Decompression Theory – Part 2: Bending Goats

by Richard Devanney:

The first section of this series on decompression theory attempted to describe the processes that determine how our bodies on and off-gas. This article continues on that theme and goes into a little more detail about what factors govern the amount and rate of on and off-gassing.

But before we proceed, it would be a good idea to do a little recap to get you back in the zone, focussing on Nitrogen (N2). At the surface the partial pressure of N2 is 0.79. Our bodies are saturated with N2 at this pressure, and through the normal process of respiration there is no net increase or decrease in the amount of it dissolved in our body tissues, they cannot hold any more at that pressure- this is what saturation means. Descending during a dive rapidly increases the ambient pressure surrounding our bodies. If we were to descend to 20m (3ATA) and stay there, eventually our tissues will be uniformly saturated at this depth, meaning that at 3ATA our tissues would have a PPN2 of 2.37. We aren’t losing any N2 because the N2 entering our lungs will also be at 3ATA (PPN2 2.37 also), so there is no diffusion gradient occurring. The only way to increase the amount of N2 in our tissues would be to descend further, say, to 30m or 4ATA (or to increase the percentage of N2 we breathe). Such a descent would increase the partial pressure of N2 in our lungs to 3.16, allowing diffusion and perfusion to work together to dissolve more N2 in our tissues until eventually the tissues go from 2.37 to 3.16 and become saturated at this pressure. This difference in partial pressures between the inspired gas mix and the tissue tension is known as the inert gas gradient (If that didn’t get you in the zone, read no further!). It is also worth noting at this point that the numbers I am using are not completely accurate, because as the gases we inhale enter the lungs they are diluted by gases that are already in the lungs, which has the effect of reducing the partial pressures slightly, but they work well enough as they are for illustrative purposes.

Now, moving on, if our bodies were all made of the same stuff, the science would be much simpler and you probably wouldn’t bother to read this. In terms of tissue types, we have blood, a brain, ligaments, cartilage, bone, fat, liver, kidneys, eyeballs, and hopefully just the one spleen. These tissues will absorb dissolved gasses at different rates depending on the gas being dissolved, and are also perfused with blood at different rates. This means that our various tissues on and off-gas at differing rates.  Decompression researchers have tried to understand these overlapping processes since 19th Century physiologist Paul Bert undertook a series of controlled experiments on the beloved canine. 22 dogs were exposed to pressures of between 7 and almost 10 atmospheres, followed by rapid decompression. Inevitably and sadly, 21 of them died.

bending-goatsJohn Haldane (pictured…. he’s the one on the left in the photo) was the first person to attempt to rigorously apply the scientific method to decompression in the early 20th Century. Haldane was a very accomplished scientist but also a little eccentric in work and life. When hosting dinner parties, he would reportedly get bored, start thinking about work and wander off to his laboratory, forgetting about his guests. On one memorable occasion, after he had been absent for a while his wife went looking for him. She found him asleep in bed. His explanation was that as he was getting changed into his formal attire for dinner, he found himself undressed and so the only logical step was to put on his nightgown and climb into bed! Despite (or because of) these quirky characteristics, he is widely considered to be the father of decompression theory. It was he who developed the first dive tables in 1908, based on his research of putting goats and family members into a hyperbaric chamber (not at the same time), and recording what happened to them after being brought back to 1ATA from different simulated depths for different times- slowly, and quickly. Pigs have the closest physiology to humans, but goats were in more plentiful supply at the time, and their ratio of body mass to cardiac output is similar to that of a lean man. He also coordinated a series of real dives with Royal Navy divers on board HMS Spanker, near the Isle of Bute in Scotland. As part of these tests, he wanted to prove that a diver could descend quickly with no ill effects. He decided that the first diver to do this should be him. So he donned the suit and helmet weighing 155 pounds and entered the water, hopefully forgetting that he had never bothered to learn how to swim.

Haldane’s son JBS Haldane, was a well-known and accomplished geneticist in his own right (Aldous Huxley based a character on him in his famous work, Brave New World). He became involved in his father’s research and was more than keen to allow himself into the chamber. Indeed, in 1906, at the tender age of 13 he found himself being thrown overboard from HMS Spanker in a diving suit that was way too big for him, as Haldane Sr. wished to prove that the decompression stops he had devised also worked on untrained people! He spent 30 minutes in a flooded diving suit on the seabed in Scotland in August. Once back on board he was wrapped in blankets and given whisky to warm him up! Sometimes the traits and antics of the scientists are as, if not more strange and interesting than the discoveries that made them famous.

Haldane Sr. was the first person to try and model what happens to the body during a dive, by proposing that so-called tissue compartments be used to model different body tissues. He used 5 compartments, all having different “half-times”. A half- time is a general scientific term most commonly used in radioactivity. It describes the time it takes for a radioactive material to decay to half the original number of atoms. But it can also be applied to uptake of gases, and for a given tissue compartment it means the time it will take for it to become half saturated, or half de-saturated with inert gas. A tissue compartment with a 5 minute half-time is known as a fast tissue compartment, and it might model the blood, whereas a 240 minute compartment is a slow tissue compartment, and may represent bone. A 5 minute compartment is so-called because on descent it will take 5 minutes for it to become 50% saturated with gas. After a further 5 minutes it will be 75% saturated, and then 87.5% after 15 minutes, then 96.88%, then 98.44%. With each cycle the compartment will become 50% more saturated compared with its previous level of saturation and full saturation. So in theory it will never be fully saturated as it is always chasing that half-way point. For practical purposes however we can consider it saturated after 6 half-time periods. You can see that the greatest rate of on-gassing occurs within the first period. Then each consecutive period produces less and less additional saturation. By ascending and therefore off-gassing, the same principle applies, but in the opposite direction.

Once a tissue compartment is fully saturated, it means that the tissue tension is at the same partial pressure as the inspired gas. When saturated, the tissues physically cannot hold any more gas at that particular ambient pressure. If we ascend, we reduce ambient pressure, which will reduce the partial pressure of the inspired gas, which, in turn will produce that inert gas gradient. Though these reductions in pressure will instigate off-gassing, the concept of half-times tell us that reaching equilibrium between the tissues and lungs takes time. Because of the delay, tissue tension will be greater than the inspired partial pressure, and may also be higher than ambient pressure. This is known as supersaturation. We need a certain amount of supersaturation in order to instigate a pressure gradient for gases to diffuse from the tissues back to the lungs.

Whilst it’s probable that during a recreational dive a fast tissue compartment may become saturated, slower compartments will not- unless you are able to do a 1,440 minute bottom time to saturate the 240 minute tissue. Now, if the tissue tension becomes higher than ambient pressure, it will become “supersaturated” during the ascent. This requires a bit of a description and a fancy table, both completely stolen from TDI instructor trainer Mark Powell’s excellent book, Deco for Divers.


Going through the example in Mark’s book, at 30m tissue 1 is saturated. Tissue 2, being a slower compartment is still on-gassing and has only reached a tissue tension of 2.50. As we ascend to 20m (3ATA), the inspired N2 has dropped to 2.37. Tissue 1 is supersaturated as the tissue tension is higher than ambient pressure and the inspired N2 partial pressure, so it begins to off-gas because of the inert gas gradient. Tissue 2 will also start to off-gas, but it is not yet supersaturated. As we ascend to 10m we can see that tissue 1 is still supersaturated, but now so is tissue 2, even though it was not supersaturated at the start of the ascent. Tying in half-times with supersaturation means that a tissue will go halfway between the current supersaturation level, back towards saturation. If supersaturation is low then it will be 50% of a short distance. If it is high it will go 50% of a large distance. For a 5 minute tissue compartment, if we reduce ambient pressure from 4ATA to 3ATA, then in 5 minutes the tissue will be at 3.5. But if I instead ascend from 4ATA to 2ATA, then there is a greater distance between the tissue tension and inspired gas tension. It’s off-gassing by 50% in both instances, but for the latter it’s 50% of a bigger difference. This means faster off-gassing.

Critical supersaturation and M-values
Although we need supersaturation to occur in order to be able to off-gas most effectively, each tissue has a theoretical limit of over-pressure, and this is known as critical supersaturation. Beyond a certain point, as the ambient pressure reduces sufficiently and the gas cannot be released quickly enough from the tissue, it will come out of solution (Henry’s law remember) and create a bubble of gas, which is of course Decompression Sickness (DCS) and rather inconvenient.

Haldane was clever enough to realise this principle in 1905, and he expressed this limit as a ratio between the inert gas tension and ambient pressure. He set it to 2:1, i.e. a diver could ascent from 2ATA to 1ATA without getting the mysterious malady of DCS as it was called at the time. This ratio was revised by Robert Workman, the nice uncle of decompression theory, in the 1960s. He changed it to 1.58:1 as long as we are only talking about N2. He reviewed previous decompression research from Haldane’s time onwards and realised it was pretty inadequate when it came to, you know, diving safely and stuff. He realised that faster tissue compartments could tolerate a higher level of overpressure than slow compartments, and also that all compartments could cope with greater overpressures as depth increases. He came up with an empirically derived equation to describe overpressure in different tissues at different depths, and called it an M-value.

So the variables that control whether tissue pressures stay within the M-value are depth, time at depth, and ascent rate. Greater depths mean greater inert gas gradients between our lungs and our tissues when we initially get to the maximum depth, meaning more gas can go into solution. Longer bottom times mean more time for saturation, which conversely means more time is required for off-gassing on ascent. Ascent rate can be analogised by imagining a balloon filled with air with a small hole in it, hovering with its legs crossed at 10m. If the balloon ascends slowly, the expanding air will be allowed the time to vent through the hole enough that the balloon will not increase in size. But if it ascends too fast, then the expanding air cannot escape quickly enough and the balloon will grow and eventually burst- critical supersaturation- reaching the M-value- #DCS. Not quite as bad or weird as realising a balloon has legs though.

Recreational divers are largely concerned with fast tissues, and NDLs and depth limits are designed to prevent too much on-gassing of slower tissues. These limits, combined with maximum ascent rates mean that divers can make a direct ascent to the surface and stay within the M-value for the leading tissues (those closest to the M-value). But for decompression diving it does get much more complicated.

Decompression dives
Remember that Haldane came up with 5 theoretical tissue compartments? They were 5, 10, 20, 40, and 75 minutes. Most dive computers now model 16. Each compartment has its own M-value which changes linearly according to depth, and the slowest compartment might be 240 minutes. A typical decompression dive on air to say 50m for 25 minutes will mean a much greater amount of on-gassing will occur compared with a no-stop dive to 40m, and now we are not just concerned with the fast tissues. On ascent, both fast, and slower tissue compartments are in danger of going over their own particular M-value at a given depth. So we need to pause to allow time for those tissue pressures to reduce. These are decompression stops. Whichever of the 16 compartments is getting close to the M-value will necessitate staying at a given depth to allow time for it to off-gas enough, then the ascent can continue until another tissue compartment again gets close to the limit, and so on and so on until eventually we reach the surface after conducting a series of stops for varying amounts of time on the way up. If we are diving on trimix now we are having to track 32 compartments- 16 for Helium (He), and 16 for N2. Ascent rate comes into play here too. On the deepest part of the dive, if I go up too slowly then I will be continuing to on-gas my slower tissues, which means reaching a decompression ceiling potentially sooner (depending on whether the ascent causes supersaturation), or extending my deco stops, or both. I need to move as fast as is allowed through the deep stops until I reach my first gas switch, so that I am minimising the amount of on-gassing of my slow tissues, but also staying within the balloon analogy for the leading tissues. Then I will need to ascend slower during the shallow stops. More on ascent rates in the last article, along with the additional complication of bubble mechanics.

The concept of M-values has been widely adopted within diving, and since Workman’s research they have been modified and tweaked by different researchers, most notably by Dr Albert Buhlmann- the Fonz of decompression research. They are still an inherent component of almost every dive agency’s tables and different manufacturer’s dive computer algorithms.

It would be very easy to drone on about M-values and produce lots of graphs that show off-gassing in individual tissues, and highlight how the reduction in inert tissue pressure and ambient pressure relates to the M-value line for that tissue during an ascent. If you’re interested in that there are lots of articles on the internet that are easy to find. It’s even better to get into a discussion about this with your dive buddies or in the classroom with an instructor. The TDI decompression procedures theory classes are the perfect opportunity. For now though give your eyes and brain a well-earned rest until the third and final installment.

Richard Devanney

References and further reading:

  • Powell, M. (2008). Deco for divers, published by Aquapress.
  • Goodman, M. (2007). Suffer and survive: The extreme life of JS Haldane.

Richard Devanney is a TDI, PADI TecRec, and SSI XR instructor currently seeking a full-time tech instructor role. He currently lives in Reykjavik, Iceland, and works as a full-time instructor/dive guide for the busy summer season, predominantly taking divers through Silfra Fissure, where the European and American tectonic plates meet. He previously managed Big Blue Tech, a successful and well-respected TDI technical diving school in Thailand. After 4 years in Thailand, he left to continue pursuing his own technical diving ambitions.

He runs a Facebook tech diver information page called zenith diving, and will be running a technical diving consultancy of the same name when he is in a position to teach technical diving again. You can contact him at or

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2 replies
  1. Rob Hall
    Rob Hall says:

    Love part I and II. Easy read and understand with a bit of humour to keep my attention.

    Not to rush you but looking forward to Part III.


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