Content uploaded by Albi Salm
Author content
All content in this area was uploaded by Albi Salm on Mar 28, 2022
Content may be subject to copyright.
2
The mapping of the DCIEM
Air-diving table
to a standard
Haldane- / Workman- /
Schreiner - algorithm
Rozenblat, Vered, Eisenstein, Salm (04/2022)
Contents:
Abstract: slide # 3 & 4
Methods: slide # 5 9
Results: slide # 10 13
Discussion: none
References: slide # 14 & 15
Bonus Material: slide # 16 18.
3
Abstract (1):
As we demonstrated recently ([1] and all the references therein) selected
air-diving schedules from the DCIEM framework ([2] & [3]) could be
recovered using a simple desktop decompression shareware with only one
additional parameter: a conservatism factor of ca. 0.9 +/- 0.05.
On just these grounds we tried to map the DCIEM AIR tables [2] 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
and implement this mapping into a shareware so that the DCIEM table
entries could be calculated with any other desktop decompression software
and thus could be:
1) compared to other published air diving tables like the MT92, USN &
NDTT [4] when the bottom depths / bottom times / surface intervalls do
not match the printed tables entries, and
4
Abstract (2):
2) extend the DCIEM air-diving framework easily 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.
The focus of this mapping here is solely on the TTS (*) of single box-
profiles with normal compressed air as the breathing-medium for the
bottom-phase, the bottom times being the maximum allowed entries from
the table [2] on the pages 1B-5 1B-18 (metric part).
Repetitive dives and other breathing-gases like Heliox call for further
research.
5
Methods (1):
All standard perfusion models (in chronological order: Haldane, Workman,
Schreiner, Ruff & Müller, Bühlmann & Hahn, …) 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:
6
Methods (2):
The LHS of equation (1) are called:
Pt,tol , M-values, critical Tissue Tensions or
MPTT (maximum permissible tissue tensions) / „red lines“ in next slide;
RHS of (1) : Pamb,tol, max , SAD (safe ascent depth) or „Ceiling“
In the DCIEM framework the following equation for (1) was derived:
(Source: [6], p. 2)
Thus, the only difference between the various models or algorithms is just
the method in calculating the „Pt“, „Pt,tol“, „“M“-value or „MPTT“. The lineup
between DCIEM and the perfusion-type models is in [1], slides # 17 & 18.
7
Methods (3)
Pamb [Bar]
Pcompartment [Bar]
45 °
1 2
1
2
Bottom Depth [m]
10 0
3
4
5
3 4 5 6
20 30 40 50
surfacing values: M0
6
P comp = Pamb / b +a
for the compartment with
half-time (HT) of 4 min :
b = 0.505
a = 1.2599
M0 = 1.0 / 0.505 + 1.2599 =>
M0 = 3.24
a = 1.2599
(Haldanes Range: 1 6 Bar)
8
Methods (4):
Slide # 7 shows simplified sketches of:
a typical Bühlmann paradigm for a fast compartment (half-time = 4 min.)
with the parameters a & b from [5], p. 158, i.e. the slope and the
axis intercept
all of the 5 Haldane compartments on one line, going through the zero-
point
these red lines are the: „M-values“, „MPTT“ or „Pt,tol“
reducing the axis-intercept, i.e. the „a“ values or the M0 values, gives a
reduction of the tolerated inert gas supersaturation
basically a „right-shift“
(
the slope „1/b“ should not be altered at whim: once a red line would
intersect with the ambient pressure line and thus the supersaturation
would vanish, which makes it impractical for real diving
)
9
Methods (5):
With the published conservatism parameter ([1]) we fitted one ZH-L16 C
parameter set of a- & b coeffcients ([5], p. 158) to obtain a maximal
similarity between printed DCIEM tables entries and a on-line calculated
run-time.
Since an original ZH-L 16 algorithm comes with 16 * 3 free parameters,
(for each of the 16 compartments: the half-time, the a- & b- coefficient
for the linear relationship from formula (1) on slide # 5)), i.e.: 48 degrees of
freedom, a mapping to virtually ANY other theory or experimental data
should be possible.
The method we used is just a geometrical right-shift of the original straight
lines for the allowed/tolerated compartmental supersaturations. Indeed, this
idea has been concocted since long from Bühlmann himself ([5], p. 157 &
159 for compartments with half-times > 27 min and on p. 131 even for
Helium!). Bühlmann called it a „Parallelverschiebung“ (= parallel shift) and
it was in the range of 12 16 % of his „theoretical a-values“.
10
Results (1):
There results the following
coefficient matrix, useable
for DIVE or any other desktop
decompression software,
provided, the Schreiner-Equation
is implemented fully and
the software allows for the
adaption of:
water density & -temperature
ascent rates
respiratory coefficient
oxygen consumption /
(i.e.: workload)
ambient air pressure
For evaluation readily available for download:
https://www.divetable.info/beta/ES-L16D.TXT
11
Results (2):
As the mother of all topical perfusion models
is called „ZH-L16x“, with:
ZH: ISO abbreviation of Zürich, a town in
Switzerland, where Albert Alois Bühlmann worked
L: linear, since the equation (1) is a linear one
16: is the number of perfused, parallel compartments and/or the number
of linearly independent coefficient pairs for nitrogen (or for Helium)
x is the version identifier:
„A“ for theoretical values
„B“ for table calculations
„C“ for dive computers on-line run-times ([5], p. 157)
Thus we kept a similar name for our matrix: ES-L 16 D to give credit to
Bühlmanns works and to honor Albert Alois.
But since our data- & build-servers are located in a data center in Esslingen
(southern germany) it is „ES“ and the version is a „D“ to reflect this
linear DCIEM simulation.
12
Results (3):
The agreement between the published/printed DCIEM table entries and the
software-derived values was nearly prefect for the reduced scope of the
TEC/recreational schedules [1] with only minimal redistribution of stopping
times between the stages.
The next slide (#13) lists the comparison between the TTS (*) of selected
schedules from 12 to 72 m bottom depth and bottom times from 40 to 360 min.
The DCIEM tables values appear, as printed in [2], as the sum of the stopping-
times and are augmented with the transit time to the surface to reach a
comparability with the (standard) TTS from DIVE.
#######################################################
(*) with the TTS = time-to-surface, defined as:
sum of all stop-times + (bottom depth / ascent speed)
13
Results (4):
Now, with the general mapping
and the broad scope of single
box-profiles on air with maximal
bottom times, i.e.: the tables
very „end“, clearly outside the
TEC/rec. scope, the agreement
is just only adequate: but the
delta times in the TTS (*), i.e.:
Δ TTS = TTSDCIEM – TTSDive 3_11
are marginal for most of the
longer schedules and the
related error is by far smaller
than the errors introduced
by the usual devices for
operational diving like
depth gauges & -monitors
or dive computers
14
Sources / References (1):
[1] Miri Rosenblat, TAU; Nurit Vered, Technion Haifa; Yael Eisenstein &
Albi Salm, SubMarineConsulting (14.03.2022) Recovery of selected
DCIEM air-diving schedules via a decompression shareware.
DOI: 10.13140/RG.2.2.15208.55046
[2] DCIEM Diving Manual, DCIEM No. 86-R-35: Part 1 AIR Diving Tables
and Procedures, Defence and Civil Institute of Environmental Medicine,
Canada, March 1992
[3] DCIEM Diving Manual, DCIEM No. 92-50: Part 2 Helium-Oxygen
Surface-Suppplied Decompression Procedures and Tables; Defence and
Civil Institute of Environmental Medicine, Canada, October 1992
[4] Miri Rosenblat, TAU; Nurit Vered, Technion Haifa; Yael Eisenstein &
Albi Salm, SubMarineConsulting (02/2021) The mapping of a french air
diving table (MT92) to a standard Haldane- / Workman- / Schreiner –
algorithm.
DOI: 10.13140/RG.2.2.34271.38567
16
Bonus Material:
Sources for
DIVE Versions 3_11
Shareware-Download and documentation for the topical
RELEASE version:
DIVE Version 3_11
https://www.divetable.info/DIVE_V3/V3e/index.htm
this RELEASE version is in one ZIP archive
whereas the topical 3_11-BETA version from 04/2022 with the
DCIEM-coefficient set for the linear simulation could be
downloaded directly as an *.exe file:
https://www.divetable.info/beta/D3_11.exe
17
The 3_11 BETA version features the linear DCIEM simulation.
It is used in the service engine of DIVE by the mnemonic „nc“
with the option 13: thus the „ES-L 16 D“ matrix is loaded into memory:
„NC“ (nitrogen coefficients):
with the option „13“ the co-
efficients part of the matrix
from slide # 10 is loaded
into the service engine of the
DIVE software.
(The „HI / LO“ values on
the very right side of the
matrix, here equal to 1.0,
could be used for a nearly
„microscopic“ fine-tuning.
This method was once called:
„Variable Gradient Method“, but is not required here in this context.)
Handling of DIVE:
18
Adaption to operational requirements
could be done via the commands / mnemonics:
ascent rate / speed („AR“)
ambient atmospheric pressure at start / end of
dive („L“)
the respiratory coefficient Rq („R“)
the ambient (water)-temperature („TE“)
the water density („DI“)
oxygen consumption / workload („W“)
The latest DIVE Version for beta testing is always staged there:
https://www.divetable.info/beta/index_e.htm
along with information on production date, size in bytes, key-word for the
new features and the checksums for verifying the download.
Fine tuning of DIVE: