk factors for DCS.<ref name="Gorman1988" /> These have been attributed to the development of a relatively high gas phase volume which may be partly carried over to subsequent dives or the final ascent of a sawtooth profile.<ref name="Wienke" />
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"
=== 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" />
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.
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===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
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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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.<ref name="Wienke 1989" />
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, and commonly uses a slightly modified exponential half-time model. 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.<ref name="Maiken" /> 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 maximize the concentration gradient, and long shallow stops, while the bubble models require slower ascents, with deeper first stops, but may have shorter shallow stops. This approach uses a variety of models.<ref name="Maiken" /><!--VPM--><ref name="Baker1998" />
==== 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"
Further research by people such as [[Robert Workman (decompression modeler)|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 ''critical pressure difference'' of 0.58 atmospheres between tissue pressure and ambient pressure. Most Haldanean tables since the mid 20th century, including the Bühlmann tables, are based on the critical difference assumption .<ref name="CMAS-ISA Tx Manual"
The '''{{visible anchor|M-value}}''' is the maximum value of absolute inert gas pressure that a tissue compartment can take at a given ambient pressure 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".<ref name="Baker1998" /><ref name="Workman 1957" />
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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.<ref name="Anttila" /> Several models of dive computer allow user input of gradient factors as a way of inducing a more conservative, and therefore presumed lower risk, decompression profile.<ref name="Perdix manual" /> Forcing a low gradient factor at the deep M-value can have the effect of increasing ingassing during the ascent, generally of the slower tissues, which must then release a larger gas load at shallower depths. This has been shown to be an inefficient decompression strategy.<ref name="Mitchell 2020" /><ref name="Mitchell 2021-3" />
The Variable Gradient Model adjusts the gradient factors to fit the depth profile on the assumption that a straight line adjustment using the same factor on the deep M-value regardless of the actual depth is less appropriate than using an M-value linked to the actual depth. (the shallow M-value is linked to actual depth of zero in both cases) <ref name="Gurr 2019"
{{expand section|More specific details on Variable gradient model|date=February 2021}}
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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.<ref name="Doolette et al 2015"
=== Saturation dives===
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=== No-stop limits ===
A no-stop limit, also called no decompression limit (NDL) is the theoretical maximum dissolved gas content of each tissue compartment of the whole body, which can be decompressed directly to surface pressure at the chosen ascent rate used by the model, without a need to stop to outgas at any depth, which has an acceptable risk of developing symptomatic decompression sickness. No decompression limit is a misnomer as the ascent at the specified ascent rate is decompression, but the term has historical inertia and continues to be used.<ref name="USNDM R6" /><ref name="Huggins Chapter 3-9"
=== Decompression ceiling ===
Once the gas loading of one or more tissue compartments exceeds the maximum level accepted for the no-stop limit, there is a minimum depth to which the diver can ascend at the appropriate ascent rate, at an acceptable risk for decompression sickness. This depth is known as the decompression ceiling. It may be considered a soft overhead, in that it is physically trivial to ascend above it, but that increases the risk of developing symptomatic decompression sickness according to the decompression model. The tissue that reaches its decompression ceiling first is called the limiting tissue.<ref name="Angelini et al 2022"
=== Decompression obligation ===
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=== Residual inert gas ===
Gas bubble formation has been experimentally shown to significantly inhibit inert gas elimination.<ref name="Hills1978" /><ref name="pmid1226586" />
A considerable amount of inert gas will remain in the tissues after a diver has surfaced, even if no symptoms of decompression sickness occur. 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.<ref name="Berghage 1978"
In repetitive diving, the slower tissues can accumulate gas day after day, if there is insufficient time for the gas to be eliminated between dives. 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.<ref name="AAUS1991"
==Decompression models in practice==
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The critical ratio 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.<ref name="Huggins 1992 Chapter 2" />
[[John Scott Haldane]] introduced the concept of [[#Tissue half times|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.<ref name="Huggins 1992 Chapter 2" /> In this early hypothesis 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.<ref name="Haldane1908" /> 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 (1 bar) 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.<ref name="Haldane1908" /> 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.<ref name="Huggins Chapter 3-2"
In the 1960s [[Robert D. Workman (physiologist)|Robert D. Workman]] of the [[U.S. Navy Experimental Diving Unit]] (NEDU) reviewed the basis of the model and subsequent research performed by the US Navy. Tables based on Haldane's work and subsequent refinements were still found to be inadequate for longer and deeper dives. Workman proposed that the tolerable change in pressure was better described as a critical pressure difference, and 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.<ref name="Huggins Chapter 3" />
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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 "[[Pyle stop (Decompression)|Pyle stop]]" is a deep stop named after [[Richard Pyle]], an early advocate of deep stops,<ref name="DecoWeenie"
:For example, a diver ascends from a maximum depth of {{convert|60|m|ft|-2}}, where the ambient pressure is {{convert|7|bar|psi|sigfig=1}}, to a decompression stop at {{convert|20|m|ft|0}}, where the pressure is {{convert|3|bar|psi|sigfig=1}}. The first Pyle stop would take place at the halfway pressure, which is {{convert|5|bar|psi|sigfig=1}} corresponding to a depth of {{convert|40|m|ft|-1}}. The second Pyle stop would be at {{convert|30|m|ft|0}}. A third would be at {{convert|25|m|ft|0}} which is less than {{convert|9|m|ft|0}} below the first required stop, and therefore is omitted.<ref name="Pyle1997" /><ref name="PyleBM" />
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The value and safety of deep stops additional to the decompression schedule derived from a decompression algorithm is unclear. Decompression experts have pointed out that deep stops are likely to be made at depths where ingassing continues for some slow tissues, and that the addition of deep stops of any kind should be included in the hyperbaric exposure for which the decompression schedule is computed, and not added afterwards, so that such ingassing of slower tissues can be taken into account.<ref name="Denoble" /> Deep stops performed during a dive where the decompression is calculated in real-time are simply part of a multi-level dive to the computer, and add no risk beyond that which is inherent in the algorithm.
There is a limit to how deep a "deep stop" can be. Some off-gassing must take place, and continued on-gassing should be minimised for acceptably effective decompression. The "deepest possible decompression stop" for a given profile can be defined as the depth where the gas loading for the leading compartment crosses the ambient pressure line. This is not a useful stop depth - some excess in tissue gas concentration is necessary to drive the outgassing diffusion, however this depth is a useful indicator of the beginning of the decompression zone, in which ascent rate is part of the planned decompression.<ref name="Deep stops"
A study by [[Divers Alert Network|DAN]] in 2004 found that the incidence of high-grade bubbles could be reduced to zero providing the nitrogen concentration of the most saturated tissue was kept below 80 percent of the allowed M value and that an added deep stop was a simple and practical way of doing this, while retaining the original ascent rate.<ref name="BMC2004" />
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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"
* 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
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<!--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"
The Goldman model differs from the Kidd-Stubbs series decompression model in that the Goldman model assumes linear kinetics, where the K-S model includes a quadratic component, and the Goldman model considers only the central well-perfused compartment to contribute explicitly to risk, while the K-S model assumes all compartments to carry potential risk. The DCIEM 1983 model associates risk with the two outermost compartments of a four compartment series.<ref name="Goldman 2007" /> The mathematical model based on this concept is claimed by Goldman to fit not only the Navy square profile data used for calibration, but also predicts risk relatively accurately for saturation profiles. A bubble version of the ICM model was not significantly different in predictions, and was discarded as more complex with no significant advantages. The ICM also predicted decompression sickness incidence more accurately at the low-risk recreational diving exposures recorded in DAN's Project Dive Exploration data set. The alternative models used in this study were the LE1 (Linear-Exponential) and straight Haldanean models.<ref name="Goldman 2010" /> The Goldman model predicts a significant risk reduction following a safety stop on a low-risk dive<ref name="Goldman"
=== 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"
These methods can vary the [[decompression stop]] depths and times to arrive at a decompression schedule that assumes a specified probability of DCS occurring, 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, given sufficient reliable data.<ref name="Vann and Dunford 2013" />
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{{Wide image|NORSOK saturation decompression.svg|2000px|Graphic representation of the NORSOK U-100 (2009) saturation decompression schedule from 180 msw, starting at 06h00 and taking 7 days, 15 hours with Oxygen partial pressure maintained between 0.4 and 0.5 bar|50%|right}}
Saturation decompression is a physiological process of transition from a steady state of full saturation with inert gas at raised pressure to standard conditions at normal surface atmospheric pressure. It is a long process during which inert gases are eliminated at a very low rate limited by the slowest affected tissues, and a deviation can cause the formation of gas bubbles which can produce decompression sickness. Most operational procedures rely on experimentally derived parameters describing a continuous slow decompression rate, which may depend on depth and gas mixture.<ref name="EOW"
In saturation diving all tissues are considered saturated and decompression which is safe for the slowest tissues will theoretically be safe for all faster tissues in a parallel model. Direct ascent from air saturation at approximately 7 msw produces venous gas bubbles but not symptomatic DCS. Deeper saturation exposures require decompression to saturation schedules.<ref name="Eckenhoff 1986"
The safe rate of decompression from a saturation dive is controlled by the partial pressure of oxygen in the inspired breathing gas.<ref name="Vann 1984" /> The inherent unsaturation due to the [[oxygen window]] allows a relatively fast initial phase of saturation decompression in proportion to the oxygen partial pressure and then controls the rate of further decompression limited by the half-time of inert gas elimination from the slowest compartment.<ref name="Doboszynski 2012"
Application of a bubble model in 1985 allowed successful modelling of conventional decompressions, altitude decompression, no-stop thresholds, and saturation dives using one setting of four global nucleation parameters.<ref name="Hoffman and Yount 1985"
Research continues on saturation decompression modelling and schedule testing. In 2015 a concept named Extended Oxygen Window was used in preliminary tests for a modified saturation decompression model. This model allows a faster rate of decompression at the start of the ascent to utilise the inherent unsaturation due to metabolic use of oxygen, followed by a constant rate limited by oxygen partial pressure of the breathing gas. The period of constant decompression rate is also limited by the allowable maximum oxygen fraction, and when this limit is reached, decompression rate slows down again as the partial pressure of oxygen is reduced. The procedure remains experimental as of May 2016. The goal is an acceptably safe reduction of overall decompression time for a given saturation depth and gas mixture.<ref name="EOW" />
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<!--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"
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.<ref name="Thalmann 1984-24" /><ref name="Thalmann 1985-5" /> Since the testing procedures are lengthy and costly, and there are ethical limitations on experimental work on human subjects with injury as an endpoint, 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.<ref name="Huggins 1992 Chapter 10"
{{expand section|NEDU comparison of deep stop/bubble model vs. shallow stop/dissolved state model and reception|date=September 2021}}
==== Efficiency of stop depth distribution ====
Deep, short duration dives require a long decompression in comparison to the time at depth, which is inherently inefficient in comparison with saturation diving. Various modifications to decompression algorithms with reasonably validated performance in shallower diving have been used in the effort to develop shorter or safer decompression, but these are generally not supported by controlled experiment and to some extent rely on anecdotal evidence. A widespread belief developed that algorithms based on bubble models and which distribute decompression stops over a greater range of depths are more efficient than the traditional dissolved gas content models by minimising early bubble formation, based on theoretical considerations, largely in the absence of evidence of effectiveness, though there were low incidences of symptomatic decompression sickness. Some evidence relevant to some of these modifications exists and has been analysed, and generally supports the opposite view, that deep stops may lead to greater rates of bubble formation and growth compared to the established systems using shallower stops distributed over the same total decompression time for a given deep profile.<ref name="Doolette and Mitchell 2013"
The integral of supersaturation over time may be an indicator of decompression stress, either for a given tissue group or for all the tissue groups. Comparison of this indicator calculated for the combined Bühlmann tissue groups for a range of equal duration decompression schedules for the same depth, bottom time, and gas mixtures, has suggested greater overall decompression stress for dives using deep stops, at least partly due to continued ingassing of slower tissues during the deep stops.<ref name="Mitchell 2020" />
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==== Altitude exposure, altitude diving and flying after diving ====
{{See also|Flying after diving|Altitude diving}}
The USAF conducted experiments on human subjects in 1982 to validate schedules for air diving no-decompression limits before immediate excursions to altitude and for altitude diving allowing immediate flying after the dive to an altitude of {{convert|8500|ft|m}}.<ref name="Bassett 1982"
Experiments with an endpoint of DCS symptoms using profiles near the no-decompression exposure limits for recreational diving were carried out to determine how DCS occurrence during or after flight relates to the length of pre-flight surface interval (PFSI). The dives and PFSI were followed by a four-hour exposure at 75 kPa, equivalent to the maximum permitted commercial aircraft cabin altitude of {{convert|8000|ft|m}}. DCS incidence decreased as surface interval increased, with no incidence for a 17 hour surface interval. Repetitive dives profiles usually needed longer surface intervals than single dives to minimise incidence. These tests have helped inform recommendations on time to fly.<ref name="Vann et al 2004" />
In-flight transthoracic echocardiography has shown that there is a low but non-zero probability of decompression sickness in commercial pressurised aircraft after a 24 hour pre-flight surface interval following a week of multiple repetitive recreational dives, indicated by detection of venous gas bubbles in a significant number of the divers tested.<ref name="Cialoni et al 2015"
{{expand section|date=December 2021}}
==Current research==
Research on decompression continues. Data is not generally available on the specifics, however [[Divers Alert Network]] (DAN) has an ongoing [[citizen science]] based programme run by DAN (Europe) which gathers data from volunteer [[Recreational diving|recreational divers]] for analysis by DAN research staff and other researchers. This research is funded by subscription fees of DAN Europe members.<ref name="About DAN research"
Listed projects (not all directly related to decompression) include:<ref name="DAN projects"
* Gathering data on vascular gas bubbles and analysis of the data
* Identification of optimised ascent profile
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Decompression is an area where you discover that, ''the more you learn, the more you know that you really don't know what is going on.'' For behind the "black-and-white" exactness of table entries, the second-by-second countdowns of dive computers, and beneath the mathematical purity of decompression models, lurks a dark and mysterious physiological jungle that has barely been explored.
— Karl E. Huggins, 1992<ref name="Huggins 1992 Intro-3"
</blockquote>
Exposure to the various theories, models, tables and algorithms is needed to allow the diver to make educated and knowledgeable decisions regarding their personal decompression needs.<ref name="Huggins 1992 Intro-2" /> Basic decompression theory and use of decompression tables is part of the theory component of training for commercial divers,<ref name="IDSA 2009"
==See also==
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== References ==
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<!--<ref name="BSAC88 tables">BSAC '88 Decompression Tables Levels 1 to 4</ref>-->
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<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="Huggins 1992 Chapter 2" >{{harvnb|Huggins|1992|loc=Chpt. 2}}</ref>
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