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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“.

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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

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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)

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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

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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

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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:

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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: