Sponges, Soda Bottles, and Safe Ascents

The Maths Your Dive Computer Does Every Two Seconds

At 30 metres, breathing air at 4 bar absolute, your body is absorbing nitrogen into its tissues at roughly four times the rate it would at the surface. Different tissues absorb and release that gas at different rates — blood and brain equilibrate quickly, fat and cartilage take hours. As you ascend and ambient pressure drops, all of that dissolved nitrogen has to come back out through the lungs. If pressure drops faster than gas can clear, the nitrogen comes out of solution as bubbles. That is decompression sickness.

Gas content models exist to track the nitrogen loading in each tissue and tell you how fast you can safely reduce pressure. Your dive computer runs one of these models — typically the Bühlmann ZHL-16C — and updates every two to four seconds throughout the dive.

How the Science Got Here

The decompression model inside your dive computer took over a century to reach its current form.

Bühlmann's ZH-L16C is the algorithm used in virtually all modern technical dive computers today.

Tissue Compartments: Rate Constants, Not Anatomy

The 16 tissue compartments in the Bühlmann model are not anatomical structures. They are mathematical representations of how different tissue types exchange gas — grouped by their perfusion rates and gas transport kinetics. A single compartment can correspond to several different tissue types that happen to behave similarly under pressure.

Each compartment is characterised by a half-time: the time it takes that compartment to reach 50% of the difference between its current nitrogen loading and the equilibrium pressure at the new depth. A 10-minute half-time means 50% saturation after 10 minutes, 75% after 20, 87.5% after 30. After six half-times — roughly 98% equilibrated — the compartment is effectively saturated or cleared. The 16 compartments in ZHL-16C span half-times from 4 minutes (fast tissues: blood, CNS, heart) to 635 minutes (slow tissues: tendon, bone, cartilage).

What Supersaturation Means

During ascent, ambient pressure drops faster than tissues can off-gas. For a period, your tissues contain more dissolved nitrogen than the surrounding ambient pressure would allow at equilibrium — they are supersaturated. Some supersaturation is inevitable and manageable. Too much supersaturation drives bubble nucleation, and bubbles cause decompression sickness.

The soda bottle analogy captures the basic physics: shake it under pressure, then open the cap slowly and the CO₂ disperses safely. Open it suddenly and you get foam. The difference in diving is that the consequences of opening the cap too fast are not trivial.

M-Values: The Tolerance Limit for Each Compartment

Each compartment has an upper gas pressure limit — the M-value — defined by Robert Workman in 1965. Rather than a fixed 2:1 ratio applying uniformly across all compartments, Workman demonstrated that each compartment has its own tolerance for supersaturation, and that tolerance varies with depth.

The Bühlmann formula:

M = M₀ + ΔM × d

M₀ is the maximum tolerable inert gas tension at the surface (1 bar). ΔM is the rate at which the M-value increases with depth. d is depth in bar. At greater ambient pressure, tissues can tolerate more absolute supersaturation before bubble formation — which is why M-values increase with depth.

Your dive computer continuously checks the nitrogen loading of each compartment against its current M-value. If any compartment approaches its limit, the computer adjusts the decompression ceiling — the shallowest depth you can safely ascend to — and extends required stop times. The compartment closest to its M-value limit at any given moment is the controlling tissue; it sets the ceiling.

Ascent Rate and Safety Stops

The rate of ascent matters independently of stop times. Standard practice is 9–10 m/min for both recreational and technical diving. Doubling the ascent rate roughly doubles to triples DCS incidence in the research record.

The final few metres carry a disproportionate risk. From 6 m to the surface, absolute pressure drops by 50% — the largest proportional change of any segment of the ascent. Technical diving guidance recommends no faster than 1 m/min over this final segment.

A staggered stop sequence reduces post-dive bubble loads more effectively than a single 5-minute stop. One minute at 9 m, two minutes at 6 m, and three minutes at 3 m has been shown in Doppler studies to reduce VGE grades by approximately 50% compared to a conventional 5-minute safety stop at 5 m.

What the Research Has Added Recently

Angelini, Tonetto, and Lang (2022) compared conventional staged stops (at fixed 3 m intervals) against ceiling-controlled ascent, where the diver follows the decompression ceiling continuously upward. Ceiling-controlled ascent was 4–12% shorter in total decompression time, because it maintains the maximum available nitrogen pressure gradient throughout the ascent. The 3-metre increment most computers use traces back to Haldane's 1908 protocol — chosen partly because of the pressure gauges available at the time, not because 3 m is physically special.

Hjelte et al. (2023) used venous gas embolism measurements by echocardiography to validate the SWEN21 dive table for the Swedish Armed Forces, designed to a target DCS risk of 1%. Across 154 dives by 47 divers, Bayesian analysis of VGE data produced an estimated DCS risk of 4.7–11.1%, substantially higher than the design target. Two per cent of dives produced clinical DCS. It is an object lesson in how difficult it is to achieve theoretical DCS risk targets in practice, and why validated algorithms and conservative ascent discipline both matter.

The Limit of These Models

Gas content models track dissolved gas only — not actual bubbles. M-values infer bubble risk through supersaturation limits, but they do not model nucleation physics or bubble growth dynamics. Subclinical bubble formation can and does occur on profiles that remain within the computer's limits. That is the gap that bubble models attempt to address, and the subject of the next article.

References

Haldane JS, Boycott AE, Damant GCC (1908) — The prevention of compressed air illness — Journal of Hygiene

Workman RD (1965) — Calculation of decompression schedules for nitrogen-oxygen and helium-oxygen dives — US Navy Experimental Diving Unit Report

Bühlmann AA (1983) — Decompression — Decompression Sickness — Springer-Verlag

Angelini SA, Tonetto L, Lang MA (2022) — Ceiling-controlled versus staged decompression: comparison between decompression duration and tissue tensions — Diving and Hyperbaric Medicine 52(1):7–15

Hjelte C, Plogmark O, Silvanius M, Ekström M, Frånberg O (2023) — Risk assessment of SWEN21 a suggested new dive table for the Swedish armed forces: bubble grades by ultrasonography — Diving and Hyperbaric Medicine 53(4):299–305

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