Decompression theory is the study and modelling of the transfer of the inert gas component of breathing gases 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, but astronauts, high altitude mountaineers, and travellers in aircraft which are not pressurised to sea level pressure, are generally exposed to ambient pressures less than standard sea level atmospheric pressure. In all cases, the symptoms caused by decompression occur during or within a relatively short period of hours, or occasionally days, after a significant pressure reduction. 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 tissues 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. 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, and provides mathematical models which attempt to predict acceptably low risk and reasonably practicable procedures for decompression in the field. Both deterministic and probabilistic models have been used, and are still in use. 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.
Physiology of decompression
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. 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. 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. In the study of decompression theory the behaviour of gases dissolved in the tissues is investigated and modeled for variations of pressure over time. 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. 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. 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 exceeds the combined external pressures of ambient pressure and the surface tension from the bubble - liquid interface, the bubble will grow, and this growth can cause damage to tissues. Symptoms caused by this damage are known as decompression sickness. The actual rates of diffusion and perfusion and the solubility of gases in specific tissues are not generally known, and they vary considerably. However, mathematical models have been proposed which approximate the real situation to a greater or lesser extent, and these models are used to predict whether symptomatic bubble formation is likely to occur for a given pressure exposure profile. Decompression involves a complex interaction of gas solubility, partial pressures and concentration gradients, diffusion, bulk transport and bubble mechanics in living tissues.
Dissolved phase gas dynamics Solubility of gases in liquids is influenced by the nature of the solvent liquid and the solute, the temperature, pressure, and the presence of other solutes in the solvent. Diffusion is faster in smaller, lighter molecules of which helium is the extreme example. Diffusivity of helium is 2.65 times faster than nitrogen. The concentration gradient, can be used as a model for the driving mechanism of diffusion. In this context, inert gas refers to a gas which is not metabolically active. Atmospheric nitrogen (N2) is the most common example, and helium (He) is the other inert gas commonly used in breathing mixtures for divers. Atmospheric nitrogen has a partial pressure of approximately 0.78 bar at sea level. Air in the alveoli of the lungs is diluted by saturated water vapour (H2O) and carbon dioxide (CO2), a metabolic product given off by the blood, and contains less oxygen (O2) than atmospheric air as some of it is taken up by the blood for metabolic use. The resulting partial pressure of nitrogen is about 0,758 bar. At atmospheric pressure the body tissues are therefore normally saturated with nitrogen at 0.758 bar (569 mmHg). At increased ambient pressures due to depth or habitat pressurisation, a diver's lungs are filled with breathing gas at the increased pressure, and the partial pressures of the constituent gases will be increased proportionately. The inert gases from the breathing gas in the lungs diffuse into blood in the alveolar capillaries and are distributed around the body by the systemic circulation in the process known as perfusion. Dissolved materials are transported in the blood much faster than they would be distributed by diffusion alone. 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. This equilibrium is called saturation. 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. 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. When the partial pressure of all gas dissolved in a tissue exceeds the total ambient pressure on the tissue it is supersaturated, and there is a possibility of bubble formation. 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. At a steady state, when the tissues have been saturated by the inert gases of the breathing mixture, metabolic processes reduce the partial pressure of the less soluble oxygen and replace it with carbon dioxide, which is considerably more soluble in water. In the cells of a typical tissue, the partial pressure of oxygen will drop, while the partial pressure of carbon dioxide will rise. The sum of these partial pressures (water, oxygen, carbon dioxide and nitrogen) is less than the total pressure of the respiratory gas. This is a significant saturation deficit, and it provides a buffer against supersaturation and a driving force for dissolving bubbles. Experiments suggest that the degree of unsaturation increases linearly with pressure for a breathing mixture of fixed composition, and decreases linearly with fraction of inert gas in the breathing mixture. As a consequence, the conditions for maximising the degree of unsaturation are a breathing gas with the lowest possible fraction of inert gas – i.e. pure oxygen, at the maximum permissible partial pressure. This saturation deficit is also referred to as inherent unsaturation, the "Oxygen window". or partial pressure vacancy. The location of micronuclei or where bubbles initially form is not known. The incorporation of bubble formation and growth mechanisms in decompression models may make the models more biophysical and allow better extrapolation. 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.
Bubble mechanics Equilibrium of forces on the surface is required for a bubble to exist. The sum of the Ambient pressure and pressure due to tissue distortion, exerted on the outside of the surface, with surface tension of the liquid at the interface between the bubble and the surroundings must be balanced by the pressure on the inside of the bubble. This is the sum of the partial pressures of the gases inside due to the net diffusion of gas to and from the bubble. The force balance on the bubble may be modified by a layer of surface active molecules which can stabilise a microbubble at a size where surface tension on a clean bubble would cause it to collapse rapidly, and this surface layer may vary in permeability, so that if the bubble is sufficiently compressed it may become impermeable to diffusion. If the solvent outside the bubble is saturated or unsaturated, the partial pressure will be less than in the bubble, and the surface tension will be increasing the internal pressure in direct proportion to surface curvature, providing a pressure gradient to increase diffusion out of the bubble, effectively "squeezing the gas out of the bubble", and the smaller the bubble the faster it will get squeezed out. A gas bubble can only grow at constant pressure if the surrounding solvent is sufficiently supersaturated to overcome the surface tension or if the surface layer provides sufficient reaction to overcome surface tension. Clean bubbles that are sufficiently small will collapse due to surface tension if the supersaturation is low. Bubbles with semipermeable surfaces will either stabilise at a specific radius depending on the pressure, the composition of the surface layer, and the supersaturation, or continue to grow indefinitely, if larger than the critical radius. Bubble formation can occur in the blood or other tissues. A solvent can carry a supersaturated load of gas in solution. Whether it will come out of solution in the bulk of the solvent to form bubbles will depend on a number of factors. Something which reduces surface tension, or adsorbs gas molecules, or locally reduces solubility of the gas, or causes a local reduction in static pressure in a fluid may result in a bubble nucleation or growth. This may include velocity changes and turbulence in fluids and local tensile loads in solids and semi-solids. Lipids and other hydrophobic surfaces may reduce surface tension (blood vessel walls may have this effect). Dehydration may reduce gas solubility in a tissue due to higher concentration of other solutes, and less solvent to hold the gas. Another theory presumes that microscopic bubble nuclei always exist in aqueous media, including living tissues. These bubble nuclei are spherical gas phases that are small enough to remain in suspension yet strong enough to resist collapse, their stability being provided by an elastic surface layer consisting of surface-active molecules which resists the effect of surface tension. 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. 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. 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. Decompression bubbles appear to form mostly in the systemic capillaries where the gas concentration is highest, often those feeding the veins draining the active limbs. They do not generally form in the arteries provided that ambient pressure reduction is not too rapid, as arterial blood has recently had the opportunity to release excess gas into the lungs. The bubbles carried back to the heart in the veins may be transferred to the systemic circulation via a patent foramen ovale in divers with this septal defect, after which there is a risk of occlusion of capillaries in whichever part of the body they end up in. Bubbles which are carried back to the heart in the veins will pass into the right side of the heart, and from there they will normally enter the pulmonary circulation and pass through or be trapped in the capillaries of the lungs, which are around the alveoli and very near to the respiratory gas, where the gas will diffuse from the bubbles though the capillary and alveolar walls into the gas in the lung. If the number of lung capillaries blocked by these bubbles is relatively small, the diver will not display symptoms, and no tissue will be damaged (lung tissues are adequately oxygenated by diffusion). The bubbles which are small enough to pass through the lung capillaries may be small enough to be dissolved due to a combination of surface tension and diffusion to a lowered concentration in the surrounding blood, though the Varying Permeability Model nucleation theory implies that most bubbles passing through the pulmonary circulation will lose enough gas to pass through the capillaries and return to the systemic circulation as recycled but stable nuclei. Bubbles which form within the tissues must be eliminated in situ by diffusion, which implies a suitable concentration gradient.
Isobaric counterdiffusion (ICD)
Isobaric counterdiffusion is the diffusion of gases in opposite directions caused by a change in the composition of the external ambient gas or breathing gas without change in the ambient pressure. During decompression after a dive this can occur when a change is made to the breathing gas, or when the diver moves into a gas filled environment which differs from the breathing gas. While not strictly speaking a phenomenon of decompression, it is a complication that can occur during decompression, and that can result in the formation or growth of bubbles without changes in the environmental pressure. Two forms of this phenomenon have been described by Lambertsen: Superficial ICD (also known as Steady State Isobaric Counterdiffusion) occurs when the inert gas breathed by the diver diffuses more slowly into the body than the inert gas surrounding the body. An example of this would be breathing air in an heliox environment. The helium in the heliox diffuses into the skin quickly, while the nitrogen diffuses more slowly from the capillaries to the skin and out of the body. The resulting effect generates supersaturation in certain sites of the superficial tissues and the formation of inert gas bubbles. Deep Tissue ICD (also known as Transient Isobaric Counterdiffusion) occurs when different inert gases are breathed by the diver in sequence. The rapidly diffusing gas is transported into the tissue faster than the slower diffusing gas is transported out of the tissue. This can occur as divers switch from a nitrogen mixture to a helium mixture or when saturation divers breathing hydreliox switch to a heliox mixture. 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. They suggest that breathing-gas switches from helium-rich to nitrogen-rich mixtures should be carefully scheduled either deep (with due consideration to nitrogen narcosis) or shallow to avoid the period of maximum supersaturation resulting from the decompression. Switches should also be made during breathing of the largest inspired oxygen partial pressure that can be safely tolerated with due consideration to oxygen toxicity.
Causative role of oxygen Although it is commonly held that DCS is caused by inert gas supersaturation, Hempleman has stated: ...This did not lead to a sufficient cut-back in the permitted decompression ratio and an allowance in the calculations is now made for high oxygen partial pressures. Whenever the partial pressure of oxygen in air (or mixture) exceeds 0.6 bar then it is considered that significant amounts of dissolved oxygen are present in the tissues and that there is an increased decompression risk. This is estimated by adding 25% to the dive depth, and proceeding with the calculations as just outlined using assumption (1). An oxygen first stop depth is thus obtained, and 5 min is spent at this depth to allow for metabolic use of the excess dissolved oxygen gas. Following this 'oxygen stop' the calculations proceed as outlined above.
Decompression sickness
Vascular bubbles formed in the systemic capillaries may be trapped in the lung capillaries, temporarily blocking them. If this is severe, the symptom called "chokes" may occur. If the diver has a patent foramen ovale (or a shunt in the pulmonary circulation), bubbles may pass through it and bypass the pulmonary circulation to enter the arterial blood. If these bubbles are not absorbed in the arterial plasma and lodge in systemic capillaries they will block the flow of oxygenated blood to the tissues supplied by those capillaries, and those tissues will be starved of oxygen. Moon and Kisslo (1988) concluded that "the evidence suggests that the risk of serious neurological DCI or early onset DCI is increased in divers with a resting right-to-left shunt through a PFO. There is, at present, no evidence that PFO is related to mild or late onset bends." Bubbles form within other tissues as well as the blood vessels. Inert gas can diffuse into bubble nuclei between tissues. In this case, the bubbles can distort and permanently damage the tissue. As they grow, the bubbles may also compress nerves as they grow causing pain. Extravascular or autochthonous[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. 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. 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 narcotic effects under high partial pressure exposure. Depending on the proportions of helium and nitrogen, these gases are called Heliox, if there is no nitrogen, or Trimix, if there is nitrogen and helium along with the essential oxygen. The inert gases used as substitutes for nitrogen have different solubility and diffusion characteristics in living tissues to the nitrogen they replace. For example, the most common inert gas diluent substitute for nitrogen is helium, which is significantly less soluble in living tissue, but also diffuses faster due to the relatively small size and mass of the He atom in comparison with the N2 molecule. Blood flow to skin and fat are affected by skin and core temperature, and resting muscle perfusion is controlled by the temperature of the muscle itself. During exercise increased flow to the working muscles is often balanced by reduced flow to other tissues, such as kidneys spleen and liver. Blood flow to the muscles is 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. Variations in perfusion distribution do not necessarily affect respiratory inert gas exchange, though some gas may be locally trapped by changes in perfusion. Rest in a cold environment will reduce inert gas exchange from skin, fat and muscle, whereas exercise will increase gas exchange. Exercise during decompression can reduce decompression time and risk, providing bubbles are not present, but can increase risk if bubbles are present. Inert gas exchange is least favourable for the diver who is warm and exercises at depth during the ingassing phase, and rests and is cold during decompression. Other factors which can affect decompression risk include oxygen concentration, carbon dioxide levels, body position, vasodilators and constrictors, positive or negative pressure breathing. and dehydration (blood volume). 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. Obesity and high serum lipid levels have been implicated by some studies as risk factors, and risk seems to increase with age. 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.
Decompression model concepts
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. 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. A recent variation on the serial compartment model is the Goldman interconnected compartment model (ICM). 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. 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.
Range of application The ideal decompression profile creates the greatest possible gradient for inert gas elimination from a tissue without causing bubbles to form, and the dissolved phase decompression models are based on the assumption that bubble formation can be avoided. However, it is not certain whether this is practically possible: some of the decompression models assume that stable bubble micronuclei always exist. The bubble models make the assumption that there will be bubbles, but there is a tolerable total gas phase volume or a tolerable gas bubble size, and limit the maximum gradient to take these tolerances into account. 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 PO2, 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. 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. Repetitive diving, multiple ascents within a single dive, and surface decompression procedures are significant risk factors for DCS. 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. 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. 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.
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.
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 have been used to generate decompression tables, and dive computers have used up to 20 compartments. 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. 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. A typical dive computer has an 8–12 tissue model, with half times varying from 5 minutes to 400 minutes. The Bühlmann tables use an algorithm with 16 tissues, with half times varying from 4 minutes to 640 minutes. 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.
Ingassing model 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. Tissue compartment half times range from 1 minute to at least 720 minutes. 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. 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 possibly bubble formation when a gas of different solubility is introduced to the breathing mixture. This model may not adequately describe the dynamics of outgassing if gas phase bubbles are present.
Outgassing models For optimised decompression the driving force for tissue desaturation should be kept at a maximum, provided that this does not cause symptomatic tissue injury due to bubble formation and growth (symptomatic decompression sickness), or produce a condition where diffusion is retarded for any reason. There are two fundamentally different ways this has been approached. The first is based on an assumption that there is a level of supersaturation which does not produce symptomatic bubble formation and is based on empirical observations of the maximum decompression rate which does not result in an unacceptable rate of symptoms. This approach seeks to maximise the concentration gradient providing there are no symptoms, 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. 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.
The critical supersaturation approach 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. 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. Further research by people such as Robert Workman suggested that the criterion was not the ratio of pressures, but the actual pressure differentials. Applied to Haldane's work, this would suggest that the limit is not determined by the 1.58:1 ratio but rather by the 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. The 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". Gradient factors are a way of modifying the M-value to a more conservative value for use in a decompression algorithm. The gradient factor is a percentage of the M-value chosen by the algorithm designer, and varies linearly between the maximum depth of the specific dive and the surface. They are expressed as a two number designation, where the first number is the percentage of the deep M-value, and the second is a percentage of the shallow M-value. The gradient factors are applied to all tissue compartments equally and produce an M-value which is linearly variable in proportion to ambient pressure.
For example: A 30/85 gradient factor would limit the allowed supersaturation at depth to 30% of the designer's maximum, and to 85% at the surface. In effect the user is selecting a lower maximum supersaturation than the designer considered appropriate. Use of gradient factors will increase decompression time, particularly in the depth zone where the M-value is reduced the most. Gradient factors may be used to force deeper stops in a model which would otherwise tend to produce relatively shallow stops, by using a gradient factor with a small first number. 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. Forcing a low gradient factor at the deep M-value can have the effect of increasing ingassing during