The mapping of a french air diving table (MT92) to a standard Haldane- / Workman- / Schreiner-algorithm

Abstract

Abstract:

The published french air diving tables MT92 ([1] & [2]) could be mapped
via a simple algebraic transformation directly to a
standard decompression algorithm based on
blood perfusion with a linear relationship between
calculated compartment inert gas overpressures and the ambient pressure.

With this mapping the MT92 table entries could be calculated with any desktop decompression software and thus compared to other published air
diving tables like DCIEM, USN & NDTT [5].

As well the MT92 framework could be extended to other than printed:
or greater bottom depths
or longer bottom times
higher pO2 during decompression
modified decompression stages

if operational requirements need an adaption of the published tables.

Full text

1
The mapping of a french air
diving table (MT92)
to a standard
Haldane- / Workman- /
Schreiner - algorithm
DOI: 10.13140/RG.2.2. -------------

2
Abstract:
The published french air diving tables MT92 ([1] & [2]) could be mapped
via a simple algebraic transformation directly to a standard decompression
algorithm based on blood perfusion with a linear relationship between
calculated compartment inert gas overpressures and the ambient pressure.
With this mapping the MT92 table entries could be calculated with any
desktop decompression software and thus compared to other published air
diving tables like DCIEM, USN & NDTT [5].
As well the MT92 framework could be extended to other than printed:
or greater bottom depths
or longer bottom times
higher pO2 during decompression
modified decompression stages
if operational requirements need an adaption of the published tables.

3
Methods (1):
All standard perfusion models (Haldane, Workman, Schreiner, …) offer the
following generic linear relationship between a tolerated inertgas over-
pressure in a theoretical (tissue-) compartment and the ambient, absolute
pressure at diving depth:

4
Methods (2):
The published parameters for the MNT92 ([1], [2], and [4] and all the
references therein) are:

5
Methods (3):
If we now identify Pcrit with Ptissue, tolerated, i.e. if we equate
eq. (1) with eq. (2) we get the following mapping

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Methods (4):
With the already published compartment parameters from: [4], p. 90
& p. 91, there results the following
coefficient matrix, useable
for standard desktop
decompression software
with the following identification
from equation (3):
A MT92 = a
B MT92 = b
For evaluation readily available for download:
https://www.divetable.info/beta/MT92.TXT

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Et voilà ! Results (0):
Comparison between the MT92 published table entries
and calculations via DIVE [3] in 5 paradigms:
(pls. cf. slides # 8 – 11 for details)
(*) TTS = time-to-surface, i.e.:
sum of all stop times + (bottom depth / ascent speed)
Paradigm
# MT92 DIVE V3 Error
TTS [min] (*)
TTS [min] (*)
circa
ΔTTS [%]
1) 12 m / 360 min
40:45 40 < 1.85
2) 33 m / 100 min
151:45 151 < 0.5
3) 42 m / 25 min
29:45 30 < 0.9
4) 42 m / 70 min
159:15 159 < 0.2
5) 60 m / 35 min
121:30 122 < 0.5

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Et voilà ! Results (1):
#1) 12 m, 360 min:
#3) 42 m, 25 min:

9
Et voilà ! Results (2):
#2) 33 m, 100 min:

10
Et voilà ! Results (3):
#4) 42 m, 70 min:

11
Et voilà ! Results (4):
#5) 60 m, 35 min:

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Discussion (1):
The agreement between the published/printed MT92 table
entries and the software-derived values is nearly perfect! The
small deviations in the TTS and the stop times per stage stem from:
Our usage of one compartment with half-time of 75 min
(not used in MT92 but in older french tables)
since fractions of minutes are unpracticable/unrealistic in a run-time /
dive plan, DIVE rounds automatically to the nearest next INTEGER minute
and, not properly defined parameters within MT92 framework:
respiratory coefficient
water temperature & density
ambient air pressure @ start / end of decompression
executive editing (proprietary to MT92)
However: these delta times in the TTS are all marginal and the related error
is by far smaller than the errors introduced by the usual devices
for operational diving like depth gauges & -monitors or O2 analyzers.

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Discussion (2):
The comparison with other air diving tables ([5]) reveals as well
that a higher physical workload i.e. higher O2 consumption is only marginally
adressed within the MT92 framework.
This could be even more so confirmed if compared to the ZH-86 system ([6]),
where the respiratory coefficient Rq = 1, and no allowance is made for
increased VO2 , thus the physical workload is neglected ([7]).
If used under such circumstances, an increased pO2 during decompression
or padding (usage of increased depth and / or bottom times for
operational dive planning than actually dived)
is strongly encouraged.

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Sources / References (1):
[1] https://www.legifrance.gouv.fr/loda/id/JORFTEXT000000690963/
accessed: 12.02.2021
[2] https://sneti.eu/wp-content/uploads/2020/06/5-Annexes-
Arr%C3%AAt%C3%A9-Mention-A-2019-TABLES-
dae_20190524_0003_0001.pdf
accessed: 12.02.2021
[3] the SubMarineConsulting Group (1991) DIVE: a decompression suite;
pls. cf. slide #16
[4] Julien HUGON: Vers une modélisation biophysique de la
décompression, T H È S E, 22 Novembre 2010
[5] Manuals for free:
https://www.divetable.info/manuals_4_free/index.htm

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Sources / References (2):
[6] "Tauchmedizin.", Albert A. Bühlmann, Ernst B. Völlm (Mitarbeiter), P.
Nussberger; 5. Auflage in 2002, Springer, ISBN 3-540-42979-4
[7] Salm, Albi (2021) Is the DGUV40 adequate for underwater-"work"?
DOI: 10.13140/RG.2.2.10079.28324

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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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The paradigm dives from above via these commands,
the input of commands and parameters are in the quotes: „ “
„d“ (simulation of a dive profile with these parameters:)
„60.“ (bottom depth)
„35.“ (bottom time)
„a“ (ascent)
the manipulation of the coefficients matrices is done via:
„nc“ (nitrogen coefficients):
with the option 12 the matrix from
slide #6 could be loaded
into the service engine of the
DIVE software.
Handling of DIVE:

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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: