January 2001

NASA/TP—2001–210196

Evidence-Based Approach to the Analysis of

Serious Decompression Sickness With

Application to EVA Astronauts

Johnny Conkin, Ph.D., M.S.

National Space Biomedical Research Institute

Lyndon B. Johnson Space Center

Houston, TX
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January 2001

NASA/TP—2001–210196

Evidence-Based Approach to the Analysis of

Serious Decompression Sickness With

Application to EVA Astronauts

Johnny Conkin, Ph.D., M.S.

National Space Biomedical Research Institute

Lyndon B. Johnson Space Center

Houston, TX

National Aeronautics and

Space Administration

Lyndon B. Johnson Space Center

Houston, Texas 77058
Available from:

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7121 Standard Drive 5285 Port Royal Road

Hanover, MD 21076-1320 Springfield, VA 22161

301-621-0390 703-605-6000

This report is also available in electronic form at http://techreports.larc.nasa.gov/cgi-bin/NTRS
iii

Contents

Page

Contents................................................................................................................................................... iii

Acronyms and Nomenclature.................................................................................................................. v

Acknowledgments................................................................................................................................... vi

Abstract ................................................................................................................................................... 1

Introduction............................................................................................................................................. 1

Method ................................................................................................................................................ 2

Data ..................................................................................................................................................... 3

Denitrogenation and the 180-Minute Half-Time Compartment......................................................... 7

Probability Function: Risk Function Model ....................................................................................... 9

Parameter Optimization and Goodness of Fit..................................................................................... 11

Results..................................................................................................................................................... 12

Best-Fit Model .................................................................................................................................... 12

Threshold for Serious DCS ................................................................................................................. 14

Model Simulations Relevant to EVA Astronauts ............................................................................... 16

Benefits From Even Limited Prebreathe............................................................................................. 17

Best Estimate for Serious DCS in EVA Astronauts ........................................................................... 19

Qualitative Assessment of Goodness of Fit........................................................................................ 20

Quantitative Assessment of Goodness of Fit...................................................................................... 23

Model Validation ................................................................................................................................ 24

Discussion ............................................................................................................................................... 25

References............................................................................................................................................... 28

Appendix A: Sources of Data Used in Analysis of Serious DCS........................................................... 31

Appendix B: Maximum Likelihood and Model Optimization ............................................................... 37

Appendix C: 258 Group Data, Literature References, and Computed Cumulative Risk

From Lowest to Highest.......................................................................................................................... 40

Notes ....................................................................................................................................................... 47

Tables

Page

Table I. A Sample of Signs and Symptoms That Qualify as Serious DCS............................................. 4

Table II. Summary of 258 Decompression Tests.................................................................................... 6

Table III. Summary of 12 Extensive Decompression Tests.................................................................... 7

Table IV. Parameter Estimates of Four-Parameter Model...................................................................... 13

Table V. Comparison of Observed and Estimated Serious DCS in 12 Tests ......................................... 20

Table VI. Results From One-Sample χ2 Test......................................................................................... 24
iv

Figures

Page

Figure 1. The 258 tests on a P2 vs. P1N2 plot................................................................................. 9

Figure 2. Observed group incidence of serious DCS in 257 tests versus

the computed rc from Eq. 4.............................................................................................. 15

Figure 3. Observed group incidence of serious DCS in 109 tests at very low rc

versus the computed rc from Eq. 4................................................................................... 15

Figure 4. Results of simulations to demonstrate changes in ri from Eq. 2...................................... 16

Figure 5. Results of simulations to demonstrate changes in rc from Eq. 4 ..................................... 17

Figure 6. The contribution of prebreathe duration toward reducing risk

in astronauts who exercise at P2 ...................................................................................... 18

Figure 7. The contribution of prebreathe duration and inactivity toward reducing risk ................. 18

Figure 8. A simulation to show the P(serious DCS) specific for conditions that astronauts

may encounter during EVAs from the ISS....................................................................... 19

Figure 9. A comparison of the estimated to the observed serious DCS in Group 2 tests................ 21

Figure 10. A comparison of the estimated to the observed serious DCS in Group 1 tests................ 22

Figure 11. The x- and y-axis are expanded to evaluate the goodness of fit in those tests

where the observed incidence of serious DCS in 206 tests was ≤ 0.05 ........................... 23

Figure 12. Observed versus estimated incidence based on 40 validation tests

not used to parameterize the probability model ............................................................... 25
v

Acronyms and Nomenclature

CI confidence interval

DCS decompression sickness

EVA extravehicular activity (space walk)

HDSD hypobaric decompression sickness databank

ISS international space station

LL log likelihood

LRT likelihood ratio test

N2 nitrogen

O2 oxygen

P(serious DCS) probability of serious decompression sickness

P1 pressure before depressurization (psia)

P1N2 computed nitrogen pressure in a theoretical tissue compartment (psia)

P2 pressure after depressurization (psia)

psia pounds per square inch absolute

rc cumulative risk (dimensionless)

ri instantaneous risk (hr -1)

SD standard deviation

SE standard error

Talt planned time spent at P2 (hr)

TR tissue ratio (P1N2 / P2, unit less)
vi

Acknowledgments

We thank Alan H. Feiveson and R. Srini Srinivasan for their reviews of the statistical

methods. We also thank Michael L. Gernhardt, Philip P. Foster, and Michael R. Powell for their

reviews of the manuscript. The National Aeronautics and Space Administration supported part

of this work through the NASA Cooperative Agreement NCC 9-58 with the National Space

Biomedical Research Institute.
1

Abstract

It is important to understand the risk of serious hypobaric decompression sickness (DCS) in

order to develop procedures and treatment responses to mitigate the risk. Since it is not ethical to

conduct prospective tests about serious DCS with humans, the necessary information was

gathered from 73 published reports. We hypothesize that a 4-hr 100% oxygen (O2) prebreathe

results in a very low risk of serious DCS, and test this through analysis. We evaluated 258 tests

containing information from 79,366 exposures in altitude chambers. Serious DCS was

documented in 918 men during the tests. Serious DCS are signs and symptoms broadly

classified as Type II DCS. A risk function analysis with maximum likelihood optimization was

performed to identify significant explanatory variables, and to create a predictive model for the

probability of serious DCS [P(serious DCS)]. Useful variables were Tissue Ratio, the planned

time spent at altitude (Talt), and whether or not repetitive exercise was performed at altitude.

Tissue Ratio is P1N2 / P2, where P1N2 is calculated nitrogen (N2) pressure in a compartment

with a 180-min half-time for N2 pressure just before ascent, and P2 is ambient pressure after

ascent. A prebreathe and decompression profile Shuttle astronauts use for extravehicular activity

(EVA) includes a 4-hr prebreathe with 100% O2, an ascent to P2 = 4.3 lb per sq. in. absolute, and

a Talt = 6 hr. The P(serious DCS) is: 0.0014 (0.00096 - 0.00196, 95% confidence interval) with

exercise and 0.00025 (0.00016 - 0.00035) without exercise. Given 100 Shuttle EVAs to date and

no report of serious DCS, the true risk is less than 0.03 with 95% confidence (Binomial

Theorem). It is problematic to estimate the risk of serious DCS since it appears infrequently,

even if the estimate is based on thousands of altitude chamber exposures. The true risk to

astronauts may lie between the extremes of the confidence intervals (0.00016 - 0.00196) since

the contribution of other factors, particularly exercise, to the risk of serious DCS during EVA is

unknown. A simple model that only accounts for four important variables in retrospective data is

still helpful to increase our understanding about the risk of serious DCS.

Introduction

In addition to the risks of launch, and the risks to move and assemble large structures in

the weightless vacuum of space during extravehicular activity (EVA), there is also a small risk of

serious decompression sickness (DCS) in astronauts and cosmonauts who perform EVAs from

the U.S. Space Shuttle, Russian Mir, and International Space Station (ISS). The decrease in

ambient pressure from the 14.7 pounds per sq. in. absolute (psia) Shuttle cabin pressure (P1), to

4.3-psia space suit pressure (P2), may cause serious DCS. Serious DCS includes signs and

symptoms broadly classified as Type II DCS, and would have ended the test early for a subject in

an altitude chamber. Many of these symptoms would prompt a hyperbaric treatment to alleviate

the symptom(s), or to reduce the likelihood of any sequela. Serious DCS is to be avoided since

death sometimes follows (7,8).
2

Serious DCS is possible if tissue nitrogen (N2) partial pressure is not reduced through

adequate denitrogenation before the decompression, if the duration of the EVA is long, and/or if

the astronaut vigorously works during the EVA. Building and maintaining the ISS will require

hundreds of EVAs. Our efforts to prevent DCS have so far been successful, but the increasing

number of EVAs required to build and maintain the ISS has caused us to reevaluate the

likelihood of a serious case of DCS. The goal of this analysis is to accurately estimate the

probability of serious DCS [P(serious DCS)] in future EVAs given information such as the

denitrogenation before the decompression, the magnitude of the decompression, the exercise

after the decompression, and the duration of the EVA. This is particularly challenging since the

overall incidence of serious DCS is less than one percent from a survey of published reports from

exposures in altitude chambers.

Estimating and controlling an event of low probability is problematic. In fact, serious

DCS defies prediction. Two scenario are often invoked to describe a rare case of serious DCS: a

small volume of gas is randomly transported through a Patent Foramen Ovale and then into a

critical tissue, or the gas is transported in venous blood shunted past the pulmonary circulation.

A bubble can also grow in a critical tissue. A practical approach to describe the risk of serious

DCS is with a multivariable statistical model. Our previous survival analysis (3) estimated the

risk of all DCS outcomes, with the assumption that reducing the risk of any symptom also

reduces the risk of a serious symptom. Here we concentrate specifically on serious DCS. We

hypothesize that a four-hr 100% oxygen (O2) prebreathe results in a very low risk of serious

DCS. We test this hypothesis through a risk function analysis of retrospective data collected

from tests in altitude chambers.

Method

We needed four items to estimate our probability model for serious DCS:

a) data that contain a dichotomous (binary) response variable and one or more

explanatory variables

b) a probability function, such as a risk function, that structures the model so that the

outcome is a probability between zero and one

c) a model that calculates decompression dose

d) a parameter estimation algorithm on a computer that uses maximum likelihood

The risk function approach combines both the probability function and dose model into a single

function without the need for additional parameters just for the probability transform. Two aims

were to estimate unknown parameters that maximize the agreement between the observed serious

DCS incidence and the estimated serious DCS, and to assess the goodness of fit of the particular

model that best fit the data.
3

Data

The data are from 258 tests of exposures in altitude chambers from 1942 to 1994, and are

available through the Hypobaric Decompression Sickness Databank (HDSD) (4). A test might

contain a few subjects, such as a unique research project, or hundreds or thousands of subjects,

such as a training flight for aviation cadets. The HDSD currently contains 456 tests, but only

258 met the selection criteria. We selected tests where males were exposed up to 8 hr in the

chamber, and ascent rate was documented. The documentation of the test had to include the

number of serious DCS cases that were observed, even if there were no cases. It was not

necessary for the author to list all the signs and symptoms of serious DCS that were observed,

but this was often done. The dichotomous response variable is Serious DCS. This category

includes, but is not limited to:

• substernal disturbances (pulmonary chokes)

• involvement of the sensory, motor, and cognitive pathways of the brain and spinal

cord

• sudden collapse (neurocirculatory collapse)

• unexplained weakness

Pulmonary chokes make up a substantial percentage of this category. Signs and symptoms of

serious DCS not specifically attributed to arterial gas embolism would also appear in this

category. Disturbances of the skin, such as rashes, mottling, paresthesia, and edema, that

appeared as the only sign or symptom were not considered serious DCS in this analysis because

there is no agreement on a classification of skin disturbances into either Type I or Type II DCS.

Disturbances involving the skin were often placed into a separate category. Also, the 20 or so

cases of death (7,8) in research and operational aviation settings since 1940 certainly qualify as

more than serious DCS, and therefore are not included in this category. Table I contains a

sample of signs and symptoms that were classified as serious DCS in the 73 reports. Adler (1)

provides an excellent description of serious DCS collected from the literature.

The 258 tests were from 73 referenced sources, and represent 79,366 altitude exposures

(see Appendix A). Twelve tests with exposures > 200 per test contributed 71,039 exposures, of

which there were 544 cases of serious DCS. This subset of data is designated as “Group 1” data.

These tests come from reports of military training and research activities involving many men

during the years of World War II. The remaining 246 tests with exposures ≤ 200 per test

contained 8,327 exposures, and documented 374 cases of serious DCS. This subset of data is

designated as “Group 2” data. The non-specific selection yielded a wide variety of tests. The

goal was to account for most of the variability in outcome with a multivariable model, and to

identify significant explanatory variables.
4

TABLE I: A SAMPLE OF SIGNS AND SYMPTOMS THAT QUALIFY

AS SERIOUS DCS

Substernal Disturbances Auditory Disturbances

unproductive cough (chokes) tinitus

dyspnea loss of hearing

neurocirculatory collapse loss of balance

disruption of motor, sensory, and cognitive

pathways in brain and spinal cord

visual field disturbances

paralysis diplopia

ataxia nystagmus

dysmetria distortion or blurring of vision

dysphagia hemianopsia

vertigo photophobia

dizziness hyper or hypoesthesia

numbness hyper or hypoalgesia

aphasia hallucinations

amnesia confusion

altered mood depression

manic behavior belligerence

disorientation scotoma

severe headache (migraine-like) nausea

bladder disturbances loss of coordination

paresis in arms or legs vomiting

cardiovascular disturbances generalized malaise (unexplained fatigue)

syncope hypovolemic shock

hypotension hyperkinesias

dyskinesia pallor

cold sweat

There are several explanatory variables available in the HDSD: the planned time at

altitude, ascent rate, whether or not repetitive exercise was performed at altitude, details about

the exercise at altitude, the test altitude, and information on the denitrogenation procedure

(prebreathe) before ascent, just to list a few. Table II shows summary statistics for important

explanatory variables in the 258 tests. The mean, standard deviation, and range are from the

258 group-tests and not the 79,366 exposures from the tests. Since the retrospective data are

from group results, the probability model for serious DCS applies prospectively to groups of men

that perform similar prebreathe and decompression procedures. The variables quantify the extent

of denitrogenation before the exposure (P1N2), information on the transition time from site
5

pressure to the test altitude (ascent time, ascent rate), the test altitude (P2), the planned duration

of a test (Talt), and information on the exercise performed at P2 (exercise frequency, exercise

type). “Exercise frequency” is the number of min of planned exercise per hr of exposure.

“Exercise type” is the type of exercise performed during prebreathe and at P2, coded into eight

categories as follows:

• 0 is no structured exercise during seated denitrogenation or at P2

• EXI is no repetitive exercise during seated denitrogenation, movements confined to lower

body at P2

• EXII is no exercise during seated denitrogenation, movements confined to upper body at P2

• EX III is no exercise during seated denitrogenation, movements of whole body at P2

• EXIV is mild exercise while sitting during denitrogenation, movements confined to upper

body while in a chair at P2

• EXV is mild exercise while sitting, supine, or head-down during denitrogenation, movements

confined to upper body at P2

• EXVI is no exercise during supine or head-down denitrogenation, movements confined to

upper body at P2

• EXVII is no exercise while head-down or sitting during denitrogenation, movements

confined to upper body while in a chair or reclined at P2

Exercises IV through VII are complex in that exercise was or was not performed at site

pressure during the prebreathe, plus body position during the prebreathe and at P2 was a variable.

These data are a small subset of information, and any variability introduced into the outcome of

serious DCS is accepted. There were not enough data in these categories (172 exposures with

four cases of serious DCS) to justify expanding the model to account for the unique test

conditions. The Results section contains how this information was evaluated. Exercises I

through VII are coded as exercise = 1 when just the presence or absence of exercise at P2 was

evaluated.
6

TABLE II. SUMMARY OF 258 DECOMPRESSION TESTS

variable mean SD range

P2 (psia) 4.66 1.76 1.92 – 10.91

P1N2* (psia) 8.60 3.04 1.52 – 12.64

Talt (hr) 3.06 1.89 0.30 – 8.00

ascent time (hr) 0.156 0.140 0.017 – 0.750

ascent rate (psia / hr) 125.1 128.0 16.7 – 672.0

exercise frequency (min/hr) 14.4** 18.6 0 – 60

additional information

1 (yes) 0 (no) tests serious DCS

serious DCS cases 918 78,448 (1.15%) 73 918

exercise type

0 6,834 72,511 73 628

EXI 2,438 72,533** 80 242

EXII 794 75,907** 44 4

EXIII 3,430 78,551** 44 39

EXIV+ 7 79,338** 1 0

EXV+ 53 79,292** 5 2

EXVI+ 92 79,253** 8 1

EXVII+ 20 79,325** 2 1

exercise type plus no exercise = 79,345** 257** 917**

SD is standard deviation.

*P1N2 (t1/2 = 180 min) was computed using Eq. 1.

** includes one test with 21 exposures and one case of serious DCS did not document the type of exercise done

at P2, so the total exposures with information on exercise type is 79,345.

The symbol + identifies 172 exposures from 16 tests with a complex exercise profile.

Table III shows specific information about Group 1 tests, plus a summary of Group 2

tests. We discuss the data as two subsets because it is instructive later when the estimated

outcomes from the model are compared to the observed outcomes from Group 1 and Group 2.

Compared to Group 2 tests, Group 1 tests have limited prebreathe time, limited time at altitude,

and limited exercise at altitude. The ascent times and test altitudes are comparable between both

sets of data. The two combined subsets complement each other by providing for a wide range of

prebreathe times, exposure times, and exercise conditions while at altitude. Our conclusions are

limited because the use of a multivariable model with retrospective data does not allow us to

analyze the influence of all the possible variables from tests that came from different facilities at

different times.
7

TABLE III. SUMMARY OF 12 EXTENSIVE

DECOMPRESSION TESTS (GROUP 1 TESTS)

ref. expo. P1N2*

(psia)

P2

(psia)

Talt

(hr)

ascent time

(hr)

exercise

at P2

serious

cases

12 223 11.60 3.00 2.0 0.156 0 11

12 204 10.95 3.00 2.0 0.156 0 4

2 343 4.48 5.00 2.5 0.042 0 0

17 245 11.31 5.22 0.3 0.105 1 0

17 379 11.31 5.22 0.3 0.105 0 0

15 9,664 11.10 3.00 1.0 0.317 0 145

15 46,683 11.20 4.36 1.0 0.350 0 327

15 4,337 11.15 4.36 1.0 0.350 0 26

15 9,738 10.70 4.36 1.0 0.350 0 19

18 434 11.51 5.95 6.0 0.025 1 0

16 585 11.51 5.95 6.0 0.033 1 1

13 204 11.03 3.00 3.0 0.217 1 12

information about the remaining 246 tests (Group 2 tests)

ref.

“a” expo.

P1N2*

(psia)

P2

(psia)

Talt

(hr)

ascent time

(hr) “b” “c”

66 8,327 74% 374

mean 8.50 4.67 3.10 0.150

SD 3.05 1.78 1.88 0.140

range 1.57 – 12.64 1.9 – 10.9 0.3 – 8.0 0.02 – 0.75

*P1N2 (t1/2 = 180 min) was computed using Eq. 1

“a” 66 is the number of references for the 246 tests

“b” the percentage of 246 tests that included repetitive exercise at P2

“c” the number of serious DCS cases in the 246 tests

Denitrogenation and the 180-Minute Half-Time Compartment

The tissue N2 partial pressure (P1N2) is an important variable in any model about DCS.

Prebreathing 100% O2 or O2-enriched mixtures before a hypobaric decompression is an

effective and often-used technique to prevent DCS. Therefore, it is necessary to account for the

use of O2-enriched mixtures before decompression using Eq. 1. Equation 1 defines how P1N2 is

calculated; it approximates a more complex process of dissolved N2 kinetics in living tissue.

Following a step-change in N2 partial pressure in the breathing medium, such as during a switch
8

from ambient air to a mask connected to 100% O2, the N2 partial pressure that is reached in a

designated tissue compartment after a specific time is:

P1N2 = P0 + (Pa - P0) * (1 - e - κt ), Eq. 1

where P1N2 = the N2 partial pressure in the tissue after t min, P0 = initial N2 partial pressure in

the compartment, Pa = ambient N2 partial pressure in breathing medium, e = base of natural

logarithm, and t = time at the new Pa in minutes. The tissue rate constant κ is defined as 0.693 /

t1/2, where t1/2 is one of six tissue N2 partial pressure half-times: 120, 180, 240, 300, 360, or

420 min in this analysis. The initial, equilibrium N2 pressure (P0) in the tissue at sea level is

taken as 11.6 psia instead of an average alveolar N2 pressure of 11.0 psia. The use of dry-gas,

ambient N2 pressure as equilibrium tissue N2 pressure (P0), and as the N2 pressure in the

breathing mixture (Pa), makes the application of Eq. 1 simple.

Figure 1 shows a vertical and horizontal array of 258 circles, which represent a total of

79,366 exposures by men in altitude chambers, on a P2 vs. P1N2 plot. The area of each circle

represents the incidence of serious DCS symptoms in a test. The largest circle is 44.8%

incidence from a test with 29 exposures and the 193 smallest circles are tests with no cases of

serious DCS. Consider the vertical array of circles located between about 10.0 and 11.6 psia on

the x-axis. These circles represent results from an ascent to P2 without the benefit of significant

denitrogenation. Notice the area of the circles appears to increase as P2 decreases for a constant

P1N2, calculated using Eq. 1 with t1/2 = 180 min. Consider also the horizontal array of circles at

about 4.3 psia on the y-axis. These circles represent results from tests at about 4.3 psia, but

which experienced a wide range of denitrogenation. Notice the area of the circles also increases

as P1N2 increases with P2 constant at about 4.3 psia. There were only six tests (24 cases of

serious DCS in 261 exposures) in the region of the graph below 2.5 psia (41,500 ft) where mild

hypoxia is expected even when 100% O2 is delivered under positive pressure in the breathing

mask. Signs and symptoms of mild hypoxia could have been misdiagnosed as serious DCS, or

could have exacerbated some cases of serious DCS.

This figures does not identify the duration of each test or whether exercise was performed

during the test. These two variables also influence the likelihood of serious DCS, and partially

explain why serious DCS appears in regions where serious DCS might not be expected. Also,

small circles in the right corner could be from tests where the exposure time was short, or there

was no exercise, or both. Finally, the observed DCS incidence, and therefore the area of each

circle, is also influenced by the number of subjects in a test, since a larger sample size is

expected to provide a better estimate of the incidence. The multivariable risk function in the next

section accounts for more than the two variables seen in this two-dimensional figure.
9

Fig. 1. The circles are 258 tests on a P2 vs. P1N2 plot. The P1N2 for each test was calculated using

Eq. 1 with t1/2 = 180 min to account for denitrogenation before ascent to P2. The area of each

circle represents the incidence of serious DCS observed during the test. Most of the large circles

appear in the lower right corner where limited denitrogenation occurred before ascent and where

the test altitudes were between 2.0 and 5.0 psia.

Probability Function: Risk Function Model

We modify and parameterize a risk function published by Van Liew (18,19) for the

analysis presented here. The instantaneous risk (ri) is a function of time and explanatory

variables associated with serious DCS. The relationship between ri and time t may be very

simple (a constant, for example) or a more complex expression such as r te i

t = ∗ −β . The

particular risk function chosen for the present analysis is:

r [ ] P N

P

EXER t e i

t = ∗



 



 ∗+ ∗∗ − χ ε

α 1 β

2

1 2 *( ) Eq. 2

where α, β, χ, and ε are unknown parameters to be estimated from data, and P1N2 (psia), P2

(psia), EXER, and Talt (hr) are the four variables associated with this four-parameter continuous

model. Equation 2 combines both mechanistic and empirical components. The change in ri with

respect to time is suggested from observations on the rate at which DCS appears (3,5,18). We

believe the ratio of P1N2 to P2 to a power α links an evolved volume of gas to the perception of
10

pain better than the ratio alone, and better than the difference in pressure alone (5). Finally, the

contributions from the type, intensity, and duration of exercise while at altitude to the risk of

serious DCS are not known. Our simple approach is to estimate a “weight” term ε to account for

the contribution of any repetitive exercise while at altitude to the risk of serious DCS.

For a test of duration Talt, the integral of ri with respect to time gives the cumulative risk

(rc). That is,

∫ =

Talt

rc ri t dt

0

( ) . Eq. 3

Using ri given by Eq. 2 in Eq. 3, we obtain the following expression for the estimated

cumulative risk:

r [ ] P N

P

EXER

T e c alt

Talt

= ∗



 



 ∗+ ∗

−+ ∗ −

χ ε β

β

α β 1

2

1

1 1 2

2 * ( ) Eq. 4

In terms of rc, the probability of serious DCS sometime before the end of the test is:

P serious DCS e rc ( ) = − − 1 Eq. 5

where e r − c is P(no serious DCS). Notice that P(serious DCS) is zero if the cumulative risk is zero

and approaches one as the risk increases. From Eq. 5, it can be seen that rc = - ln[1 - P(serious

DCS)], where ln is natural log. Notice that rc is dimensionless. The derivative of rc with respect

to time is ri, so ri = d(- ln[1 - P(serious DCS)]) / dt, or the rate in a finite interval of time at which

serious DCS appears in the data set.

This analysis was limited because the specific time of serious DCS (failure time) reported

for each subject and the actual duration of some exposures that were shorter than the planned

duration were not available. Recall that Talt is the duration of the planned test. Serious DCS

occurred during the interval from the start of the test on arriving at P2 to the end of the planned

test. When serious DCS occurred, the subject was removed (locked out) from the chamber, and

the test was allowed to proceed, or the entire test was stopped, thus censoring the failure time for

those subjects who may have gone on to develop serious DCS. A subject with mild pain-only

symptoms may have been allowed to continue the test. However, a subject with intense painonly symptoms, but not serious DCS, would have been removed from the chamber. It is not

known if that subject would have progressed to a serious symptom. These complexities mean

that the model likely underestimates the true risk of serious DCS since an unidentified subset of

men without serious DCS were removed from the tests early for various reasons. These

unidentifiable cases were still assigned the Talt of the test and coded as “0” for not having
11

serious DCS. Those subjects with serious DCS were coded as “1”, and also assigned the Talt of

the test, no matter when the sign or symptom appeared.

Parameter Optimization and Goodness of Fit

The SYSTAT (ver. 5.03) Nonlin module (21) was used to estimate unknown parameters in the

model, with optimization employing the Quasi-Newton algorithm. The P(serious DCS) was

computed using Eq. 5 and iteratively adjusted using data to optimize the model parameters

through the likelihood function. Maximum likelihood optimization in our application entails

minimization of the summed positive log likelihood (LL) number, and the details are covered

elsewhere (2, 20, 21), and in Appendix B. The best-fit continuous model from this statistical

approach does not necessarily mean that there is a good fit of the model to the data. Goodness of

fit of the best-fit model provides information about how confident one can be in the estimate of

serious DCS.

One method to assess goodness of fit is to compare the LL numbers for three models: the null

model, the discontinuous model, and the best-fit continuous model, using the Likelihood Ratio

Test (LRT) (10). The LRT is used to compare two models that differ by at least one parameter.

It can determine if the best-fit continuous model is statistically better than the other two models:

the null and discontinuous (20). The test involves comparing the LLs of two models, the

restricted and unrestricted, fitted to the same data set. A restricted model can contain a single

constant, the null model. The null model is a constant-probability model based on the mean

serious DCS incidence of all the individuals in the data set. A large LL results with the null

model since no explanatory variables are used to “explain” the outcome. In the same data set, a

small LL from a discontinuous, or saturated, model is defined as the best, or perfect LL based on

the definition that the DCS incidence in each group result is the true DCS incidence. The

discontinuous model has as many degrees of freedom as there are tests, 258 in this case. The

best-fit continuous model based on theory would not perfectly predict the observed DCS

incidence in all tests, so the summed LL would always exceed the summed LL for the

discontinuous model. Equation 6 calculates the LL for the discontinuous model:

n

LL = Σ ln [(1 - ci) (no serious dcsi

) * ( ci ) (serious dcsi)], Eq.6

i = 1

where "n" is the number of groups, ln is natural log, ci is the fraction of subjects with serious

DCS in group "i", (no serious dcsi) is the number of subjects without serious DCS in group "i",

and (serious dcsi) is the number of subjects with serious DCS in group "i".

The restricted model always has fewer degrees of freedom than the unrestricted model. The idea

is to test if the addition of one or more parameters to the unrestricted model is better than the null
12

model by testing the hypothesis that the additional parameter has a zero value. The value of the

Likelihood Ratio statistic is calculated as two times the difference in the LL between the

unrestricted and restricted models. The statistic follows an approximate χ2 distribution with

degrees of freedom equal to the difference in the degrees of freedom between the unrestricted

and restricted models. The value of the statistic and the degrees of freedom are entered into a χ2

table to find the corresponding p-value. A p-value < 0.05 indicates that the null hypothesis

should be rejected, i.e., that the additional parameter is not zero. In addition to determining if the

best-fit continuous model is statistically superior to the null or discontinuous models with the

LRT, it is possible to approximate a goodness of fit of the continuous model by comparing the

LL of the model to the LLs of the null and discontinuous models. The percent improvement over

the null model is calculated as: [(LL null model - LL continuous model) / (LL null model - LL

discontinuous model)].

Results

Best-Fit Model

Table IV shows the four parameters, parameter estimates, standard errors, T-ratios, and

correlation matrix for the best-fit model selected from a list of several competing models (not

shown). All four fitted parameters were significant enough to remain in the model. The best-fit

model accords with observations in that limited prebreathe before ascent, or ascent to a high

altitude, or a lengthy exposure time, or exercise at altitude results in a greater risk of serious

DCS. Six half-times from 120 to 420 min at 60-min intervals were evaluated once a promising

model was developed. The LL for the best model improved by eight units on going from a 360-

to a 180-min half-time compartment. A faster half-time compartment amplifies small differences

in prebreathe times, thus indicating that prebreathe time is an important explanatory variable.

Modifying the model with inclusion of information on specific exercise type and ascent

rate did not improve the fit; the additional parameters were not statistically significant. Also,

fitting several models without the data from 16 tests with complex exercise profiles (172

exposures with four cases of serious DCS (see Table II) did not improve the overall goodness of

fit. There was no systematic change in the parameter estimates or the standard error of the

estimates in the best-fit model. The largest change was a 6% decrease in the value of the scale

term χ. The probability estimates for the model based on 79,194 exposures for various

simulations (not shown) were within the 95% confidence intervals of the best-fit model based on

79,366 exposures.
13

TABLE IV. PARAMETER ESTIMATES OF

FOUR-PARAMETER MODEL

Parameter Estimate Asymptotic SE T-ratio

χ (scale) 0.000613 0.000133 4.60

β (rate) 1.794 0.219 8.19

α (power) 4.267 0.142 30.0

ε (weight) 4.752 0.548 8.67

SE is standard error, T - ratio is the ratio of the estimate to the SE of the estimate, and an absolute

value > 1.96 indicates that the p - value for the estimate is < 0.05 for the test that the true parameter

value is zero.

ASYMPTOTIC CORRELATION MATRIX

χβαε

χ 1.000

β 0.660 1.000

α -0.781 -0.085 1.000

ε 0.408 0.663 -0.121 1.000

Other candidate models with various combinations of the parameters and the four

explanatory variables in the context of Eq. 2 were tried. Expressing N2 supersaturation as a

difference in pressure [P1N2(t1/2) - P2] was not as good as when supersaturation was expressed

as a ratio of pressures [P1N2(t1/2) / P2]. Adding a power term α to the pressure ratio

dramatically improved the model (LL = 4273 with α compared to 4556 without α), as was the

case in a previous effort (5). The addition of the scale parameter χ was statistically justified.

The LL was 4314 without the parameter and improved by 41 units when included in the model

(p < 0.001 from the LRT). Also, the correlation matrix in Table IV shows that this parameter is

not highly correlated with the three other parameters, another indication that it is not redundant

and contributed to the description of the data.

The LL number for the four-parameter continuous model was 4273, compared to 5006 for

the null model, and 1191 for the discontinuous model. The continuous model was statistically

better than the null model, but not as good as the discontinuous model, in both cases p < 0.0001

from the LRT. The null model estimated the best risk of serious DCS for any exposure to be

0.0115, the mean incidence in the data set, with narrow 95% confidence interval of 0.0108 to

0.0123. The improvement of the continuous model over the null model was about 19%.

Two simpler expressions for ri were also evaluated, ri = γ, a constant, and ri = t. For

ri = γ, integration with respect to t gives rc = γ Talt, which is a straight line passing through the
14

origin with slope = γ. This rc with the three parameters (χ, α, ε) gave a LL of 4306. For ri = t, rc

= Talt 2 / 2, so there was no additional term to parameterize. This rc, also with the three

parameters, gave a LL of 4478. Neither model was statistically superior to the ri defined in Eq. 2

(LL = 4273), which also included a fourth fitted parameter, β. We also evaluated the standard

logistic regression model in the Logit module of SYSTAT (21). Given the same four variables

and four parameters, the LL was worse at 4333 (results not shown). We interpret this as

evidence that our efforts to understand serious DCS in mechanistic terms have advantage over a

non-mechanistic approach. We conclude that these data required a risk function that first

increases and then decreases in time, just as seen in two other models that describe the P(DCS)

(3) and the P(forced descent DCS) (18,19).

Threshold for Serious DCS

The model describes the data and the data indicate that even at low decompression stress (low

values of rc), there is a risk of serious DCS (Appendix C). Figure 2 shows a comparison of the

observed group incidence from 257 tests with the computed rc from Eq. 4 to facilitate a

discussion about a “threshold” for serious DCS over the entire range of the data. A threshold

means that a minimum decompression stress must be exceeded before an outcome is observed.

One data point at rc = 0.588, with an observed incidence of serious DCS of 27% from a test with

29 men, is excluded from Fig. 2 so that data from the remaining 257 tests could be clearly

displayed. Since rc is a function of four variables, it is possible to have a high or low value

depending on the magnitude of the variables. Notice that the calculated P(serious DCS), the

solid line from Eq. 5, is nearly linear, and passes through the origin. But it is not possible on

Fig. 2 to see information at very low values of rc, so the examination of threshold is continued by

evaluating data at very low rc.

Figure 3 shows the observed group incidence of serious DCS over a range of very low rc

values. There were just six cases of serious DCS in 3,687 exposures (109 tests) with rc ≤ 0.0045.

The lowest value of rc with a case of serious DCS was 0.00145, and was from a test with ten

males with a single case of serious DCS. There were 2,178 exposures in 56 tests below this

value of rc where no case was reported. A 4-hr prebreathe followed by a 6-hr exposure to

4.3 psia that does not include exercise provides an rc = 0.000254, well below the value of rc

where a case of serious DCS was reported. If exercise is included in the exposure, then rc =

0.00146. Finally, in Group 1 tests, the lowest value of rc was 0.00469 in 9,738 exposures

associated with 19 cases of serious DCS. Even though the model extrapolates P(serious DCS) to

rc = 0 (curve on Fig. 3), there is an interval between zero and 0.00145 where no case has been

reported.
15

Fig. 2. Observed group incidence of serious DCS in 257 tests versus the computed rc from Eq. 4.

Notice at rc < 0.07 that there is a wide range of incidence. Due to the range of the x-axis, a

“threshold” interval for serious DCS cannot be seen. The solid line is the calculated P(serious

DCS) using Eq. 5, which is approximately linear because 1 – e –r

c ≈ rc for small values of rc.

Fig. 3. Observed group incidence of serious DCS in 109 tests at very low rc versus the computed rc

from Eq. 4. In the interval rc ≤ 0.0045 there were only six cases of serious DCS in 3,687 exposures

from 109 tests, and no cases in the interval rc ≤ 0.00145. This is an interval where the combinations of

prebreathe and decompression procedures can be adjusted such that no case of serious DCS is expected.
16

Model Simulations Relevant to EVA Astronauts

Figures 4, 5, 6, 7, and 8 pertain to hypothetical scenarios where the values of the explanatory

variables are in the range of the data, and in a range of interest to astronauts who perform EVAs.

The scenarios reflect lengthy prebreathes, with ascent to 4.3 psia, exposure times up to 6 hr (the

length of a typical EVA), and with or without repetitive exercise being performed while at

4.3 psia. Figure 4 shows ri changing through time at altitude for two prebreathes (3 – 4 hr), a test

altitude of 4.3 psia, and with or without repetitive exercise at altitude. The rate at which serious

cases of DCS occur in these simulations as a function of time at altitude approaches zero after

about 4 hr. Figure 5 shows rc as it increases through time at altitude for the same conditions as

in Fig. 4. The accumulation of additional risk is minimal after about 3 hr at altitude.

Fig. 4. Results of simulations to demonstrate changes in ri from Eq. 2. The rise and fall of ri over

a short interval of time is also observed in other categories of DCS outcomes.
17

Fig. 5. Results of simulations to demonstrate changes in rc from Eq. 4. There is a limited

accumulation of additional risk after about 3 hr.

Benefits From Even Limited Prebreathe

Figure 6 shows the P(serious DCS) from Eq. 5 as a function of time at altitude in scenarios that

include exercise at 4.3 psia with no prebreathe before ascent, or prebreathes of 0.5, 1.0, 2.0, or

3.0 hr. Notice the significant reduction in the P(serious DCS) with a limited prebreathe of 0.5 hr

of O2 compared to the case with no prebreathe. There is about a 40% reduction in risk at the

sixth hr after a 0.5-hr prebreathe compared to no prebreathe [(0.073 - 0.045 ) / 0.073 = 0.4], and

about a 60% reduction in risk after a 1-hr prebreathe [(0.073 - 0.028 / 0.073 = 0.6]. Figure 7

shows the P(serious DCS) as a function of time at altitude in simulations without exercise at

4.3 psia with no prebreathe before ascent, or prebreathes of 0.5, 1.0, 2.0, or 3.0 hr. The y-axis

scale is expanded compared to Fig. 6 to clearly show the lower risk when exercise is not

performed at altitude. Notice that there is about a fivefold decrease in the P(serious DCS) for

each case in this figure compared to the cases in Fig. 6. It is important to prebreathe 100% O2, at

least for 30 min, before ascent and to limit exercise while at altitude to avoid serious DCS.
18

Fig. 6. The contribution of prebreathe duration (indicated by labels) toward reducing risk in

astronauts who exercise at P2. The probability curves are specific to an exposure to 4.3 psia. The

ratio of P1N2 to P2 for the 180-min half-time compartment with no prebreathe before ascent is

2.69, and decreases by half to 1.34 after a 3-hr prebreathe.

Fig. 7. The contribution of prebreathe duration (indicated by labels) and inactivity toward

reducing risk. The shapes, but not the magnitudes, of the probability curves are the same as in Fig.

5 since the contribution of exercise toward serious DCS is a constant in the model. Note that the

y-axis scale is twice as large as in that of Fig. 6.
19

Best Estimate for Serious DCS in EVA Astronauts

Figure 8 shows the P(serious DCS) as a function of time at altitude after a 4-hr prebreathe in

scenarios with and without exercise at 4.3 psia. Notice in this figure, as well as in Figs. 6 and 7,

that the P(serious DCS) increases rapidly over the first 3 hr, and then increases only slightly for

the remainder of the altitude exposure. The model reflects the observation in the data that most

signs and symptoms of serious DCS occur early in the altitude exposure, a period in which to be

vigilant. The examples shown in Figs. 4 - 8 are specific for a prebreathe procedure available to

astronauts who perform EVAs. Unfortunately, astronauts’ actual exercise during EVA and the

denitrogenation associated with adaptation to microgravity is not well understood. Therefore,

our best estimate of risk for serious DCS is between the extremes of the 95% confidence

intervals at the sixth hr of altitude exposure, between 0.00016 (0.016%) and 0.00196 (0.196%).

There has not been a case of serious DCS (or any DCS) in the previous 100 Shuttle EVAs.

Using the binomial distribution, we can say that the one-sided 95% upper bound on the risk of

serious DCS is no greater than 0.03, or about 15 times greater than our worst-case estimate of

0.00196 for a “typical” Shuttle EVA. By the same logic, it would require 1660 EVAs without

serious DCS to have confidence in our worst-case estimate.

Fig. 8. A simulation to show the P(serious DCS) specific for conditions that astronauts may

encounter during EVAs from the ISS. The wide confidence intervals for estimates that include

exercise reflect the limited understanding of how exercise influences the likelihood of serious DCS,

and also the limited amount of data that included information about exercise. The 95% confidence

intervals were calculated based on a propagation of errors formula (11). The intervals provide a

defined range for the estimate, but do not establish the accuracy of the estimate.
20

Qualitative Assessment of Goodness of Fit

Equation 4 is the expression for decompression dose that was the best-fit of various

candidate models regardless of the strength of the relationship between the dependent and

independent variables. Goodness of fit, after obtaining the model with the best fit, is a measure

or impression of agreement between the estimated outcome and the observed outcome. Without

a goodness-of-fit assessment it is possible to be unjustifiably confident in an estimate of

P(serious DCS) as a function of the explanatory variables. Table V shows a comparison between

the observed and estimated cases of serious DCS from Group 1 tests. In about half of the tests

the model performed well. But in several large tests, the model either over- or underestimated

the observed cases. Overall, the model overestimated 84 out of 544 observed cases of serious

DCS.

TABLE V: COMPARISON OF OBSERVED AND ESTIMATED SERIOUS DCS

IN 12 TESTS (GROUP 1 TESTS)

Ref. Exp. serious cases

observed

serious cases

estimated estimated - observed

12 223 11 11.5 -0.5

12 204 4 8.3 4.3

2 343 0 0.04 0.04

17 245 0 0.7 0.7

17 379 0 0.2 0.2

15 9,664 145 205 60

15 46,683 327 266 -61

15 4,337 26 24 -2

15 9,738 19 45 26

18 434 0 8.0 8

16 585 0 10 10

13 204 12 49 37

totals 71,039 544 628 overestimated 84 cases

Figures 9 and 10 graphically show how well Eq. 5 described the data. Figure 9 shows the

observed incidence for Group 2 tests compared to the estimated incidence from the model. The

area of each circle is proportional to the number of subjects in the test. The smallest circle

indicates a test with two subjects while the largest indicates a test with 195 subjects. There were

374 cases of serious DCS in 8,327 exposures in these 246 tests. Tests below the identity line

were underestimated, and those above the line were overestimated. Although difficult to see due
21

to the scales used, tests along a vertical line at zero observed group incidence may at first seem to

indicate that the model severely overestimates the risk of serious DCS in these tests. However,

tests along the horizontal line at zero observed group incidence on Fig. 2 with rc < 0.07 are

associated with other tests in that range that show group incidence up to 33%. The estimated risk

from the model does balance the variability seen in these data at low rc, so the estimated

incidence seen along the y-axis is reasonable even when the observed incidence is zero for

several tests. The visual goodness of fit based on group incidence is limited because the

precision of group incidence is greatly influenced by the number of subjects in a group.

Fig. 9. A comparison of the estimated to the observed serious DCS in Group 2 tests. The area of a

circle is proportional to the number of men in a test. At this scale, the model appears to underestimate

the observed incidence as evident by the scatter of tests below the identity line. Looking at the data

from zero to 10% on an expanded scale, the model appears to overestimate the observed incidence.

The model does not systematically over- or underestimate the observed incidence over the entire

range of the data. The cluster of circles near the origin represents 191 tests with serious DCS < 0.03.

Figure 10 shows the observed incidence compared to estimated incidence for Group 1

tests. Data from tests with large number of men contribute more to the model, so larger circles

are located nearer to the identity line in Fig. 10 compared to Fig. 9. There were 544 cases of

serious DCS in 71,039 exposures in these 12 tests. Except for one test far above the identity line,

the model reasonably estimated the observed group incidence. This is not surprising since the

parameters for the model are influenced by the large number of exposures contained in these

tests. The position of all the circles on Figs. 9 and 10 gives an impression of a reasonable fit of

Eq. 5, given the simple formulation of the model, the realization that random variability in the
22

outcome will not be completely accounted for, and the limitation of these figures to provide an

assessment of goodness of fit.

Fig. 10. A comparison of the estimated to the observed serious DCS in Group 1 tests. The area of

a circle is proportional to the number of men in a test, but not the same proportionality as in Fig. 9.

Observed and estimated appear in better agreement than in Fig. 9, which is expected due to the

larger sample size and greater influence on the model parameters.

We continue to evaluate goodness of fit by expanding the observed group incidence along

the y-axis from zero to 5%. Figure 11 shows positive estimated incidence for tests along a vertical

line at zero observed group incidence. This indicates that the model overestimates the risk of

serious DCS in these tests. However, the tests along a horizontal line of zero observed group

incidence on Fig. 2 with rc < 0.07 are associated with other tests in that range that show group

incidence up to about 33%. Figure 3 shows more clearly the P(serious DCS) through a region

where the group incidence was mostly zero, at very low rc ≤ 0.0045. The estimated risk from the

model does balance the variability seen in the data at low rc. The overestimation at very low rc is

partially due to fitting the model through a wide range of rc so that extrapolating the model to very

low rc is associated with some risk, even in a region where no cases were observed. This explains

the appearance of the circles along the y-axis at a zero observed group incidence.
23

Fig. 11. The x- and y-axis are expanded to evaluate the goodness of fit in those tests where the

observed incidence of serious DCS in 206 tests was ≤ 0.05. Three tests are not shown: n = 12 with

an estimated incidence of 12.3%, but an observed incidence of zero percent; n = 14 with an

estimated incidence of 6.1%, but an observed incidence of zero percent; and n = 21 with an

estimated incidence of 11.7%, but an observed incidence of 4.8%.

Quantitative Assessment of Goodness of Fit

A computational method, as opposed to the previous visual method, is also available to

assess goodness of fit. Equation 7 is the One-Sample χ2 Test. The test compares an observed

distribution to a theoretical one. The null hypothesis is that there is no difference between the

distributions; any difference observed is simply due to chance. In the case where estimated

always equals observed, the summed χ2 is zero.

k

χ2 = ∑ Oi – Ei  2 / Ei Eq. 7

 i = 1

where Oi = observed number in ith bin, Ei = expected number in ith bin, and k = number of bins.

We accept the null hypothesis if the p-value is ≥ 0.05 for the computed χ2, and n – 4 is the

degrees of freedom, where n = 10 bins that the 258 tests were distributed into. The four in the

calculation of the degrees of freedom is because there are four parameters estimated in the model.

The data were combined into ten bins such that the estimated cases at very low values of rc were

about two. To reject the null hypothesis at p < 0.05 would require a computed χ2 be < 12.59,
24

based on six degrees of freedom (from a χ2 table). The summed χ2 from Table VI was 118.5,

with a resulting p-value <0.00001. Three bins, numbers 3, 6, and 8, show significant

overestimation of serious DCS, while bins 4 and 9 show significant underestimation. Based on

this analysis, we reject the null hypothesis, and conclude that the model does not account for all

the variability observed in the outcome of serious DCS.

TABLE VI. RESULTS FROM ONE-SAMPLE χ2 TEST

bin tests exposures observed estimated χ2

1 1 – 70 2,564 4 2.03 1.89

2 71 - 91 696 0 1.85 0.85

3 92 - 112 10,197 21 47.46 14.75

4 113 - 133 51,586 354 293.14 12.63

5 134 - 154 525 2 4.61 1.47

6 155 - 175 2,106 2 34.73 30.85

7 176 - 196 777 28 16.77 7.52

8 197 - 217 8,485 163 229.36 19.20

9 218 - 238 1,349 111 68.03 27.14

10 239 - 258 1,081 233 217 1.18

totals 258 79,366 918 915 118.51

Model Validation

A final method to assess goodness of fit is to evaluate, or validate, Eq. 5 with data not

used to initially parameterize the model. Forty tests that provided 723 exposures are available

that did not meet the initial selection criteria in that data on ascent rate was not available, and

Talt was not limited to 8 hr. The mean and standard deviation for variables in the 40 tests are:

P2 = 5.05 ± 1.83 psia, Talt = 4.3 ± 2.2 hr, TR based on 180 min t1/2 = 1.33 ± 0.69, and exercise

was present in 67% of the tests. Thirty-eight of the tests (637 exposures) had no case of serious

DCS. The P(serious DCS) was computed for each test with Eq. 5, and the product of the

probability and number of subjects in each test gives the estimated number of cases. The model

estimated 2.5 cases in the 637 exposures where there were no observed cases. One test with

56 exposures had two cases of serious DCS, and the model estimated 14.8. The observed

incidence in this test was 3.6% and the estimated was 26.4%. This test was particularly stressful

in that an ascent to 3.0 psia was made with no prebreathe, and exercise was done over a 2-hr

exposure. A second test with 30 exposures had a single case, and the model estimated 2.3 cases.

This test was the same as above, except the exposure was 0.5 hr. Figure 12 shows the observed

incidence compared to estimated incidence in the 40 tests. The model in a separate data set
25

overestimates the observations from stressful decompressions, but performed reasonably well

with decompressions that provided some protection from DCS.

Fig. 12. Observed versus estimated incidence based on 40 validation tests not used to parameterize

the probability model.

Discussion

Estimating any low probability event is a challenge. One advantage here is that cases of

serious DCS were not likely missed compared to pain-only outcomes. A bias not to report a

pain-only symptom is a constant concern in training, and even research settings. Subjects, often

pilots and other aircrew in training, may have been reluctant, for fear of disqualification, to report

mild symptoms during their training. Also, different investigators undoubtedly had different

criteria for what qualified as a bonafide case of DCS, but a case of serious DCS would not likely

be missed.

On the whole, Eq. 5 accounted for the observed group incidence, with 915 cases estimated

and 918 observed in the complete data set. But there are notable cases where the model

underestimated the risk. For example, there were three large circles below the identity line on

Fig. 8 where the observed group incidence was between about 33% and 40%, but the estimated

incidence was about 20%. The model often estimated very low incidence in tests with no cases

of serious DCS, both in data used to fit the model and data used to validate the model. However,

the model often overestimated the number of cases in those tests where serious DCS was
26

observed. We regard this as a limitation of the model since we cannot assume that the

overestimation was due to a bias not to report a serious symptom. Clearly there is room for

improvement, both in the model and the addition of other important explanatory variables, which

are not available to us.

The addition of ascent rate as an explanatory variable did not improve the model, and yet

this was expected to be important. Since tests with "explosive decompressions" were excluded

from the HDSD, it may be that the range of remaining ascent rates was not great enough for this

variable to make a significant contribution to the model, as it was in another model (18).

Another limitation of the model is that it only applies to men. Using the model to estimate the

risk for women may not be valid because this assumes that men and women respond equally to a

stressful decompression, which has not been established. We also assume the contribution of any

exercise toward the risk of serious DCS is constant regardless of the combinations of other

variables in the model, and this is certainly not true. Finally, including information about the

frequency of exercise and eight classifications of the type of exercise did not improve the model.

Limitations of this analysis are the lack of additional information about the individuals in the

test, the absence of the failure time when the serious DCS symptom first appeared, the censoring

of failure time in some tests that ended prematurely for other reasons, and our simple probability

model. A model based only on four variables and fitted to retrospective data will not accurately

estimate the risk of serious DCS for all possible hypobaric decompressions, including decompressions

in astronauts adapted to microgravity. It is likely that our simple model based on results from

men in altitude chambers would apply to similar men doing similar tasks in future altitude

exposures, but we are less confident that it will apply to men and women during EVA. However,

combining a few important variables into an abstraction of the true decompression dose that is

then statistically optimized to a DCS response is a practical means to estimate the risk of serious DCS.

Our motivations to understand the variables associated with serious DCS were to quantify

the risk from previous EVAs and then, if necessary, to develop new procedures to prevent it

during future EVAs from the ISS. At no time in the past have EVAs had such a significant role

in the success of a program as they will have with the ISS construction. The increased number of

EVAs increases the likelihood of a serious case of DCS. Knowing how different explanatory

variables reduce the risk of serious DCS can be exploited as prebreathe procedures are

developed. Figure 3 showed an interval at rc ≤ 0.00145 where no serious DCS was ever

reported. Future denitrogenation and decompression procedures for ISS should place EVA

astronauts within this interval. However, the influence on the incidence of serious DCS from

variables involved in adapting to and working within a space suit in microgravity are unknown.

Changes in body fluid volumes, distributions, and resulting pressures within the circulatory

system in space may influence the efficiency of denitrogenation, or the likelihood to form

bubbles in the tissues and blood. For example, inactivity of the lower body before and during

exposures in hypobaric chambers, called adynamia, has been shown to reduce the incidence of
27

DCS and venous gas emboli returning to the lungs (6,14). If this also applies to astronauts

during EVA, then an important variable to reduce risk is missing from the model that would

make the model more applicable to astronauts.

There is another practical aspect to knowing the risk of serious DCS for astronauts. The

cost in terms of materials and training to provide for hyperbaric treatment capability on the ISS is

not trivial. If there were no risk of DCS, then there would be no reason to provide an expensive

treatment capability. This was the case during the Skylab program where 70% O2 at a total

pressure of 5.0 psia was breathed while in the space station. The engineering of the life support

system assured that there was no risk of DCS since there was no N2 supersaturation in the tissues

during EVAs in the 3.75-psia space suit. Supersaturation defines a condition where the sum of

all gas tensions (pressure) in a tissue exceeds the ambient pressure. Since DCS is not

“engineered” out of the current U.S. and Russian space station programs, there is a finite risk of a

serious case of DCS even when prebreathe procedures are accepted as safe. The difficult issue is

to decide how much risk of serious DCS is acceptable to not require a hyperbaric treatment

capability given that other less aggressive but still effective treatment options now exist. An

option on the ISS and Mir does include returning the injured crewman to earth for a hyperbaric

treatment, which would not be an option for a Mars mission.

In conclusion, Eq. 5 serves as a guide to quantify how manipulation of four variables before and

after a depressurization can change the P(serious DCS) so that an acceptable level of risk is

achieved. The estimate of risk applies to a group, not an individual, since there was no

information about individuals in the model. Although we might be confident in a low estimate

of risk in astronauts, it is not yet possible to identify which astronaut would be at greatest risk.

Our worst-case estimate of serious DCS is 0.0019 (0.19%) for astronauts with the equivalent of a

4-hr prebreathe. This corresponds to a condition in which one case was reported in 2,498

exposures from 65 tests. Is this risk acceptable? Whereas it might be reasonable to accept the

risk of a “pain-only” symptom (Type I DCS) under conditions where immediate treatment is

available, it is unlikely that anyone would accept, or allow, a significant risk of serious DCS,

regardless of the treatment capability. What defines a significant or acceptable risk of serious

DCS is debatable. It depends on many factors such as the importance of success for a particular

EVA, the availability of DCS treatment, and the programmatic impact to the National

Aeronautics and Space Administration in the event of a serious case of DCS during an EVA.
28

References

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2. Beard S, Allen TH, et al. Comparison of helium and nitrogen in production of bends in simulated

orbital flights. Aerospace Med 1967; 38:331-37.

3. Conkin J, Kumar KV, Powell MR, Foster PP, Waligora JM. A probabilistic model of hypobaric

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Aviation Medicine Report 458. San Antonio: Randolph Field, 1944; pp. 1-46.

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13. Motley HL, Chinn HI, Odell FA. Studies on bends. J Aviat Med 1945; 16:210-34.

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in simulated microgravity. NASA Technical Memorandum 104762. Houston: Johnson Space

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15. Sedov AV, Mazin AN, et al. Probability of altitude decompression disorders when breathing

oxygen containing human waste gases. Kosmicheskaya Biologiya I Aviakosmicheskaya

Meditsina 1980; 14:36-39. USA Translation In: Space Biology and Aerospace Med 1980; 14:49-

53.

16. Smedal HA, Brown EB, et al. Incidence of bends pain in a short exposure to simulated altitudes of

26,000, 28,000, and 30,000 feet. J Aviat Med 1946; 17:67-70.
29

17. Vakar MI, Mazin AN, et al. Relationship between onset of altitude-decompression disorders in man

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30
31

Appendix A: Sources of Data Used in

Analysis of Serious DCS

====================================================================

1. Adams JD, Dixon GA, Olson RM, et al. Preventing of bends during space shuttle EVAs using

staged decompression. 1981 Preprints of the Aerospace Medical Association Scientific Meeting,

55-6, 1981. (AD144*)

2. Adams JD, Olson GM, Dixon GA. Use of the doppler precordial bubble detector in altitude

decompressions. Preprints of the 1981 Annual Scientific Meeting of the Aerospace Medical

Association, 260-61, San Antonio, Tx, 1981. (AD150)

3. Allen TH, Maio DA, Bancroft RW. Body fat, denitrogenation and decompression sickness in

men exercising after abrupt exposure to altitude. Aerospace Med 1971; 42:518-24. (NW130)

4. Allen TH, Maio DA, Beard SE, Bancroft RW. Space-cabin and suit pressures for avoidance of

decompression sickness and avoidance of decompression sickness and alleviation of fire hazard. J

Appl Physiol 1969; 27:13-17. (AD611)

5. Anthony RA, Clarke RW, Liberman A, et al. Temperature and decompression sickness. CAM

Report No. 136, 1943. (AD1430)

6. Anthony RA, Clarke RW, Liberman A, et al. Effects of local compression, impairment of

venous return, and arterial tourniquet upon the intensity of established "bends" pain. CAM Report

No. 143, 1943. (AD1431*)

7. Balldin UI, Borgstrom P. Intracardial bubbles during decompression to altitude in relation to

decompression sickness in man. Aviat Space Environ Med 1976; 47:113-16. (AD237*)

8. Barer AS, Golovkin LG, et al. Probability of casson disease while wearing a space suit when

exiting from a spacecraft with an atmosphere close to that of earth. Kosmicheskaya Biologiya I

Aviakosmicheskaya Meditsina 1979; 13:37-42. USA Translation In: Space Biology and Aerospace

Med 1979; 13:53-59. (AD817)

9. Barer AS, Vakar MI, et al. Probability of casson disease after pressure drop from 840 to 308

mmHg. Kosmicheskaya Biologiya I Aviakosmicheskaya Meditsina 1982; 16:26-28. USA

Translation In: Space Biology and Aerospace Med 1982; 16:34-37. (AD818*)

10. Bateman JB. Susceptibility to decompression sickness: The effect of prolonged inhalation of

certain nitrogen-oxygen mixtures compared with those of exposure to pure oxygen. CAM Report

364, NRC, 1944. (AD47)

11. Beard S, Allen TH, et al. Comparison of helium and nitrogen in production of bends in

simulated orbital flights. Aerospace Med 1967; 38:331-37. (AD238)
32

12. Behnke AR. The value of preliminary oxygen inhalation for the prevention of decompression

sickness during high altitude flight. National Research Council, Office of Scientific Research and

Development. Report #114, 1942. (AD63*)

13. Bridge EV, Henry FM, et al. Nature and incidence of symptoms during and after artificial

decompression to 38,000 feet for ninety minutes with exercise during exposure. J Aviat Med 1944;

15:1-12. (AD64)

14. Bridge EV, Henry FM, Williams OL, et al. Chokes: A respiratory manifestation of

aeroembolism in high altitude flying. Ann Inter Med 1945; 22:398-407. (AD1318)

15. Cheetham RW. Incidence of decompression sickness in individuals tested in a decompression

chamber situated at 4,700 feet. J Aviat Med 1947; 18:279-88. (AD1701)

16. Chernyakov IN, Glazkova VA, et al. Prevention of decompression disease applicable to

conditions of multiple emergence into space. Kosmicheskaya Biologiya I Aviakosmicheskaya

Meditsina 1976; 10:23-26. USA Translation In: Space Biology and Aerospace Med 1976; 10:33-

38. (AD83)

17. Conkin J, Dierlam JJ. The impact of exercise and other factors on the incidence of venous gas

emboli and decompression sickness in bends test 1,2, and 3. Houston: Johnson Space Center,

Technology Inc., Contract NASA-16880, Project 0211-91, 1984. (AD91*)

18. Conkin J, Edwards BF, Waligora JM, Horrigan DJ Jr. Empirical models for use in designing

decompression procedures for space operations. Houston: Johnson Space Center, NASA Technical

Memorandum 100456, 1987. (1*)

19. Conkin J, Edwards BF, Waligora JM, Stanford J Jr, Gilbert JH III, Horrigan DJ Jr. Updating

empirical models that predict the incidence of aviator decompression sickness and venous gas

emboli for shuttle and space station extravehicular operations. Houston: Johnson Space Center,

NASA Technical Memorandum 100456 Update, 1990. (ADNEW*)

20. Cooke JP. Interruption of denitrogenation by air-breathing. USAF School of Aerospace

Medicine, Brooks AFB. Under NASA-MSC Contract T-82170, 1975. (NW119*)

21. Cooke JP, Bollinger RR, Richardson B. Prevention of decompression sickness during a

simulated space docking mission. Aviat Space Environ Med 1975; 46:930-33. (AD616*)

22. Cooke JP, Robertson WG. Decompression sickness in simulated Apollo-Soyuz space

missions. Aerospace Med 1974; 45:297-300. (AD118*)

23. Damato MJ, Highly FM, et al. Rapid decompression hazard after prolonged exposure to 50

percent oxygen-50 percent nitrogen atmosphere. Aerospace Med 1963; 34:1037-40. (AD612)

24. Degner EA, Ikels KG, Allen TH. Dissolved nitrogen and bends in oxygen-nitrogen mixtures

during exercise at decreased pressure. Aerospace Med 1965; 36:418-25. (AD116*)
33

25. Dixon GA, Adams JD, Olson RM, Fitzpatrick EL. Validation of additional prebreathing times

for air interruption in the Shuttle EVA prebreathing profile. 1980 Preprints of the Aerospace

Medical Association Scientific Meeting, Anaheim, Ca., 16-17, 1980. (AD61*)

26. Dixon GA, Adams JD, Harvey WT. Decompression sickness and intravenous bubble

formation using a 7.8 psia simulated pressure-suit environment. Aviat Space Environ Med 1986;

57:223-228. (AD126*)

27. Dixon GA, Krutz RW. Evaluation of 9.5 psia as a suit pressure for prolonged extravehicular

activity. 23rd Annual SAFE Symposium Proceedings, 122-23, 1985. (AD431*)

28. Eatock BC, Gray GW, Ford GS. Evaluation with doppler ultrasonic bubble detection of

standard Canadian forces aeromedical training altitude profiles. Canadian Forces School of

Aeromedical Training. DCIEM Technical Communication No. 83-C-07, Downsview, Ontario,

1983. (AD159*)

29. Ferris EB, Webb JP, Engel G, Brown EW. A comparative study of decompression sickness

under varied conditions of exercise, altitude, and denitrogenation. CAM Report No. 363, 1944.

(AD1438*)

30. Ferris EB, Webb JP, Ryer HW, Engel GL, Romano J, Blakenhorn MA. The protective value

of preflight oxygen inhalation at rest against decompression sickness. Washington D.C.: NRC

Comm. on Aviation Med., Report No. 132, 1943. (AD73*)

31. Ferris EB, Webb JP, Ryer HW, Engel GL, Romano J, Blakenhorn MA. The influence of

physical activity and physical relaxation on susceptibility to decompression sickness. Washington

D.C.: NRC Comm. on Aviation Med., Report No. 126, 1943. (AD72*)

32. Gray JS. Present status of the problem of decompression sickness. The Army Air Force

School of Aviation Medicine, Randolph Field, Texas. Report #458, pp. 1-46, 1944. (AD615)

33. Gray JS. Aeroembolism induced by exercise in cadets at 23,000 feet. Randolph AFB: Army

Air Force, School of Aviation Med., Report No. 227, 1944. (AD76)

34. Gray JS, Mahady SCF. The prevention of aero-embolism in cadets at 45,000 feet by

denitrogenation. CAM Report No. 315, 1944. (AD1436)

35. Gray JS, Mahady SCF, Masland RL. Studies on altitude decompression sickness III. The

effects of denitrogenation. J Aviat Med 1946; 17:606-10. (AD1708)

36. Henry FM. Effects of exercise and altitude on the growth and decay of aviator’s bends. J Aviat

Med 1956; 27:250-59. (AD67)

37. Ivy AC, Atkinson AJ, Adler HF, et al. Incidence of symptoms of "bends and chokes" at 47,500

feet for one hour without exercise with intermittent pressure breathing. Washington D.C.: NRC

Comm. on Aviation Med., Report No. 370, 1944. (AD1025)

38. Ivy AC, Atkinson AJ, Adler HF, et al. Pertaining to the effect of dextroamphetamine and

preoxygenation plus dextroamphetamine on the incidence of bends and incapacitating bends and
34

chokes at 40,000 feet, for one hour. Washington D.C.: NRC Comm. on Aviation Med., Report No.

113, 1942. (AD1028)

39. Krutz RW, Dixon GA. The effects of exercise on bubble formation and bends susceptibility at

9,100 m (30,000 ft; 4.3 psia). Aviat Space and Environ Med 1987; 58(9,Suppl.):A97-9. (AD322*)

40. Krutz RW, Dixon GA, Harvey WT. Minimum pressure for a zero-prebreathe pressure suit.

Fifteenth Intersociety Conference on Environmental Systems. SAE Report No. 851315, San

Francisco, Ca., 1-3, 1985. (AD35*)

41. Kumar KV, Calkins DS, Waligora JM, Gilbert JH, Powell MR. Time to detection of

circulating microbubbles as a risk factor for symptoms of altitude decompression sickness. Aviat

Space Environ Med 1992; 63:961-64. (AD1506*)

42. Larrabee MG, Lilly JC, Comroe JH Jr., Hodes R. Decompression sickness during exposures to

38,000 feet, accompanied by exercise. Evaluation of a classification procedure. Washington D.C.:

NRC Comm. on Aviation Med., Report No. 137, 1943. (AD1024)

43. Lawrence JH, Tobias CR, et al. A study of aero medical problems in a liberator bomber at

high altitude. J Aviat Med 1945; 16:286-310. (AD1704)

44. Mackenzie CG, Riesen AH. The production of moderate exercise of a high incidence of

bends. JAMA 1944; 124:499-501. (AD619)

45. Maio DA, Allen TH, Bancroft RW. Decompression sickness in simulated Apollo spacecabins. Aerospace Med 1969; 40:1114-18. (AD614)

46. Maio DA, Allen TH, Bancroft RW. Decompression sickness and measured levels of exercise

on simulated Apollo missions. Aerospace Med 1970; 41:1162-65. (AD117)

47. Marbarger JP, Kadetz W, Variakojis D, Hansen J. The occurrence of decompression sickness

following denitrogenation at ground level and altitude. J Aviat Med 1957; 28:127-133. (AD245*)

48. McIver RG, Beard SE, et al. Treatment of decompression sickness in simulated space flight.

Aerospace Med 1967; 38:1034-36. (HB143*)

49. Motley HL, Chinn HI, Odell FA. Studies on bends. J Aviat Med 1945; 16:210-34. (AD911)

50. Norfleet WT. Protocol for flying after diving and NASA DCS Database. Houston: Johnson

Space Center, 1992. (AD1622*)

51. Olson RM, Adams JD, Dixon GA. Effects of repeated altitude exposure on the incidence of

decompression sickness. Aerospace Med., Assn., Preprints, Washington, D.C., 101-102, 1979.

(AD69*)

52. Olson RM, Dixon GA, et al. An evaluation of the ultrasonic precordial bubble detector.

Preprints of the 1981 Annual Scientific Meeting of the Aerospace Medical Association, 10-11. San

Antonio, Tx, 1981. (AD149*)
35

53. Olson RM, Krutz RW, et al. An evaluation of precordial ultrasonic monitoring to avoid bends

at altitude. Aviat Space Environ Med 1988; 59:635-39. (AD424*)

54. Powell MR, Waligora JM, Kumar KV. Hypobaric decompression in simulated null gravity; a

model using chair-rest adynamia. Undersea Biomed Res 1995; 22 (Suppl):67. Also NASA DCS

Database. Houston: Johnson Space Center, 1994. (AD1801*)

55. Powell MR, Waligora JM, Norfleet WT, Kumar KV. Project ARGO-gas phase formation in

simulated microgravity. Houston: Johnson Space Center, NASA Technical Memorandum 104762,

1993. (AD1619*)

56. Robinson TW. High altitude endurance test. Randolph AFB: Army Air Force, Aeromedical

Lab., Eng. Division, ENG-49-696-1E, 1943. (AD712*)

57. Robinson TW, Donnelly DP. High altitude tolerance tests. Randolph AFB: Army Air Force,

Aeromedical Lab., Eng. Division, ENG-49-696-1G, 1944. (AD713*)

58. Ryder HW, Engel GL, et al. An assay of dextro-amphetamine for its protective value in

decompression sickness. Washington D.C.: NRC Comm. on Aviation Med., Report No. 112,

1943. (AD1722*)

59. Sedov AV, Mazin AN, et al. Probability of altitude decompression disorders when breathing

oxygen containing human waste gases. Kosmicheskaya Biologiya I Aviakosmicheskaya Meditsina

1980; 14:36-39. USA Translation in: Space Biology and Aerospace Med 1980; 14:49-53. (AD85)

60. Smedal HA, Brown EB, et al. Incidence of bends pain in a short exposure to simulated

altitudes of 26,000, 28,000, and 30,000 feet. J Aviat Med 1946; 17:67-70. (AD243)

61. Smead KW, Krutz RW, Dixon GA, Webb JT. Decompression sickness and venous gas emboli

at 8.3 psia. 24th Annual SAFE Symposium, 196-99, 1986. (AD430*)

62. Smith HW. The effect of anoxia on the incidence of decompression sickness at 35,000 feet.

No. 2 Clinical Investigation Unit, RCAF, Regina, 1943. (HB134*)

63. Smith HW, Manning GW. The relationship between daily urinary output and the incidence of

decompression sickness. Report to Director of Medical Service (Air). No. 2 Clinical Investigation

Unit, RCAF, Regina, 1942. (HH25)

64. Vakar MI, Mazin AN, et al. Relationship between onset of altitude-decompression disorders

in man and barametric pressure level during intensive physical exercise. Kosmicheskaya Biologiya

I Aviakosmicheskaya Meditsina 1977; 4:83-85. USA Translation in: Space Biology and Aerospace

Med 1977; 4:112-15. (AD816)

65. Vann RD, Gerth WA. Factors affecting tissue perfusion and efficacy of astronaut

denitrogenation for extravehicular activity. F.G. Hall Hypo/Hyperbaric Center, Duke University

Medical Center, Durham NC, March 31, 1995. (AD1807*)

66. Walder DN. Studies in the susceptibility to decompression sickness. University of Bristol,

Bristol England. Thesis for Doctor of Medicine, 1947. (HH214*)
36

67. Waligora JM, Horrigan DJ Jr, Conkin J. The effect of extended O2 prebreathing on altitude

decompression sickness and venous gas bubbles. Aviat Space Environ Med 1987; 58(9,

Suppl):A110-12. (AD18*)

68. Webb JP, Engel GL, et al. The effect of pressure breathing on decompression sickness under

different altitude conditions. University of Cincinnati College of Medicine Report No. 385, 1944.

(AD79*)

69. Webb JT, Krutz RW, et al. An annotated bibliography of hypobaric decompression sickness

research conducted at the crew technology division, USAF School of Aerospace Medicine, Brooks

AFB, Texas from 1983-1988. USAFSAM-TP-88-10, Brooks AFB, Tx., 1988. (AD432)

70. Webb JT, Olson RM, et al. Oxygen toxicity during five simulated eight-hour EVA exposures

to 100% oxygen at 9.5 psia. 18th Intersociety Conference on Environmental Systems. SAE Report

881071, 1988. (AD422*)

71. Webb JT, Pilmanis AA. Breathing 100% oxygen compared with 50% O2: 50% N2 reduces

altitude-induced venous gas emboli. Aviat Space Environ Med 1993; 64:808-12. (AD1721)

72. Webb JP, Ryder HW, Engel GL, Romana J, Blankenhorn MB, Ferris EB. The effect of

susceptibility to decompression sickness of preflight oxygen inhalation at rest as compared to

oxygen inhalation during strenuous exercise. Washington D.C.: NRC Comm. on Aviation Med,

Report No. 134, 1943. (AD249*)

73. Williams OL, Lyons WR, et al. The use of drugs for the prevention of decompression

sickness. J Aviat Med 1946; 17:602-05. (AD1706*)

 ====================================================================

The code in the parentheses identifies the location of the report in J. Conkin’s filing system, and

the * identifies that information exists on the individuals who participated in the test.
37

APPENDIX B: MAXIMUM LIKELIHOOD AND MODEL

OPTIMIZATION

=====================================================================

Maximum likelihood is the preferred method to optimize unknown parameters in a model

when the response variable is dichotomous. Maximum likelihood provides the probability that

y = 1 given a value for "x", and is the method of choice when modeling a probability. The goal

is to find a model that best describes the relationship between a response variable and a set of

independent explanatory variables formulated into a model. The estimated P(serious DCS) is

written as a function of the altitude exposure data, and the favored model:

P(serious DCS) = ƒ (altitude exposure data, model), B1

where ƒ is a risk function that the altitude exposure data and model are structured within.

The probability of no serious DCS is:

P(no serious DCS) = 1 - P(serious DCS). B2

If "y" is the actual outcome of serious DCS for a subject, where y = 0 for no serious DCS

and y = 1 for serious DCS, then the estimated probability of the outcome is:

P(outcome) = P(serious DCS) y * (1 - P(serious DCS)) (1 - y), B3

or in a more general form:

P(yi) = (π(xi)) yi * (1 - π(xi)) (1 - yi

) yi = 1,0 B4

where π(xi) is the conditional mean [P(serious DCS)] as modeled and for subject "i" with

covariates xi.

If the observed outcome is serious DCS (y = 1), then A3 gives P(serious DCS) from the

probability model, Eq. 5 for example, and if the observed outcome is no serious DCS (y = 0), the

equation gives P(no serious DCS), also from the probability model since [1 - P(serious DCS)] =

P(no serious DCS). In the case where the probability model is always correct, P(outcome) equals

one. In the case where the probability model is always wrong, the P(outcome) equals zero. The

total estimated probability of all outcomes is given by the likelihood function:

n n

L = Π P(outcome), or L = Π (π(xi)) y

i (1 - π(xi)) (1 - yi

), B5

 i = 1 i = 1
38

where "n" is the number of subjects in the data set. A perfect model would produce a likelihood

of one. The likelihood function expresses the probability of the observed data as a function of

the unknown parameters. The maximum likelihood estimates of these parameters are chosen so

as to maximize this function. Thus, the resulting estimates are those that agree most closely with

the observed data.

The value of "L" is very small since it is the product of numbers between one and zero. It

is convenient to take the natural logarithm of "L" to produce the log likelihood (LL) function:

n

 LL = Σ ln(P(outcome)), B6

 i = 1

or

 n

LL = Σ (yi ln(π(xi)) + (1 - yi) ln(1 - π(xi))), B7

 i = 1

and expanded with the definition of P(outcome):

 n

LL = Σ [yi ln(P(serious DCS)i) + (1 - yi) ln(1 - P(serious DCS)i)]. B8

 i = 1

The value of LL is negative because it is the summation of the logarithms of positive

numbers ≤ to one. The smallest negative number defines the best fit of the model to the

observations. Note that even models with poor goodness of fits are still optimized to the data

since the fitting routine provides a best fit to any model.

The SYSTAT Nonlin module estimates unknown parameters of nonlinear models. The

module provides the option to construct a LOSS statement that is different from the standard

least squares LOSS statement. In least squares, the idea is to minimize the sum of squared

deviations of the observed values of "y" from the estimated values (y^) based upon the model,

and data are used to estimate all unknown parameters in a model. Maximum likelihood

estimation is accomplished in the Nonlin module by specifying the negative of the LL function

as the LOSS statement. Parameter estimation in the Nonlin module is structured to minimize the

positive LL, which is the same as maximizing the negative LL. The Quasi-Newton minimization

technique is used to fit nonlinear models. The LOSS statement is:

LOSS = - (SERIOUS * ln(ESTIMATE) + NOSERIOUS * ln(1 - ESTIMATE)), B9
39

where SERIOUS is the number of subjects in a group test with serious DCS, and NOSERIOUS

is the remaining subjects in the test without serious DCS, and ESTIMATE is the evaluated

P(Serious DCS). The computer evaluates the probability model (Eq. 5) for the first row of data

in the data set with initial values for unknown parameters. The LL is then calculated from

Eq. A9 for the same row of data using the ESTIMATE from the probability model. This

procedure is repeated over all 258 rows in the data set and the LL is summed over all rows. A

small adjustment is made in the values of the fitted parameters, based on the Quasi-Newton

procedure, such that the summed LL is less than the previous summation. Iterations continue for

parameters in the probability model to minimize the summed LL and until a predetermined

convergence criterion is reached. In addition to parameter estimation using maximum likelihood,

the module also computes asymptotic standard errors and the asymptotic correlation matrix by

estimating the Hessian matrix after iterations have stopped, both of which are used in computing

95% confidence intervals for the estimates of P(serious DCS).
40

APPENDIX C: 258 GROUP DATA, LITERATURE

REFERENCES, AND COMPUTED CUMULATIVE RISK

FROM LOWEST TO HIGHEST

Number of

male subjects

Number of serious

DCS cases

Cumulative risk

computed from Eq. 4

Literature

reference for data

11 0 0.0000221 67

20 0 0.0000311 24

54 0 0.0000599 24

7 0 0.0000613 30

12 0 0.0000805 17

343 0 0.0001117 11

57 0 0.0001126 24

17 0 0.0001553 17

19 0 0.0001592 67

33 0 0.0002140 47

8 0 0.0002528 17

11 0 0.0002623 55

12 0 0.0003011 18

12 0 0.0003014 18

9 0 0.0003041 19

2 0 0.0003299 50

12 0 0.0003312 18

19 0 0.0003356 19

14 0 0.0003562 50

4 0 0.0003663 18

17 0 0.0004067 46

33 0 0.0004119 47

6 0 0.0004713 28

25 0 0.0004923 24

30 0 0.0005199 24

379 0 0.0005257 60

65 0 0.0005257 60

10 0 0.0006456 54

15 0 0.0006963 46

52 0 0.0007049 24

14 0 0.0007335 17

6 0 0.0007447 28

169 0 0.0007592 60

80 0 0.0007592 60

2 0 0.0007707 10

19 0 0.0007984 46

29 0 0.0008692 45

28 0 0.0008937 67

19 0 0.0009187 46
41

Number of

male subjects

Number of serious

DCS cases

Cumulative risk

computed from Eq. 4

Literature

reference for data

92 0 0.0011149 60

156 0 0.0011149 60

33 0 0.0011359 47

17 0 0.0011393 12

31 0 0.0011900 24

9 0 0.0012870 54

6 0 0.0012870 54

7 0 0.0012870 54

54 0 0.0013241 24

12 0 0.0013351 23

23 0 0.0014542 67

7 0 0.0014542 65

16 0 0.0014542 65

10 0 0.0014542 65

9 0 0.0014542 65

10 0 0.0014542 65

12 0 0.0014542 65

10 1* 0.0014542 65

12 0 0.0014841 23

11 0 0.0014888 21

31 0 0.0016031 3

12 0 0.0016620 23

8 0 0.0017443 40

29 0 0.0018096 45

137 0 0.0018110 3

70 0 0.0019010 46

14 1** 0.0020534 65

8 0 0.0020534 65

18 1*** 0.0020534 65

15 1**** 0.0020534 65

11 0 0.0020534 65

10 0 0.0020534 65

11 0 0.0021070 17

6 0 0.0021483 4

116 0 0.0021483 4

6 0 0.0021632 69

11 0 0.0021736 70

12 0 0.0021736 70

12 0 0.0021736 70

12 0 0.0021744 70

20 0 0.0021931 27

12 0 0.0022104 23

33 0 0.0022975 47

15 0 0.0023138 18

12 0 0.0023795 70
42

Number of

male subjects

Number of serious

DCS cases

Cumulative risk

computed from Eq. 4

Literature

reference for data

16 0 0.0026148 25

16 0 0.0027148 40

33 0 0.0029726 3

10 0 0.0029937 45

71 0 0.0030242 60

245 0 0.0030242 60

17 0 0.0031507 44

10 1 0.0031617 30

5 0 0.0032571 9

5 0 0.0033582 7

9 0 0.0034521 40

12 0 0.0035851 18

12 0 0.0035879 18

12 0 0.0036410 20

14 0 0.0037336 39

10 0 0.0038969 65

10 0 0.0038969 65

35 0 0.0040997 17

20 0 0.0041304 9

20 0 0.0042329 61

10 0 0.0042690 71

12 0 0.0043211 18

65 0 0.0043674 60

144 0 0.0043674 60

22 NASA 1+ 0.0044859 17

19 0 0.0045711 25

13 0 0.0046881 20

9738 19 0.0046882 49

12 0 0.0046883 20

15 0 0.0046885 20

26 1 0.0048661 3

10 0 0.0049007 45

31 0 0.0051126 26

31 0 0.0051133 26

10 0 0.0051670 71

18 0 0.0051889 1

32 0 0.0052850 26

9 0 0.0053272 2

10 0 0.0054088 20

11 0 0.0054088 20

10 0 0.0054089 20

43 0 0.0054927 69

3 0 0.0055450 17

4337 26 0.0055902 49

46683 327 0.0057076 49
43

Number of

male subjects

Number of serious

DCS cases

Cumulative risk

computed from Eq. 4

Literature

reference for data

13 0 0.0061861 17

17 0 0.0062445 20

143 0 0.0064134 60

122 0 0.0064134 60

5 0 0.0065557 7

17 0 0.0066437 44

17 0 0.0067401 44

10 0 0.0068550 71

4 0 0.0070485 48

6 0 0.0072742 16

29 0 0.0075382 4

21 0 0.0075683 22

11 0 0.0080222 45

8 0 0.0081807 12

29 0 0.0081995 4

25 0 0.0085500 69

29 0 0.0085567 4

117 0 0.0087149 33

29 0 0.0087802 4

12 0 0.0090126 23

10 0 0.0092788 71

62 0 0.0101890 34

62 0 0.0101890 32

11 0 0.0117627 19

11 NASA 2++ 0.0117627 19

68 0 0.0119851 8

15 0 0.0121555 55

59 NASA 0+++ 0.0121555 41

14 NASA 1++++ 0.0121555 55

22 0 0.0123891 22

42 0 0.0135366 52

14 0 0.0135366 2

23 0 0.0136429 51

23 0 0.0136429 51

195 0 0.0142129 33

82 0 0.0149730 53

143 0 0.0152264 8

4 0 0.0157824 12

83 0 0.0161814 15

100 0 0.0162003 32

585 0 0.0182575 59

434 0 0.0182575 64

24 1 0.0182826 62

126 0 0.0182826 63

15 0 0.0185912 8
44

Number of

male subjects

Number of serious

DCS cases

Cumulative risk

computed from Eq. 4

Literature

reference for data

35 0 0.0188430 3

23 3 0.0200716 56

23 3 0.0200716 56

50 0 0.0204305 38

35 2 0.0207115 66

55 8 0.0207115 66

128 0 0.0209092 32

38 0 0.0214761 69

14 0 0.0214761 39

90 0 0.0217385 35

90 0 0.0217385 35

17 0 0.0225183 44

27 0 0.0227023 72

27 5 0.0227023 30

13 0 0.0232692 29

8 0 0.0234289 9

20 0 0.0237584 9

21 0 0.0237584 9

24 2 0.0240438 57

24 5 0.0240438 57

36 0 0.0241504 23

14 0 0.0245397 29

180 1 0.0254102 32

14 0 0.0269339 44

7664 145 0.0270627 49

27 5 0.0283400 31

27 5 0.0283400 31

14 2 0.0290479 29

93 0 0.0298568 32

78 0 0.0300170 8

35 0 0.0308453 3

14 3 0.0309177 48

29 0 0.0310131 4

14 1 0.0321544 44

5 0 0.0323172 7

145 0 0.0325107 32

6 0 0.0347234 4

49 0 0.0352455 64

25 0 0.0358841 12

18 0 0.0382146 44

15 1 0.0387692 44

18 0 0.0387692 44

15 0 0.0387731 36

204 4 0.0415954 32

50 0 0.0427898 38
45

Number of

male subjects

Number of serious

DCS cases

Cumulative risk

computed from Eq. 4

Literature

reference for data

105 1 0.0427898 38

84 0 0.0454109 59

77 6 0.0455288 35

121 12 0.0459043 5

112 18 0.0459043 5

223 11 0.0532187 32

23 7 0.0537845 56

23 3 0.0537845 56

33 3 0.0587407 12

27 3 0.0608337 72

27 0 0.0608337 72

27 3 0.0608337 30

14 1 0.0623528 29

14 1 0.0623528 29

29 2 0.0624716 68

14 0 0.0625533 29

24 8 0.0644286 57

24 8 0.0644286 57

94 20 0.0853625 14

29 11 0.1022634 68

29 10 0.1213644 68

21 1 0.1244325 73

12 0 0.1315500 23

24 5 0.1630117 58

24 6 0.1630117 58

27 2 0.1630117 31

14 4 0.1670823 29

14 1 0.1670823 29

14 1 0.1670823 29

14 2 0.1670823 29

50 3 0.1790864 37

29 13 0.2158145 68

167 60 0.2230230 13

90 36 0.2257103 14

136 44 0.2257103 14

118 12 0.2260429 43

36 2 0.2640416 6

204 12 0.2748659 42

29 8 0.5882192 68

* from Duke University (1995), numbness in right hand that appeared 1 hr into test, and cleared

on descent from 4.3 psia to site pressure. No hyperbaric treatment provided.
46

** from Duke University (1995), dizziness, nausea, and hot flash in head. No hyperbaric

treatment provided.

*** from Duke University (1995), blurred vision during test. Treatment Table 6 provided.

**** from Duke University (1995), numbness and tingling in left shoulder. Treatment Table 6

provided.

+ from NASA/JSC (1982), sudden onset of fatigue, cold sweat, and skin mottling on chest after

report of pain in right knee. No hyperbaric treatment provided, but 2 hr of ground level oxygen.

++ from NASA/JSC (1989), first case reported pain in right knee, headache, and later blurred

vision. No hyperbaric treatment provided, but 2 hr of ground level oxygen. Second case

reported pain in hands, pain in right knee, then later pain behind right eye with throbbing

headache. Treatment Table 6 provided.

+++ from NASA/JSC (1990), classified as Type II based only on skin mottling on right side of

chest 2 hr into exposure, but not counted as serious DCS in this analysis. Treatment Table 5

provided.

++++ from NASA/JSC (1992), had skin mottling on chest during test plus hypotension on

standing after test, which may have been due to an extensive bed rest period. Treatment Table 5

provided.
47

NOTES

t

S(t) = e – H(t) = e [ - ∫ h(x) dx], where H(t) = rc and h(x) = ri.

 0

ri does not have to be a function of time, but the integration of ri with respect to time will

accumulate risk.

F(t) = 1 – S(t)

P(serious DCS) = 1 - e -rc,

let P(serious DCS) = y and rc = x, and solve for rc

y + e-x = 1

e-x = 1 - y

-x = ln(1 - y)

x = - ln(1 - y)

=====================================================================

rc = - ln[1 - P(serious DCS)] = Eq. 2 =

0.000613 * TR4.267 * (1 + (exer * 4.752)) * [(1 / 1.7942) * (1 - (1.794 * Talt + 1) * e-1.794 *

Talt)]

ri = d(- ln[1 - P(serious DCS)]) / dt = Eq. 4 =

0.000613 * TR4.267 * (1 + (exer * 4.752)) * (t * e-1.794 * t)]

four hr prebreathe (4.6 / 4.3 = 1.069), with exercise at 4.3 psia, and after six hr at 4.3 psia.

r

i = ********* is the rate d(- ln[1 - P(serious DCS)]) / dt at the second hr. The integration with

respect to Talt over the two hr gives:

r

c = - ln[1 - P(serious DCS)] = 0.00146

Rpt# 382 is the one without exerfreq included (n = 21)
48

Threshold of Serious DCS at Low rc

at rc ≤ 0.0045 there are 109 tests with total exposures = 3,687. There are six tests with serious

DCS:

exposures serious serfrac rc institution

4-hr PB, 6-hr no exercise at 4.3 psia 0.000254 computed from model

10 1 10% 0.00145 Duke, 1995

4-hr PB, 6-hr exercise at 4.3 psia 0.00146 computed from model

14 1 7.1% 0.00205 Duke, 1995

18 1 5.5% 0.00205 Duke, 1995

15 1 6.7% 0.00205 Duke, 1995

10 1 10% 0.00316 NRC Comm. on Aviat. Med., 1943

22 1 4% 0.00449 NASA staged 10.2 psia

9,738 19 0.2% 0.00469 report by Motley, 1945

26 1 3.8% 0.00487 report by Allen, 1971

4,337 26 0.6% 0.00559 report by Motley, 1945

46,683 327 0.7% 0.00571 report by Motley, 1945

Ï

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 January 2001 NASA Technical Paper

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Evidence-Based Approach to the Analysis of Serious Decompression Sickness With

Application to EVA Astronauts‘

 

6. AUTHOR(S) 

Johnny Conkin, Ph.D., M.S.* 

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Lyndon B. Johnson Space Center

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S-875

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13. ABSTRACT (Maximum 200 words)

It is important to understand the risk of serious hypobaric decompression sickness (DCS) to develop procedures and treatment

responses to mitigate the risk. Since it is not ethical to conduct prospective tests about serious DCS with humans, the necessary

information was gathered from 73 published reports. We hypothesize that a 4-hr 100% oxygen (O2) prebreathe results in a very low

risk of serious DCS, and test this through analysis. We evaluated 258 tests containing information from 79,366 exposures in altitude

chambers. Serious DCS was documented in 918 men during the tests. A risk function analysis with maximum likelihood optimization

was performed to identify significant explanatory variables, and to create a predictive model for the probability of serious DCS. Useful

variables were Tissue Ratio, the planned time spent at altitude, and whether or not repetitive exercise was performed at altitude. A

prebreathe and decompression profile Shuttle astronauts use for extravehicular activity (EVA) includes a 4-hr prebreathe with 100%

O2, an ascent to P2 = 4.3 lb per sq. in. absolute, and a Talt = 6 hr. Given 100 Shuttle EVAs to date and no report of serious DCS, the

true risk is less than 0.03 with 95% confidence. It is problematic to estimate the risk of serious DCS since it appears infrequently, even

if the estimate is based on thousands of altitude chamber exposures. The true risk to astronauts may lie between the extremes of the

confidence intervals since the contribution of other factors, particularly exercise, to the risk of serious DCS during EVA is unknown. A

simple model that only accounts for four important variables in retrospective data is still helpful to increase our understanding about

the risk of serious DCS.

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pressure reduction; decompression sickness; hypobaric atmospheres; altitude chamber;

tissue ratio; extravehicular activity 60 

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