On the statistical probability of contracting a decompression sickness after a single scuba dive on air within a no-decompression-limit

Abstract

On the statistical probability of contracting a decompression sickness after a single scuba dive on air within a no-decompression-limit

The P(DCS) is the statistical probability of contracting a decompression
sickness, the NDL are the so-called „No Decompression Limits“, the time
limits for dives where a direct ascent to the surface is still possible, i.e.
without decompression stops.

Since there is variance in these NDLs from different agencies, we set out
to analyze them with already published methods of assessing the P(DCS).

Thus the somewhat lengthy title could have been condensed to:

On the P(DCS) from a single air dive within NDL

The NDL from some recreational air dives from various training agencies are contrasted and analyzed with 3 published methods from the USN NEDU [1], [2] & [4].

Full text

1
On the statistical probability of
contracting a decompression
sickness after a single scuba
dive on air within a no-
decompression-limit
DOI: 10.13140/RG.2.2.: t.b.d.!

2
Abstract:
The P(DCS) is the statistical probability of contracting a decompression
sickness, the NDL are the so-called „No Decompression Limits“, the time
limits for dives where a direct ascent to the surface is still possible, i.e.
without decompression stops.
Since there is variance in these NDLs from different agencies, we set out
to analyze them with already published methods of assessing the P(DCS).
Thus the somewhat lengthy title could have been condensed to:
On the P(DCS) from a single air dive within NDL
The NDL from some recreational air dives from various training agencies
are contrasted and analyzed with 3 published methods from the USN
NEDU [1], [2] & [4].

3
Methods:
The P(DCS) estimation is implemented according to [1], p. 8 &
Table 2, p.11:

4
Methods:
with ASE: asymptotic standard errors
LOGIT: logistic regression function
P(DCS) : probability of decompression sickness
With D: bottom depth [fswg], T: bottom time [min], TDT: total decompression
time [min]; a,b,c,d,f,g: the parameters according to Table 2, p.11.

5
Methods:
Whereas DIVE [3] uses metric units, the input of D has to be converted
from m to fwsg, the TDT being as well a parameter for free input as TTS.
As well a very similar model, the so-called „Combination Model“ [2] is
implemented by the same token. This model added 240 EAN / saturation
dives to the calibration data set, thus the parameters are different ([2],
p. 204):

6
Methods:
The 3rd. method implemented is the so-called „P-No-Stop Model“, a
probabilistic model based on ca. 2.000 experimental no-stop dives on air /
EAN [4].
The LOGIT regression function and the parameter set thus different from [1]
& [2]; source [4], Table 3 on p. 14:

7
Methods:
Sample outputs from DIVE [3]; Version 3_09
(pls. cf. next slides) for a single dive on air
to 100 feet  30.48 m, 17 min; TTS: 3 min
as input for the P(DCS) dialogue [i.e.:
bottom depth / ascent rate=30 m / 10 m / min]
DIVE [3]; Version 3_09 has implemented
nine (9) published methods for the
estimation of P(DCS); here,
only 5 are showed in this screen shot.
For this presentation, we use only the methods designated here as:
IVa & IVb (yellow display) from [1] and [2] because the calibration data
sets fit to the scenario of a single air dive to a NDL and calculation of the
P(DCS) at the end of the bottom time, i.e.: prior to ascent. The other
methods are not relevant here.
Due to the ASE, we have the upper & lower error margins of these 2
methods calculated.

8

9
Methods:
Sample output from the 3rd. method implemented,
the “P-No-Stop Model” [4],
for a dive on air to
bottom depth: 30.48 m, 20 min bottom time:
Due to the ASE, we have the upper & lower error margins calculated.

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Results (1):
(*) used by nearly all agencies until the 90‘s
(**) used by: ZH-86, BSAC 88, SSI, PADI RDP, NAUI 2001
(***) DECO 2000 by Dr. Max Hahn, used by major D-A-CH agencies
Bottom
depth:
100 feet /
30.48 m
Bottom
time
[min]:
P(DCS)
IV a: P(DCS)
IV b: P(DCS)
P-No-Stop
Model:
Table /
Agency
USN 1957
(*) 25 0.04155 0.03836 0.05402
(**) 20 0.02507 0.02596 0.02275
DECO 2000
(***) 15 0.01478 0.01705 0.00831
- / - 12 0.01064 0.01301 0.00422

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Results (2):
Bottom depth:
100 feet / 30.48 m
Bottom time:
20 min
TTS = TDT
[min]: P(DCS)
IV a: P(DCS)
IV b: P(DCS)
P-No-Stop
Model:
Ascent Rate
60 feet/min 1.7 0.02552 0.02622 0.02275
10 m / min 3 0.02507 0.02596 0.02275
5 m / min 6 0.02411 0.02540 0.02275
2.5 m / min 12 0.02237 0.02435 0.02275
1.25 m / min 24 0.01953 0.02248 0.02275

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Discussion:
(*) used by nearly all training agencies
until the 90‘s
(**) used by:
ZH-86: the Zuerich Air Table ZH-L16 A from A. A. Buehlmann
BSAC 88: British Sub-Aqua Club 1988 table by Hempleman et al.,
SSI: USN doppler-reduced NDL by Scuba Schools International, 1996
PADI RDP, the Recreational Dive Planner from Prof. Assoc of Diving Instructors
NAUI 2001, the RGBM table from National Assoc. of Underw. Instructors
(***) DECO 2000 by Dr. Max Hahn, used by major D-A-CH training agencies
[D: germany, A: austria, CH: switzerland]
All 3 methods / models suggest the following:
the reduction in ascent speed or increase in TTS decreases the P(DCS) only
insignificantly, whereas to reduce the P(DCS) significantly for this 30 m dive,
an „NDL“ of ca. 11

12 min has to be applied.

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private remark:
We would like to thank the USN NEDU, the Naval Experimental Diving Unit
of the United States Navy!!!
For all their excellent reports: with superb clarity, outstanding quality in
terms of documentation, diving technology and statistical wisdom!
Without these fine works, our world of modern diving would have been
much more un-safe!

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Sources / References:
[1] H. D. Van Liew, E. T. Flynn (December 2004)
A SIMPLE PROBABILISTIC MODEL FOR ESTIMATING
THE RISK OF STANDARD AIR DIVES; USN NEDU TR 04-41 TA 01-07
[2] H. D. VAN LIEW, E. T. FLYNN (2005) A simple probabilistic model for
standard air dives that is focused on total decompression time. UHM 2005,
Vol. 32, No. 4, 199 - 213
[3] the SubMarineConsulting Group (1991) DIVE: a decompression suite;
pls. cf. next slide
[4] H. D. Van Liew, E. T. Flynn (December 2004) PROBABILITY OF
DECOMPRESSION SICKNESS.IN NO-STOP AIR DIVING, TA 01-07
NEDU TR 04-42

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Bonus Material:
Source for
DIVE Version 3_09
Download free of charge:
DIVE V 3_09
(https://www.divetable.info/DIVE_V3/index.htm)
 and the german manual
https://www.divetable.info/DIVE_V3/DOXV3_0.pdf
The release train for
the english version (V3_04) is somewhat slower …
DIVE V 3_09 is not compatible with all older versions!
https://www.divetable.info/DIVE_V3/V3e/index.htm

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Fine tuning could be done via the commands:
 ascent rate („AR“)
ambient atmospheric pressure at start („L“)
the respiratory coefficient („R“)
the ambient (water)-temperature („te“)
the water density („di“)
Buehlmann Safety Factor („B“)
last stop depth („LS“)
And with: „a“ we recieve the complete decompression prognosis;
i.e.: the stop times in min per stage, modulo 3 m
and the responsible leading compartment & the rounded up TTS in
min. The latest DIVE Version for beta testing is always staged there:
https://www.divetable.info/beta/index.htm
along with information on production date, size in bytes, new features and
the checksums for verifying the download.
Fine tuning of DIVE:

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The paradigm dive from above via
these commands,
the input of commands and
parameters are in the quotes: „ “
„d“ (simulation of a box profile with these parameters:)
„30.48“ (bottom depth)
„17.“ (bottom time)
the P(DCS) dialogue is invoked with: „pdcs“
pls. cf. slides #6 & 7
the methods IVa & IVb depend on the TDT / TTS, so this is an input
parameter, the TTS (time-to-surface ) = sum of all stop times +
max. bottom depth / ascent rate
 The „P-NO-STOP Model“ is started with: „bpa“ (for „Box Profile Air“)
Handling of DIVE: