Decompression model developed by John Scott Haldane
Haldane's decompression model is a mathematical model for decompression to sea level atmospheric pressure of divers breathing compressed air at ambient pressure that was proposed in 1908 by the Scottish physiologist, John Scott Haldane (2 May 1860 – 14/15 March 1936), who was also famous for intrepid self-experimentation.
Haldane prepared the first recognized decompression table for the British Admiralty in 1908 based on extensive experiments on goats and other animals using a clinical endpoint of symptomatic decompression sickness. The model, commented as "a lasting contribution to the diving world", was published in the "Journal of Hygiene". 
Haldane observed that goats, saturated to depths of of sea water, did not develop decompression sickness (DCS) if subsequent decompression was limited to half the ambient pressure. Haldane constructed schedules which limited the critical supersaturation ratio to "2", in five hypothetical body tissue compartments characterized by their halftime. Halftime is also termed Half-life when linked to exponential processes such as radioactive decay. Haldane's five compartments (halftimes: 5, 10, 20, 40, 75 minutes) were used in decompression calculations and staged decompression procedures for fifty years.
Previous theories to Haldane worked on "uniform compression", as Paul Bert pointed in 1878 that very slow decompression could avoid the caisson disease, then Hermann von Schrötter proposed in 1895 the safe "uniform decompression" rate to be of "one atmosphere per 20 minutes". Haldane in 1907 worked on ""staged decompression" – decompression using a specified relatively rapid ascent rate, interrupted by specified periods at constant depth – and proved it to be safer than "uniform decompression"" at the rates then in use, and produced his decompression tables on that basis.
Previous work.
Paul Bert.
Paul Bert (17 October 1833 – 11 November 1886) was a French physiologist who graduated at Paris as doctor of medicine in 1863, and doctor of science in 1866. He was appointed professor of physiology successively at Bordeaux (1866) and the Sorbonne (1869). Paul Bert was given the nickname of "Father of Aviation Medicine" after his work, "La Pression barometrique" (1878), a comprehensive investigation on the physiological effects of air-pressure, which pointed out that the symptoms of caisson disease could be avoided by means of very slow decompression. However, his work did not furnish data about safe decompression rates.
Schrötter.
Anton Hermann Victor Thomas Schrötter (5 August 1870 – 6 January 1928), an Austrian physiologist and physician who was a native of Vienna, was a pioneer of aviation and hyperbaric medicine, and made important contributions in the study of decompression sickness. He studied medicine and natural sciences at the Universities of Vienna and Strasbourg, earning his medical degree in 1894, and during the following year receiving his doctorate of philosophy. He was active in many fields of medicine and physiology. His first interest from 1895 was the investigation and combating of caisson disease, and during his tenure in Nussdorf he studied the numerous diseases that have occurred and was looking for ways of treatment and prevention.
His published report in 1900 with Dr. Richard Heller and Dr. Wilhelm Mager, on air pressure disease is considered the basic German-language work of diving and hyperbaric medicine. Schrötter, Heller and Mager framed rules for safe decompression and believed that the decompression rate of one atmosphere (atm) per 20 minutes would be safe. Leonard Erskine Hill and Greenwood decompressed themselves without serious symptoms after exposure to .
Haldane's work.
The Admiralty Committee needed to frame definite rules for safe decompression in the shortest possible time for deep diving, and hence, Haldane was commissioned in 1905 by the UK Royal Navy for this purpose, to design decompression tables for divers ascending from deep water.
In 1907 Haldane made a decompression chamber to help make deep-sea divers safer and produced the first decompression tables after extensive experiments with animals. In 1908 Haldane published the first recognized decompression table for the British Admiralty. His tables remained in use by the Royal Navy till 1955.
"The Prevention of Compressed Air Illness" was published in 1908 by Haldane, Boycott and Damant recommending staged decompression. These tables were accepted for use by the Royal Navy.
Haldane introduced the concept of half-times to model the uptake and release of nitrogen into the blood in different body tissues, and suggested five body tissue compartments with half times of 5, 10, 20, 40 and 75 minutes.
In his hypothesis, Haldane predicted that if the ascent rate does not allow the partial pressure of the inert gas (nitrogen) in each of the hypothetical tissues to exceed the environmental pressure by more than twice (2:1 ratio), then bubbles will not form in these tissues.
Basically this meant that one could ascend from a depth of  – an ambient pressure of  – to () or from () to the surface () when saturated, without a decompression problem. To ensure this, a number of decompression stops were incorporated into the ascent tables.
The ascent rate and the fastest tissue in the model determine the time and depth of the first stop. Thereafter, the slower tissues determine when it is safe to ascend further.
Outline.
Haldane ran his experiments on some animals, illustrating the difference between different kinds of animals such as goats, guinea-pigs, mice, rats, hens and rabbits, but his main work and results were done on goats and men.
Haldane stated in his paper: "In order to avoid the risk of bubbles being formed on decompression, it has hitherto been recommended that decompression should be slow and at as nearly a uniform rate throughout as possible. We must therefore carefully consider the process of desaturation of the body during slow and uniform decompression", hence the outline of his work is noted:
* As regards to oxygen, the amount in simple solution in arterial blood will increase, but as soon as blood reaches body tissues, the extra dissolved oxygen will be used up so that venous blood will exhibit slight increase in partial pressure of oxygen.
* As regards to carbon dioxide, the experiments of Haldane and Greenwood showed that partial pressure of CO2 in the alveolar air remains constant with the rise of atmospheric pressure, hence, there can be no increase in CO2 in blood during exposure to compressed air.
* As regards to nitrogen, considerations should be taken for the saturation in body tissues.
* For short diving periods of less than seven to eight minutes with no repetitive dive: Haldane's experiments on goats showed that sudden decompression in less than a minute after exposures up to four minutes at , equivalent to of sea water, goats did not develop any symptoms, even when exposures were raised to six minutes in some cases. This coincides with reports at that time from the Mediterranean of skilled Greek divers, diving to who, should their gear become entangled on the bottom, will cut their air-pipe and line, and blow themselves up to the surface in less than a minute.
* With dives exceeding a few minutes or brief repetitive dives: Hill and Greenwood compressed themselves to , equivalent to of sea water, a very high pressure and risky experiment, and had bends after decompression. The saturation curves of their experiment for parts of the body were published in 1908.
* Bends, the commonest symptom. The limb, most commonly the fore-leg.
* Temporary paralysis, symptom to general deficiency of oxygen
* Pain, continuous bleating 
* Permanent paralysis, usually immediately after decompression
* Illness, impossible to identify any local symptoms, sometimes blind
* Dyspnoea and death
* Mechanical symptoms are not important, if goat suffered ear troubles during compression
* staged decompression on different pressures, and different decompression times, and included also comparison with uniform decompression. Results showed that a certain minimum pressure is required to give symptoms on goats and that duration of exposure to high pressures with different decompression times had also an influence.
* Experiments compared between different types of animals and their susceptibility to decompression symptoms, and compared influence of size between short and long exposures, and decompression time.
* Experiments on blood mass and volume of goats showed apparently no relation to susceptibility.
* Pathological observations on them post-mortem appearances of goats after decompression, showed practical importance in connection with the size of bubbles found in blood. Pathological changes underlying the chief symptoms were sufficiently noticed, except for bends. The exact cause of bends was not known.
Main results of Haldane’s work.
This work is published in "The Prevention of Compressed-air Illness" book. Results are published in same book under "Summary" in pages 424 and 425. The main conclusions of his decompression model are:
Further developments on Haldane's principles.
The 2:1 ratio proposed by Haldane was found to be too conservative for fast tissues (short dives) and not conservative enough for slow tissues (long dives). The ratio also seemed to vary with depth. The ascent rates used on older tables were , but newer tables now use .
Haldane's related work and research.
Haldane had many other related researches:
formula_1
where,
"T": tension (pressure) of gas in tissues
"T"0: initial tension
"T"N2: current nitrogen tension
"T"f: final tension
"t"0: compartment half-time
"t": current time
Contradicting work.
Although Haldane's model remains the basis for modern decompression tables, Haldane's first decompression tables proved to be far from ideal. Haldane's equation is used by many dive tables and dive computers today, even though, a growing number of decompression models contradict its assumptions such as the 
* Asymmetry of saturation phenomena of inert gases (uptake and elimination),
* Desaturation according to Hempleman's memorandum and those of Thalmann, taking into account circulating bubbles, VPM, Reduced gradient bubble model.
References.
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