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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).



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


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.


Understanding Oxygen Toxicity: Part 1 – Looking Back

In this first of a two-part series, Diver Alert Network’s Reilly Fogarty examines the research that has led to our current working understanding of oxygen toxicity. He presents the history of oxygen toxicity research, our current toxicity models, the external risk factors we now understand, and what the future of this research will look like. Mind your PO2s!




By Reilly Fogarty

Header photo courtesy of DAN

Oxygen toxicity is a controversial subject among researchers and an intimidating one for many divers. From the heyday of the “voodoo gas” debates in the early 1990s to the cursory introduction to oxygen-induced seizure evolution that most divers receive in dive courses, the manifestations of prolonged or severe hyperoxia can often seem like a mysterious source of danger. 

Although oxygen can do great harm, its appropriate use can extend divers’ limits and improve the treatment of injured divers. The limits of human exposure are tumultuous, often far greater than theorized, but occasionally–and unpredictably–far less.  

Discussions of oxygen toxicity refer primarily to two specific manifestations of symptoms: those affecting the central nervous system (CNS) and those affecting the pulmonary system. Both are correlated (by different models) to exposure to elevated partial pressure of oxygen (PO2). CNS toxicity causes symptoms such as vertigo, twitching, sensations of abnormality, visual or acoustic hallucinations, and convulsions. Pulmonary toxicity primarily results in irritation of the airway and lungs and decline in lung function that can lead to alveolar damage and, ultimately, loss of function. 

The multitude of reactions that takes place in the human body, combined with external risk factors, physiological differences, and differences in application, can make the type and severity of reactions to hyperoxia hugely variable. Combine this with a body of research that has not advanced much since 1986, a small cadre of researchers who study these effects as they pertain to diving, and an even smaller group who perform research available to the public, and efforts to get a better understanding of oxygen toxicity can become an exercise in frustration. 

Piecing together a working understanding involves recognizing where the research began, understanding oxygen toxicity (and model risk for it) now, and considering the factors that make modeling difficult and increase the risk. This article is the first in a two-part series. It will cover the history of oxygen toxicity research, our current models, the external risk factors we understand now, and what the future of this research will look like. 

Early Research

After oxygen was discovered by Carl Scheele in 1772, it took just under a century for researchers to discover that, while the gas is necessary for critical physiological functions, it can be lethal in some environments. The first recorded research on this dates back to 1865, when French physiologist Paul Bert noted that “oxygen at a certain elevation of pressure, becomes formidable, often deadly, for all animal life” (Shykoff, 2019). Just 34 years later, James Lorrain Smith was working with John Scott Haldane in Belfast, researching respiratory physiology, when he noted that oxygen at “up to 41 percent of an atmosphere” was well-tolerated by mice, but at twice that pressure mouse mortality reached 50 percent, and at three times that pressure it was uniformly fatal (Hedley-White, 2008). 

Interest in oxygen exposure up to this point was largely medical in nature. Researchers were physiologists and physicians working to understand the mechanics of oxygen metabolism and the treatment of various conditions. World War II and the advent of modern oxygen rebreathers brought the gas into the sights of the military, with both Allied and Axis forces researching the effects of oxygen on divers. Chris Lambertsen developed the Lambertsen Amphibious Respiratory Unit (LARU), a self-contained rebreather system using oxygen and a CO2 absorbent to extend the abilities of U.S. Army soldiers, and personally survived four recorded oxygen-induced seizures. 

Kenneth Donald, a British physician, began work in 1942 to investigate cases of loss of consciousness reported by British Royal Navy divers using similar devices. In approximately 2,000 trials, Donald experimented with PO2 exposures of 1.8 to 3.7 bar, noting that the dangers of oxygen toxicity were “far greater than was previously realized … making diving on pure oxygen below 25 feet of sea water a hazardous gamble” (Shykoff, 2019). While this marked the beginning of the body of research that resembles what we reference now, Donald also noted that “the variation of symptoms even in the same individual, and at times their complete absence before convulsions, constitute[d] a grave menace to the independent oxygen-diver” (Shykoff, 2019). He made note not just of the toxic nature of oxygen but also the enormous variability in symptom onset, even in the same diver from day to day. 

The U.S. Navy Experimental Diving Unit (NEDU), among other groups in the United States and elsewhere, worked to expand that understanding with multiple decades-long studies. These studies looked at CNS toxicity in: immersed subjects with a PO2 of less than 1.8 from 1947 to 1986; pulmonary toxicity (immersed, with a PO2 of 1.3 to 1.6 bar, and dry from 1.6 to 2 bar) from 2000 to 2015; and whole-body effects of long exposures at a PO2 of 1.3 from 2008 until this year. 

The Duke Center for Hyperbaric Medicine and Environmental Physiology, the University of Pennsylvania, and numerous other groups have performed concurrent studies on similar topics, with the trend being a focus on understanding how and why divers experience oxygen toxicity symptoms and what the safe limits of oxygen exposure are. Those limits have markedly decreased from their initial proposals, with Butler and Thalmann proposing a limit of 240 minutes on oxygen at or above 25 ft/8 m and 80 minutes at 30 ft/9 m, to the modern recommendation of no greater than 45 minutes at a PO2 of 1.6 (the PO2 of pure oxygen at 20 ft/6 m). 

Between 1935 and 1986, dozens of studies were performed looking at oxygen toxicity in various facets, with exposures both mild and moderate, in chambers both wet and dry. After 1986, these original hyperbaric studies almost universally ended, and the bulk of research we have to work with comes from before 1986. For the most part, research after this time has been extrapolated from previously recorded data, and, until very recently, lack of funding and industry direction coupled with risk and logistical concerns have hampered original studies from expanding our understanding of oxygen toxicity. 

Primary Toxicity Models

What we’re left with are three primary models to predict the effects of both CNS and pulmonary oxygen toxicity. Two models originate in papers published by researchers working out of the Naval Medical Research Institute in Bethesda, Maryland, in 1995 (Harabin et al., 1993, 1995), and one in 2003 from the Israel Naval Medical Institute in Haifa (Arieli, 2003). The Harabin papers propose two models, one of which fits the risk of oxygen toxicity to an exponential model that links the risk of symptom development to partial pressure, time of exposure, and depth (Harabin et al., 1993). The other uses an autocatalytic model to perform a similar risk estimate on a model that includes periodic exposure decreases (time spent at a lower PO2). The Arieli model focuses on many of the same variables but attempts to add the effects of metabolic rate and CO2 to the risk prediction. Each of these three models appears to fit the raw data well but fails when compared to data sets in which external factors were controlled.  

Comparison of predicted and recorded oxygen toxicity incidents by proposed model (Shykoff, 2019).

The culmination of all this work and modeling is that we now have a reasonable understanding of a few things. First, CNS toxicity is rare at low PO2, so modeling is difficult but risk is similarly low. Second, most current models overestimate risk above a PO2 of 1.7 (Shykoff, 2019). This does not mean that high partial pressures of oxygen are without risk (experience has shown that they do pose significant risk), but the models cannot accurately predict that risk. Finally, although we cannot directly estimate risk based on the data we currently have, most applications should limit PO2 to less than 1.7 bar (Shykoff, 2019).  

NOAA Oxygen Exposure Limits  (NOAA Diving Manual, 2001).

For the majority of divers, the National Oceanic and Atmospheric Administration’s (NOAA) oxygen exposure recommendations remain a conservative and well-respected choice for consideration of limitations. The research we do have appears to show that these exposure limits are safe in the majority of applications, and despite the controversy over risk modeling and variability in symptom evolution, planning dives using relatively conservative exposures such as those found in the NOAA table provides some measure of safety. 

The crux of the issue in understanding oxygen toxicity appears to be the lack of a definitive mechanism for the contributing factors that play into risk predictions. There is an enormous variability of response to hyperoxia among individuals–even between the same individuals on different days. There are multiple potential pathways for injury and distinct differences between moderate and high PO2 exposures, and the extent of injuries and changes in the body are both difficult to measure and not yet fully understood. 

Interested in the factors that play into oxygen toxicity risk and what the future of this research holds? We’ll cover that and more in the second part of this article in next month’s edition of InDepth.

Additional Resources:

  1. Shykoff, B. (2019). Oxygen Toxicity: Existing models, existing data. Presented during EUBS 2019 proceedings.
  2. Hedley-Whyte, John. (2008). Pulmonary Oxygen Toxicity: Investigation and Mentoring. The Ulster Medical Journal 77(1): 39-42.
  3. Harabin, A. L., Survanshi, S. S., & Homer, L. D. (1995, May). A model for predicting central nervous system oxygen toxicity from hyperbaric oxygen exposures in humans
  4. Harabin, A. L., Survanshi, S. S. (1993). A statistical analysis of recent naval experimental diving unit (NEDU) single-depth human exposures to 100% oxygen at pressure. Retrieved from
  5. Arieli, R. (2003, June). Model of CNS O2 toxicity in complex dives with varied metabolic rates and inspired CO2 levels
  6. NOAA Diving Manual. (2001). 

Two Fun (Math) Things:


The Theoretical Diver: Calculating Oxygen CNS toxicity

Reilly Fogarty is a team leader for risk mitigation initiatives at Divers Alert Network (DAN). When not working on safety programs for DAN, he can be found running technical charters and teaching rebreather diving in Gloucester, MA. Reilly is a USCG licensed captain whose professional background includes surgical and wilderness emergency medicine as well as dive shop management.

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