PresentationPDF Available

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



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“
An agile implementation of the “K-value”:
a severity index for CNS- and pulmonary
Miri Rosenblat, Nurit Vered, Albi Salm @
06 01 / 2021, DOI: t.d.b.
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
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“:
pls. cf. chapter „Handling of DIVE“. Error reports and enhancement requests are very
welcomed, via e-mail to our head of lab:
Overview: K-Value calculations for
CNS-OT risc @ ca. 1 % & P-OT < - 2 % ΔVC:
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.
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
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
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):
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
% 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
From the bottom phase of the example above (pls. cf. slide # 3) we get the following
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
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
[1] Arieli, R., A. Yalov, and A. Goldenshluger. Modeling pulmonary and CNS O2
toxicity and estimation of parameters for humans. J Appl Physiol 92: 248256,
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:
[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.
[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
An agile implementation of the “K-value”:
a severity index for CNS- and pulmonary
[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,
[8] Vered, Nurit; Rosenblat, Miri (2021) Synopsis: Fact Sheet & PoC
[9] Salm, Albi (2012) Mother Nature is a Bitch: beyond a pO2 of 1.6
TDM, Vol 07 / 2012, p. 16 - 22
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:
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
but the german manual for the old, the 3_09, still holds,
Update will follow in a couple of months:
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!
The workaround is to use the english manual with the new 3_10:
The mnemonics to control DIVE are in english, anyway.
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.“ „zoffers 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].
Handling of DIVE Version 3_10 (3)
With the „kmnemonic / 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 („ **** “)
Handling of DIVE Version 3_10 (4)
Once again: „k“ , and the new pO2 set to3.“ 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.
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 „zor in black-&-white in the log file, for later documentation /
Et voilà ! The ASCII log-file from: C:\DIVE\PROT\PROTOCOL.TXT (*):
(*): proper installation on hard disk C: required
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 relatedmishaps“ (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!
Handling of DIVE Version 3_10 (7)
As already pointed out in the „Preamblesection:
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-isbasis. 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
givefriendly 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!
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: „Kwe recieve the K-Value Plan subroutine (slides # 7 & 8; 13 & 14)
Fine tuning of DIVE:
...  the K-value indices for CNS-& P-OT from Ran Arieli et al.  the ESOT for P-OT as a replacement for the UPTD The physiologic rationale and the calculations are described in [1] & [3], resp. in all the references of [1] and [4]. ...
... The handling of Ran Arielis K-values are described in [4], along with operational examples and hints for the used tool. ...
... The calculation of ESOT / K-values are described in-depth in [1] & [4] and all the references therein. ...
Full-text available
This communication is on the implementation of a tool to calculate the new oxygen exposure indices, i.e. the indices concerning the oxygen toxicity (-OT) for the central nervous system (CNS-) and the whole body, the pulmonary (P-)system, pls. cf. ref. [1] & [4] and all the references therein. It is not intendend to discuss the scientific background nor the physiological or statistical rationale of these new indices. As well it is not intended to give any guidelines, which one of these new indicators should be used. Instead, we only want to point out that there are already tools available for these tasks at hand, pls. cf. ref. [2]. That is, the tool relieves the inclined user (i.e.: diver, instructor, manager, LST, DMO, …) of the calculation needed for ESOT and Arieli K-values and / or of errors through look-up of the tabulated versions [3], p. 27 & 28, resp. the rounding errors, intrinsic to all tabulated values. Additional, the tool displays the standard, seasoned Ox-Tox indices from the NOAA / USN, i.e. the %CNS and the OTU oxygen exposure doses for easy & straightforward comparison with other tools and/or dive computers.
... der recovery-function implementiert. Ein paar kleine, praxisorientierte Beispiele (auf englisch) sind auf dem RESEARCHGATE Portal zum anschauen; Quelle: [16]. ...
Full-text available
Überblick über Hintergründe & Anwendungen des "K-Wert"- Algorithmus. Der K-Wert ist ein "severity index" zur CNS- & P-OT, den Schädigungen durch hyperbaren Sauerstoff von Ran Arieli et al. [1] bis [5] und alle darin genannten Referenzen.
Full-text available
During our evaluation of some ZH-L16x Helium coefficients [1], we found certain interesting aspects on how dive computers calculate a box dive profile with Heliox21 mixture as the sole breathing gas and how diving contractors would handle the same profile in a completely different way. One keyparameter for our comparison was the K-Value index for CNS-OT [2].
Full-text available
Abstract: We compiled lists/descriptions of errors found in the standard diving medicine literature. Methods: We scanned our diving medicine archives and looked there for already existing error-reports; typos etc. were ignored. Results: Severe errors are appearing more frequently in monographs. Omnibus Volumes, written by teams of experts, are obviously more resilient to errors. Discussion / Recommendations: Single authors / editors should consult with expert teams prior to publication. If you want to contribute to our list, we would be very happy if you send an e-mail to our head of lab:
Full-text available
Patients undergoing hyperbaric oxygen therapy and divers engaged in underwater activity are at risk of central nervous system oxygen toxicity. An algorithm for predicting CNS oxygen toxicity in active underwater diving has been published previously, but not for humans at rest. Using a procedure similar to that employed for the derivation of our active diving algorithm, we collected data for exposures at rest, in which subjects breathed hyperbaric oxygen while immersed in thermoneutral water at 33°C (n = 219) or in dry conditions (n = 507). The maximal likelihood method was employed to solve for the parameters of the power equation. For immersion, the CNS oxygen toxicity index is K I = t2 × PO210.93, where the calculated risk from the Standard Normal distribution is Z I = [ln(K I 0.5) - 8.99)]/0.81. For dry exposures this is K D = t2 × PO212.99, with risk Z D = [ln(K D 0.5) - 11.34)]/0.65. We propose a method for interpolating the parameters at metabolic rates between 1 and 4.4 MET. The risk of CNS oxygen toxicity at rest was found to be greater during immersion than in dry conditions. We discuss the prediction properties of the new algorithm in the clinical hyperbaric environment, and suggest it may be adopted for use in planning procedures for hyperbaric oxygen therapy and for rest periods during saturation diving.
Full-text available
In Special Operations Forces (SOF) closed-circuit rebreathers with 100% oxygen are commonly utilised for covert diving operations. Exposure to high partial pressures of oxygen (PO2) could cause damage to the central nervous system and pulmonary system. Longer exposure time and higher PO2 leads to faster development of more serious pathology. Exposure to a PO2 above 1.4 ATA can cause central nervous system toxicity, leading to a wide range of neurologic complaints including convulsions. Pulmonary oxygen toxicity develops over time when exposed to a PO2 above 0.5 ATA and can lead to inflammation and fibrosis of lung tissue. Oxygen can also be toxic for the ocular system and may have systemic effects on the inflammatory system. Moreover, some of the effects of oxygen toxicity are irreversible. This paper describes the pathophysiology, epidemiology, signs and symptoms, risk factors and prediction models of oxygen toxicity and their limitations on SOF diving.
Full-text available
Oxygen toxicity is a problem in diving and can have fatal consequences in the water. Various aspects of oxygen diving have been studied in dry hyperbaric chambers, but there is a lack of information on in-water diving using closed-circuit oxygen apparatus. We collected 2527 dive reports from 473 closed-circuit oxygen divers (a mean of 5.2 reports per diver), and analyzed the relationships between various symptoms and their dependence on depth and diving time. No CNS oxygen toxicity-related symptoms were reported at a depth of 2 m seawater (msw), but their proportion increased at depths from 3 to 6 msw. We found that CNS oxygen toxicity-related symptoms appeared in 2.5% of dives conducted at a Po2 of 119 kPa. The main symptoms and signs reported were headache: 4.5%; nausea: 2.6%; hyperventilation: 2.6%; heavy breathing: 2.4%; dizziness: 1.6%; hiccups: 1.5%; bloody sputum: 1.4%; cold shivering: 1.1%; tinnitus: 0.9%; difficulty maintaining a steady depth: 0.9%; disorientation: 0.6%; tiredness: 0.5%; tingling in the limbs: 0.4%; hearing disturbances: 0.4%; a choking sensation: 0.4%; extreme effort: 0.4%; and loss of consciousness: 0.3%. Environmental factors, light vs. dark and temperature, had no effect on symptoms. The number of symptoms increased with diving time. Divers who experienced amnesia, facial twitching, hearing disturbances (p < 0.001), and disorientation (p < 0.014) were prone to suffer loss of consciousness. It was found that some divers are more sensitive to oxygen than others (p < 0.0001).
Background: The risk of oxygen toxicity has become a prominent issue due to the increasingly widespread administration of hyperbaric oxygen (HBO) therapy, as well as the expansion of diving techniques to include oxygen-enriched gas mixtures and technical diving. However, current methods used to calculate the cumulative risk of oxygen toxicity during an HBO exposure i.e., the unit pulmonary toxic dose concept, and the safe boundaries for central nervous system oxygen toxicity (CNS-OT), are based on a simple linear relationship with an inspired partial pressure of oxygen (PO2) and are not supported by recent data. Methods: The power equation: Toxicity Index = t2 × PO2c, where t represents time and c represents the power term, was derived from the chemical reactions producing reactive oxygen species or reactive nitrogen species. Results: The toxicity index was shown to have a good predictive capability using PO2 with a power c of 6.8 for CNS-OT and 4.57 for pulmonary oxygen toxicity. The pulmonary oxygen toxicity index (PO2 in atmospheres absolute, time in h) should not exceed 250. The CNS-OT index (PO2 in atmospheres absolute, time in min) should not exceed 26,108 for a 1% risk. Conclusion: The limited use of this toxicity index in the diving community, after more than a decade since its publication in the literature, establishes the need for a handy, user-friendly implementation of the power equation.
The power expression for cumulative oxygen toxicity and the exponential recovery were successfully applied to various features of oxygen toxicity. From the basic equation, we derived expressions for a protocol in which PO(2) changes with time. The parameters of the power equation were solved by using nonlinear regression for the reduction in vital capacity (DeltaVC) in humans: %DeltaVC = 0.0082 x t(2)(PO(2)/101.3)(4.57), where t is the time in hours and PO(2) is expressed in kPa. The recovery of lung volume is DeltaVC(t) = DeltaVC(e) x e(-(-0.42 + 0.00379PO(2))t), where DeltaVC(t) is the value at time t of the recovery, DeltaVC(e) is the value at the end of the hyperoxic exposure, and PO(2) is the prerecovery oxygen pressure. Data from different experiments on central nervous system (CNS) oxygen toxicity in humans in the hyperbaric chamber (n = 661) were analyzed along with data from actual closed-circuit oxygen diving (n = 2,039) by using a maximum likelihood method. The parameters of the model were solved for the combined data, yielding the power equation for active diving: K = t(2) (PO(2)/101.3)(6.8), where t is in minutes. It is suggested that the risk of CNS oxygen toxicity in diving can be derived from the calculated parameter of the normal distribution: Z = [ln(t) - 9.63 +3.38 x ln(PO(2)/101.3)]/2.02. The recovery time constant for CNS oxygen toxicity was calculated from the value obtained for the rat, taking into account the effect of body mass, and yielded the recovery equation: K(t) = K(e) x e(-0.079t), where K(t) and K(e) are the values of K at time t of the recovery process and at the end of the hyperbaric oxygen exposure, respectively, and t is in minutes.
DIVE: a decompression suite
the SubMarineConsulting Group (1991) DIVE: a decompression suite;
Mother Nature is a Bitch: beyond a pO 2 of 1
  • Albi Salm
Salm, Albi (2012) Mother Nature is a Bitch: beyond a pO 2 of 1.6