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Gradient Factors in a Post-Deep Stops World

World-recognized decompression physiologist and cave explorer David Doolette explains the new evidence-based findings on “deep stops,” and shares how and why he sets his own gradient factors. His recommendations may give you pause to stop (shallower).

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by Associate Professor David J. Doolette

Gradient factors are mechanisms which modify the decompression stops prescribed by the Buhlmann ZH-L16 decompression algorithm. ZH-L16 is a “gas content” algorithm, which tracks the uptake and elimination of inert gas in notional tissue compartments and schedules decompression stops to not exceed specified maximum permissible inert gas partial pressures in the compartments. When such maximum permissible inert gas partial pressures are specified for decompression stop depths, they are referred to as M-values.

Gradient factors (GF) modify M-values (and consequently allowed gas supersaturation) to a fraction of the difference between ambient pressure and the original M-value. Thus, GF 80 modifies the M-value to 80% of the difference between ambient pressure and the original M-value. Typical proprietary implementations of the GF method require the diver to select two gradient factors: GF low modifies the M-values for the deepest decompression stop, and GF high modifies the M-value for surfacing (often designated as GF low/high, e.g. GF 20/80). The algorithm then interpolates a series of modified M-values in between these two user-specified points. If the GF low is set less than 100%, this forces deeper stops to limit supersaturation in the fast tissues early in the ascent, and setting the GF high to less than 100% will produce longer, shallower stops to reduce supersaturation in the slower tissues in the latter phase of the ascent

In contrast to gas content decompression algorithms, bubble decompression algorithms (VPM-B is one such algorithm familiar to GUE divers) characteristically prescribe deeper decompression stops. In simple terms, bubble decompression algorithms favor deeper stops to limit supersaturation and thereby bubble formation early in the decompression, whereas traditional gas content decompression algorithms favor a more rapid ascent to maximize the inspired–tissue gradient of inert gas partial pressures to maximize tissue inert gas washout.

New Findings on Deep Stops

Deep stops came to the attention of early technical divers in the form of empirical “Pyle stops,” a practice serendipitously developed by ichthyologist and technical diving pioneer Richard Pyle, arising from a requirement to vent the swim bladders of fish specimens collected at great depth before arriving at his first decompression stop. There followed a strong trend toward the adoption of bubble algorithms, and also for the use of gradient factors to force gas content algorithms to impose deep stops (for instance, using GF low values of 30% or less). Based largely on supportive anecdotes, a widespread belief emerged among technical divers that deep-stop decompression schedules are more efficient than shallow-stop schedules. Efficiency, in this context, means that a schedule of the same or even shorter duration has a lower risk of DCS than some alternative schedule.

However, since about 2005, evidence has been accumulating from comparative decompression trials that shows deep stops are not more efficient, and possibly less efficient, than shallow stops.

However, since about 2005, evidence has been accumulating from comparative decompression trials that shows deep stops are not more efficient, and possibly less efficient, than shallow stops. Most studies have used venous gas emboli (bubbles) as an indicator of comparative risk of decompression sickness (DCS). Blatteau and colleagues compared dives using French Navy air and trimix decompression tables (relatively shallow stop schedules) to experimental schedules with added deep stops and longer total decompression time (similar to Pyle stops). Despite longer total decompression time, the deep stops schedules resulted in either the same or more VGE than the shallow stops schedules, and some cases of DCS.1

Photo courtesy of GUE Archives.

Spisni and colleagues compared trimix dives conducted using a deep stops schedule (ZH-L16 with GF 30/85) to an even deeper stops schedule with longer total decompression time (a UDT version of ratio deco) and found no difference in VGE.2 An as-yet-unpublished study compared trimix dives using a DCAP shallow stops schedule to a ZH-L16 GF 20/80 deep stops schedule with similar total decompression time, and the deep stops schedule resulted in significantly more VGE.3 A large study conducted by the U.S. Navy compared the incidence of DCS in air decompression schedules for 30 minutes bottom time at 170 fsw bottom for a gas content algorithm with the first stop at 40 fsw (shallow stops) or a bubble algorithm with the first stop at 70 fsw (deep stops). The shallow stops schedule resulted in 3 DCS in 192 man-dives and the deep stops schedule resulted in 11 DCS in 198 man-dives.4

What To Do About Gradient Factors

The emerging body of evidence against deep stops suggest common gradient factor setting should be modified to de-emphasize deep stops. Fraedrich validated dive computer algorithms by comparing them to well-tested U.S. Navy decompression schedules, including the schedules from the deep stop study outlined above. For that dive, ZH-L16 with a GF low >55% (e.g. GF 55/70) produced a first decompression stop between 70 and 40 fsw.5 Tyler Coen at Shearwater Research Inc. noted that GF settings recommended by Fraedrich modify ZH-L16 M-values so that approximately the same level supersaturation is allowed at all stop depths. To understand this requires delving a little further into M-values.

The emerging body of evidence against deep stops suggest common gradient factor setting should be modified to de-emphasize deep stops.

M-values are typically a linear function of stop depth. In older algorithms such as ZH-L16, the M-value generating functions have a slope greater than one (in ZH-L16, the slopes are the reciprocals of the “b” parameters), resulting in increasing supersaturation allowed with increasing stop depth. In more modern algorithms developed by the U.S. Navy since the 1980s, including the one used to produce the shallow stops schedule in the study outlined above, the slope of the M-value generating functions are generally equal to one, so that the same level of supersaturation is allowed at all stop depths. This results in modestly deeper stops than older algorithms, but still relatively shallow stops compared to bubble models.

With this information in mind, I set my GF low to roughly counteract the ZH-L16 “b” parameters (I have been using Shearwater dive computers with ZH-L16 GF in conjunction with my tried and true decompression tables for about three years). In ZH-L16, the average of “b” parameters is 0.83. I choose my GF low to be about 83% of the GF high, for instance GF 70/85. Although the algebra is not exact, this roughly counteracts the slope of the “b” values. This approach allows me to believe I have chosen my GF rationally, is not so large a GF low as I am unable to convince my buddies to use it, and satisfies my preference to follow a relatively shallow stops schedule.

This article was prepared by Assoc. Professor Doolette in his personal capacity. The opinions expressed in this article are the author’s own and do not reflect the view of the Department of the Navy or the United States government.

Header image: Joakim Hjelm

1. Blatteau JE, Hugon M, Gardette B. Deeps stops during decompression from 50 to 100 msw didn’t reduce bubble formation in man. In: Bennett PB, Wienke BR, Mitchell SJ, editors. Decompression and the deep stop. Undersea and Hyperbaric Medical Society Workshop; 2008 Jun 24-25; Salt Lake City (UT). Durham (NC): Undersea and Hyperbaric Medical Society; 2009. p. 195-206.

2. Spisni E, Marabotti C, De FL, Valerii MC, Cavazza E, Brambilla S et al. A comparative evaluation of two decompression procedures for technical diving using inflammatory responses: compartmental versus ratio deco. Diving Hyperb Med 2017;47:9-16.

3. Gennser M. Use of bubble detection to develop trimix tables for Swedish mine-clearance divers and evaluating trimix decompressions. Presented at: Ultrasound 2015 – International meeting on ultrasound for diving research; 2015 Aug 25-26; Karlskrona (Sweden).

4. Doolette DJ, Gerth WA, Gault KA. Redistribution of decompression stop time from shallow to deep stops increases incidence of decompression sickness in air decompression dives. Technical Report. Panama City (FL): Navy Experimental Diving Unit; 2011 Jul. 53 p. Report No.: NEDU TR 11-06.

5. Fraedrich D. Validation of algorithms used in commercial off-the-shelf dive computers. Diving Hyperb Med 2018;48:252-8.


Additional Resources:

PADI recently published an excellent post, “Evolving Thought on Deep Decompression Stops,” by John Adsit, on the subject of Deep Stops.

Alert Diver magazine published a profile and interview with Doolette in the Fall of 2016.

The Math behind the ZH-L16 Model: Bühlmann established, by means of many hyperbaric chamber experiments with volunteers, how much supersaturation the individual tissue compartments can tolerate without injury. He expressed the relationship through the following equation:

pamb. tol. = (pt. i.g. – a) ·b

or

pt. tol. i.g. = (pamb / b) + a

pamb. tol. – the ambient pressure tolerated by the tissue

pt. i.g. – the pressure of the inert gas in the tissue

pt. tol. i.g. – tolerated (excess)pressure of the inert gases in the tissues

pamb – current ambient pressure

a, b – parameters of the model ZH-L16 for each tissue. “a” depends on the measure unit of pressure used, while “b”  represents the steepness of the relationship between the ambient pressure pamb. and the pressure of inert gas in the tissue pt. i.g. The first equation shows which lower ambient pressure pamb. tol. will still be tolerated at the actual pressure of inert gas in the tissues pt. i.g. The lower equation shows which level of supersaturation pt. tol. i.g. can be tolerated at a given ambient pressure pamb for a given tissue.


Dr. David Doolette began scuba diving in 1979 and was introduced to the sinkholes and caves of Australia in 1984. Around this time, he alternated between studying for his B.Sc. (Hons.) and working as a dive instructor, when he developed an interest in diving physiology. He planned and conducted some of the first technical dives in Australia in 1993. Since being awarded his Ph.D. in 1995, he has conducted full time research into decompression physiology, first at the University of Adelaide, and since 2005 at the U.S. Navy Experimental Diving Unit in Panama City, Florida.

He has been a member of the Undersea Hyperbaric Medical Society since 1987, received their 2003 Oceaneering International Award, and is a member of their Diving Committee. He has also been a member of the South Pacific Underwater Medicine Society since 1990 and served as the Education Officer for five years. He is a member of the Cave Diving Association of Australia, the Australian Speleological Federation Cave Diving Group, Global Underwater Explorers, and the Woodville Karst Plain Project. He remains an avid underwater cave explorer, both near his home in Florida and abroad.


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Finland’s Newly Established Scientific Diving Academy

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by Edd Stockdale
Header image: Antarctic research as part of Science Under the Ice project Photo by @scienceundertheice.

While exploring the aquatic realm, many divers often encounter objects of interest but are unaware of the historical or scientific value to the fields of archaeology, geology, or biology. Even if they suspect their find might be important, they are untrained in how to treat such a find with an investigative approach.

Scientific diving, separate from sport, recreational, or commercial diving, requires occupational training specific to science-led, underwater activities with the purpose of collecting data and/or samples. This type of diving is important both to research, as well as to policy making, because divers with this specific training and background can make the quantitative or qualitative-based assertions necessary to implement the findings. There is a necessary and important distinction between professional scientific divers and the “citizen science” trained divers who are essential in building public awareness, particularly in conservation projects. 

The necessary training and the regulation of professional scientific diving varies widely from country to country, both in regulation requirements, as well as in practice. In many countries, scientific work is classified as commercial diving, and regulations are set accordingly. At the opposite extreme, underwater scientific activity can be conducted by anyone certified to dive.

Structured approaches were developed to mitigate the abuses that both of these approaches might create—one such approach was specifically from the American Academy of Underwater Sciences, formed in 1977. AAUS, in 1982, received an exemption from commercial diving standards through self-regulation. In Europe, the process of establishing a recognized training standard was slower because many different European countries had different regulations; however, in 2007, after collaborative efforts by leading researchers, the European Scientific Diving Committee was formed. This agency became the European Scientific Diving Panel (ESDP) in 2008. ESDP established the standards for both Advanced European Scientific Diver (AESD) and European Scientific Diver (ESD) that are recognized by its member countries. 

One of the  early members in the establishment of ESDP, Finland, has experienced a decrease in scientific dive training options but no decrease in the demand for trained divers because of the increased amount of marine research and monitoring Finland carries out. To fill this void in suitably trained divers and to develop a new generation of marine researchers, a group of leading representatives from various institutions have successfully sought funding to establish a new, centralized training center—the Finnish Scientific Diving Academy (FSDA) at the University of Helsinki Tvarminne Zoological Station. FSDA is located on the shore of the Baltic Sea. 

Archeologist taking video for photogrammetry model of Garpen by Rikka Tevali, Photo by Finnish Heritage Agency.

The Academy’s primary objective is to train European standard professional scientific dive training for AESD certification, but this is far from its only goal. In addition to the six-week core program, plans are in place for adding dive training to undergraduate and early career research students to stimulate future generations of field-based marine researchers. Courses for divers who want to gain more experience or to develop skills for citizen-science-based projects with shorter timescales are also in the cards, making the Academy a truly centralized base for all aspects of scientific dive activities, one that can offer expertise across the disciplines.

With its location on the Gulf of Finland, this training will predominantly specialize in cold-water based approaches, though training options in other locations are always a possibility to cover different conditions. Taking advantage of the ice conditions in Finnish winter’s polar research dive training, which, combined with easier access and facilities already established, makes the option to train for polar projects—without the logistical hassle of actually getting to research stations in those regions—a realistic possibility. 

Included into the development concept of the FSDA is not only the concentration on classical scientific diving protocols, but also a widening the scope. It is often ironic that all the different areas of diving contain techniques that can overlap to benefit each other but are not taught or communicated; for example, skills used in a cave diving survey could easily benefit an ecological study or archeological field work. Therefore, the coordinator position for the FSDA requires a background in not just scientific, but technical and other areas of diving with the aim to integrate these skills into these areas into the programs.  

As a result, in the future, courses will likely be offered for specific evolving technological options, developing techniques, or specialist subjects that research teams need in order to carry out projects. Training may also be offered for more advanced diving, including mixed gas and rebreathers, to expand the ranges and environments to carry out scientific work. 

At the other end of the spectrum, driven by the growing need for more studies of aquatic regions combined with reduced funds for research, citizen science or the involvement of non-professional volunteers becomes more relevant all the time. 

Training options for divers looking to develop these skills vary dramatically, and they may not be familiar with research institutions where expertise is highly appreciated. 

Due to the need for scientific consistency in work carried out, divers not only need high levels of diving ability, but also an understanding of the project goals that are important for the results to be valid. Such training is specialized, but done and implemented correctly, provides scientists with the resources of capable dive teams, which is one of the long term goals of the FSDA. These programs will also aim to cover more specialized fields of study or the application of different diving procedures, both from the requirements perspective of project leaders looking for teams of “citizen scientists,” as well as from the divers themselves. 



Overall, the creation of the Finnish Scientific Diving Academy is exciting for both the scientific and regular diving communities, as it aims to address reduced access to specialized training while developing newer techniques and raising awareness of the importance of how research into the marine world is carried out, whether it is surveying a 400-year-old shipwreck or the ecology of a reef.

The FSDA has been initially funded by the Antero and Merja Parma Foundation and Weisell Foundation for three years with aims to secure more funding to remain long term and is coordinated by Edd Stockdale. The first courses will begin in April 2022. Queries should be sent to Edd Stockdale


Edd Stockdale has worked in scientific and technical diving for over a decade and joined as Badewanne team member in 2019. He is the coordinator of the newly established Finnish Scientific Diving Academy at the University of Helsinki, which was established to develop scientific diving training to further research abilities and develop new approaches to data collection in cold water based science.  When not working on research diving, Edd can be found exploring the mines and wrecks in the Nordic region or planning the next adventure. He is supported by Divesoft as well as Santi, Halcyon, and REEL Diving in Scandinavia. 

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