Choosing Gradient Factors
Coffee ground reading or science?
In recent years, more and more dive computers have come onto the market that calculate with the Bühlmann algorithm ZHL-16C. More or less plausible pairs of gradient factors can be found as presets, and some divers even set what they personally consider to be the best. If you simply ask around online, you get a rather interesting range.
How do divers usually choose their GFs? As a rule, they stick with what is preset in the computer or take what their last dive instructor told them. Very few have a well-founded decision behind their choice, and among those there are very different positions.
How can we choose gradient factors according to rational criteria, and where are the limits of current knowledge?
First, as a reminder:
What are Gradient Factors?
Most people have come across this plot in various forms. It is used to explain the saturation and desaturation of a single model tissue, and it can be used to explain basic concepts quite well.
Anyone who has dealt with gradient factors has certainly already understood what an M-value is and where the M-line comes from, which sets a limit to the supersaturation of a tissue. The M-value is always the maximum pressure that a tissue can tolerate. It is made up of the current ambient pressure and the tolerated supersaturation. If you calculate the M-value for a tissue for each ambient pressure and enter it in the plot, you can connect these points to form the M-line. In Bühlmann logic, the M-line is not parallel to the pressure equalization line, but has a slightly greater slope. The model assumes that tissue at depth, under a higher ambient pressure, can tolerate a greater supersaturation than at the surface.
It is clear that the M-line is not a rigid boundary beyond which something bad happens, but a line that has been drawn into the spongy zone of increasing risk for plausible reasons and with some empiricism behind it. And this is exactly where the gradient factors come into play: The risk that is accepted in the “original” Bühlmann model seems too great to many today. Most people want to make their dives a little safer.
Therefore, the M-line is shifted. To do this, the tolerated supersaturation is taken – not the entire M-value, but the M-value minus the ambient pressure – and a percentage of this supersaturation is determined that is still considered justifiable. This allows the M-line as a whole to be shifted into the safer area, and the supersaturation becomes lower overall. Or, and this is probably more common at the moment, you decide to tolerate different supersaturations at different moments of ascent. In this case, you need two gradient factors: GF Low and GF High. This is then represented by a pair of values: first Low, then High, e.g. GF 55/70.
The GF Low determines the maximum accepted inert gas overpressure in the tissue when the first stop is reached, and the GF High determines the maximum accepted inert gas overpressure in the tissue when the surface is reached. In the plot, the colored lines represent the simply shifted M-lines, and the black line (slightly curved) shows how the limit would run with GF40/80.
So far, so good: You move the boundaries further away from the original M-line, and staying further away from the boundaries certainly leads to a lower risk. But how exactly should you choose them?
GF High: Lower is always better – but extends the Deco
The GF High is the “simpler” value. Its choice is basically related to how much risk you want to accept. The higher it is, the greater the supersaturation that you accept at the end of the dive, and a higher supersaturation is clearly associated with a higher DCS risk.
You don’t really know that much about which factors play a role in DCS, and there is a lot that cannot be explained by supersaturation alone. Different people react differently to the same dive profile, and even the same diver can come out of the water very differently after identical dives on different days. But what you do have is data from real diving accidents.
DAN has analyzed the dive profiles in a larger data collection of 320 DCS cases. The maximum achieved GF was extracted from the profiles – in most cases this was certainly the one when the surface was reached. The result: 73.7% of the DCS cases “only” reached GFs between 70 and 90%. The vast majority of cases therefore occurred even though the divers had adhered to all recognized limits.
Maximum Gradient Factor Reached and DCS
Evaluation of data from 320 DCS cases in the DAN database: Which maximum gradient factors were reached?
Of course, the data is missing an extremely important piece of information, namely how many dives were actually carried out in which areas. If only 2.5% of the DCS cases came out of the water with GF over 100, this does NOT mean that dives in which an even higher gradient factor is reached are safer. The lower numbers there are due to the fact that dives in these areas are only very rarely carried out. However, it is interesting to see the extent to which the reported cases are reduced below a maximum achieved gradient factor of approx. 60. This is certainly not because these dives are rare. Globally, a very large number of no- Deco dives are made, often far away from the no- Deco limits and with a lot of time in the shallows. GFs of less than 60 are therefore certainly very common in practice, but do not appear as often in accident dives.
Most divers now opt for a GF High between 70 and 80. Those who have opted for a lower one often argue that they are no longer the youngest, and most of those who have set a higher one say that they would like to spend a little more time in the shallows if it works out. The fact that a lower supersaturation at the end of the dive is a good idea if you want to be as safe as possible seems to have become known in the meantime.
GF Low: Strong opinions, little reliable knowledge
While a lower GF High has a clear, demonstrable and logically comprehensible effect, when choosing the GF Low we enter an area in which there is a lot of speculation because there is little valid data. Simply setting the GF Low lower does not automatically make the dive more conservative, as we will see shortly.
The idea of setting the GF Low significantly lower than the GF High can be traced back to the bubble models with their deeper stops and the hope that deeper Deco stops can prevent or at least control bubble growth from the outset. This may even be true – but if you stop deep, some tissues continue to saturate relevantly here, and must then also desaturate later. The Deco therefore becomes significantly longer. If you don’t want that, but use deeper stops in a Deco profile of the same length as one with shallower stops, you tend to come out of the water with a higher supersaturation. And that in turn seems to be riskier according to all logic and all studies than coming to the surface with a lower supersaturation with the same length of Deco.
Therefore, there has been a tendency for some years not to set the GF Low too low.
Among the well-founded proposals for choosing GF Low, one stands out that suggests a correction to the model. The “original” M-values in the Bühlmann model allow a higher inert gas supersaturation at depth than what would be acceptable upon reaching the surface. Bühlmann already made the line slightly flatter compared to Workman’s M-values, but even this slope is now being questioned. As a prominent critic of this idea, David Doolette argues, among others, that this behavior of the model may not entirely align with current understanding. One can therefore attempt to compensate for this part of the model using gradient factors and accept the same level of supersaturation at every depth. This can be achieved by setting GF Low to 83% of GF High, and this practice has gained some acceptance in recent years.
Is this the very best idea of all? In the end, nobody knows. However: Combining a relatively low-risk GF High of 70 with a GF Low of 55 can be quite a good idea, and this has been practiced by quite a few technical divers in recent years.
The Belgian military: A bit odd, but by no means safer
But even that seems too low to some.
In recent years, a paper from circles of the Belgian military has been discussed among Tekkies. This was partly received as “the military takes GF Low=GF High, and would even prefer GF Low to be even higher than GF High, which is certainly safer than what we do!”
But stop – is that really the case? And what exactly did the Belgians do?
The starting point was that the Belgian military had introduced Shearwater computers and now wanted instructions on setting optimal GFs. So far, the US Navy tables and the DCIEM tables were the basis on which dives were carried out, and these tables are considered empirically validated and sufficiently safe. The aim was therefore to find pairs of values that match the tables mentioned as closely as possible. It then turned out that values in the approximate range of 100/75 to 100/90 produce similar profiles to those of the DCIEM air Deco table.
It is important to note that the aim was not to make the dives as safe as possible, but to find a balance between safety and efficiency that was acceptable to the military. Our goals when we go diving for fun in our free time may be very different.
Now there’s a technical catch: the firmware on Shearwater computers does not accept a GF Low greater than GF High. As a compromise, it was suggested to choose GF Low and GF High symmetrically, with 90/90 being the pair that was most often recommended under most boundary conditions. Likewise, the advice was that if you want to reduce risk, you should reduce the values symmetrically. Up to that point, this is certainly not particularly controversial. GFs of 90/90 produce a relatively long no-decompression time and brisk Deco, and if that has worked well for them with tables so far, they can keep doing it.
However, there is one part of this study that we view very critically. It also recommended not using values lower than 75/75.
How did they arrive at that? The argument at this point drew, among other things, on the NEDU study from 2011 on deeper decompression profiles after deep air dives. The profiles used there can be roughly reproduced if, in Bühlmann terms, you use GF 100/40 for the profile with the shallower stops, and GF 45/70 for the one with the deeper stops. Because the profile with the shallower stops performed significantly better, the conclusion was drawn that the higher GF Low should generally be preferred.
Now, it’s certainly plausible to argue that a low GF Low is not efficient and can create disadvantages if you then lack time in the shallows to keep supersaturation at the surface limited. But the equally long ascent with the deeper stops not only had the lower GF Low—it also had a higher GF High, a component you can’t simply ignore.
So you can’t conclude from this that, for example, GFs of 60/60 are more dangerous than 80/80 or 90/90. After all, the maximum supersaturation reached is still more strongly limited thanks to the also-low GF High. It just takes more time—which, in recreational diving, we do have.
GF Low for civilians
So what should you take away regarding GF Low when it comes to where you should best invest extra time to reduce risk? In most cases, the answer would certainly be “at the shallow stops, to reduce GF High.” We clearly advise against reducing GF Low at the expense of GF High (so that it would increase), and against shifting time from shallow to deep.
GF Low with Trimix
When it’s no longer just about nitrogen, but helium comes into play, the discussion changes again.
When it comes to helium, the Bühlmann model works on the assumption that it diffuses 2.65 times faster than nitrogen. Therefore, all tissues have significantly shorter half-lives, they saturate and desaturate faster. The tissues that have already been saturated much more strongly at depth then consequently require deeper first stops in the Deco in order to slowly reduce this more massive supersaturation again. Deco profiles with gases with a high helium content will therefore generally have deeper stops than those with more nitrogen. Since the slower tissues continue to saturate at these stops – we already know that – the stops in the shallows must also be correspondingly longer in order to reduce this additional supersaturation as well. This effect is known as the “Helium Penalty”.
The basis for this, namely the assumption that helium behaves so fundamentally differently in the body than nitrogen, has been questioned in recent years. Here too, it was a study by the NEDU that provided relevant evidence: In rebreather dives with Heliox or Trimix, there were more DCS cases among the Trimix divers with the same ascent profile – although the dived profile with Heliox was considered significantly riskier.
It is therefore increasingly doubted that the deeper stops that are considered necessary with helium are actually necessary. However, the state of research is far from sufficient to simply throw proven models overboard. If some Tekkies simply conceal the helium content from the dive computer, even though they are diving Trimix – a practice that is sometimes reported under the table – this is not something we would recommend for imitation. However, it would certainly be worth considering not artificially making the stops EVEN deeper within the tested model – and that means setting the GF Low higher than you would with air.
And what should I set now?
What you can say is: The lower the GF High, the lower the risk. A very low GF Low does not appear to make sense according to all available data. But whether it should be 50/70, or 75/75, or 60/80, or rather 80/80 – somewhere in this area you will probably settle on what you consider reasonable.
Anyone who has already had DCS and wants to try not to let any bubbles form at all may choose very low GFs – some have decided to ascend very slowly with GF20/50 and are very satisfied with it. Those who are more risk-averse will opt for something like 60/85. But many now separate their default settings to some extent from what they actually do: Simply staying in the shallows a little longer after the end of the Deco is always good, and if you follow the GF, you can also see how quickly you get down to 70 or even 60 – especially if there is a Deco gas involved.
Some also take different GFs depending on the dive. Apparently, the same gradient factor is not always equally risky: The higher the overall load, i.e. the deeper and longer the dive, the higher the risk. Which is perhaps not entirely surprising: If you don’t have a leading tissue during the ascent, but many tissues are at their supersaturation limit at the same time, right down into the middle tissues, this puts a greater strain on the body than if only a single tissue has just limited the dive. For more extreme dives, it may make sense to choose lower gradient factors – even if this noticeably prolongs the decompression, of course.
So there is no one setting that is always right for everyone. Year after year, small new findings are added at various points, and we would not dare to predict what we will consider safe in 20 years.
To read up on the studies mentioned:
Cialoni, D., Pieri, M., Balestra, C., & Marroni, A. (2017). Dive risk factors, Gas Bubble formation, and decompression illness in recreational SCUBA diving: Analysis of DAN Europe DSL data base. Frontiers in Psychology, 8. https://doi.org/10.3389/fpsyg.2017.01587
De Ridder, S., Pattyn, N., Neyt, X., & Germonpré, P. (2023). Selecting optimal air diving gradient factors for Belgian military divers: more conservative settings are not necessarily safer. Diving and Hyperbaric Medicine, 53(3), 251–258. https://doi.org/10.28920/dhm53.3.251-258
Doolette, D. J. (2019, May 29). Gradient Factors in a Post-Deep Stops World. InDEPTH. https://indepthmag.com/gradient-factors-in-a-post-deep-stops-world/
Doolette, D. J., Gault, K. A., & Gerth, W. A. (2015). Decompression from He-N2-O2 (Trimix) bounce dives is not more efficient than from He-O2 (Heliox) bounce dives. https://apps.dtic.mil/sti/tr/pdf/AD1000575.pdf
Doolette, D. J., Gerth, W. A., & Gault, K. A. (2011). Redistribution of Decompression stop time from shallow to deep stops increases incidence of decompression sickness in air decompression dives. https://apps.dtic.mil/sti/citations/ADA561618
