An agile implementation of the "K-value": a severity index for CNS-and pulmonary oxygen-toxicity

Abstract

The K-value power functions for the central nervous system and pulmonary oxygen toxicity (CNS-OT, P-OT) are described in: [1], [2], [3], [4] & [5],
pls. cf. chapter „References“.

As Ran et al. would have it ([3], abstract), there is a need for an implementation.
Which is what we did ([6], [7], [8], [9]).

„Agile“ means here, in the context of IT-projects: a failure rate of 20 % is subliminally
accepted … Which is why we put the software on the BETA TEST site of „DIVE“

Full text

An agile implementation of the “K-value”:
a severity index for CNS- and pulmonary
oxygen-toxicity
1
Miri Rosenblat, Nurit Vered, Albi Salm @ www.SMC-de.com
06 01 / 2021, DOI: t.d.b.
Preamble:
The K-value power functions for the central nervous system and pulmonary oxygen
toxicity (CNS-OT, P-OT) are described in: [1], [2], [3], [4] & [5], pls. cf. chapter
„References“.
As Ran et al. would have it ([3], abstract), there is a need for an implementation.
Which is what we did ([6], [7], [8], [9]).
„Agile“ means here, in the context of IT-projects: a failure rate of 20 % is subliminally
accepted … Which is why we put the software on the BETA TEST site of „DIVE“:
https://www.divetable.info/beta/index.htm
pls. cf. chapter „Handling of DIVE“. Error reports and enhancement requests are very
welcomed, via e-mail to our head of lab: director@SMC-de.com

Overview: K-Value calculations for
CNS-OT risc @ ca. 1 % & P-OT < - 2 % ΔVC:
2
power functions:
K = t2 * pO2 c
CNS-OT: K < 26,108 t in min. pO2 in atm c = 6.8
P-OT: K < 244 t in hours pO2 in atm c = 4.57
recovery function:
Krecovery = Kend * e - (τ * trecovery )
τ = time constant: 0.079; trecovery in min.

3
K-Value Calculation, e.g. CNS-OT:
bottom phase:
e.g.: 1.1 atm pO2, 60 min
K bottom = [60 * 1.1 3.4 ]2 = [ 82.9 ]2 = 6,883
decompression phase:
e.g.: 6.25 m @ 100 % O2, 15 min
K deco = [15 * 1.6 3.4 ]2 = [74.1]2 = 5,498
K-Value for the complete dive:
K = [60 * 1.1 3.4 + 15 * 1.6 3.4 ]2 = 24,684
Depth Time

4
K-Value Calculation, e.g. CNS-OT:
Example I: say, you have a diver down, working @ 1.1 atm pO2, now for 60 min
at the baseplate of your wind power station. Her decompression obligation becomes
significant. But now you need to get her up asap due to surface surge, swell, …
whatever. How can you decompress her most efficient, but quite safely?
The CNS-OT K-value for her bottom phase (pls. cf. slide #3) is: K bottom = 6,883
For one decompression phase, say: 6.25 m @ 100 % O2 we have: K deco = 5,498
For these 2 stages we get: K = 24,684. So how much have you left @ 3m?
How long could you leave her instead @ 9m?
For a 1% CNS risk you have left 26,108 – 24,684 = 1,424 K-units.
Looks like a lot: but it‘s not!
This is already ca. 24,684 / 26,108 = 0.9454, i.e. more than 94 % of one Kmax:
(pls. cf. slide # 6) so this translates to less than 1 min @ 3 m …
For the same accepted risk, the time frame @ 9m is approx. 8 min.
For a ca. 2 % risk, the times @ 6 and @ 9 m are, respectively: ca. 32 or 17 min.
Pls. cf. the slides # 7 & 8.

An agile implementation of the “K-value”:
a severity index for CNS- and pulmonary
oxygen-toxicity
5
Kbottom = t2 * pO2 c
KDive = [t * pO2 c/2 + tdeco * pdecoO2 c/2 ]2
Since Kbottom is defined via known t & pO2, as well for hyperoxic multi-level
exposures ([1], Appendix A), there results a quadratic equation in the
standard form for tdeco with the free parameters:
pdecoO2 and K = Kmax(CNS/P risc) :
[α + β * tdeco ]2 – Kmax = 0 
α2 – Kmax + 2 * α * β * tdeco + (β * tdeco )2 = 0
α β

K max definitions ([3], p. 155, 157):
6
CNS-OT: K < 26,108 @ 1 % CNS risk
K < 58,571 @ 2 % CNS risk
K < 196,811 @ 4 % CNS risk
K < 432,700 @ 6 % CNS risk
P-OT: K < 244 @ - 2 % ΔVC
K < 1,220 @ - 10 % ΔVC
For these 6 values of Kmax we evaluate with the already calculated 2 K-values
for CNS-OT & P-OT of the topical hyperoxic exposure (= the actual dive) the
following:
% of Kmax
time in [min] (for CNS-OT) or [h] (for P-OT) to reach Kmax
for an intended / required target pO2 as a free input-parameter. The target pO2
is the pO2 for the final or any other decompression stage.

An agile implementation of the “K-value”:
a severity index for CNS- and pulmonary
oxygen-toxicity
7
From the bottom phase of the example above (pls. cf. slide # 3) we get the following
output:
 i.e.: the final decompression should not be substantially longer than 15 min;
or ca. 30 min, if you opt for a 2 % CNS risk.

An agile implementation of the “K-value”:
a severity index for CNS- and pulmonary
oxygen-toxicity
8
The target pO2 (default = 1.6 atm) could be set to any other intended / required
value, for e.g.: 1.9 atm:

An agile implementation of the “K-value”:
a severity index for CNS- and pulmonary
oxygen-toxicity
9
References:
[1] Arieli, R., A. Yalov, and A. Goldenshluger. Modeling pulmonary and CNS O2
toxicity and estimation of parameters for humans. J Appl Physiol 92: 248–256,
2002; 10.1152/japplphysiol.00434.2001.
[2] Aviner B, Arieli R and Yalov A (2020) Power Equation for Predicting the Risk of
Central Nervous System Oxygen Toxicity at Rest. Front. Physiol. 11:1007.doi:
10.3389/fphys.2020.01007
[3] Arieli R. Calculated risk of pulmonary and central nervous system oxygen
toxicity: a toxicity index derived from the power equation. Diving and Hyperbaric
Medicine. 2019 September 30;49(3):154-160. doi: 10.28920/dhm49.3.154-160.
PMID:31523789.)
[4] Arieli, R., Shochat, T., and Adir, Y. (2006). CNS toxicity in closed-circuit oxygen
diving: symptoms reported from 2527 dives. Aviat. Space Environ. Med. 77, 526–
532.

An agile implementation of the “K-value”:
a severity index for CNS- and pulmonary
oxygen-toxicity
10
References:
[5] Wingelaar TT, van Ooij P-JAM and van Hulst RA (2017) Oxygen Toxicity and
Special Operations Forces Diving: Hidden and Dangerous. Front. Psychol. 8:1263.
doi: 10.3389/fpsyg.2017.01263
[6] the SubMarineConsulting Group (1991) DIVE: a decompression suite;
[7] Vered, Nurit; Rosenblat, Miri (2021) Synopsis: some collateral aspects of DCS,
DOI: http://dx.doi.org/10.13140/RG.2.2.22131.66087
[8] Vered, Nurit; Rosenblat, Miri (2021) Synopsis: Fact Sheet & PoC
https://www.researchgate.net/publication/349504991_Synopsis_Fact_Sheet_PoC_f
or_DIVE_Proof_of_Concept_for_a_free-shareware_decompression_suite
[9] Salm, Albi (2012) Mother Nature is a Bitch: beyond a pO2 of 1.6
TDM, Vol 07 / 2012, p. 16 - 22
[10] http://divingresearch.scripts.mit.edu/militarydivingdata/

11
Handling of DIVE Version 3_10 (1)
Download free of charge from the DIVE Version 3 BETA TEST site:
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.
DIVE V 3_10 is now (as per 06/2021) at an early deployment stage
(https://www.divetable.info/beta/D3_10.exe)
but the german manual for the old, the 3_09, still holds,
Update will follow in a couple of months:
https://www.divetable.info/DIVE_V3/DOXV3_0.pdf
Please, note: since the release train for
the english version (V3_04) is somewhat slower …
DIVE V 3_10 is not compatible with all older versions!
https://www.divetable.info/DIVE_V3/V3e/index.htm
The workaround is to use the english manual with the new 3_10:
The mnemonics to control DIVE are in english, anyway.

12
Handling of DIVE Version 3_10 (2)
Example II: say, we had a tender after a HBOT session @ 2 atm pO2,
30 min. Suddenly an urgent CO intox comes in: you need to put her
again in the chamber due to lack of staff.
What would her CNS- & P-OT parameters look like?
Set the mixture to oxygen („m“ „1.“) (*) and the parameters for the
1st. exposure: „d“ „10.1“ „30.“ „z“ offers all parameters relevant to the dive:
(*): the „“ are here only for clarity: for proper input, omit the „“ but not the dot .
Forget the german text, focus on the pure numbers …  )
The figures in line 4, designated as CNS & OTU are the values inherited from NOAA
in 1991, using a linear extrapolation beyond 100 % / 1.6 atm with USN contingency
exposure values [9].

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Handling of DIVE Version 3_10 (3)
With the „k“ mnemonic / command you invoke the K-Value Plan dialogue,
using the already calculated CNS- & P-OT K-values to project into the
Kmax values (pl. cf. slide # 6) for the next required / planned hyperoxic exposure,
the default being 1.6 atm:
The 1% & 2% risk values are already exceeded, so there is no time left („ **** “)

14
Handling of DIVE Version 3_10 (4)
Once again: „k“ , and the new pO2 set to „3.“ atm:
Et voilà ! There results a ca. 8 min @ 3 atm time frame for an approx. 6 % risk of an
CNS-OT episode to appear and ca. 1 h for a decrement of 2 % vital capacity or
2½ h for an approx. 10 % decrement in VC.

15
Handling of DIVE Version 3_10 (5)
Once you let her breathe a normoxic mixture ( „m“ „.21“ „0“ „0“ )
during surface interval, say 30 min („d“ „0.“ „30.“ ),
you follow the recovery function (from [1] to [5]),
again via „z“ or in black-&-white in the log file, for later documentation /
evaluation:
Et voilà ! The ASCII log-file from: C:\DIVE\PROT\PROTOCOL.TXT (*):
(*): proper installation on hard disk C: required

16
Handling of DIVE Version 3_10 (6)
We hard-coded these K-values, the exponents c (pls. cf. slides # 2 & 6)
and the connected risk numbers into the DIVE FORTRAN source code and thus
took them for granted. But they are not!
If you look at the data scatter ([2], tables 1 & 2; [3], Fig. 3; and [4]) and that multi-
collinearity is not adressed properly, it is obvious, that a couple of thousands
CNS episodes are needed to get the proper statistics.
This both translates to approx. 100,000 additional dives to be analyzed. But the
data is already out there: for e.g. the USN has collected more than 145,000 dives
on MK-25 and 29,000 on MK-16 systems during a ca. 7 year period [10] with
14 rebreather related „mishaps“ (not specified) in the 0 to 30 feet depth bins.
The first derivative of a dose-reaction function is an underlying normal
distribution. But this idea from the central limit theorem holds only for large,
very large numbers. Which underlines the above. I.e.: there is leeway in the
risk predictions and thus in the such derived c and K-values.
So, please, consider all of the above & the refs. as a start of a cooperation,
run as an iterative process!

17
Handling of DIVE Version 3_10 (7)
As already pointed out in the „Preamble“ section:
DIVE Version 3_10 is a BETA Test version,
in an early deployment stage. Chances are, there are errors!
Pls. notify them to us: we will appreciate it.
As well if you have feature requests.
Et voilà !
Basically, the DIVE software is for free, i.e.:
the software is provided on an „as-is“ basis. A full-blown english version 3_11
and a new english handbook will need some months, so take the german
3_10 in conjunction with the old english manual. But anyway we promise to
give „friendly support“:
We want you to help get your job done!
If we could assist or if you have any questions:
do not hesitate to contact us per e-mail.
We would even set up on short notice an on-line session,
usually via CISCO Webex ®, free of charge!
Promise!

18
For hyperbaric exposures with or without immersion
a fine tuning could be done via the commands:
 ascent rate („AR“)
ambient atmospheric pressure („L“)
the respiratory coefficient („R“)
physical workload / oxygen consumption („W“)
the ambient (water)-temperature („te“)
the water density („di“)
Buehlmann Safety Factor („B“)
last stop depth („LS“)
Gradient Factors High- & -Low („gf“)
a host of 9 alternative perfusion models („nc“)
And, as well, features like:
in-depth P(DCS) analysis with various models
pulmonary R-/L (right-to-left) shunting according to A. A. Buehlmann
oxygen-effects during decompression with pO2 > 1.6 atm, like:
bradycardia and vasoconstriction
latency during change of breathing mix
reduced perfusion rates through low ambient temperature
And with: „K“ we recieve the K-Value Plan subroutine (slides # 7 & 8; 13 & 14)
Fine tuning of DIVE: