*This is a contributed post by Doug Fraedrich in which he reports on a recent paper by him and which is also mentioned in Doolette’s blog post I just commented on. *

Recently I published a methodology on how to set conservatism factors on commercial dive computers based on published probability of decompression sickness (DCS) data and statistical summaries/models thereof, (Reference 1.) That paper described the general methodology on how to adjust the conservatism of several different algorithms; this note will focus specifically on setting gradient factor levels for the Bühlmann ZHL-16C algorithm.

The basic methodology is to use the output of probabilistic models from the literature that were derived from many well-documented experimental man-trials of known dive profiles. Then pick a probability of DCS isopleth curve and use those to set gradient factors (or conservatism factors) such that the algorithm will output the No-stop time or total decompression time (TDT) specified by that isopleth. This was done for three metrics: no-stop times for short recreational dives profiles, total decompression time for longer/deeper decompression dives and “first stop depth” for decompression dives. There were no probabilistic models for first stop depths/decompression profiles, so for this metric, we used data from a NEDU controlled experiment, which compared P_{DCS}outcomes of dives of the same depth, bottom time and same TDT but with different stop profiles (Reference 2.) This NEDU study was performed specifically to assess the effect of deep versus shallow profiles as dictated by dual-phase vs tissue-loading algorithms.

So now to apply the methodology from that paper to the task of setting Gradient Factor levels for the Bühlmann ZHL-16C algorithm. From previous publications on the topic of gradient factors, we know that the value GF-Hi mainly affects total decompression time and GF-Lo affects the depth of the first stop. For GF-Hi, we will use the probabilistic model from a new study on No Stop Times by Howie et al. (Reference 3.) Using their criteria of 0.1 % serious DCS, we pick several point-pairs of depth and No-stop time and iteratively run theBühlmann ZHL-16C algorithm (specifically MultiDeco version 4.12)with different values of GF-Hi and match at what level the algorithm allows for a direct ascent at each individual depth-bottom time pair. The corresponding value of GF-Hi is 80.

As mentioned above, for GF-Lo, we use the US Navy NEDU study on deep stops, Reference 2. In the NEDU study, the maximum depth was 170 fsw, the bottom time was 30 minutes, the ascent rate was 30 fsw/min and the TDT for both profiles was 180 minutes. The group of divers who started their first stop at 40 fsw (for 9 minutes) had significantly lower P_{DCS}(*P*= 0.0489 one-sided, Fisher Exact Test) than the group that stopped first at 70 fsw (for 12 minutes). Since there is not sufficient information to know exactly where between the two tested depths is optimal, this test case used the two depths as a maximum and minimum for the first stop criterion. For that dive profile, MultiDeco was iteratively run varying GF-Lo to see which levels of GF-Lo yield the two limiting first stop depths. This procedure indicates that GF-Lo should be higher than 55 (this was previously reported in Reference 1.) If you pick the mid-point of the two first stop depths between those profiles (assuming the optimal point is somewhere in the middle and not at either extreme) the resulted in GF-Lo being on the order of 70.

Of course, the above setting for GF-Hi was based on no-decompression dives which had a relatively low value of PrT of ~10-12 (Pressure Root Time is an indicator of the severity of the dive exposure where P = pressure in bar, T = dive time in minutes, Reference 4.)We know from Reference 4 that historically, the incidence of DCS is significantly higher for dives with a PrT > 25 and we know from Reference 1 that the required value of GF-Hi for ZHL-16C needs to decrease as the PrT of the dives increases. So to set GF-Hi for higher PrT decompression dives, we re-visited methods and models presented by Van Liew and Flynn, where they were specifically assessing the suitability of the US Navy’s decompression schedule (used at that time) by fitting data on single-level, non-repetitive, nitrogen-oxygen dives from the US Navy Decompression Database to a logistic regression that resulted in P_{DCS}isopleths as a function of bottom time and TDT (Reference 5).We limited the domain of applicability of the current study to PRT< 40, so we used the “StandAir” Model which Van Liew andFlynn based ondata from standard air dives which had depths of less than 190 fsw and bottom times of less than 720 minutes. They assessed the StandAir statistical model to be reasonable except at the two depth extremes (nominally < 60 fsw and > 190 fsw). Van Liew and Flynn compared TDT required by the algorithm-under-test to the P_{DCS}isopleths from their statistical model, and found that the TDT required by the algorithm-under-test lay between the 2% and 3% P_{DCS}isopleths and thus deemed the algorithm acceptable for US Navy use. In the current study, we selected the 3% P_{DCS}isopleth as an initial standard of comparison as a compromise between managing DCS risk while not requiring excessive total decompression times. Note that in their analysis, they combined data from all dives that had the same depth and bottom time, thus their PDCS results are averaging over many different (non-optimal) decompression profiles.

The process here is similar to what was described above using the No Stop Data, only with the Deco dives, it was a trio of data values of: depth-bottom time-TDT (at the 3% PDCS isopleth curve.) MultiDeco was iteratively run to match TDT for the input values of Depth and bottom time. The value of GF-Hi was noted and plotted against the PrT of the dive profiles used. These results are summarized in Figure 1.

Note the curve in Figure 1 is of sigmoid shape: It is flat at both low and high levels of PrT with a transition in between. These results are based on dive profiles with observed DCS symptoms, and there are many more dives at the lower end of the PrT scale than the higher; so generally speaking the “error bars” start off small on the left side of the graph and get bigger as PrT increases. The point at which it levels out is considered somewhat uncertain.

To summarize:

- GF-Lo is recommended to be >= 55
- The recommended level of GF-Hi depends on the PrT of the dive, but is never greater than 80. It decreases with increasing PrT of the dive (to a point)
- While the uncertainty at the low end (say PrT < 25) is low, it increases with PrT (i..e. more research is needed in this part of the domain.)

References:

- Fraedrich DS, Validation of algorithms used in commercial off-the-shelf dive computers, Diving and Hyperbaric Medicine, V48 No 4 , 2018
- Doolette DJ, Gerth WA, Gault KA. Redistribution of decompression stop time from shallow to deep stops increases incidence of decompression sickness in air decompression dives. NEDU TR 11-06, Panama City FL; 2011.
- Howie, LE, Weber PW, Hada E, Vann RD, Denoble PJ, The probability and severity of decompression sickness, PLoS ONE 12(3): e0172665,2017
- Balestra C. Dive computer use in recreational diving: Insights from the DAN-DSC database. In: Blogg SL, Lang MA, Møllerløken A, editors. Proceedings of validation of dive computers workshop. 2011 Aug 24 Gdansk. Trondheim: Norwegian University of Science and Technology; 2012. p. 99–102.
- Van Liew HD, Flynn ET. A simple probabilistic model for standard air dives that is focused on total decompression time. Undersea Hyperb Med
*.*2005;32:199–213.