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Variable Gradient Model: An Approach To Create More Efficient Decompressions

British tech pioneer and inventor Kevin Gurr has been building dive computers since the early 1990s, including the world’s first mixed gas diving computer, the VR3, which he launched in 1997, through his former company VR Technology Ltd. based in Dorset, UK. He also designed and built three sport rebreathers. Now the Maritime Technology Officer at Avon Protection managing military rebreathers, Gurr discusses an innovative modification of gradient factors that he developed for use with his various devices.



by Kevin Gurr

Header Image: by K. Davidson for Halcyon.

This article is not designed to go into the finite detail of decompression modeling; other people have achieved this far more successfully. It is intended as a snapshot view of what is currently available in Avon Protections’ MCM100 military rebreather, which I helped design, hopefully with a level of technical clarity so that the reader can evaluate for themselves the merits of the differing methods.

The human body cannot currently be mathematically modelled. Not only are individuals different because of age, fitness, pulmonary and cardiac (PFO) defects, but they also vary on a daily basis due to hydration, stress, exercise, micro-nuclei generation, and many other factors. 

So how does the diving community conduct thousands of safe dives per year? Some experimentation has historically been done to produce ‘reasonably safe’ decompression tables that ‘fit’ most people for a shallow water (primarily air diving) environment. In modern technical diving, much of the deeper diving we do is simply an extrapolation of the early shallow water research. We now know that this does not always work. 

Shallow water diving is relatively well documented and we have historical figures to work with, which  is only just starting to occur with deeper diving. Let’s review the basic decompression theory so that we may investigate possible ways to deal with the problem.

Consider the Buhlmann system of decompression: it is assumed that each of the hypothetical tissue compartments can safely experience an over-pressurization during a reduction in pressure (ascent) after a pressurized exposure (time at depth) which has allowed them to absorb gas.

The subsequent decompression profile that is generated on the ascent should not exceed the tolerated over-pressure value, or M value — a theoretical construct for the theoretical controlling tissue compartment within the body, in order to avoid decompression illness (DCI). As each compartment comes into play and the relevant M value is reached, a decompression stop profile is generated.

Figure 1 represents a very simplistic example involving just one of the fast tissues which will control the primary ascent phase. The M value for this compartment is shown as a straight line. If the diver controls the ascent, the inert gas loading in the compartment will stay on or below the M value line. If they do this, let’s assume they are using 100% of the available M value, which means there’s no extra safety margin for that dive; they are theoretically diving right on the edge of the model. 

Graph courtesy of Kevin Gurr.

For a typical bounce dive, Buhlmann standard practice has been to allow a rapid ascent to the first stop to generate a high level of off-gassing. Doing this, the gas loading in the fastest compartment will be on or near saturation at the bottom depth (the slow tissues are only partially saturated). This means that the fastest compartments will control the initial ascent since their gas loadings will be near or on the tolerated over-pressure value (M value). The first stop depth is set when the controlling (fast) compartment is nearest to the M value. The example only shows up to a point where the first stop starts and does not detail the other compartments or the remaining decompression. 

Using gradient factor terminology, the M value line is the 100/100 reference. The first 100 describes how close (in percentage) to the M value line the first stop is, and the second 100 describes how close the final stop is. Thus 100/100 has no added safety margin compared to the M value. In the complete picture, each compartments’ M value and each compartments’ internal pressure right through to the end of the dive (not just to the stop as drawn) would be displayed on the graph each with the same 100/100 gradient. The slower compartments would reach their M value during the final decompression phases while the faster compartments control the deeper decompression.

The gradient factor system modifies the M value by taking a percentage of the difference between the M value and the ambient pressure value. As a simple example to illustrate how Gradient factors work, using 80% of the M value as the controlling value (80/80 line) produces a line on the graph (figure 2) below the 100/100 line, having the effect of reducing the compartments allowed over-pressure value and generating a deeper decompression stop. 

Graph courtesy of Kevin Gurr.

Again, in the complete picture all the adjusted M values and compartment pressures would be plotted, adding safety to the whole decompression profile.

As most of these early dissolved gas based tables were formulated around relatively shallow water air range dives, they do not suit deep water dives, although historically they have often been extrapolated for use in deep-water. While these tables have a varying solution for different depths they were depth limited.

So what about Pyle stops? Technical diving pioneer, ichthyologist Richard Pyle developed a practical solution that divers could understand for modifying the decompression profile to reduce the excessive over-pressurization of the controlling compartment at the deep stops. He found that by stopping and venting a fish’s swim bladder below the first tabular stop depth, he ‘felt better’ at the end of the decompression. He was in effect allowing the faster compartments’ pressure to reduce before ascending to the tabular first stop and not reach its M value peak. 

The downside of this was that other compartments were still on-loading gas, which could generate an additional decompression obligation in shallow water. He was applying a safety factor that only had an effect on the deeper stops. This had the potential to allow the slower compartments to become closer to their M value during the shallow water decompression phase unless additional safety factors were applied.

Now we move onto bubble models (VPM etc.). Put very simply, bubble models attempt to explain the growth phases of inert gas bubbles and their subsequent effects. These models focus on the first part of the ascent where the bubbles grow, and by doing so, claim they can lead to a predicted reduction of the decompression obligation in shallow water. However, because of this decompression reduction, some dives generated decompression stress which could not be explained. In recent years, these bubble growth models have gone through several iterations as a result, and new evidence suggests that “deep stops” generated by bubble models may not be more efficient than shallower decompression.

A common (but complicated) solution to reduce the problem was to combine what was known about shallow water decompressions (Buhlmann) with the deep water bubble model. We know this is still an incomplete solution as phenomena such as arterial bubbles and other effects are not taken into account. Bubble models give an explanation and provide a working model of what Richard Pyle tried to implement practically from a technical divers standpoint. 

A recent tool, which provides a simpler solution between Buhlmann and the bubble models, has been to use gradient factors with a dissolved gas model which in turn modifies the M values of the controlling compartments (Baker). This has the effect of combining a bubble with a dissolved gas model style decompression profile.

Gradient factors can further mimic bubble models by using two different gradient factors to control the decompression: one that primarily references the deep stops, and one the shallow. 

So a 20/80 gradient factor, which has been commonly used on deeper dives, would allow an over-pressure value of 20% (instead of 100%) of the difference between the ambient pressure and the allowed M value for the controlling compartment of the first or “deep stop” and 80% (instead of 100%) of the M value for the controlling compartments’ pressure difference at the shallow stop. The stops in between are calculated by drawing an over-pressure value line between the two points and plotting the new adjusted M values for each compartment in between. It assumes a linear calculation between the adjusted first and last M values. 

In Figure 3 let’s assume that compartment 4 controls the deep stop and compartment 16 the shallow stop. Again, for clarity, the on-going compartment inert gas loading reductions are not shown past the M value point, neither are all the other compartment M values.

Graph courtesy of Kevin Gurr.

The major drawback of gradient factors is that the factors applied need to be adjusted for each depth/time exposure. For example, if you used the same 20/80 gradient factor for an 80 m dive, on a 30 m dive you might have an excess of decompression in shallow water because we know from experience that a gradient factor of close to 100/100 is reliable for this shallow water dive. 

What does this mean? First, it is not necessarily appropriate to apply one gradient factor to a range of dive depths. What works deep may not work shallow. Secondly, it means just applying gradient factors in the first place may be too coarse a solution. Just drawing a straight line between the M value points and assuming the mid-water decompression follows this linear approach may not work. So how do we generate a refinement?

Stochastic modelling has been around in diving for some time. Decompression tables are generated based on statistical dive data of incidents; basically, points are plotted on a graph and an algorithm generated. So how could we use this to improve gradient factor modelling? Assuming the 100/100 factor is OK for a certain shallow dive and the 20/80 is OK for a particular deep dive, would it not be best to have a varying gradient factor depending on depth/time exposure and other factors? If we can be fairly certain of key decompression times for a range of depth/time exposures that are ‘safe’ and generate reasonable decompressions, we could use them to generate a gradient factor that varies accordingly. My term for this approach is a Variable Gradient Model (VGM).

VGM has the ability to use stochastic data and historically ‘proven’ decompression values in an algorithm and automatically adjust it for a range of depth/time exposure scenarios. The VGM software can be embedded into the dive computer, for example, in the MCM100, and its parameters can be adjusted using the screen below. Note that I also used VGM in my previous company’s [VR Technology Ltd.] VRx computers.

The Ace, Ace Profile, VR3, VRx dive computers designed and built by Kevin Gurr, VR Technology Ltd.

In summary, a VGM profile has the effect of padding the stops at certain decompression points while reducing stop times at others for a specific exposure scenario. What’s more, it changes them again automatically for different exposure scenarios and allows varying degrees of user input dependent on the application. VGM is a useful tool based on our current culminated experience. It brings together in one approach much of what we know and may help predict some of that which we do not.

Once data is available, many other variables could be built into a VGM matrix, such that with time and information it could continuously evolve to give increasingly accurate decompression predictions. While the modelling of the human body eludes us, VGM would appear to be a good solution to the current issues.

Additional Resources:


 Gradient Factors in a Post-Deep Stops World by David Doolette.


Kevin Gurr has been involved with Technical Diving since its inception in Europe. As well as being the first Technical Diving instructor outside the USA, he has led and been a part of many expeditions; the first sport dives on the Britannic in 1997, treasure hunting in the Pacific (and several other locations World-wide), filmmaking, and a dive on the Titanic in the MIR submarines to name a few.

As an engineer and diver he has developed several ground breaking products for the diving industry from trimix computers to rebreathers, including the Ace Profile, VR3, VRx computers, Pro Planner desktop decompression software, and the Ouroboros, Sentinel, Explorer and the MCM100 rebreathers. He lives in Dorset, England with wife Mandy, daughters Leyla and Amberlee, Neo the black Labrador, and various motorcycles.


The Thought Process Behind GUE’s CCR Configuration

GUE is known for taking its own holistic approach to gear configuration. Here GUE board member and Instructor Trainer Richard Lundgren explains the reasoning behind its unique closed-circuit rebreather configuration. It’s all about the gas!




By Richard Lundgren
Header photo by Ortwin Khan

Numerous incidents over the years have resulted in tragic and fatal outcomes due to inefficient and insufficient bailout procedures and systems. At the present time, there are no community standards that detail:

  • How much bailout gas volume should be reserved
  • How to store and access the bailout gas 
  • How to chose bailout gas properties

Accordingly, Global Underwater Explorers (GUE) created a standardized bailout system consistent with GUE’s holistic gear configuration, Standard Operating Procedures(SOP), and diver training system. The system was designed holistically; consequently, the value and usefulness of the system are jeopardized if any of its components are removed.  

Bailout Gas Reserve Volumes

The volume of gas needed to sustain a diver while bailing from a rebreather is difficult to assess, as many different factors impacts the result— including respiratory rate, depth and time, CO2 levels, and stress levels. These are but a few of the variables. All reserve gas calculations may be appropriate under ideal conditions and circumstances, but they should be regarded as estimates, or predictions at best.

The gas volume needed for two divers to safely ascend to the first gas switch is referred to as Minimum Gas (MG) for scuba divers. The gas volume needed for one rebreather diver to ascend on open-circuit during duress is referred to as Bailout Minimum Gas (BMG). The BMG is calculated using the following variables:

Consumption (C): GUE recommends using a surface consumption rate (SCR) of 20 liters per minute, or 0.75 f3 if imperial is used.

Average Pressure (AvP or average ATA): The average pressure between the target depth (max depth) to the first available gas source or the surface (min depth)

Time (T):  The ascent rate should be according to the decompression profile (variable ascent rate). However, in order to simplify and increase conservatism, the ascent rate used in the BMG formula is set to 3 meters/10 ft per minute. Any decompression time required before the gas switch (first available gas source) must be added to the total time. One minute should be added for the adverse event (the bailout) and one minute additionally for performing the gas switch.

BMG = C x AvP x T

Note that Bailout Minimum Gas reserves are estimations and may not be sufficient! Even though catastrophic failures are unlikely, other factors like hypercapnia (CO2 poisoning) and stress warrants a cautious approach. 

Decompression bailout gas volumes are calculated based on the diver’s actual need (based on their decompression table/algorithm), and no additional reserve is added. 

It should be noted that GUE does not endorse the use of “team bailout,” i.e. when one diver carries bottom gas bailout and another diver carries decompression gas based on only one diver’s need. A separation or an equipment failure would quickly render a system like this useless.

Common Tech Community Rebreather Configuration

  • Backmount rebreather (note side mount rebreathers are gaining in popularity)
  • Typically, three-liter oxygen and a three-liter diluent cylinder on board (each hold 712 l/25 f3) 
  • Bailout gas in one or more stage bottles which could be connected to an integrated Bailout Valve (BOV).
Divers on the AP Diving Inspiration rebreather in typical backmount configuration. Photo by Martin Parker.
Cave diver in the DiveSoft Liberty sidemount rebreather. Photo courtesy of Marissa Eckert.

Containment and Access

Rather than carry bailout minimum gas (BMG) in a stage bottle, which is typical in the rebreather diving community, GUE has designed its bailout system as a redundant open-circuit system consisting of two 7-liter, 232 bar cylinders (57 f3 each) that are integrated into the rebreather frame, and called the “D7” system, i.e. D for doubles, 7 for seven liter. Note that GUE has standardized the JJ-CCR closed-circuit rebreather for training and operations.

Photo by Kirill Egorov.

These cylinders, each with individual valves, are linked together using a flexible manifold. This system holds up to 3250 liters of gas (114 f3), of which only about 10% is used by the rebreather as diluent. Hence, close to 3000 liters (106 f3) is reserved for a bailout situation. This gives a tremendous capacity and flexibility in a relatively small form factor for dives requiring additional gas reserves (when direct ascent is not possible or desirable). 

The following advantages were considered when designing the bailout system:

  • The D7 system is consistent with existing open-circuit systems utilized by GUE divers. A bailout system that is familiar to the user will not increase stress levels, which is important. A GUE diver will rely on previous experience and procedures when most needed.
  • The system contains the gas volumes needed according to the GUE BMG calculations as well as the diluent needed for a wide range of dive missions.
  • The system is fully redundant and has the capacity to isolate failing components, like a set of open-circuit doubles and still allowing full access to the gas.
  • The overall weight of the system is less, compared to a standard system with an AL11 liter (aluminum 80 f3) bailout cylinder. In addition, it contains 800-900 liters/20-32 f3 more gas available for a bailout situation compared to the AL11 liter system. Weight has been traded for gas.
  • The system does not occupy the position of a stage bottle which allows for additional stages or decompression bottles to be added.
  • If the ISO valves on each side were closed, the flex manifold can be removed and the cylinders transported individually while still full.

Bailout gas can be accessed quickly by a bailout valve (BOV), which is typically configured as a separate open-circuit regulator worn on a necklace, consistent with GUE’s open-circuit configuration. However, some GUE divers use an integrated BOV. After evaluation of the situation, while breathing open-circuit from the BOV, the user can transition to a high-performance regulator worn on a long hose if the situation calls for it.

The long hose is carried under the loop when diving the rebreather. The chances of having to donate to another GUE rebreather diver is low, as both carry redundant bailout. Still, GUE maintains that the capacity to donate gas must be present. The process is more likely to involve a handover of the long hose rather than a donation. 

Photo by Jesper Kjøller.

Still, if needed, such a donation is made possible by either removing the loop temporarily or by simply donating the long hose from under the loop. 

Bailout decompression gasses are carried in decompression stage bottles. If more than three bottles are needed, the bottles that are to be used at the shallowest depths are carried on a stage leash (i.e. a short lease that clips to your side D-ring to carry multiple stage bottles). Maintaining bottle-rotation techniques and capacity through regular practice is important and challenging, as this skill is rarely used with the rebreather.

Bailout Gas Properties

The choice of bailout gas is extremely important, as survival may well depend on it. It is not only the volume that is important, the individual gas properties will decide if the bailout gas will be optimal or not. As the D7 system contains both the diluent and bailout gas, both gasses share the same characteristic. The following gas characteristics must be considered when choosing gas:


The equivalent (air) gas density depth should not exceed 30 meters/100 ft or 5.1 grams/liter. This is consistent with the latest research by Gavin Anthony and Simon Mitchell that recommends that divers maintain maximum gas density ideally below 5.2 g/l, equivalent to air at 31 m/102 ft, and a hard maximum of 6.2 g/l, the equivalent to air at 39 m/128 ft. You can find a simple gas density calculator here.

Ventilation is impaired when diving, due to several factors which increase the work of breathing (WOB); when diving rebreathers, the impairment is even more so. High gas density, for example, when diving gas containing no or low fractions of helium, significantly decreases a diver’s ventilation capacity and increases the risk of dynamic airway compression. CO2 washout from blood depends on ventilation capacity and can be hindered if a high-density gas is used. The impact of density is very important, and the risk of using dense gases is not to be neglected. Note that this effect is not limited to deep diving. Using a dense gas as shallow as 30 meters/100 ft reduces a diver’s ventilation capacity by a staggering 50%.


The (air) equivalent narcotic depth should also not exceed 30 m/100 ft, or PN2=3.16. Rebreathers and emergency situations are complex enough without further being aided by narcosis.

Oxygen Toxicity

The PO2 should be limited to allow for long exposures. GUE operating standards call for a maximum PO2 for bottom gases of 1.2 atm, a PO2 of 1.4 for deep decompression gases, and a PO2 of 1.6 for shallow decompression gases. GUE recommends using the next deeper GUE standard bottom gas for diluent/bailout when diving a rebreather in combination with GUE standard decompression gases.

Bailout gasses are not chosen in order to give the shortest possible decompression obligation. They are chosen in order to give the best odds of surviving a potentially life-threatening situation. 

Two GUE CCR divers in California. Photo by Karim Hamza.

In Summary

GUE’s D7 bailout system is flexible and contains the rebreather’s diluent as well as bailout gas reserves needed for a range of different missions. The familiarity the system, along with the knowledge that they are carrying ample gas reserves, gives GUE divers peace of mind. Choosing gases with properties that will aid a diver in duress while dealing with an emergency completes the system.

GUE did not prioritize the ease of climbing boat ladders or reducing decompression by a few minutes. These are more appropriately addressed with sessions at the gym, combined with finding aquatic comfort. Nothing prevents a complete removal of the entire system at the surface if an easy exit is needed.

Founder of Scandinavia’s Baltic Sea Divers and Ocean Discovery diving groups, and a member of GUE’s Board of Directors and GUE’s Technical Administrator, Richard Lundgren has participated in numerous underwater expeditions worldwide and is one of Europe’s most experienced trimix divers. With more than 4000 dives to his credit, Richard Lundgren was a member of the GUE expeditions to dive the Britannic (sister ship of the ill-fated Titanic) in 1997 and 1999, and has been involved in numerous projects to explore mines and caves in Sweden, Norway, and Finland. In 1997, in arctic conditions, he performed the longest cave dive ever carried out in Scandinavia. Richard’s other exploration work has included the 1999 filming of the famous submarine, M1, for the BBC; the side scan sonar surveys of the Spanish gold galleons outside Florida’s Key West in 2000; and the search for the Admiral’s Fleet, an ongoing project that has already led to the discovery of more than 40 virgin wrecks perfectly preserved in the cold waters of the Swedish Baltic Sea.

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