The history of Haldanian decompression models

Nowadays, diving is a very safe sport, but this wasn't always the case: in its earlier days, especially when diving was primarily a tool for a mission rather than an activity for leisure, a lot of early workers subjected to increased atmoshperic pressures reported feeling strange "aches" when returning to a normal pressure (which is known today to be decompression sickness). There was a necessity to create protocols for the ascents during dives (and other expeditions where workers were subjected to higher pressure) and ensure a safe return.

Haldanian Models are early decompression models, which were in the form of diving tables, and the first recognized as such, used in staged decompression for various users, such as mines/tunnel workers, early divers, and more. Although they are some of the oldest decompression models, the newer versions are still widely used today, even in the most modern dive computer; the most commonly used decompression algorithm is the Bühlmanm ZH-L16C model (which we will talk about later on), which is a more recent version of Haldane's decompression model, also known as a Neo-Haldanian model.

This is the story of trial and error, and how, over the years, divers and scientists have made diving a safer practice.

First instances of Decompression Sickness

To understand exactly why decompression models came to fruition, let's first jump back in time to the first instances of decompression sickness and understand the necessity of developing tables for safely executing missions under increased atmospheric pressure.

If you attempt to guess when the first case of decompression sickness was recorded, a reasonable guess would be when scuba diving started gaining traction in the 1940s, with Jacques Cousteau creating the first Aqua-Lung prototypes, or maybe a bit before then, in the 1800s, when caissons started being used for workers in mines, tunnels, or other various submerged environments? The reality is that the first recorded case of decompression sickness is believed to have originated in 1670.

Introducing Robert Boyle: Robert Boyle (1627 - 1691) was an English-Irishman known for being a philosophist, chemist, and physicist (amongst many other things). He is regarded to be one of the pioneers of chemistry and scientific methodology. Boyle's Law is named after him (this law states that at constant temperature, the volume of gas is inversely proportional to its absolute pressure, which is also a very important concept in scuba diving). The reason why we're interested in him in this case is that he was working on a series of experiments (the ethics of which can be questioned); by operating an air pump, which would drain the air out of a "receiver", in which he would place various animals, and observing how withdrawing air affected each animal. In a particular case, he observed that a viper was showing signs of distress after removing the air, as a bubble formed in the aqueous humor of one of its eyes. Without even knowing what it was or why it happened, Robert Boyle described the first instance of DCS.

Here is the passage, by Robert Boyle, theorizing the action of these "small bubbles" and describing the viper being affected by it:

Note, that the two foregoing Experiments were made with an eye cast upon the inquiry, that I thought might be made; Whether, and how far the destructive operation of our Engin upon the included Animal, might be imputed to this, that upon the withdrawing of the Air, besides the removal of what the airs presence contributes to life, the little Bubble generated upon the absence of the Air in the Bloud, juyces, and soft parts of the Body, may by their Vast number, and their conspiring distension variously steighten in some places, and stretch in others, the Vessels, espetially the smaller ones, that convey the Bloud and Nourishment; and so by choaking up some passages, and vitiating the figure of others, disturb or hinder the due circulation of the Bloud? Not to mention the pains that such distensions may cause in some Nerves, and membranous parts, which by irritating some of them into Convulsions may hasten the death of Animals and destroy them sooner by occasion of that irritation, that they would be destroyed by the bare absence of loss of what the Air is necessary to supply them with. And to show, how this production of Bubbles reaches even to very minute parts of the Body, I shall add on this occasion (hoping that I have not prevented my self on any other,) what may seem somewhat strange, what I once observed in a Viper, furiously tortured in our Exhausted Receiver, namely that it had manifestly a conspicuous Bubble moving to and fro in the waterish humour of one of its Eyes. - Robert Boyle, Philosophical Transactions N.63 pp. 2044

Although at this point, diving in its current form was still far from existing, Robert Boyle, unbeknownst to him, had shown a link between a reduction in pressure and bubbles forming in the body.

To observe the next recorded case of decompression sickness, we would have to jump almost 170 years into the future, in 1840, towards the end of the first industrial revolution: at this point, a lot of technological progress had been made, and the use of heavier machinery became widespread. Specifically, caissons, or pneumatic caissons, were being used in mines and tunnels, and for other water-related projects, such as building bridges.

You can probably imagine the problem: workers were exposed for multiple hours to an increased atmospheric pressure, and when the work was done, they would exit the caisson (you can make the parallel between that and a fast ascent after a long dive) with their tissues supersaturated in nitrogen. Reports of workers encountering issues upon exiting the caissons were appearing: limb pain, numbness, dizziness, etc... To be specific, the first two instances of DCS relating to caissons were noted by French geologist Jacques Triger in 1841, when two of his workers (miners) surfaced after being subjected to an increased atmospheric pressure of 2.4 atmospheres for 4.25 hours: They reported feeling a sharp pain in their left arm, knees, and left shoulders (although they were subsequently treated by massaging the areas with alcohol, and the pain dissapeared the next day - keep in mind, at this time, no one had any idea what the issue was, and the idea of "recompression" would only appear later on).

Before making any subsequent observations or advancements, more news of workers encountering this mysterious "illness" was appearing, especially as use of the caisson was becoming more and more widespread. In the following years, caisson workers and miners reported many of those cases, and as we'll see in the next part, even after starting to understand what this "illness" was and how to treat it, it was still a mostly dark area for scientists.

Pre-Haldanian Models and Theories

Although calling them "models" is a bit of a stretch, early researchers were slowly starting to figure out what was happening, and even though no real model, tables, or algorithm (as we have today) existed, procedures and standards were slowly starting to be put in place.

The first notable advancements were made in 1847 in Lourches, a town situated in northern France. During the digging of the Avaleresse-la-Naville mine, miners were used for excavation and were exposed to various pressures, sometimes up to 4.25 atmospheres. On this operation, a total of 64 caisson workers were used at various pressures, 6 to 7 of them being used at a time at intervals of 4 hours. The compression and decompression would be stretched over 30 minutes. There were several instances of decompression illnesses amongst workers, some more severe than others: many workers were presenting nausea, breathing difficulties, muscle spasms/contractions, limb pain, and, in some cases, even death. B. Pol (who was the mining company's surgeon), and T.-J.-J. Watelle (a doctor) were asked to examine all the incidents that were happening. They made various important observations:

• Younger workers seemed to be more "immune" to these effects, as of the 25 incidences observed, only 1 of the incidents included a 28-year-old. (5 were 30-40 years old, and 19 were 40+ years old).
• Workers seemed to be unaffected by these effects while under pressure: they would only appear upon decompression. B. Pol writes, "decompression only is to be feared".
• The gravity of the illness seemed to be proportional to the depth the diver went to and the time they spent there (we now know that the more time you spend at depth, the more nitrogen saturates your body).
• Some symptoms seemed to improve upon recompression.

While all these observations are now known to be correct to an extent, the actual origin of these symptoms was still unknown, and we would have to wait 10 years, until 1857, for the German physiologist Felix Hoppe-Seyler to propose the theory that the origin of the illnesses and deaths of the workers originated from the formation of bubbles. In 1861, Eugène Bucquoy went a step further and hypothesized that it was the gas dissolved in the tissues that reverted to their gaseous form upon decompression. He then compared the action of those gas bubbles to an embolism caused by the injection of air in the veins.

It would be a few years until a man by the name of Paul Bert would create the first real foundations of decompression theory. Paul Bert (1833-1886) was a French physiologist, zoologist, and politician (although his scientific career was more successful than his political one) known for his work La Pression Barométrique, published in 1878, which is more or less known as the basis for modern hyperbaric physiology and set the stage for the following discoveries. In it, he published a few discoveries:

• He identified the gas that would form bubbles upon decompression to be nitrogen. He explains that nitrogen is dissolved in our body at a higher partial pressure and would force itself out of solution into bubbles as the pressure is reduced. For this reason, he speaks of keeping the speed of decompression as slow and constant as possible.
• He showed that oxygen therapy was effective for treating decompression sickness.
• As the variation of pressure affects the content of the gas we breathe, it modifies the amount of oxygen we are exposed to, and can cause hypoxia if the pressure is too low, and it can cause hyperoxia if it is too high. This hyperoxia can lead to oxygen toxicity (and specifically at very high partial pressures, can lead to CNS, or Central Nervous System Oxygen toxicity, also known as the Paul Bert Effect).

Although he acted as a very important stepping stone for decompression theory in the realm of scuba diving, he actually first became interested in pressure-related maladies because of high-altitude activities such as mountaineering or hot-air balloon expeditions. As a matter of fact, he is known as the "father of aviation physiology".

At the dawn of the 19th Century, the cause of decompression sickness started being understood and the culprit (Nitrogen) had been exposed! Nevertheless, only the first part of the problem had been solved: the next issue was going to be finding how to preventing DCS. For that to happen, scientists would need to define clear protocols explaining how to limit nitrogen exposure and create decompression plans for safe ascents; this is where J.S. Haldane, would come in.

John Scott Haldane

John Scott Haldane (1860-1936) is probably one of the most important people regarding the history and research of decompression theory: he is often referred to as the father of decompression theory, and his research was the pillar for the more current models we still use today (it is the reason why some of our current models are called neo-haldanian models). Born in 1860 in Edinburgh, Scotland, He graduated from the Edinburgh University Medical School in 1884. He was known as a physiologist, physician, and philosopher. Other than decompression sickness, he was known for studying many incidents, including (but not limited to): countering the use of poisonous gas during the First World War; silicosis; the oxygen tent; and the Haldane effect. He was also known for experimenting on himself and on his son to learn more about the potential effects of harmful gases. If that wasn't already impressive enough, he also founded the Journal of Hygiene, which published a lot of diving-related studies in the following years.

Haldane becomes especially relevant to us in 1906, when he was tasked by the Royal Navy to create protocols, rules, and standards for safe decompressions. He began studying the effects of various compression and decompression schedules on goats and humans, and developed the first diving tables, which were published in 1908 in his Journal of Hygiene. The paper was titled "The prevention of Compressed-Air Illness".

Of all the contents in the paper, we can take away some key points that are crucial to Haldanian models and made them a revolution in the realm of decompression theory:

• Haldane considered 5 parts of the body in which the nitrogen saturation/desaturation would take place independently. Each of those "parts" (which we know today as a compartment) saturates/desaturates at a different rate, which would depend on their half-time. Haldane's first compartments had half-times of 5, 10, 20, 40, and 75 minutes.
• To avoid bubbles forming, there couldn't be a pressure difference between the nitrogen dissolved in the body and the ambient nitrogen pressure greater than 1:2.

To read more about Haldane's discovery, the following points detail the summary of his research (taken directly from the paper The Prevention of Compressed-Air Illness, A. E. BOYCOTT, G. C. C. DAMANT AND J. S. HALDANE pp. 424-425):

SUMMARY.

The time in which an animal or man exposed to compressed air becomes saturated with nitrogen varies in different parts of the body from a few minutes to several hours. The progress of saturation follows in general the line of a logarithmic curve and is approximately complete in about five hours in man and in a goat in about three hours.

The curve of desaturation after decompression is the same as that of saturation, provided no bubbles have formed.

Those parts of the body which saturate and desaturate slowly are of great importance in reference to the production of symptoms after decompression.

No symptoms are produced by rapid decompression from an excess pressure of 15 pounds, or a little more, to atmospheric pressure, i.e. from two atmospheres absolute to one. In the same way it is safe to quickly reduce the absolute pressure to one-half in any part of the pressure scale up to at least about seven atmospheres: e.g. from six atmospheres (75 pounds in excess) to three (30 pounds), or from four atmospheres to two.

Decompression is not safe if the pressure of nitrogen inside the body becomes much more than twice that of the atmospheric nitrogen.

In decompressing men or animals from high pressures the first part should consist in rapidly halving the absolute pressure: subsequently the rate of decompression must become slower and slower, so that the nitrogen pressure in no part of the body ever becomes more than about twice that of the air. A safe rate of decompression can be calculated with considerable accuracy.

Uniform decompression has to be extremely slow to attain the same results. It fails because it increases the duration of exposure to high pressure (a great disadvantage in diving work), and makes no use of the possibility of using a considerable difference in the partial pressure of nitrogen within and without the body to hasten the desaturation of the tissues. It is needlessly slow at the beginning and usually dangerously quick near the end.

Decompression of men fully saturated at very high pressures must in any case be of very long duration: and to avoid these long decompressions the time of exposure to such pressures must be strictly limited. Tables are given indicating the appropriate mode and duration of decompression after various periods of exposure at pressures up to 90 pounds in excess of atmospheric pressure.

The susceptibility of different animals to compressed-air illness increases in general with their size owing to the corresponding diminution in their rates of circulation.

The individual variation among goats in their susceptibilitv to caisson disease is very large. There is no evidence that this depends directly on sex, size or blood-volume: there is some evidence that fatness and activity of respiratory exchange are important factors.

Death is nearly always due to pulmonary air-embolism, and paralysis to blockage of vessels in the spinal cord by air. The cause of " bends" remains undetermined; there are reasons for supposing that in at least many cases they are due to bubbles in the synovial fluid of the joints.

In essence, Haldane established a few ideas that are still adopted to this day in modern decompression algorithms: firstly, the nitrogen permeating and saturating our body doesn't just diffuse in and out of it in one block, but it saturates some parts of it faster than others. Additionally, the saturation process follows a logarithmic curve. Secondly, the risk of bubbles forming originated from a pressure differential between a supersaturated tissue and the surrounding nitrogen ambient pressure. He also highlights the importance of those so-called "slow tissues" (he calls them those parts of the body which saturate and desaturate slowly) regarding their importance in bubble formation.

The decompression tables Haldane published went on to be used for the next half-century. Nevertheless, it was still a new model, and although quite revolutionary for its time, it was still far from perfect. As we will see in the next part, the next decades were spent refining Haldane's model and tweaking its parameters.

US Navy's research

out of all the organizations invested in this research, the biggest contributors at that period were surely the U.S. Navy.

From the 1910s onwards, for the best part of a century, the U.S. Navy conducted many dives with the goal in mind to improve Haldane's tables. The initial force in this research was led by Chief Gunner George D. Stillson; the goal was to allow the Navy divers to go deeper than 18m safely. The research started in 1912, and 3 years later, in 1915, the Department of Construction and Repair published "Report On Deep Diving Tests", which contained the first U.S. dive tables (also known as the C&R tables). This report describes around 100 different diving tests undergone by Navy divers at various depths, but also talks about various topics such as the equipment used by divers, safety procedures, recompression procedures, and even the procedures of diving on a rebreather.

The culmination of this research was the establishment of the Deep Sea Diving School in Rhode Island and the revision of their diving manual in 1916.

Over the course of the next years, the tables published by Stillson would allow the navy to successfully carry out many missions, such as salvaging the debris of the USS-F4: the USS-F4 was a submarine that sank to a depth of 93m (306 feet) on the 25th of March 1915, and killed 21 men. The navy divers successfully recovered the submarine and the bodies. This allowed the victims to be given a proper ceremony and burial (although only 4 were ever identified), and the reason for the submarine's demise to be investigated (it was determined that the battery acid was leaking on the steel hull).

During the recovery of the USS-F4, divers experienced severe signs of vertigo in the water (which we now know to be narcosis). This led to the start of experimental dives using helium, as it was observed to have a positive effect on divers at depth. A few years later, in 1927, the US Navy published its Air Decompression Tables.

As the 20th century progressed, so did the research, and although more refined decompression tables had already been published, the innovations were by no means slowing down. One of the most important observations was made by J.A. Hawkins, C.W. Schilling, and R.A. Hansen in the 1930s, when they realized that the maximum supersaturation ratio of 2:1 was off: the faster tissues (lower half-times) could actually handle a higher supersaturation ratio, while the slower compartments (higher half-times) were more "sensitive" and had a lower ratio. After 3 years and 2143 experimental dives, they came up with the following revised supersaturation ratios in the 5 Haldanian compartments:

Based on these new ratios, O.D. Yarbrough, a US Navy decompression researcher, hypothesized that the first two compartments (5 and 10 minutes) had such a big supersaturation ratio that they could essentially be ignored. Consequently, in 1937, he published a model that only used the 20, 40, and 75-minute compartments, although the ratios used for the remaining compartments were more conservative:

However, this 3-compartment model didn't stick around for very long: one persisting issue was long-deep dives, which the current models didn't seem to describe properly, and as such, in 1956, the U.S. Navy once again published a revised table, which not only reinstated the 5 and 10 minute compartments but also added a 120 minute compartment. This new compartment was based on a series of experiments conducted in the 1940s by Otto Van Der Aue, the captain of the naval medical research in the Navy. Otto's experiments consisted of multiple dives divided into three separate compression/decompression schedules:

1. The first schedule was a compression at 10m for a duration of 24 hours, followed by a direct ascent to the surface. Out of four divers, none suffered DCS
2. The second schedule was a compression at 10m for a duration of 36 hours, followed by a direct ascent to the surface. Out of four divers, two suffered DCS.
3. The third schedule was a compression at 36m for 12 hours, followed by a (de)compression at 10m for 24h, before ascending to the surface. Out of two divers, both suffered DCS.

This experiment not only showed the necessity of using lower ratios for deeper tissues with a higher half-time, but also opened the possibility of adding additional compartments with longer half-times. For the next years, the air table published by the U.S. Navy using 6 compartments was the standard for diving.

Robert Workmann

Robert D. Workman was a medical doctor, part of the U.S. Navy Experimental Diving Unit (NEDU), and a Captain in the Medical Corps. As longer and deeper dives were still posing an issue to the realm of decompression theory, Workman was tasked with refining the model even further.

He came up with a revolutionary idea (which still stands to this day): the supersaturation ratios, instead of being a fixed value for each compartment, would actually vary with depth. Workman figured out a "maximum tolerated supersaturation pressure" for each compartment at each depth; this value would come to be known as an "M-Value". This M-value could be calculated easily as it was represented by a simple linear function: each compartment had a distinct M0 (which represents the M-value at the surface), and a slope ΔM (which represents how much the M-value increases as depth increases), which could be used to calculate the value of any compartment at any depth.

On top of allowing models to compute more precise M-values, Workman added three additional compartments: on top of the 6 compartments that were already being used (5, 10, 20, 40, 80, and 120 minutes), the three new ones had even longer half-times of 160, 200, and 240 minutes. Those compartments would represent even deeper tissues, the idea being to take into account the high supersaturation that takes place for longer and deeper dives. The ratio (which we can now call M-value) for those new compartments would be even smaller.

To calculate these "M-Values", one could use the following table, published in 1965 by Workman:

Workman allowed decompression scientists to view the limit as a maximum allowed pressure of dissolved nitrogen instead of fixed ratios, and allowed divers to venture deeper safely. Surely, since the original tables by Haldane were published, Workman's research was the biggest improvement made towards decompression theory. We would have to wait around another 20 years for the next big breakthrough in decompression theory.

Bühlmann's models

Albert Alois Bühlmann (1923-1994) was a physician based in Switzerland. Although not a diver, he made some of the biggest contributions to decompression theory; in fact, his models are still the most widely used in diving computers and decompression software. Bühlmann was interested in physiology (and particularly respiration) at high altitudes and high pressures.

Bühlmann's involvement in deep diving actually started in 1959 (6 years before Workman would publish his tables), when Hannes Keller, a Swiss diver and mathematician, started to pursue deep diving. He developed mix-gas tables, an effort that went on to be supported by Bühlmann. Bühlmann advised Hannes on which gas mix he should use: this was later put into practice in Lake Zurich, where Hannes reached a depth of 120m (393 feet), and later in Lake Maggiore, where he got to 222m (728 feet).

A problem that would quickly come to be recognized by Bühlman is the fact that the decompression models that existed at this point in time didn't seem to properly account for diving at altitude: as a matter of fact, he was based in Switzerland, and a lot of the lakes there (in which the dives would take place) are at high altitudes. Swiss military divers would follow the decompression plan, but appeared to get DCS at an abnormally high rate. When looking at the work published by Workman, the "surface M-value" actually corresponds to the "M-value at sea-level pressure", which is different from the reduced ambient pressure at high altitude. Bühlmann went on to expand on Robert Workman's existing model, generalizing the M-values calculation to be able to compute them at pressures lower than 1 atmosphere.

Another question that would come up had to do with the compartments and half-times: we originally went from 5 compartments (following the work published by Haldane) to 9 compartments (used in Robert Workman's work). The question begged itself: How many compartments exactly are there? What are the deepest parts of our body, where nitrogen takes significantly longer to diffuse in and out of? To answer these questions, Bühlmann began his research, funded by the US Navy and Shell Oil. His research was published in 1983 in a book titled Dekompression-Dekompressionskrankheit (which translates to Decompression-Decompression sickness). In this first version, there were a total of 12 compartments, and he named his model ZH-L 12 (ZH stands for Zürich, L stands for Linear, and 12 stands for the 12 compartments used in the model).

In 1986, a new set of tables was published, which had 16 compartments: those 16 compartments are still in use today. This model was known as ZH-L 16, or ZH-L 16A. Each compartment had a pair of coefficients a and b, determined empirically, which could be used to calculate the maximum tolerated dissolved nitrogen pressure of a certain compartment at any ambient pressure using the following formula:

There were slight modifications made to the original values published, as it was found that the a coefficient for the mid-range compartments was not conservative enough. Two new sets of values were published: the ZH-L 16B, and the ZH-L 16C. Although they were both more conservative than the first set published, the B set was meant to be used for dive tables, whereas the C set was meant to be implemented on dive computers for real-time calculations. Today, the ZH-L 16C model is still one of the most widely used decompression models found on diving computers.

Below can be found the values for the ZH-L 16C set:

To get a good idea of the difference between Workman's and Bühlmann's M-values, observe the following graph, which shows the M-value line calculated for the 6th compartment using both models:

If we want to resume Bühlmann's work:

• He generalized the tolerated pressures for each compartment (M-values) for any ambient pressure, even sub-atmospheric pressures.
• He introduced the remaining compartments we use today(10-16), taking into account the deepest tissues, with half-times of up to 635 minutes (10 and 1/2 hours) for the last compartment.
• Comparing the M-values to Workman's M-value (for the same ambient pressure), Bühlmann's were even more conservative.

Other Neo-Haldanian models

Although the ZH-L16C remains the most common model used to this day, there are a handful of other models based on Haldane's work that are used sparingly. Such models include:

• The Thalman Algorithm (VVAL 18) is a model developed by the US Navy, originally created for divers using the Mk15 Rebreather. It considers that although the saturation of tissues is exponential, the desaturation process follows a linear curve.
• MN90 Decompression tables are tables developed and used by the French Navy.
• DCIEM Sport Diving Tables is a nonlinear model developed by the Canadian Military.

Many other decompression models exist (RGBM, Varying Permeability model, Thermodynamic model, etc...) and although they are interesting and present their own specificity, they diverge from Haldanian models and deserve their own article.