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Decompression-Calculations for Trimix Dives with PC-Software; Gradient Factors: do they repair defective algorithms or do they repair defective implementations?

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If there is more than one inertgas in the breathing mixture, the calculation of the decompression-time t d has to be done numerically. We analyzed 480 square dive-profiles in the TEC/REC range with one freeware, two commercially available software-packages and via numerical methods (depth range: 30-80 m, bottom times: 20-60 min, helium percentage: 5-80 %, only normoxic mixes i.e.: no travel-or enriched deco gases, only ZH-L model, no adaptions with gradient factors). There are significant differences in the calculation of the decompression-times t d with trimix gases, obviously dependent on the helium percentage. In the present analysis, these differences do not come from variations in the decompression algorithms.
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Decompression-Calculations for Trimix Dives with PC-Software;
Gradient Factors: do they repair defective algorithms or do they
repair defective implementations?
If there is more than one inertgas in the breathing mixture, the calculation of the
decompression-time td has to be done numerically. We analyzed 480 square dive-profiles in
the TEC/REC range with one freeware, two commercially available software-packages and
via numerical methods (depth range: 30 - 80 m, bottom times: 20 - 60 min, helium
percentage: 5 - 80 %, only normoxic mixes i.e.: no travel- or enriched deco gases, only ZH-L
model, no adaptions with gradient factors). There are significant differences in the calculation
of the decompression-times td with trimix gases, obviously dependent on the helium
percentage. In the present analysis, these differences do not come from variations in the
decompression algorithms.
decompression, diving theory, mixed gas, models, simulation, technical diving, trimix
Side Note:
This is an abbreviated version of a paper which appeared in: CAISSON 2011, 26(3): 4 – 12.
Several parts of this paper I presented during a lecture for which I was invited to the
scientific meeting of the GTUEM ( , 03/20/2011 in Regensburg, Germany;
the abstract is under: CAISSON 2011, 26(1): 61. The extended german version you will find
An „Algorithm“ is just a mathematical rule for inert gas bookkeeping during an exposure to
overpressure. An „Implementation“ is the practical translation of this algorithm into a piece of
software, be it for a dive computer or a desktop deco software. A „Gradient Factor“ is a factor
< 1. It is used to multiply the allowed / tolerated inertgas partialpressures in the various body
tissues; thus a more conservative decompression method is forced via mathematics. With
“ZH-L” a certain group of disolved gas deco models is denoted, the researchers names are:
Haldane, Workman, Schreiner, Mueller, Ruf, Buehlmann and Hahn (pls. cf. the references).
The classical, perfusion-limited decompression algorithms after Haldane et al. describe the
absorption of inert gases per compartment through a mono-exponential function. Normally
the term „Haldane Equation“ is used:
Pt(t) = Palv0 + [Pt0-Palv0] e-kt (1)
Variable Definition
Pt(t) inertgas partialpressure within a compartment with the constant k [Bar] at time t
after an instantaneous change in pressure
Pt0 initial partialpressure of the inertgas within the compartment at time t=0 [Bar]
Palv0 the constant partialpressure of the inertgas in the alveoli [Bar], for t = 0 and thus for
all t due to the boundary conditions
k a constant, dependent on the compartment [min-1], with k = ln 2 / τ
t time [min]
The exponent k is basically the perfusion rate, i.e. the inverse of the half-time τ of a model
tissue. These model tissues are called „compartments“. The adaption of a purely
mathematical algorithm to a physiological system is done via a flock of these compartments,
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typically 6, 9 or 12, 16 and sometimes as well 20 (or even more). The variability comes with
the different halt-times into play. A typical spectrum of these half-times is from 1.25 to 900
minutes; for e.g. in a dive computer for professional use, the EMC-20H from Cochran and the
corresponding desktop deco-software Analyst 4 (
The mainstream sources for these perfusion algorithms are wellknown and listed in the
appendix. But now we want to try something new and draw upon a source which is relatively
rarely used:
[102] Hills, Brian Andrew (1977), Decompression Sickness, Volume 1,
The Biophysical Basis of Prevention and Treatment
Formula (1) is on page 111, the relationship between the half-times and the perfusionrate is
on page 113.
Limits of the perfusion-models:
The perfusion-models for Air/Nitrox/EAN and Heliox as breathing gases are based
worldwide on a very broad number of well-documented dives. They are mathematically
straightforward and have since the papers of Buehlmann ([4], [5], [65]) enjoyed popular
implementations in many dive computers and PC programs (Desktop-Deco-Software). The
technical diver as such wants to dive deeper / longer and thus is inclined to forget the trusted
envelope. Nonetheless this envelope is already published at length (e.g. in [63], p. 449 and
463) and is dealing with a couple of the following points, here just as a short overview and
not limited to:
only „inertgas-bookkeeping“, only mono-exponential for one compartment
these compartments are all in a parallel circuit, the linear connections like spleen ->
liver & bowel -> liver are not considered
inconsistent consideration of the metabolic gases O2, CO2 and H2O
„uneventful“ decompression, only the gas in solution is considered and not the free
gas phase (bubbles)
no allowance is made for short-term pressure changes which are small against the
fastest half-times
the calculation of inert gas saturation and de-saturation is done in a symmetrical
manner, i.e. with the identical coefficient in the exponential terms of (1)
clientele / biometrics and adaption are not reflected in the algorithms
as well not these circumstances, which affect tec divers even more due to massive
impact on blood-perfusion: workload, temperature and excessive oxygen partial
and: the 2nd. inert gas; the 2nd. (n-th) repetitive dive; and, and, and, …
Just a small choice of sources to these points:
Thalmann, ED; Parker, EC; Survanshi, SS; Weathersby, PK. Improved probabilistic
decompression model risk predictions using linear-exponential kinetics. Undersea Hyper.
Med. 1997; 24(4): 255 – 274;
Tikuisis, P; Nishi, RY. Role of oxygen in a bubble model for predicting decompression illness.
Defence R&D Canada, 1994; DCIEM-94-04;
Doolette DJ, Gerth WA, Gault KA. Probabilistic Decompression Models With Work-Induced
Changes In Compartment Gas Kinetic Time Constants. Navy Experimental Diving Unit,
Panama City, FL, USA; in: UHMS Annual Scientific Meeting, St. Pete Beach, Florida, June 3-
5, 2010, Session A6.
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Hahn MH. 1995. Workman-Bühlmann algorithm for dive computers: A critical analysis. In:
Hamilton RW, ed. The effectiveness of dive computers in repetitive diving. UHMS workshop
81(DC)6-1-94. Kensington, MD: Undersea and Hyperbaric Medical Soc.
Trimix tables:
For Heliox (oxygen & helium mixtures) there is a great abundance of validated tables: quite
in contrary to Trimix (oxygen, helium and nitrogen). There are none (almost). Surely enough
there is anecdotal evidence of sucessfull trimix-decompressions, but limited to a couple of
custom mixes, with a limited group of test persons and limited in the dive profiles. But
„validated“ here means a completely other league of game. It is a journalled procedure in a
decompression chamber, run for a big number of various depth/time combinations, each of
them with big numbers of dives. The journal is a detailed and reproducible log of the
following parameters: biometrics of test persons, time of the day, depth, time, ascent- and
descent-rates, surface intervall (even multi-day), breathing gas composition and- humidity/ -
temperatures, temperatures in the chamber and wet-pot, type of immersion and work-load.
The outcomes (DCS or # of doppler detected bubbles) have to be checked via double-
blinded operators. And when the number of test-persons exceeds the 3-digit limits and the
number of test-dives is in the 4- or even 5-digit range (as with NEDU, DCIEM and COMEX
tables) then there might be a certain tenacity. But none of the known trimix tables is meeting
these requirements. Maybe a laudable exception is the NOAA Trimix 18/50 Table from
Hamilton Research Ltd., 1993, 1998.
Just for the fun of it we draw from the „Journal of Applied Physiology“ the number and
temporal distribution of research papers concerning “trimix“ (title & keyword) from 1948 to
2010 and compared with other topics (Tables (1a) & (1b)):
Table 1a
The papers concerning „air“ are in brackets and only to compare the absolute numbers since
the relationsship to exposure to overpressure is not always the case. The first paper was
around 1976; the graph below shows the last 20 years and features a peak in the year 2007.
This results from short discussion-papers concerning the (in)-validity of Henry’s Laws,
especially with binary (half/half) gas-mixtures:
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Table 1b
The somewhat singulary paper in 2010 is from Ljubkovic et al. (pls. cf. the references), and
reflects very well our topic here, however with a VPM / bubblemodel and is really interesting
for hyperbaric (-diving) physicians. But generally speaking we have here the tendency that
trimix plays only a somewhat junior role in serious research. To put it bluntly:
the heavily exposed trimix diver is his own guinea pig.
The decompression time td for un-ary mixes (i.e. only one inertgas like EAN or heliox) can be
calculated directly with the Haldane equation (1). This is documented already and elsewhere
(for e.g.: ), here is the analytic expression for the
decompression time t = td:
t = - τ / ln2 * ln[ (Pt(t) - Palv0) / (Pt0 - Palv0) ] (2)
The criteria for „safe“ decompression within the perfusion-models is a simple linear (straight
line) equation ([65], p. 117, resp.: [102], p. 119 ff):
Pt.tol.ig = Pamb / b + a (3)
Variable Definition
Pt.tol.ig tolerated inert gas partial pressure, for each compartment, (analog to M) [Bar],
the sum of all inert gas partial pressures
a limit of a theoretical ambient pressure of 0 Bar, i.e. the axis intercept [Bar]
Pamb ambient pressure, absolute pressure of all breathing gases [Bar]
b 1/b pressure gradient: increase per unit of depth (dimensionsless), i.e.: the slope of
the straight line
These a-/b-coefficients are constants, tabulated for look up, e.g.: in [4] p. 27, in [5] p. 108 &
109, as well in [65] on p. 158.
A direkt mapping of equation (3) onto other perfusion models, e.g. the „M-Value“ model of
Workman or Schreiner, is done via a comparison of the parameters and the conversion of
the SI-units to imperial; described elsewhere and, as well, here: )
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During the course of the century the number and absolute values of the coefficients changed
from author to author: this is mostly the reflection of an increasingly conservative
decompression, that is: longer deco stops (pls. cf. Egi et al.).
The analytical expression (2) is only possible with one inert gas, in this case N2 . With more
than one inert gas the calculation of td has to be done numerically, via an approximation
procedure, that is: by trial-and-error. With Tri-Mix we have 2: N2 (nitrogen) and He (helium).
Thus we have to calculate the inert gas absorption for these 2 separately. This is a standard
procedure, already described by Buehlmann in [65], p. 119:
Pt(t) = Pt, He(t) + Pt, N2(t) (4)
The differences are in the molecular weights, the solubility coefficients and the diffusion
constants (pls. cf.: Rostain JC, Balon N. Nitrogen Narcosis, the High Pressure Nervous
Syndrome and Trimix. In: Moon RE, Piantadosi CA, Camporesi EM (eds.). Dr. Peter Bennett
Symposium Proceedings. Held May 1, 2004. Durham, N.C.: Divers Alert Network, 2007; as
well: [102], p. 118)
But now the criteria for „safe“ ascent has to be adapted as well to 2 inert gases, (3) changes
simply to (3*):
Pt.tol.ig = Pamb / b* + a* (3*)
Here as well there is a simple procedure to determine these new a* and b* -coefficients. The
old a- and b-coefficients (table look-up) for both of the gases are normalized with the
prevailing inert gas partial pressures for each of the compartments (pls. see the remark in
[54] on p. 86). Thus we have for any combination of a- and b-values for each compartment at
any time t:
a* = a (He + N2) = [( Pt
He * aHe ) + ( Pt
N2 * aN2)] / ( Pt
He + Pt
N2 )
b* = b (He + N2) = [( Pt
He * bHe ) + ( Pt
N2 * bN2)] / ( Pt
He + Pt
N2 ) (5)
Pls. see as well the examples in [4], p. 27; [5], p. 80 and Rodchenkov et al, p. 474.
The ascent criteria is now time-dependent by itself, the a*- & b*-coefficients are via (5)
married with the time-dependent exponential expressions of saturation/desaturation and no
longer any constants as per air/EAN or heliox.
The mapping of the compartment halftimes from N2 to He is normally done according to
Graham‘s law with the square root of the proportion of the molecular weights (i.e.: ca. 2.65).
This factor is now keyed in, uniform to all compartments. And exactly at this point we meet
the criticism of serious researchers in the field: D‘ Aoust et al, p. 119 & 121; as well: Lightfoot
et al, p. 453 and: Voitsekhovich, p. 210. In experiments we see the perfusion rates quite
differently! The pivotal 2.65 is, so it seems, really valid only for saturation exposures
(Berghage et al, p.6). But saturation is a state which even the bold tec-diver does not reach
easily … (Well, there are bold divers and there are old divers. But there are no ... Ok, Ok:
you already know the rest of the story ...)
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To put it simply: the deco time td is now on the left and the right hand side of eq. (2), a simple
analytical expression to solve for td is not possible due to the exponential sums. How can we
then evaluate td ?
Basically there are at least 3 simple methods. We look at them only skin-deep because they
are described elsewhere (for e.g.:
A) „Trial-and-Error“: for small increments in time, e.g. 1 second or 0.1 minute, we
calculate all relevant terms and check if the ascent criteria is met. This is called a
classical „numerical“ solution.
B) „Quasi-Analytical“: we accept tacitly an error by using eq. (2) without changes. Thus
we consider the a*-/b*-coefficients as constants for each phase of the
C) An approximation method: all the exponential terms are approximated via a
polynomial expression, aka „Taylor Expansion“ (Bronstein, Chapter: Expansion in
For commercially available off-the-shelf (COTS) desktop deco software method A) should be
preferred since the computing power of topical PC hardware does not impose any waiting-
time for the users. Thus quite in contrary to standard mix gas diving computers. Due to the
relatively high cost of development for water-proof hardware and, in comparison to other
mobile electronic devices like SmartPhones, virtually negligible lot sizes, there are regularly
no full-custom ASICs in favour of relatively cheap standard chips. These standard chips are
somewhat “slower” and brilliant in a gigantic energy consumption ...
The numerical solution A) consumes, in comparison to method B) more computing power
and thus time and more variables and memory: all of the 3 we do not have plenty under
water! It is thus self-evident to insinuate method B) where cost are at premium and we need
a result on the spot
How is this handled with commercial standard products? The crux is that producers of dive
computer hardware and deco software are regularly not willing to answer such inquiries with
hints to company secrets. Or, answers are cryptic and thus give room for conjecture!
But to answer this question halfway satisfactorily, we have developed the following
experimental method: 480 square dive profiles from the TEC- and REC- domain with the
depth range: 30 - 80 m (6 profiles at 10 m distance), and bottom times : 20 - 60 min (5
profiles in 10 min increase), with helium fractions: 5 - 80 % (16 profiles in 5% increments),
only with one normoxic mix (i.e.: no travel gases and no EAN deco mixes) have been
evaluated each with 4 software products and compared:
two commercially available off-the-shelf deco softwares,
one Freeware/Shareware version of DIVE (source: , version 2_900), and, as well
a private version 3_0 of DIVE.
This version 3_0 had implemented exactly the method A), the public version 2_900 is flawed
with the “blunder” of method B). For the 2 COTS products there are no reliable statements
available despite insistent and repeated inquiries.
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As a first step, these 4 products have been tested against each other with 40 different air-
and 40 different Nitrox/EAN32 profiles. Thus we checked the actual convergence of the
numerical method A with the COTS products. As one paradigm we have the following table
(2) with the TTS values for a square dive to 40 m with the bottom times ranging from 20 to
60 minutes:
Table (2): TTS vs. the 4 products; TTS = time-to-surface, i.e. sum of all deco stop times +
time for ascent
As well a sensitivity analysis was made for the numerical solution in order to make sure that
minor variations in the starting parameters do not lead to mathematical artefacts. In the end
we compared the 4 against the „Gold Standard“, the „Zuerich 1986 table for air dives“ (ZH-
86) of A. A. Buehlmann ([65], p. 228). Here we have deviations of + / - 2 min per deco stage,
as well sometimes the staging begins 3 m deeper in comparison to the table. This comes
mainly from the different sets of coefficients: the ZH-86 table uses the ZH-L 16 B set ([65], p.
158), whereas deco software or dive computers are using normally the ZH-L 16 C set ([65],
l.c.). As well printed tables are treating truncations in a completely different way than dive
computers. Even the great ex-champion from the NEDU (the United States Navy
Experimental Diving Unit), Cptn. Dr. Edward Thalmann had to admit, that a published diving
table does not jars with a computer-output:
“I think some were just manually adjusted. They just went in and empirically added
five minutes here and five minutes there, yeah.”
(Source: Edward Thalmann, [113] Naval Forces under the Sea: The Rest of the Story, p. 63
– 70, 197, 274, 361 and as well, the CD “Individual Interviews”).
Similar things may have been happened as well with OSHA tables for caisson/tunnel work
(until 1979). But these have been coined as „typographical errors“ (Kindwall, p. 342).
To force comparability all the calculations are based solely on the set ZH-L 16 C ([65], p.
158) and there are no manipulations via gradient factors. As well there are slight adaptions of
the dive profiles via ascent- and descent rates to make sure that the bottom times and the
inert gas doses are matching.
Evidently there are significant differences in the calculation of the deco times in dependence
of the helium-fraction and the amount of decompression obligations, vulgo the inert gas
dose, see chart (2). These differences are not due to variations in the decompression
algorithm but rather exclusively through different ways of calculation.
40 m, Nitrox/EAN 32 bottom times [min]: 20' 30' 40' 50' 60'
TTS DIVE 2_900 8 16 28 42 55
TTS DIVE 3_0: numerical solution 7 17 28 40 57
TTS COTS product 3 5 15 28 41 53
TTS COTS product 4 7 16 28 41 54
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Chart (2) shows the deviation of the TTS in dependence of the helium fraction, here as an
example for a dive to 40 m with a bottom time of 40 min.:
x axis: percentage of helium in the breathing mix: from 10 to 80 %
y axis: Delta TTS is a difference of the numerical solution to an arithmetic mean out of the 3
TTS according to: Σ (td,1 + td,2 + td,3) / 3 ; the td,i being the calculated td of the products i = 1 -
3 (DIVE 2_900, product 3, product 4). The x axis is defined as the zero baseline of the TTS
of the numerical solution. An “error” in [minutes] is coined as the deviation (Delta TTS) of this
mean value against the TTS of the numerical solution. The calculation of this arithmetic
mean was superimposed by the strong closeness of the td from the 3 products. The absolute
errors (see the vertical error margins) are increasing with the increase of the inert gas dose
and with the increase of the helium fraction. The above represented curve progression is
more or less universal for all of the 480 square profiles. Speaking simplified, qualitatively:
in the region of the helium fractions 5 % up to ca. 25 % the TTS is overrated: positive
error; i.e. the TTS is too great, the decompression is too conservative.
in the region of helium fractions which is relevant to most tec divers, that is ca. 30 –
ca. 40 %, the error vanishes: Delta TTS -> 0, and
increases with increasing helium fraction. In this region the error is negative, i.e. the
TTS is too small, the decompression is too liberal.
The results of the 2 COTS products and DIVE 2_900 came very close to each other thus a
somewhat similar calculation method is supposed. But this „similar“ method means in plain
language: the „blunder“ of DIVE 2_900 could be repeated in the implementations of the 2
COTS products ... To put it even more bluntly: the relative identity of the absolute values and
the prefix leave room for the guesswork that the 2 COTS products are using method B). Well,
there are quite a couple of other factors who could have been responsible for these
deviations. To name just a few:
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undocumented gradient factors
a respiratory coefficient unequal to 1
another weighting of other inert gases
another weighting of the water density
„empirically“ adapted a-/b coefficients, especially for helium and as a consequence:
small deviations from the original helium ZH-L spectrum of half-times (i.e. a mismatch
of a and b with the half time)
utilisation of the so-called „1b“ compartment instead or additive to compartment „1“
([65], p. 158);
ascent rates varying with depth
different approach to truncations
„Walking stick“ solutions for software implementations due to restrictions of the hardware
have been quite common in the early days of dive computers: for e.g. there was a product in
europe which could only interpolate linearly between stored values instead of calculating a
full-blown saturation/desaturation. But even today there are implementations which rely on a
modified ZH-L instead of the promised (advertised) RGBM model ...
But it seems that there are implementations taking this topic seriously. Amongst others there
is a shareware with a VPM model
( „The analytic, logarithmic
expression for stop times ... was replaced with a numerical solution of the restriction on the
sum of He and N2 partial pressures.“ As well you could check in the C-source code of the
OSTC, the „Open Source TauchComputer“ (german for: open source dive computer):
e_c_part2/p2_deco.c )
What shall we do with these, admittedly rather theoretical considerations? By no means this
should made be a public example for the developers. And in no case there is ample evidence
to draw any solid conclusions, as described above. These are the reasons not to reveal any
brand names. As well there is to consider, at least in Germany, the fair trade law, especially
the §§ 4, 5 and 6.
But the situation stays very unsatisfying concerning the intransparent status of some
implementations and the lack of open documentation of the „defaults“ and constants. To put
it in tec-lingo:
Is there really a ZH-L inside when the label reads ”ZH-L”???
But the clear message is the following: a decompression time in a digital display, be it on a
dive computer or a PC, is subject to interpretation! And this not so much due to errors in the
measurements (pressure, time, temperature, ...) and other statistical contemplations but
rather due to the method of programming and the choice of a solution for a mathematical
algorithm; i.e.: the software technology, the implementation. The range for these
interpretations is not only in ppm or per mill but rather, dependent on the inert gas dose and
the helium fraction , in the one- or even two digit percent range …
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To answer the question posed in the title finally:
1) Yes, with gradient factors we could repair defective perfusion algorithms. But the
perfusion models work by far more satisfying than the topical hype around the bubble
models tells. To underline this one with a historical one-liner:
“Haldane works if you use it properly!”
(R.W. Hamilton, Decompression Theory: 17th UHMS workshop, p. 135; 1978)
2) Yes, we need gradient factors to haul up to the safe side bad or negligent
implementations for mix gases!
In a nutshell we have it here for a dive (depth 42 m, bottom time 25 min, mix: 20 % O2, 80 %
He) on chart (3): it is a screen copy of DIVE Version 3_0:
Chart (3):
at first we see a couple of deep stop strategies and then the projection in details: the 1st.
block (according to method B) with the deco stages and the TTS @ ca. 64 min is likely to be
found with the COTS programs. The 2nd block (TTS = 78, method A) is the numerical
solution, not truncated. For a printed table or a COTS product the rounding-on at every deco
stage would result in a TTS of ca. 81 min. Application of gradient factors (block 3) with for eg.
GF high = 0,9 and GF low = 0,65 yields a TTS of ca. 93 min. Thus feigning a safety buffer of
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93 – 64 = ca. 30 min which we do NOT have in reality, because the „real“ numerical solution
converges @ ca. 81 min.
Thus the deviations are in an order of magnitude where even the differences between the
various deco models / algorithms become blurred, pls. look at table A in: The discussions on which model is
„better“ and which became here and there sometimes overheated could now be put into a
cooler context. To put this one as well into tec-lingo:
„It doesn’t matter which model you use, provided it has a sound
implementation!“ (© Albi, CE 2009)
are for the entire crew of GTUEM for the possibility to give a lecture on this topic at the 12. th
scientific meeting of the GTUEM 03/20/2011 in Regensburg/Germany. Especially to Willi W.
(Prof. Dr. Willi Welslau, president of GTUEM, Vienna) for a constant peer review and to
Jochen D. (Prof. Dr. Jochen D. Schipke, University Medical Center for experimental surgery,
Duesseldorf) for the lot of editorial work and for patience with my oft unorthodox approach.
As well to a couple of my tec-diving students @ PADI Israel.
The numbers in square brackets [ ] relate to the corresponding entry in a book list at:
the other internet links are pointing to the abstract page at the Rubicon research repository:
The sources for the perfusion algorithms are the following, generally well-known and
respected and the already cited famous standard books of diving medicine, pls. cf.:
CAISSON 2010; 25(1): 9;
Boycott, A.E., Damant, G.C.C., & Haldane, J.S.: The Prevention of Compressed Air
Illness, Journal of Hygiene, Volume 8, (1908), pp. 342-443
Workman, Robert D. "Calculation of Decompression Tables for
Nitrogen-Oxygen and Helium-Oxygen Dives," Research Report 6-65, U.S. Navy
Experimental Diving Unit, Washington, D.C. (26 May 1965)
Schreiner, H.R., and Kelley, P.L. "A Pragmatic View of Decompression," Underwater
Physiology Proceedings of the Fourth Symposium on Underwater Physiology, edited
by C.J. Lambertsen. Academic Press, New York, (1971) pp. 205-219
Müller, K. G.; Ruff, S.:
- Experimentelle und Theoretische Untersuchungen des Druck-Fall Problems, DLR,
Forschungsbericht 71-48, Juli, 1971; as well:
Seite 12
- Theorie der Druckfallbeschwerden und ihre Anwendung auf Tauchtabellen, DVL /
Bericht – 623/ 1966
[4] Dekompression - Dekompressionskrankheit, A. A. Bühlmann, Springer, 1983, ISBN 3-
[5] Tauchmedizin (Barotrauma, Gasembolie, Dekompression, Dekompressionskrankheit) A.
A. Bühlmann, Springer, 1993, ISBN 3-540-55581-1
[54] Enzyklopädie des Technischen Tauchens, Bernd Aspacher
[62] "Diving & Subaquatic Medicine", Carl Edmonds, Lowry, Pennefather, Walker, 4 th. Ed.,
Arnold, ISBN 0-340-80630-3
[63] "Benett and Elliott's Physiology and Medicine of Diving" Alf Brubakk, Neuman et al., 5 th
Ed. Saunders, ISBN 0-7020-2571-2
[64] "Textbook of Hyperbaric Medicine.", Kewal K. Jain; 3rd. Revised Ed., Hogrefe & Huber,
ISBN 0-88937-203-9
[65] Tauchmedizin, Albert A. Bühlmann, Ernst B. Völlm (Mitarbeiter), P. Nussberger; 5.
Auflage in 2002, Springer, ISBN 3-540-42979-4
[75] "Bove and Davis' DIVING MEDICINE", Alfred A. Bove, 4 th. edition, Saunders 2004,
ISBN 0-7216-9424-1
[102] Hills, Brian Andrew (1977), Decompression Sickness, Volume 1, The Biophysical
Basis of Prevention and Treatment, John Wiley & Sons, Ltd.. ISBN 0 471 99457 X.
[113] Naval Forces Under the Sea: The Rest of the Story; 2007, Best Publishing Company,
ISBN-13: 978-1-930536-30-2, ISBN-10: 1-930536-30-5
Berghage TE (ed). Decompression Theory. 17th Undersea and Hyperbaric Medical Society
Workshop. UHMS Publication Number 29WS(DT)6-25-80. Bethesda: Undersea and
Hyperbaric Medical Society; 1978; 180 pages.
Berghage, T.E., T.D. David and C.V. Dyson. 1979, Species differences in decompression.
Undersea Biomed. Res. 6(1): 1 – 13
Bronstein – Semendjajew: Taschenbuch der Mathematik, Verlag Harri Deutsch
D’Aoust, B.G., K. H. Smith, H.T. Swanson, R. White, L. Stayton, and J. Moore. 1979,
Prolonged bubble production by transient isobaric counter-equilibration of helium against
nitrogen. Undersea Biomed. Res. 6(2): 109 -125
Egi SM, Gürmen NM. Computation of decompression tables using continuous compartment
half-lives. Undersea Hyper Med 2000; 27(3): 143 – 153.
Kindwall, EP. Compressed air tunneling and caisson work decompression procedures:
development, problems, and solutions. Undersea Hyperb. Med. 1997 Winter; 24(4): 337 –
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decompression. In: Shilling CW, Beckett MW, eds. Underwater physiology VI. Proceedings of
the sixth symposium on underwater physiology. Bethesda, MD, 1978: 449 – 457
Ljubkovic M, Marinovic J, Obad A, Breskovic T, Gaustad SE, Dujic Z. High incidence of
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Moon RE, Piantadosi CA, Camporesi EM (eds.). Dr. Peter Bennett Symposium Proceedings.
Held May 1, 2004. Durham, N.C.: Divers Alert Network, 2007
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COCHRAN Consulting Inc.;
COMEX: Compagnie Maritime d'Expertises;
DAN: Divers Alert Network;
DCIEM (old label, now): Defence Research and Development Canada;
Journal of Applied Physiology:
NEDU: Navy Experimental Diving Unit;
NOAA: National Oceanic and Atmospheric Administration;
resp. NOAA diving:
OSHA: Occupational Safety and Health Administration;
(the topical caisson tables are at: Part Number 1926.)
UHMS: Undersea & Hyperbaric Medical Society;
Version of: 14.09.2011 19:13 # words: 4989
... There is a wealth of data in this report, Ref. [1] and the topical conference paper: "update per 03 / 2021" [1a] and as well a huge data base, not fully exploited: 30 graphs like Chart (2), pls. cf. next slide underlining the basic messages: ...
Full-text available
Background Information on the "update 03 / 2021" to the 2011 paper from Decompression-Calculations for Trimix Dives with PC-Software; Gradient Factors: do they repair defective algorithms or do they repair defective implementations?
Full-text available
Synopsis: some collateral aspects of DCS A collection of papers / essays / presentations and their URLs at, related to DCS (decompression sickness), PBPK (physiologically based pharmaco-kinetic models), diving and their somewhat remote, unusal or at least, unorthodox aspects.
SCUBA diving is associated with generation of gas emboli due to gas release from the supersaturated tissues during decompression. Gas emboli arise mostly on the venous side of circulation, and they are usually eliminated as they pass through the lung vessels. Arterialization of venous gas emboli (VGE) is seldom reported, and it is potentially related to neurological damage and development of decompression sickness. The goal of the present study was to evaluate the generation of VGE in a group of divers using a mixture of compressed oxygen, helium, and nitrogen (trimix) and to probe for their potential appearance in arterial circulation. Seven experienced male divers performed three dives in consecutive days according to trimix diving and decompression protocols generated by V-planner, a software program based on the Varying Permeability Model. The occurrence of VGE was monitored ultrasonographically for up to 90 min after surfacing, and the images were graded on a scale from 0 to 5. The performed diving activities resulted in a substantial amount of VGE detected in the right cardiac chambers and their frequent passage to the arterial side, in 9 of 21 total dives (42%) and in 5 of 7 divers (71%). Concomitant measurement of mean pulmonary artery pressure revealed a nearly twofold augmentation, from 13.6 ± 2.8, 19.2 ± 9.2, and 14.7 ± 3.3 mmHg assessed before the first, second, and the third dive, respectively, to 26.1 ± 5.4, 27.5 ± 7.3, and 27.4 ± 5.9 mmHg detected after surfacing. No acute decompression-related disorders were identified. The observed high gas bubble loads and repeated microemboli in systemic circulation raise questions about the possibility of long-term adverse effects and warrant further investigation.
In an effort to bring together the diverse laboratory-animal decompression studies, a literature review and statistical evaluation were undertaken. Although 22 different species that had been used in decompression studies were identified, systematic data were available for only 7 of these species: man, goat, dog, guinea-pig, rat, hamster, and mouse. Mathematical functions using physiological data on these seven species were developed to estimate 1) saturation time (the time for the body to equilibrate after an increase in hydrostatic pressure), and 2) no-decompression saturation-exposure limits (the maximum saturation-exposure pressure from which an abrupt return to 1 ATA can be tolerated). Data from man, rat, and mouse were used to develop physiological relationships for two additional decompression variables: change in pressure-reduction limits associated with increased exposure pressure and time to onset of decompression symptoms. Finally, data on rats for two other decompression variables, gas elimination time and optimum decompression stop time, are discussed in the hope that this will stimulate additional animal laboratory research in other mammalians. The general functional relationships developed in this paper provide a preliminary and rough means for extrapolating among species the decompression results obtained during animal laboratory experiments.
The production of systemic gas bubbles by isobaric counter-equilibration of helium against 5 atmospheres saturated nitrox (0.3 ATA O2 in both mixes) in awake goats was demonstrated. Sixteen animal exposures (8 dives, 2 animals per dive) to a sudden isobaric gas switch from saturation on N2 to He were conducted; 8 saturations occurred at 132 fsw and 8 at 198 fsw. Central venous bubbles were detected acoustically by means of a Doppler ultrasonic cuff surgically implanted around the inferior vena cava of each animal. Bubbles occurred from 20 to 60 min after the switch in both the 132 fsw and 198 fsw exposures, but were not always present in the 132 fsw exposure, and did not persist for as long. Bubbles or other Doppler events were often detected for the entire isobaric period-12 h-following the gas switch in the 198 fsw exposures. Decompressions were conducted according to the USN saturation tables and were uneventful, with only occasional bubbles. Supersaturation ratios calculated to have occurred for a considerable period after the gas switch were approximately 1.15 (tissue gas tension pi, divided by ambient hydrostatic pressure, P) with maxima at 1.26 for the faster tissues. These values are limiting ones in USN decompression only for the slower tissues. In general, therefore, these results argue for reducing the permissible ascent criteria for the faster tissues-assuming bubbles are to be avoided-and allowing more time at stops for non-saturation decompression. Gas switches from a more soluble to a less soluble and/or more rapidly diffusing gas should therefore be avoided until physiological limits are well worked out.
Multinational experience over many years indicates that all current air decompression schedules for caisson and compressed air tunnel workers are inadequate. All of them, including the Occupational Safety and Health Administration tables, produce dysbaric osteonecrosis. The problem is compounded because decompression sickness (DCS) tends to be underreported. Permanent damage in the form of central nervous system or brain damage may occur in compressed air tunnel workers, as seen on magnetic resonance imaging, in addition to dysbaric osteonecrosis. Oxygen decompression seems to be the only viable method for safely decompressing tunnel workers. Oxygen decompression of tunnel workers has been successfully used in Germany, France, and Brazil. In Germany, only oxygen decompression of compressed air workers is permitted. In our experience, U.S. Navy tables 5 and 6 usually prove adequate to treat DCS in caisson workers despite extremely long exposure times, allowing patients to return to work following treatment for DCS. Tables based on empirical data and not on mathematical formulas seem to be reasonably safe. U.S. Navy Exceptional Exposure Air Decompression tables are compared with caisson tables from the United States and Great Britain.
There is no consensus on the number of compartments and the half-lives (T1/2) used in the calculation of inert gas exchange and decompression sickness (DCS) boundary in existing dive tables and decompression computers. We propose the use of a continuous variable for the tissue half-lives, allowing the simulation of an infinite number of compartments and reducing the discrepancy between different algorithms to a single DCS boundary expression. Our computational method is based on the premise that M-values can be expressed in terms of T1/2 and ambient pressure (D). We combined the surfaces defined by M(D,T1/2) and tissue tension H(t,T1/2) to plan decompression. The efficiency and applicability of the method is investigated with four different DCS boundaries. The first two utilize the M-value relations proposed by Bühlmann and Wienke to derive no-D limits for sea level. The third boundary is defined by a surface fitted to the empirical M-values of US Navy, Bühlmann tables, US Air Force, and our altitude diving data. This expression was used to design the decompression procedure for a multilevel dive at 11,429-ft altitude and was used in six man dives in the Kaçkar Mountains, Turkey. Although precordial bubbles were observed in two dives, there were no cases of DCS. The fourth DCS boundary is constructed with the addition of a constraint that forces calculated M-values to stay below the available M-values. This constraint aims the highest degree of "conservatism". As an application of the new boundary, the method is used to derive decompression stop diving schedules for 11,429-ft altitude. The concept of continuous tissue half-lives is applicable to different types of gas exchange and DCS boundary functions or to a combination of different models with a desired level of conservatism. It has proved to be a useful tool in planning decompression for undocumented modes of diving such as decompression stop diving or multilevel diving at altitude. The algorithm can easily be incorporated into dive computers.
The sources for the perfusion algorithms are the following, generally well-known and respected and the already cited famous standard books of diving medicine
The numbers in square brackets [ ] relate to the corresponding entry in a book list at: the other internet links are pointing to the abstract page at the Rubicon research repository: The sources for the perfusion algorithms are the following, generally well-known and respected and the already cited famous standard books of diving medicine, pls. cf.: CAISSON 2010; 25(1): 9;