So, I'm not the only one with fundamental concerns as to the nature of this dispute.
Guys, Please. Rate your approaches to decompression modeling in two categories on a 1 to 10 scale:
Deterministic vs. Probabilistic.
Deterministic versus probabilistic is tangential to the debate, which has been about empirical comparison of different schedules, in the case of the trimix study the schedules compared had the same stops and times but the breathing gases were different – how the stops and times were arrived at does not really matter. However, in case anyone is interested…
First thing to appreciate is that there is a difference between a model, which is the description of a system, and an algorithm which is a method of controlling the system via the model. For instance, in a deterministic gas content algorithm like the ZH-L16 decompression algorithm, the model is the gas uptake and washout in a collection of compartments. This model is meant to represent DCS-sites in the human body. The model input is a dive profile (depth/breathing gas history) and the output is the point-in-time compartment gas pressures. The deterministic algorithm is the control of the maximum allowed supersaturation in these compartments by specification of a safe ascent depth (using “a” and “b” values or “m-values”
for those point-in-time gas pressures.
The fundamental difference between deterministic and probabilistic algorithms is the output of the underlying model. Probabilistic decompression models estimate the probability of DCS (PDCS) from a dive profile. The probabilistic models are typically much like the models underlying decompression algorithms, in that bubble volume and/or gas supersaturation in a collection of compartments is calculated from the dive profile. However, they have an additional step in that PDCS is calculated from the bubble volume or gas supersaturation history. This PDCS could be a function of the maximum point-in-time supersaturation or maximum bubble volume, but typically, because it results in much better estimates, PDCS is a function of the time-integral of supersaturation or bubble volume over the whole dive profile. A probabilistic decompression algorithm evaluates candidate schedules searching for an optimum schedule. This optimum can be one of two things: 1) the lowest estimated PDCS for a specified total decompression time or 2) the shortest total decompression time that results in a target PDCS.
Another difference between deterministic decompression algorithms and probabilistic decompression models is how the parameters (e.g. half-times, m-values etc.) are chosen. A deterministic algorithm is usually developed by trial and error. Schedules are produced from a trial set of parameters and then some of those schedules are man-tested. If the incidence of DCS is too high, a more conservative set of parameters is used to generate a new set of schedules and these are man-tested, and so on. To calibrate a probabilistic decompression model (and in this case it is the underlying model, not the algorithm), dive profiles with known DCS outcome (usually historical data from previous traditional decompression trials) are used as model input and the model parameters (for instance compartment half-times, tissue gas permeabilities at the bubble surface) are adjusted, using formal statistical methods, to get the closest fit to the outcome data. As on oversimplification, if the calibration database was comprised of dive profile A dived 100 times with one DCS and profile B dived 100 times with 20 DCS, the best model parameters will those that result in PDCS estimate for profile A closest to 1% PDCS and estimate for profile B closest to 20%. Typical calibration data sets are larger, do not need to have duplicates of the same profile (but usually do), and should have about 10 DCS cases for every estimated parameter. Just to clarify a misconception, once he model is calibrated, the database is no longer required.
No 1-10 rating, but some advantages of the probabilistic approach over the deterministic are:
Probabilitic models can be calibrated with existing data, without conducting new trials ( although validation trials are still a good idea).
Probabilistic models are a purer embodiment of the information in the calibration data.
Probabilistic models can be used to estimate PDCS and therefore evaluate any dive profile, for instance something downloaded from a dive computer or a schedule prescribed by any algorithm.
Probabilistic algorithms are more flexible. A good example is handling a missed stop. A deterministic algorithm has no way to handle a missed stop, it can either pretend you are at the missed stop or calculate a new, shorter schedule based on the greater gradient for gas washout at the shallower stop - neither is the best answer. A probabilistic algorithm could give you the PDCS estimate if you continue on the remainder of the original schedule or calculate a new schedule at the original target PDCS.
David Doolette
