How likely is DCS? How an algorithm predicts decompression sickness from a dive profile

Understanding risk is not the same as fear. Quite the opposite — when you know where a number comes from and what moves it, fear gives way to calm control. This article is for people who want to look under the hood: how can a handful of numbers describing a profile — depth, time, gases, ascent rate — be turned into a probability of decompression sickness (DCS)? And why two seemingly similar decisions on the ascent produce wildly different risk.

Two questions, two kinds of model

A classic dive computer and the tables answer a yes/no question: "from this depth, am I allowed to go shallower yet?". That is a planning model. In recreational and technical diving the reigning one is Bühlmann ZH-L16C with Gradient Factors: it splits the body into 16 "tissue compartments" that on-gas nitrogen at different rates, and makes sure that in none of them does the gas tension cross an allowed limit (the M-value). The output is a ceiling and a stop schedule — but still a "yes/no" answer.

A predictive model answers a different question: "how likely is it that THIS particular profile ends in DCS?". Because DCS is a random event — the same profile in the same person ends well one time and badly another. Instead of a hard limit we get a probability: P(DCS). And it is that — the probabilistic model — that is the subject of this piece.

How the algorithm computes a probability

The idea that ties this whole family of models together was set out by Weathersby, Homer and Flynn in "On the likelihood of decompression sickness" (Journal of Applied Physiology, 1984). It goes like this: at every instant of a dive there is an instantaneous hazard rate that rises when a tissue is supersaturated with inert gas relative to ambient pressure. The total probability is computed as in survival analysis — from the sum (integral) of that hazard over the whole dive:

Here G is the cumulative hazard, g_i are the weights of the individual risk compartments, and r_i(t) is the instantaneous risk in compartment i. That last term grows with supersaturation — with the excess of gas tension in the tissue over ambient pressure, divided by that pressure:

Risk does not build up on the bottom. It accrues mostly on the ascent and for many hours after you leave the water — when the pressure drops and the tissues are still loaded.

That is the key intuition, and it is right there in the formula: when P_i ≤ P_amb (you are deep, the tissue is still on-gassing), the risk is zero. It rises only once ambient pressure falls below the tissue tension — that is, on the ascent and at the surface. This is why the integral runs over the standard 24-hour observation window after the dive (most DCS symptoms appear within it; this window is also a calibration parameter of the model). The specific algorithm I use here is LE1nt — a linear-exponential variant from the Thalmann / US Navy (NMRI) line. Three "risk compartments" (separate from the Bühlmann tissues, with their own time constants) sum their contributions to G, and the result maps onto a probability in a trinomial form: no DCS / mild / serious. The formula shown above is the historical binomial foundation (Weathersby, 1984); the specific numbers in this article come from its trinomial refinement (the model multiplies the cumulative hazard by a factor a+1, with a≈0.116), which raises them by a dozen-or-so percent relative to 1−e^(−G) alone.

There is one more nuance worth knowing: in the linear phase of the model the risk in the intermediate compartment is computed not from the gas tension itself but from a "load" that, once it crosses a certain threshold, washes out linearly — more slowly than exponentially. That is precisely why the intermediate tissues stay supersaturated and dangerous long after you leave the water.

How do we know the numbers mean anything? The coefficients were fitted by maximum likelihood to the BIG292 dataset — 3322 real experimental dives from the US, UK and Canadian navies, in which 190 cases of DCS were recorded. Real human data, not theory. The LE1nt coefficients come from the open-access paper by Howle et al. (PLoS ONE, 2017), and the exact kinetics from Howle, Weber and Vann (Computers in Biology and Medicine, 2009).

The same family also describes the role of oxygen (Parker, Survanshi, Weathersby, 1998) and newer, more detailed coupled perfusion–diffusion models (the two parts of "Probabilistic pharmacokinetic models of DCS", 2017 and 2018). All answer the same question — with varying fidelity to physiology:

• Weathersby 1984 — the foundation: DCS as a random event, risk from a hazard integral, maximum-likelihood fitting.
• The LE / LEM line (Thalmann, NMRI98) — risk from inert-gas tension; LEM adds a separate effect of oxygen.
• LE1nt (Howle 2017) — the trinomial version: it distinguishes mild from serious DCS; this is what the simulator below uses.
• PK models (2017/2018) — coupled perfusion–diffusion, closest to bubble physics; more complex, the same logic.

A plan is not risk — enter Gradient Factors

Before we compute risk we need a plan — a stop schedule. That is governed by Gradient Factors (GF): two conservatism dials laid over Bühlmann. GF Low (e.g. 30%) says how close to the M-value you may come at the first, deepest stop — a lower value forces earlier, deeper stops. GF High (e.g. 70%) says how loaded you may be at the moment you surface — a lower value lengthens the shallow stops. "GF 30/70" is exactly that pair. GF 100/100 is raw Bühlmann with no margin; the lower you go, the more conservative and the longer the decompression. GF changes the plan, and the probabilistic model turns each plan into a single number — P(DCS).

Example: 40 m for 40 minutes, air + EAN50 + oxygen

Take a concrete, demanding dive: 40 metres, 40 minutes on the bottom on air, with an EAN50 cylinder for decompression (switched at about 21 m) and pure oxygen on the shallow stops. The plan is computed on ZHL-16C + GF, the risk with LE1nt. Here is the same profile under different GF settings (decompression time includes the stops and gas switches):

• GF 100/100 (no margin): ~25 min of decompression, P(DCS) ≈ 0.99%.
• GF 70/85: ~35 min, P(DCS) ≈ 0.78%.
• GF 50/85: ~37 min, P(DCS) ≈ 0.75%.
• GF 40/85 (a typical "technical" setting): ~38 min, P(DCS) ≈ 0.74%.
• GF 30/70 (conservative): ~47 min, P(DCS) ≈ 0.58%.
• GF 20/60 (very conservative): ~56 min, P(DCS) ≈ 0.47%.

A pattern emerges: every extra minute of decompression lowers the risk, but with diminishing returns. Going from GF 100/100 to 40/85 lengthens the ascent by half (×1.5) and shaves a quarter off the risk. Tightening further to 20/60 adds another dozen-plus minutes (and a lot of oxygen exposure — CNS), yet trims only fractions of a percent. For context: a calm recreational dive (18 m for 50 min on air, GF 85/85) sits at P(DCS) around 0.2% in this model — several times less than our technical "forty".

The best way to feel it is to try it yourself. The simulator below computes the plan and the risk live — with the same engine as the numbers in this article (Bühlmann ZH-L16C + GF and the LE1nt model), verified directly against a full dive simulator. Drag the depth, time and GF sliders, toggle the deco gases on and off, and watch what happens to the probability:

What really happens when you cut decompression short

Here is the most interesting part. Back to the GF 30/70 plan (47 min of decompression, P(DCS) ≈ 0.58%), and let us commit three ascent "sins", each scored with the same model. First the extreme: straight to the surface, with no stops at all. Then two subtler ones: removing exactly ⅓ of the decompression time (about 16 minutes) — once from the deep stops, once from the shallow ones.

• Full decompression (47 min): P(DCS) ≈ 0.58% — the reference.
• Cut ⅓ of the time from the DEEP stops: P(DCS) ≈ 0.62% — the risk barely changes (×1.06).
• Cut ⅓ of the time from the SHALLOW stops: P(DCS) ≈ 1.20% — the risk doubles (×2.1).
• Straight to the surface, no stops: P(DCS) ≈ 1.99% — more than three times as much (×3.4).

The chart shows the same thing from the time axis. With full decompression (the calm line) the risk stays negligible even through the whole ascent — the stops keep the tissues below the supersaturation threshold — and ends gently near 0.58%. Going straight up (the red line) starts earlier and climbs to ~1.99%, and most of that increase happens only AFTER you leave the water. It is not the bottom that is dangerous, but the return.

Back to the numbers: we removed exactly the same number of minutes, yet the effect is drastically different depending on WHICH minutes we cut. Why? Because the shallow stops are what finish off-gassing the compartments that lead at the moment of surfacing. The last pressure jump — from 3–6 metres to zero — is the largest in relative terms and the most dangerous; do it with the slow tissues still loaded and the hazard shoots up. The deep stops mainly govern the fast tissues, which are not the limiting ones at surfacing anyway — shortening them changes almost nothing.

This is not just a model artefact. A US Navy experiment (NEDU, 2011) compared two schedules of the same length head to head: one emphasising deep stops, the other shallow. The deep-stop version produced MORE cases of DCS — because it kept the slow tissues loaded for longer. Hence the modern shift toward higher GF Low. Our simulator says exactly the same: a minute spent shallow is worth more, for safety, than a minute spent deep.

If you ever had to shorten your decompression — and the plan is NOT to — the last few metres are the ones you must never give back.

What this model does not know

Honesty is part of safety, so plainly: this is an educational model with limits. The numbers illustrate the mechanism — they are not a dive plan or medical advice.

• The calibration domain is air and nitrox at sea level. Helium (trimix), altitude diving and closed-circuit rebreathers (CCR) are already extrapolation beyond the data.
• The model does not know you: your hydration, sleep, exertion, temperature, a patent foramen ovale (PFO), the form of the day. These can shift the risk more than a few minutes of stops.
• The absolute percentage is uncertain to within a factor of 2–3× and depends on the calibration dataset — this particular variant (LE1nt on the BIG292 set) reads LOWER than models calibrated directly on the navy data (NMRI98), so do not treat these percentages as a pessimistic, "safe" upper bound. What is reliable and instructive are the COMPARISONS: by how much the risk rises when you change the profile.
• No model replaces training, your own computer and tables, and plain common sense in the water.

What it means for you

We do not compute risk to be afraid, but to make better decisions, calmly. Three things stay with you from this lesson: decompression works and it pays to do it in full; conservatism (lower GF) buys safety, but with diminishing returns and an oxygen cost; and if anything were to go wrong — the shallow, "boring" stops are the ones you guard most.

That calm, informed relationship with the numbers is what I teach on my courses — from the first breath to planning dives where charts like these stop being abstract. Because the point is to understand, not just "press OK on the computer" — the rest is your decision, made with a clear head.