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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.

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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.


Dive Deeper:

InDepth: Variable Gradient Model: An Approach To Create More Efficient Decompressions by Kevin Gurr

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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Risk-Takers, Thrill-Seekers, Sensation-Seekers, and … You?

It’s likely that many in our community no longer think of tech diving as a risky activity, or perhaps even appreciate how important taking risks may be to one’s personal health—let alone that of our species. Fortunately, InDEPTH’s copy editing manager Pat Jablonski dived deep into the origins, meaning, and benefits of regularly taking risks, and even offers a thrill-seeking quiz for your edgy edification. What have you got to lose?

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by Pat Jablonski. Title photo courtesy of Katelyn Compton Escott.

“Life without risk is not worth living.” – Charles Lindbergh

What defines a risk? What is involved in taking a risk?

Difficult questions to answer, because something that feels risky to one person might be yawn-worthy to another. Risk taking, unscientifically, is something you do that gets your blood up, raises your heartbeat, awakens your senses, and makes you hyper-aware of your surroundings.

Surely we can agree that the Covid pandemic has added an unexpected level of risk to everyday life. Add poor drivers, mass shootings, contentious politics, global climate change, and many are left believing that meeting each day is risky enough. But that’s not true for people who identify as risk-takers or thrill-seekers.

“Everyone has a ‘risk muscle’. You keep in shape by trying new things. If you don’t, it atrophies. Make a point of using it once a day.” – Roger Von Tech

There are many activities that go to the trouble of defining the level of risk involved with a specific activity, and while that’s not the purpose of this article, you should know that scuba diving ranks fairly high on the risky behavior scale–higher than skydiving and rappelling. And, cave/wreck diving or freediving isn’t on any risk scale we could locate. We can assume it’s up there—near or at the top.

Fock A. Analysis of recreational closed-circuit rebreather deaths 1998–2010 Diving and Hyperbaric Medicine. 2013 Volume 43, No. 2. With the caveat that they are “best guess numbers,” Fock concluded that rebreather diving is likely 5-10x as risky as open circuit scuba diving, accounting for about 4-5 deaths per 100,000 dives, compared to about 0.4 to 0.5 deaths per 100k dives for open circuit scuba. This makes rebreather diving more risky than skydiving at .99/100k, but far less risky than base-jumping at 43 deaths/100k. The current belief is that rebreather diving has gotten safer.

Divers are a fairly small niche group for many reasons. One of them could involve the degree of danger associated with the sport. Answer this: Do dry land people ever ask you why you would want to take such a chance with your life in order to go where you weren’t meant to go? 

It’s a reasonable question, albeit a hard one to answer.

Photo courtesy of Glen Kwan

“A life without risk is a life unlived, my friend.” – Big Time Rush

Kevin Costner’s Waterworld aside, humans have (yet) to be born with gills or webbed toes. Still, there you are. You’ve spent unmentionable amounts of money. You’ve carved out a whole day, or maybe weeks, away from your to-do list. You’re suited up and look like an alien. You’re on a quest to explore the aquatic world where you’re able to breathe only with a cumbersome apparatus. You’re planning to explore inner space! You’re going to delve into that amazing realm that’s off limits to most people. 

You may look all matter-of-fact, cool as a cucumber, another day at the office, but it’s a thrill, isn’t it? Inside, you’re a kid with butterflies in your tummy who’s getting away with something big and exciting. Okay, it’s true–you and your team are highly trained, your equipment is top-notch, every box is checked off, and you are behaving responsibly. However, you’d have to be in a coma to not realize that what you’re about to do is taking a risk. Who doesn’t know that people have died doing what you’re doing? Answer honestly: How much more exhilarating is the experience when you know it’s not a walk in the park? Our own Michael Menduno admitted that “the feeling of being more alive lasted for days” after a dive.

So, you’re a diver. Does that mean you’re a risk taker? A thrill seeker? A sensation seeker?

Let’s dive into that subject, first by taking a little quiz, shall we? 

Photo courtesy of SJ Alice Bennett

From A Death Wish to Life Is Precious

In the past, too many mental health professionals treated risky behavior like a disease in need of a cure, focusing on the negative side of risk, even using government funding to address risky behavior and stamp it out. 

Before that, Sigmund Freud might have even believed that thrill seekers had a death wish; in fact, it’s what was believed for many years. 

Modern-day science doesn’t support either theory.

“Only those who will risk going too far can possibly find out how far one can go.” – TS Elliot

For our purposes, we’re focusing on the positive aspects of taking chances, pushing boundaries, and seeking experiences that make life feel . . . more alive. Richer. Fuller. We want to examine what goes into the psyche of a person (like you?) who is enthusiastically willing to engage in an activity already identified as dangerous, possibly even by the people who are engaging in it, and hear what some experts on the subject have to say about such people.

Photo courtesy of Jen MacKinnon

The University of Michigan’s Daniel Kruger proposes that taking chances is a fundamental part of human nature going all the way back to our ancient ancestors—prehistoric humans who had to constantly put their safety on the line in their fight for survival. Think fighting off a wooly mammoth with a stick. Kruger believes we have consequently retained many of those same instincts today, and he believes that it’s a good thing. 

This writer, who is related to a major risk-taker, has always believed that heart-quickening experiences are essential for a well-lived life. I’m convinced and have long proposed that those pulse-pounding moments are often accompanied by a deepened understanding of and appreciation for one’s life—perhaps all life. And I’m happy to report that current science confirms that belief.

“If you are not willing to risk the unusual, you will have to settle for the ordinary.” – Jim Rohn

Dr. Kruger is one of the scientists who proposes that taking risks means “seeking that moment when life feels most precious.

This should not be news for you diving adventurers out there.

Nature vs. Nurture: Born That Way or Learned To Love Adventure

Another scientist, Marvin Zuckerberg, affirms the theory that risk taking is in our DNA. “Certain people have high sensation-seeking personalities that demand challenges and seek out environments that most people’s brains are geared to avoid.” I’ll go out on a limb and say that underwater caves or shipwrecks would qualify as environments most would avoid.

Dr. Cynthia Thompson, the researcher behind a 2014 study from the University of British Columbia, was early to look at the genetic factors that might make a person predisposed to participating in extreme sports, ones that are typically defined as activities where death is a real possibility. The results of her study revealed that risk-takers shared a similar genetic constitution, a genetic variant that influences how powerful feelings are during intense situations.

Photo courtesy of Steve Boisvert

Most scientists agree that personality is a complicated mix of genetic and environmental influences. The “nature vs. nurture” dilemma is alive and well. Dr. Thompson concluded that people who engaged in so-called high-risk sports were not impulsive at all, not reckless either. Instead, “they’re highly skilled masters of their discipline who take a very thoughtful approach to their sports.”

A study conducted in 2019 examined human boundaries, people who pushed them to their limits and beyond, and what made those people tick. Zuckerman labeled such people “sensation seekers” and defined them as “people who chase novel, complex, and intense sensations, who love experience for its own sake, and who may take risks to pursue those experiences.” Is that you?

“History is full of risk-takers. In fact, you could say that risk-takers are the ones who get to make history.” – Daniel Kruger

Other experts posit an alternate theory—one proposing that modern society in the age of seatbelts, guardrails, child-proof caps, safety precautions, laws, rules, and regulations has dulled the sense of survival. In other words, life has flattened out and no longer feels exciting, or risky. So, is one of the reasons we seek excitement because of boredom? 

Maslow’s Theory of Self-actualization

I don’t honestly know who was the first proponent of risk-taking being a positive thing, but the work of Abraham Maslow, the founder of humanistic psychology, was one of the first. Maslow became one of the most influential psychologists of the twentieth century, and he developed a theory of human motivation that advocates for “peak experiences.” Peak experiences are not attained without risk.

“One can choose to go back toward safety or forward toward growth. Growth must be chosen again and again; fear must be overcome again and again” – A Maslow

He proposed that, in addition to meeting basic needs, all humans from birth seek fulfillment in terms of what he called self-actualization—finding their purpose/being authentic. Self-actualization involves peak experiences—those life-altering moments that take us outside ourselves, make us feel one with nature, and allow us to experience a sense of wonder and awe. Maslow also believed that those who were able to have such peak experiences tended to seek them out rather than waiting for the next random occurrence. Hence the anticipation of the next dive?

“Do one thing every day that scares you.” – Anonymous

Photo courtesy of Adam Haydock

Out of Your Comfort Zone Into A World of Wonder

Psychologist Eric Brymer from Queenstown University of Technology in Brisbane, Australia, has spent years studying extreme athletes and has this to say: “They’re actually extremely well-prepared, careful, intelligent, and thoughtful athletes with high levels of self-awareness and a deep knowledge of the environment and of the activity.”

Recent research backs up what some extreme sports athletes have been saying for years, even if only to themselves.

“What participants get from extreme sports is deeply transformational, a sense of connecting with a deep sense of self and being authentic, a powerful relationship with the natural world, a sense of freedom,” says Brymer. “They get a strong sense of living life to its fullest as if touching their full potential.”

Brymer’s comments mirror what Maslow, the founder of humanistic psychology, said back in the 1940s.

We’re not advocating for taking stupid chances (such as diving without proper training, or necessary precautions) and we don’t believe anyone reading this article does that. We simply intended to focus on the scientific evidence that supports adventurers—people who get a thrill from an activity that offers—as a bonus; a chance to feel awakened from the mundane and thrust into a world of wonder. 

Risk-takers and sensation- or thrill-seekers chase unique experiences. Often, those experiences bring awareness of important issues or increase essential knowledge about the planet we share. Many people overanalyze and dither when faced with an unfamiliar situation; they shy away from unsettling circumstances. Risk-takers face the unknown and trust themselves to prevail. Learning to scuba dive, for example, pushes people out of their comfort zone, takes them into a realm foreign and mysterious. Diving forces divers to pay complete attention to a task, to focus with laser-like precision in order to conquer misgivings, and to attain a skill that few others have. Confidence comes with accomplishment. Leadership emerges. Fear is overcome. 

Sensation-seekers see potential stressors as challenges to be met rather than threats that might defeat them. With action, resilience develops. High sensation-seekers report lower perceived stress, more positive emotions, and greater life satisfaction. Engaging in extreme activities brings them peace. 

What does it bring you?

Dive Deeper

Bandolier: Risk of dying and sporting activities

National Geographic: What Makes Risk Takers Tempt Fate? Recent research suggests that genetic, environmental, and personal factors can make people take on risky—even potentially fatal—challenges.

Healthday: Taking Risks By Chris Woolston HealthDay Reporter


Pat Jablonski heads up the copy edit team for InDEPTH. She is a blogger, a writer of stories, a retired tutor, English writing teacher, and therapist. She’s a friend, a wife, a proud mother and grandmother. She is also a native of Florida, having spent most of her life in Palm Beach County. She has a B.A. in English from FAU in Boca Raton and an M.S.W. from Barry University in Miami. She learned to swim in the ocean, a place she thinks of as home, but she doesn’t dive.

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