Modeling pulmonary and CNS O2 toxicity and estimation of parameters for humans

The power expression for cumulative oxygen VCe × e 0.42 + 0.00379P O 2t, where VCt is the value at the end of the hyperoxic exposure, nervous system CNS oxygen toxicity in K t = Ke × e

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Modeling pulmonary and CNS O2 toxicity and

estimation of parameters for humans

R Arieli 1 , A Yalov 2 , and A Goldenshluger 3

ABSTRACT

10.1152/japplphysiol.00434.2001 The power expression for cumulative oxygen

VCe × e ( 0.42 + 0.00379P O

2)t, where VCt is the

value at the end of the hyperoxic exposure,

nervous system (CNS) oxygen toxicity in

K t = Ke × e 0.079t , where K t and Ke are the values of K at time t of the recoveryprocess and

hyperbaric oxygen; pulmonary oxygen toxicity; central nervous system oxygen toxicity

TOP

ABSTRACT

INTRODUCTION QUANTITATIVE EXPRESSIONS FOR SELECTING THE PARAMETERS FOR APPENDIX A

APPENDIX B REFERENCES

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INTRODUCTION

HYPERBARIC OXYGEN (HBO) is encountered in clinical treatment in the hyperbaric

recovery process The toxic process itself,

oxygen species (ROS) and increased injury,

may differ from the steady-state production

state and in which recovery may occur

In the present report, we shall introduce the general power equation for any form of

TOP ABSTRACT

INTRODUCTION

QUANTITATIVE EXPRESSIONS FOR SELECTING THE PARAMETERS FOR APPENDIX A

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QUANTITATIVE

EXPRESSIONS FOR

OXYGEN TOXICITY

Quantification Principles

We assumed that an oxygen-damaged

measurable physiological variable (DMG) may have the same relationship with time t

P O 2 Effect

the hydroxylradical is d[·OH]/dt = k2(k1[X ][H+]PO2)2 t3(k3[Fe2+] + k4 × k1 × t × PO2),

PO2

Time Effect

DMG t2 (2)

Power Equations

TOP ABSTRACT INTRODUCTION

QUANTITATIVE EXPRESSIONS FOR

SELECTING THE PARAMETERS FOR APPENDIX A

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(1) where a is a constant related to the units of measured damage, and c is for the said

(2) where K is the cumulative oxygen toxicity index A symptom may appear when K reaches

Complex Exposures

Eqs A2-A5) that the cumulativeoxygen toxicity indexes, either the parametric DMG or

(3)

(4)

solved for their integral forms

(5)

(6)

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Recovery Equations

The power equation, which was developed by using the non-steady-state production of

It has been suggested that recovery from oxygen toxicity in normoxia follows an

(7)

and

(8)

SELECTING THE

PARAMETERS FOR

HUMANS

Because the basic processes of toxicity and

recovery are common to all mammals, the

be applied to humans with the appropriate

TOP ABSTRACT INTRODUCTION QUANTITATIVE EXPRESSIONS FOR

SELECTING THE PARAMETERS FOR

APPENDIX A APPENDIX B REFERENCES

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related topulmonary oxygen toxicity and expressed by the reduction in VC,and the other

Pulmonary Values

There are enough data to derive the parameters for pulmonary oxygen toxicity in the

c = 4.57, where DMG = % VC (where VC is the reduction in VC), time t is expressed

0.42 + 0.00379 P O

hyperoxic exposure

View larger version (19K):

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[in a new window]

Fig 1 Reduction of vital capacity ( VC) in

equation

[in this window]

[in a new window]

Fig 2 Recovery of human VC as a function of

except for the 106-kPa exposure in Eckenhoff et al., when the first 33 h of the recovery process were at

50 kPa Lines represent the solution of the

exponential recovery Inset: recovery after exposure

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[in this window]

[in a new window]

Fig 3 Time constant ( ) for the recovery of

human VC, calculated from the data presented in

The line represents the linear regression solution

In developing our approach to recovery, we assumed that recovery depends on the level

The US Navy recommended oxygen exposure limits that would result in a 2% change in

CNS Oxygen Toxicity Values

Background power equation and recovery. For CNS oxygen toxicity, the data for convulsions

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between 1994and 1999) The mean data and the line representing the predictionof the

[in this window]

[in a new window]

Fig 4 Latency to central nervous system (CNS)

( ) and 2 SD (bars) are shown, together with the

no of measurements The line represents the power equation

MODULATORS OF CNS OXYGEN TOXICITY. The two principal modulators affecting CNS

For the metabolic rate effect, CNS oxygen toxicity will develop faster during exercise or

Therefore the ratio

(9)

function of PO2 (4)

(10)

and

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(11)

[in this window]

[in a new window]

Fig 5 Latency to CNS oxygen toxicity in the rat

by which it is represented

D × PCO2 Replacing t in the powerequation will yield = t2 PO = (C D × PCO2)2

(12)

(13)

and

(14)

3

(15)

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VARIABILITY. Our laboratory has shown that there is individual sensitivity to CNS oxygen

RECOVERY TIME CONSTANT IN HUMANS. Because measurements were not made in any other mammals, it would only be reasonable to guess that the use of body mass (BM)

human = rat (BMhuman/BMrat) 0.25 = 0.079 min 1, where BMrat is rat BM, BMhuman is human

BM, human is human , and rat is rat It is interesting to note that our suggestionagrees

CNS parameters in humans The parameters for the power equation can be derived by

(17)

For comparison, we applied the same analysis of CNS oxygen toxicity to our rat data To

P < 0.0001 2 for both parameters The power of PO2 with the data for the 395exposures,

The parameters solved by using the model for human hyperbaric exposures were

c = 15.0 (SE = 1.8) and K c = 5.28 × 109 (P < 0.0001 2 for both parameters and = 1.35)

(16)

intervals

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[in this window]

[in a new window]

Fig 6 Percent risk of CNS oxygen toxicity as a

calculation were derived from human hyperbaric

We gathered reports of 2,039 closed-circuit oxygen dives from the Israel Navy SEALS

distribution will now be

(17)

It is interesting that the same power c (6.8) was solved for both rats and humans This

For each diving depth, we calculated the percentage of symptoms at 1-h intervals The

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View larger

version (21K):

[in this window]

[in a new window]

Fig 7 Percentage of symptoms related to CNS oxygen

shown in the top left of each panel, and the no of dives is shown in the top right , Risk calculated from the parameters

derived from hyperbaric exposures (exp); , risk calculated from the parameters derived from both hyperbaric exposures and diving

We used our model with the parameters derived from the hyperbaric experiments and

[in this window]

[in a new window]

Fig 8 Percent risk of CNS oxygen toxicity as a

calculation were derived from both hyperbaric experiments and diving

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View this table:

[in this window]

[in a new window]

Table 1 Calculation of the risk of CNS oxygen toxicity within

the limits suggested by the US Navy

Two versions of the power equation describing CNS oxygen toxicity in humans were 5.28 × 109 = t2 (PO2/101.3)15.0 for an O2 of 0.9 l/min and 2.31 × 108 = t2(PO2/101.3)6.8 for

In conclusion, the power equation is a simplified expression derived from the principles

APPENDIX A

Calculation of Cumulative Oxygen Toxicity

When P O 2 Is Not Constant

TOP ABSTRACT INTRODUCTION QUANTITATIVE EXPRESSIONS FOR SELECTING THE PARAMETERS FOR

APPENDIX A

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from which it follows that

(A1)

The expressions

and

from which it follows that

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and

Thus

(A3)

For all-or-none effects, DMG should be replaced by K, and the parameter a should be

omitted, giving

(A4)

or

(A5)

APPENDIX B

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Solution of the Parameters of the Power

Equation

The power equation describes the increasing

risk of CNS oxygen toxicity as K approaches

(B1)

(B2) where y i = min(t i , c i), i = I (ti ci) , and c iare the censor variables, and i is the indicator

Considering t as the response variable, one can write

Thus c and K can be estimated by using parametric regression techniques for the survival

data The idea is that

follows

TOP ABSTRACT INTRODUCTION QUANTITATIVE EXPRESSIONS FOR SELECTING THE PARAMETERS FOR APPENDIX A

APPENDIX B

REFERENCES

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value,if t has the smallest extreme value distribution, then e t has a Weibull distribution;

In our computations, we used the smallest extreme value distribution The results

The risk can then be calculated from the normal distribution

(B3)

ACKNOWLEDGEMENTS

The authors thank R Lincoln for skillful editing and Y Roth for assistance with the

FOOTNOTES

The opinions and assertions contained herein are the private ones of the authors and are

Institute

Address for reprint requests and other correspondence: R Arieli, Israel Naval Medical

The costs of publication of this article were defrayed in part by the payment of page

Received 4 May 2001; accepted in final form 21 September 2001

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78: 454-459, 1998

5 Arieli, R, and Ertracht O Latency to

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598-603, 1999

6 Arieli, R, and Gutterman A Recovery

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182-187, 1997

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Shupak A Thermal status of wet-suited divers using closed circuit O2 apparatus in sea

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10 Butler, FK, Jr, and Thalmann ED Central nervous system oxygen toxicity in

11 Clark, JM, Jackson RM, Lambertsen CJ, Gelfand R, Hiller WDB, and Unger

TOP ABSTRACT INTRODUCTION QUANTITATIVE EXPRESSIONS FOR SELECTING THE PARAMETERS FOR APPENDIX A

APPENDIX B

REFERENCES

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J APPL PHYSIOL 92(1):248-256

American Physiological Society

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