Review of Human Lethality Estimates for Chlorine Inhalation Douglas R. Sommerville John J. Bray...

Review of Human Lethality Estimates for Chlorine InhalationReview of Human Lethality Estimates for Chlorine Inhalation

Douglas R. Sommerville

John J. Bray

Raymond E. Jablonski

Sharon A. Reutter-Christy

Erin E. Shelly

Douglas R. Sommerville

John J. Bray

Raymond E. Jablonski

Sharon A. Reutter-Christy

Erin E. Shelly

13 January 200913 January 2009

DISCLAIMER: The findings presented in this briefing are not to be construed as an official Department of the Army or Department of Homeland Security position unless so designated by other authorizing documents.

Distribution is Unlimited--Available for Public Release (PAO # 100804, 6 January 2009, US Army ECBC, ATTN: AMSRD-ECB-RT-IM, Aberdeen Proving Ground, MD. 21010-5424)

UNCLASSIFIED/UNLIMITED


Eighth Symposium on the Urban Environment

89th Annual American Meteorological Society Meeting

Phoenix, AZ

Eighth Symposium on the Urban Environment

89th Annual American Meteorological Society Meeting

Phoenix, AZ

UNCLASSIFIED/UNLIMITED2


Acknowledgements Acknowledgements

● Work funded by the Chemical Security Analysis Center (CSAC), US Department of Homeland Security, Aberdeen Proving Ground, MD

● Work documented in CSAC technical reporto Report Number CBRNIAC-SS3-628, January 2008

● Authors are from following organizationso ECBCo CSACo Optimetrics, Inc., Abingdon, MD



Purpose and Application of StudyPurpose and Application of Study

● Reevaluate the human lethality estimate for chlorine inhalation exposure as a function of

o exposure duration

o population basis (military versus general population)

● Estimates are to be used in risk assessments involving

chlorine airborne releases

o atmospheric transport and dispersion (ATD) models



General ApproachGeneral Approach

● Literature Review

● Data collection and reduction of mammalian lethality data

● Statistical analysis of mammalian lethality data

● Modeling of relationship between subpopulation and

general population

o Application of Crosier (2007)—Available from DTIC, AD# A465827

o Brief description of Crosier Model shown in backup slides

● Investigation of sensitivity of ATD model predictions to

changes in toxicity estimate parameters



Toxicity Parameters InvestigatedToxicity Parameters Investigated

● Variability in human toxic response: kTL or kC

o Probit slope with respect to toxic load or vapor concentration

● Time dependence of toxicity: n

o Toxic load exponent (TLE)

o Toxic load = CnT

● Median effective quantities

o LCT50 – Lethal Concentration Time for 50% of individuals exposed

o LTL50 – Lethal Toxic Load for 50% of individuals exposed



Shallow versus Steep Probit SlopesShallow versus Steep Probit Slopes

Dose

10 100

No

rmit

s

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Cu

mu

lati

ve P

rob

abili

ty (

Per

cen

t)

1

2

5

10

20

30

405060

70

80

90

95

98

99

Dose

10 100

No

rmit

s

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Cu

mu

lati

ve P

rob

abili

ty (

Per

cen

t)

1

2

5

10

20

30

405060

70

80

90

95

98

99

Dose

10 100 1000

Pro

ba

bili

ty D

en

sit

y

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Dose

10 100 1000

Pro

ba

bili

ty D

en

sit

y

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Median Effective

Dose

ED50 = 100

Probit Slope (m) = 3 Probit Slope (m) = 10

The probit slope is a measure of a population’s variability in

their responses to a toxicant

Shallow

Short & Wide

Steep

Tall & Narrow

Dose

10 100

No

rmit

s

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Cu

mu

lati

ve P

rob

abili

ty (

Per

cen

t)

1

2

5

10

20

30

405060

70

80

90

95

98

99

Dose

10 100

No

rmit

s

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Cu

mu

lati

ve P

rob

abili

ty (

Per

cen

t)

1

2

5

10

20

30

405060

70

80

90

95

98

99

Dose

10 100 1000

Pro

ba

bili

ty D

en

sit

y

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Dose

10 100 1000

Pro

ba

bili

ty D

en

sit

y

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Median Effective

Dose

ED50 = 100

Probit Slope (m) = 3 Probit Slope (m) = 10

The probit slope is a measure of a population’s variability in

their responses to a toxicant

Shallow

Short & Wide

Steep

Tall & Narrow



Importance of Establishing the Time Dependence of ToxicityImportance of Establishing the Time Dependence of Toxicity

Exposure Duration (minutes)

10 100

Med

ian

Eff

ecti

ve D

osa

ge

(EC

T5

0)

(mg

-min

/m3)

0.4

0.5

0.6

0.8

1.0

1.3

1.6

2.0

2.5

Haber's LawUnderestimates Toxicity

Haber's LawOverestimates Toxicity

Haber's Rule

Toxic Load Model (with N > 1)

Value for toxic load exponent (n) and constant (kxx) is agent and

scenario specific

Protective Enough?

Overprotective?Unnecessary Stress?

Exposure Duration (minutes)

10 100

Med

ian

Eff

ecti

ve D

osa

ge

(EC

T5

0)

(mg

-min

/m3)

0.4

0.5

0.6

0.8

1.0

1.3

1.6

2.0

2.5

Haber's LawUnderestimates Toxicity

Haber's LawOverestimates Toxicity

Haber's Rule

Toxic Load Model (with N > 1)

Value for toxic load exponent (n) and constant (kxx) is agent and

scenario specific

Protective Enough?

Overprotective?Unnecessary Stress?



Literature ReviewLiterature Review

● Identification of general references/sources

● Previously reported human estimates

● Existing mammalian lethality data

● Historical record of industrial accidents involving chlorine



General References/Sources used for Initial Identification of Chlorine Toxicity StudiesGeneral References/Sources used for Initial Identification of Chlorine Toxicity Studies

● Acute Exposure Guideline Levels (AEGL) for Chlorine (2004)

● Third Edition of Lees’ Loss Prevention in the Process Industries

(Chapter 18: “Toxic Releases”)

● Chlorine Toxicity Monograph (1988) published by the Major Hazards

Assessment Panel

● Edgewood CB Center Technical Library and Historical Research &

Response Team



Previous Human Lethality EstimatesPrevious Human Lethality Estimates

● Studies with estimates for median lethal dosageo US Coast Guard sponsored studies for Vulnerability Model

■ Eisenberg et al. (1975)

■ Perry and Articola (1980)

o ten Berge and van Heemst (1983)

o Rijnmond Report (1982)/Harris and Moses (1983)

o Withers and Lees (1985)

● Many existing estimates for threshold lethal dosages were

not used for this analysiso Purpose was to determine median lethal dosage and probit slope

(whole distribution) not just the tail of the distribution



Existing Mammalian Lethality DataExisting Mammalian Lethality Data

● Searched for experimentally measured median lethal dosages in mammalso Whenever possible, underlying response data were obtained

● Used only studies where mammals were exposed for a specified period of time and then removed from the chamber for observation o Gas-until-death studies not used

■ Such studies generally produce higher median lethal dosages relative to fixed duration and observe studies

■ Example: the often cited Weedon et al. (1940) was not used in this study because it was a gas until death study

o Median dosages not associated with a duration were not used



Scope of Existing Mammalian Lethality DataScope of Existing Mammalian Lethality Data

● 29 individual median lethal inhalation dosages were found

and/or calculated

o Collected from 18 studies and sources dating back to 1882

o Eight mammalian species represented (mouse, rat, guinea pig,

rabbit, cat, dog, sheep and goat)

o Data discovered in previously “forgotten” US government technical

reports

o In some cases, LCT50 was not originally reported and was

subsequently calculated in this study using the reported response

data



Median Lethal Dosage as a Function of Exposure Duration for Chlorine InhalationMedian Lethal Dosage as a Function of Exposure Duration for Chlorine Inhalation

Time (minutes)

1 10 100

LC

T5

0 (m

g-m

in/m

3 )

1e+3

1e+4

1e+5

1e+6 Eisenberg et al. (General)Perry & Articola (General)Rijnmond Report (General)ten Berge & van Heemst (General)Withers & Lees (Average)

LCT50 (Chlorine Vapor) vs Exposure Duration

MouseRat

DogGoat

Guinea Pig

RabbitCat

Sheep

Human Estimates



Historical Record—Accidental Chlorine ReleasesHistorical Record—Accidental Chlorine Releases

● Accidental releases (up to 50 tons)

o Fatalities (with one exception) occurred within about 400 meters of the actual point of release

o Most fatalities occurred within 250 meters

o Largest number of fatalities from a release is around 60 (Romania in 1939)

o Marshall (1977) estimated that there are on average 0.3 to 0.8 fatalities per metric ton of an accidental industrial release



Historical Record—Civilian Exposure (?) at Second Ypres (1915)Historical Record—Civilian Exposure (?) at Second Ypres (1915)

● Marshall noted that there are no reported civilian

casualties from the first wartime use of chlorine at the

Second Battle of Ypres (1915)

o Germans released 168 tons over 4 mile front

o Civilians in Ypres were about 6 kms from the front



Current ATD Model Predictions and the Historical RecordCurrent ATD Model Predictions and the Historical Record

● Current atmospheric transport & dispersion (ATD) model predictions more often than not greatly overestimate the downwind hazard from a chlorine release

o Example: LC50 plume extending 650 to 1100 meters downwind for a 1000 kg release (Franks et al. (1996))

● Possible explanations

o ATD models are over-predicting the downwind transport of chlorine■ Inadequate knowledge of atmospheric chemistry of chlorine and/or heavy gas transport (?)

o The human lethality estimates are over-predicting the toxicity■ The point of the present study

o Combination of both of the above factors



Data ReductionData Reduction

● Probit slope and LCT50 from response data

o Probit slope—from probit analysis

o LCT50—from either probit analysis or maximum likelihood estimation (MLE)

● Species properties—minute volume (VM) and body mass (M)

o Obtained average values for non-anaesthetized mammals from Bide et al. (2000)

● Convert inhalation dosages into nominal doses for allometric

modeling

● Detailed statistical analysis of individual studies for toxic load

exponent estimateo Bitron and Aharonson (1978)—mouse lethality study



Response Variance—Probit Slope EstimateResponse Variance—Probit Slope Estimate

● Response variance assumption:o Healthy lab animals [=] healthy (military) humans

● Variance estimated via weighted average of experimental

probit slopeso Slopes calculated from eight studies

o Weights equal the inverse of the square of the standard error

■ Hence, less precise values had less influence on the final estimate

o Average equals 7.96 (95% CI of 7.21 to 8.71)--rounded to 8.0 for

subsequent calculations for the general population

● This approach was not used by previous researchers in the

derivation of their probit slope estimates



Allometric Modeling ResultsAllometric Modeling Results

● Lethality is a slight function of species body mass—LCT50

increases with body mass

o Ratio of LCT50s

■ Man to Mouse = 2.25

■ Man to Dog = 1.18

■ Man to Goat = 1.07

● Allometric modeling was less useful for time dependence of lethality

o Toxic load exponent equals 2.7 with 95% CI of 2.1 to 4.0

■ Wide error bars are an issue

● Chlorine is a not a Haber’s Rule chemical (n = 1), but what is the value of its toxic load exponent?



Experimental Values of Chlorine Toxic Load Exponent from Previous StudiesExperimental Values of Chlorine Toxic Load Exponent from Previous Studies

● Only two suitable lethality studies found with exposures at several exposure durations

o Bitron and Aharonson (1978) 476 male mice

■ ten Berge and van Heemst calculations (1983)

□ n = 3.5 (95% CI of 2.5 to 4.5)

□ Based upon fit of LCT50 values

■ Present study re-calculation of n from Bitron and Aharonson data

□ n = 3.36 (95% CI of 2.99 to 3.73)

□ Based upon probit analysis of original binary response data

o Zwart and Woutersen (1988) rats and mice (n is suspect)

■ Curvature in log(LCT50) versus log(T) plot (n < 1 for 5 to 30 minutes)



Experimental Values of Chlorine Toxic Load Exponent from Previous Studies (cont.)Experimental Values of Chlorine Toxic Load Exponent from Previous Studies (cont.)

● Weedon et al. (1940) was not included in this group

o Gas to death to study

o Only involved 16 rats and 8 mice

o n roughly equals 1.8

● One human study (non-lethal, threshold effects) involved

exposures at several exposure durations—Anglen (1981)

o n = 1.9



Human Estimates of Chlorine Toxic Load Exponent from Previous StudiesHuman Estimates of Chlorine Toxic Load Exponent from Previous Studies

● ten Berge and van Heemst (1983) o Took average of values from Bitron and Aharonson (1978) and

Anglen (1981) for a value of n = 2.75

o Right answer for wrong reason?

o Should not mix toxic load exponents from two different toxic

mechanisms

■ Systemic respiratory poisoning (Bitron and Aharonson)

■ Eye and throat irritation (Anglen)



Human Estimates of Chlorine Toxic Load Exponent from Previous Studies (cont.)Human Estimates of Chlorine Toxic Load Exponent from Previous Studies (cont.)

● Withers and Lees (1985)

o Took average of values from Bitron and Aharonson (1978) and Weedon

et al. (1940) for a value of n = 2

o However, Bitron and Aharonson is far superior to Weedon et al.

■ Number of animals (476 (BA) versus 24 (W))

■ Gas and observed (BA) versus gas to death (W)

● MHAP and Harris and Moses (1983) concluded that n = 2.75 is the

best value based upon their separate reviews of all the known

chlorine lethality data



Human Estimates of Chlorine Toxic Load Exponent from Present StudyHuman Estimates of Chlorine Toxic Load Exponent from Present Study

● A value of 2.75 is recommended for the human estimate● This estimate is based upon three factors

o Bitron and Aharonson (1978) is the only previous experimental study that produced suitable data for a toxic load exponent

■ n = 3.36 (95% CI of 2.99 to 3.73) (based on re-calculation of original BA data)

o Toxic load exponent value from allometric fit of total mammalian lethality dataset (present study)

■ n = 2.7 (with 95% CI of 2.1 to 4.0) ■ Error bars overlaps the value of Bitron and Aharonson

o The need for caution■ Have only one TLE value available from acceptable experimental work■ Too high of a TLE value for human estimate will underestimate chlorine

toxicity at longer exposure durations

● The value of 2.75 was chosen as a conservative estimateo Additional experimental work is needed



Human Estimate of Chlorine Toxicity from Present Study (Military)Human Estimate of Chlorine Toxicity from Present Study (Military)

● YN is a normit

o YN = -1, 0 and 1 for 16, 50 and 84% response, respectively

● Probit slopeo Slope (kTL) equals 2.91 for toxic load basis

o Slope (kC) equals 8.0 for vapor concentration basis

■ kC = n x kTL

● C is in mg/m3 and T is in minutes

2.75

2.75 10

50

31.52 2.91 log

or

L C T 6.79x10

NY C T



Human Estimate of Chlorine Toxicity from Present Study (General Population)Human Estimate of Chlorine Toxicity from Present Study (General Population)

● Derived from military estimate using the method of Crosier (2007)● YN is a normit

o YN = -1, 0 and 1 for 16, 50 and 84% response, respectively

● Probit slopeo Slope (kTL) equals 2.18 for toxic load basiso Slope (kC) equals 6.0 for vapor concentration basis

■ kC = n x kTL

● C is in mg/m3 and T is in minutes

2.75

2.75 10

50

22.698 2.18 log

or

L C T 2.58x10

NY C T



Chlorine Toxicity Estimates from Present Study and Modified Rijnmond Report (General Population)Chlorine Toxicity Estimates from Present Study and Modified Rijnmond Report (General Population)

● Upper bound on estimate● Assumes toxicity can be

modeled allometricallyo Human toxicity closer to that

of larger mammals in dataset

Present Study

2.75

2.75 10

50

22.698 2.18 log

or

L C T 2.58x10

NY C T

2.75

2.75 9

50

21.710 2.18 log

or

L C T 9.09x10

NY C T

Rijnmond Report (Modified)

● Lower bound on estimate● Probit slope was modified from

original Rijnmond equation to match that of present work

● Assumes human toxicity should be modeled as an average of existing mammalian data



Median Lethal Dosage as a Function of Exposure Duration for Chlorine InhalationMedian Lethal Dosage as a Function of Exposure Duration for Chlorine Inhalation

Time (minutes)

1 10 100

LC

T5

0 (m

g-m

in/m

3 )

1e+4

1e+5

1e+6Present Work (Military)

Rijnmond Report (General)ten Berge & van Heemst (General)Withers & Lees (Average)Present Work (General)

LCT50 (Chlorine Vapor) vs Exposure Duration

MouseRat

DogGoat

Guinea Pig

RabbitCat

Sheep

Human Estimates



Sensitivity Analysis of New Human Estimates via ATD Model RunsSensitivity Analysis of New Human Estimates via ATD Model Runs

● Comparison of the historical record versus model predictions of the

probability of lethality as a function of downwind distance

● Scenario modeled using HPAC

o Catastrophic release of 50 tons of chlorine liquid

o Flat and open terrain

o Three different atmospheric conditions

■ Low wind (1 m/sec), clear sky, nighttime (2 am), “stable” condition

□ Pasquill Stability Category F—produced the longest downwind distances

■ Moderate wind (5 m/sec), cloudy day, “neutral” condition

□ Pasquill Stability Category D

■ Low wind (2 m/sec), clear sky, daytime (2 pm), “unstable” condition

□ Pasquill Stability Category B



Sensitivity Analysis of New Human Estimates via ATD Model Runs (Cont)Sensitivity Analysis of New Human Estimates via ATD Model Runs (Cont)

● HPAC output

o Concentration time history for each model run at downwind distances of 0.2

km, 0.5 km, 1.0 km, 1.5 km and 2.0 km along center-line of plume

o Histories were then numerically integrated using several different human

toxicity estimates

■ Present study

■ Previous studies

■ Modification of present study—examine the sensitivity of plots to changes in

toxicity parameters

□ 2 x 2 matrix of toxic load exponent values and probit slopes

o Produced plots of probability of lethality as function of downwind distance



Probability of Lethality as a Function of Downwind Distance--Comparison of Several Toxicity EstimatesProbability of Lethality as a Function of Downwind Distance--Comparison of Several Toxicity Estimates

● Based on concentration-time profile from HPAC simulation

o 50 ton release of chlorine

o PS Category F

● Several toxicity equations used to translate profile into lethality probability

● Historical industrial record

o Almost no deaths beyond 0.4 km

Probability of Lethality as a Function of Downwind DistancePasquill Stability Class F

Downwind Distance (km)

Pro

bab

ilit

y o

f L

eth

ality

0.10.25

1

2.55

10

20

3040506070

80

90

9597.5

99

99.7599.9

Present Work (General Population)

Withers & Lees (Average Population)

Rijnmond Report

ten Berge & van Heemst

Haber's Rule (LCT50 = 9500 mg-min/m3 & kC = 6)



Probability of Lethality as a Function of Downwind Distance--Comparison of Better Toxicity EstimatesProbability of Lethality as a Function of Downwind Distance--Comparison of Better Toxicity Estimates



o Two extremes of atmospheric stability

● Several toxicity equations used to translate profile into lethality probability



Probability of Lethality as a Function of Downwind Distance


0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 2.00.1 1.0

Pro

bab

ility

of

Let

hal

ity

0.10.25

1

2.55

10

20

3040506070

80

90

9597.5

99

99.7599.9

Present Study--Stability B

Present Study--Stability F

ten Berge & van Heemst--Stability B

ten Berge & van Heemst--Stability F

Rijnmond--Stability B

Rijnmond--Stability F



● Lethality probability (probability scale) versus log(Downwind Distance) plots

Toxicity Parameter Sensitivity AnalysisToxicity Parameter Sensitivity Analysis

● Two by two matrix of low and high values for probit slope and TLE

o Probit slope values of 3 and 6

o TLE values of 1.85 and 2.75


Pro

bab

ility

of

Let

hal

ity


Pro

bab

ility

of

Let

hal

ity

Change in slope rotates plot Change in TLE shifts plot

Increasing TLEIncreasing

Slope


Pro

bab

ility

of

Let

hal

ity


Pro

bab

ility

of

Let

hal

ity



Pro

bab

ility

of

Let

hal

ity


Pro

bab

ility

of

Let

hal

ity


Pro

bab

ility

of

Let

hal

ity


Pro

bab

ility

of

Let

hal

ity


Increasing TLEIncreasing

Slope



Probability of Lethality as a Function of Downwind Distance—Probit Slope and TLEProbability of Lethality as a Function of Downwind Distance—Probit Slope and TLE



o PS Category F

● Two by two matrixo PS of 3 and 6

o TLE of 1.85 and 2.75

● All toxicity curves share a common LC50 value at 2 minutes

o 4750 mg/m3



Probability of Lethality as a Function of Downwind DistancePasquill Stability Class F


Pro

ba

bil

ity

of

Le

tha

lity

0.10.25

1

2.55

10

20

3040506070

80

90

9597.5

99

99.7599.9

LTL50 = 2.582 x 1010, kC = 6.0 & n = 2.75

LTL50 = 1.267 x 107, kC = 6.0 & n = 1.85

LTL50 = 2.582 x 1010, kC = 3.0 & n = 2.75

LTL50 = 1.267 x 107, kC = 3.0 & n = 1.85

For all four toxic load relationships shown,

the two minute LC50 = 4750 mg/m3.



SummarySummary

● Reasonable bounds on the estimate for human chlorine lethality for the general population have been establishedo Present study (upper boundary)

■ Allometric fit

o Modified Rijnmond Report (lower boundary)■ Human equivalent to average of all mammals

● Quantitative estimate for the probit slope was derivedo Weighted average of experimental probit slopes has not been done

previously

● Defensible value derived for toxic load exponento Based primarily on value from Bitron and Aharonson

o Collaboration from allometric fit from present study

● ATD model using new lethality estimate provides reasonable predictions of downwind distance of lethality plumes



Dependence of Toxic Effect on Duration—Toxic Load ModelDependence of Toxic Effect on Duration—Toxic Load Model

● E(CnT)XX = kXX or

ECTXX = kXX (1/n) * T(n - 1)/n

o When n equals one, Haber’s Rule is obtained

● The approach is based more on empirical observations than on basic biological theories

● Equation needs to be derived empirically on an individual toxicant basis from acute toxicity experiments where both C and T are varied

o n is also dependent on the toxicological endpoint, poisoning mechanism, route of exposure, etc.

● Biologically, it has been postulated that n provides an empirical measure of the agent’s detoxification rate

o n > 1 corresponds to significant detoxification

● Operationally, n is also dependent on the exposure scenario

o Post-exposure decontamination

o Absence or presence of clothing (in case of percutaneous exposures)



Anatomy of a Bell CurveAnatomy of a Bell Curve

Dose

10 100 1000

Pro

ba

bili

ty D

en

sit

y

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

-- Standard Deviation

(1 / ) -- Probit Slope ( m )

ED50 -- Median

Effective Dose

= log (ED50) Base Equation

Z standard normalrandom variable



Normit Transformation of Percent ResponseNormit Transformation of Percent Response

CurveParameters

Median EffectiveDose

ED50 = 100

Probit Slope

m = 3



Example of Probit Analysis from ECBC Low Level Toxicology ProgramExample of Probit Analysis from ECBC Low Level Toxicology Program

Dosage (mg-min/m3)

100 1000

No

rmit

s

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Cu

mu

lati

ve P

rob

abili

ty (

Per

cen

t)

1

2

5

10

20

30

405060

70

80

90

95

98

99

Percent Lethality versus GB Concentration-Time (mg-min/m3)Female Sprague-Dawley Rats (GB Inhalation, 10 Minutes)

From Mioduszewski, et al. (2001)

Quantal Data

Dosage Deaths Exposed

153 0 10

187 1 10

218 4 10

271 8 10

343 10 10

Median EffectiveDosage

LCT50 = 231 mg-min/m3

Probit Slope

m = 14.1

Red Quantal Points are Off-Scale



t T

N

t

TL C t dt0

(CT)1 = (CT)2

If TLR 1

(CNT)1 (CNT)2

Physiological effects from dosage (CT)1 may differ from dosage (CT)2

(CT)1 (CT)2

Toxic Load Model versus Haber’s RuleToxic Load Model versus Haber’s Rule

If N = 1, Above Equation Reduces Haber’s Rule

Real Life Toxicology Laboratory

t T

N

tNT

C t dt

TLRC T

0

Toxic Load Ratio (TLR)

If TLR = 1

(CNT)1 = (CNT)2

Toxic Load (TL)



Subpopulation-Population RelationshipCrosier Model

Subpopulation-Population RelationshipCrosier Model

● Final product the result of a series of three reports

o Crosier and Sommerville (2002), ECBC-TR-224, AD A400214

o Crosier (2003), ECBC-TR-337, AD A417162

o Crosier (2007), ECBC-TR-534, AD A465827—final version of model

● Premises of mathematical model

o The distribution of log(doses) for a healthy subpopulation is located completely within

the distribution formed by the general population

o Distribution of the log(doses) for the two populations are normal

■ However, based on theory, the subpopulation cannot be normal, but the normal distribution

has been shown by Crosier (2007) to be an useful approximation for the subpopulation

● To use model, only three parameters are needed

o Percent size of subpopulation relative to the total population—subpopulation healthy

enough for military service estimated to equals 30% of total population

o Probit slope and median effective dosage for one of the populations



Examples of Possible Relative Positions of Subpopulation and Population Bell CurvesExamples of Possible Relative Positions of Subpopulation and Population Bell Curves

Subpopulation Distributions (Shaded Areas) as Function of Subpopulation Mean & St. Dev.

Feasible value pairs do not always produce realistic distributions (see )

MaxMean

CentroidMax Ratio

Editor



Final Recommended Position for Relative Positions of Subpopulation and Population Bell CurvesFinal Recommended Position for Relative Positions of Subpopulation and Population Bell Curves

●Editor Model—located at yellow crosso Max difference in means between two bells,

with subpopulation distribution still approximately normal

o Location:

■ SP Standard Deviation: 0.744

■ SP Mean: 0.900

● Tail Model—located at upper end of dashed line

o This is the point providing the greatest difference in means between the two bell curves

o However, subpopulation deviates extremely from a normal distribution

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Review of Human Lethality Estimates for Chlorine Inhalation Douglas R. Sommerville John J. Bray...

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