PBPK Model for Lead: PBPK Model for Lead: Uncertainties and Parameter Uncertainties and Parameter

EstimationEstimation

byby

Sangam Uma ReddySangam Uma Reddy

Thesis SupervisorDr. Mukesh Sharma

OverviewOverview

Introduction Introduction

Objective of the studyObjective of the study

Literature reviewLiterature review

Methodology Methodology

Results and discussionResults and discussion

ConclusionsConclusions

LeadLead

Versatile heavy metalVersatile heavy metal Extensively usedExtensively used Cheap, useful, easy to mine, physical properties Cheap, useful, easy to mine, physical properties

- ubiquitous in air, food, water and soil- ubiquitous in air, food, water and soil Cumulative Neurotoxin, no known biological Cumulative Neurotoxin, no known biological

functionfunction one of most hazardous substances (ATSDR)one of most hazardous substances (ATSDR)

Usage of LeadUsage of Lead

BatteriesBatteries PigmentsPigments Rolled/ExtrusionsRolled/Extrusions AmmunitionsAmmunitions Cable SheathingCable Sheathing Petrol AdditivesPetrol Additives

73%

11%

6%

2%

3%2%

1% 2%

Batteries Pigments Rolled Ext.Ammunition Cable Sheathing Petrol AdditivesAlloys Miscellaneous

Source: ILZSG, 1997Source: ILZSG, 1997

Effects of LeadEffects of Lead

Damage Central Nervous SystemDamage Central Nervous System Causes reduction in IQ and attention spanCauses reduction in IQ and attention span Affects mental and physical developmentAffects mental and physical development Reading and learning disabilities, hyperactivity Reading and learning disabilities, hyperactivity

and other behavioral problemsand other behavioral problems Impairs formation of Hemoglobin, thus AnemiaImpairs formation of Hemoglobin, thus Anemia Irreversible brain damageIrreversible brain damage Even death at higher concentrationEven death at higher concentration

However…However… Lead continues to be in environment after several Lead continues to be in environment after several

years of unleaded gasoline (Morisawa years of unleaded gasoline (Morisawa et al.et al. 2001) 2001) – Why?– Why?

After phase out of lead from gasoline:After phase out of lead from gasoline: Immediate drop in airImmediate drop in air Exposure continues:Exposure continues:

FoodFood WaterWater SoilSoil Air ???Air ???

Objective of the studyObjective of the study

““To estimate the parameter values (KETo estimate the parameter values (KELILI and and KEKEKIKI) of PBPK model using the observed ) of PBPK model using the observed blood and urine lead levelsblood and urine lead levels””

Routes of humans exposureRoutes of humans exposure

Exposure MechanismExposure Mechanism

• IngestionIngestion Absorption - 50% in Absorption - 50% in childrenchildren

- 10% in adults- 10% in adults• RespirationRespiration Absorption - 50% in children Absorption - 50% in children and adultsand adults

• DermalDermal Absorption Absorption - Insignificant- Insignificant

6%

41% 53%

Food Water Air

Source: Tripathi Source: Tripathi et al.et al., 1997, 1997

DistributionDistribution

BloodBlood Soft tissueSoft tissue BoneBone

Liver, Kidneys, Brain and Muscle

Excretion Urine Bile Sweat Nails Hair

95% of the Pb body burden in bones (O’Flaherty, 1993)

Blood lead level…Blood lead level…

Lead health effects are manyLead health effects are many indicated by blood lead levels (PbB)indicated by blood lead levels (PbB)

PbB – an important biomarkerPbB – an important biomarker

Acceptable levels of PbB Acceptable levels of PbB – – 10 10 g/dLg/dL

0

10

20

30

40

50

60

1965 1970 1975 1985 1991

Source: CDC, 1991Source: CDC, 1991

PBPK ModelPBPK Model PBPK - Physiologically Based Pharmacokinetic ModelPBPK - Physiologically Based Pharmacokinetic Model

mathematical description of uptake and disposition of mathematical description of uptake and disposition of substances to quantitatively describe relationship substances to quantitatively describe relationship among critical biological processamong critical biological process

Requires chemical substance-specific Requires chemical substance-specific physicochemical parameters and species-specific physicochemical parameters and species-specific physiological and biological parametersphysiological and biological parameters

Numerical estimates of parameters are incorporated Numerical estimates of parameters are incorporated with set of differential and algebraic equations that with set of differential and algebraic equations that describes the pharmacokinetic processdescribes the pharmacokinetic process

PBPK model for a chemical substancePBPK model for a chemical substance

Model RepresentationModel Representation

Model ParameterizationModel Parameterization

Model SimulationModel Simulation

Model ValidationModel Validation

Source: Krishna and Anderson, 1994

PBPK Model for LeadPBPK Model for Lead

LungsLungs

Rapidly Perfused TissuesRapidly Perfused Tissues

Slowly Perfused TissuesSlowly Perfused Tissues

BoneBone

KidneyKidney

LiverLiver

Gastrointestinal TractGastrointestinal Tract

Venous BloodVenous Blood Arterial BloodArterial Blood

InhalationInhalation ExhalationExhalation

QQ QQCCvenven CCartart

CCven,RAven,RA

CCven,SLven,SL

CCven,BOven,BO

CCven,KIven,KI

CCven,LIven,LI

AALULU

AAGIGI

KEKEKIKI

KEKELILI

QQRARA

QQSLSL

QQBOBO

QQKIKI

QQLILI

Source: Morisawa Source: Morisawa et al.et al., 2001, 2001

PBPK Model for LeadPBPK Model for Lead

LILILIGIGILIvenartLILI

LI VCKEDACCQdt

dCV

,

KIKIKIKIvenartKIKI

KI VCKECCQdt

dCV

,

RAvenartRARA

RA CCQdt

dCV ,

SLvenartSLSL

SL CCQdt

dCV ,

BOvenartBOBO

BO CCQdt

dCV ,

Liver

Kidney

Rapid Perfused TissuesRapid Perfused Tissues

Slow Perfused TissuesSlow Perfused Tissues

Bone

PBPK Model for LeadPBPK Model for Lead

i

iiven P

CCp ,

iveniveniveniven CpKBIND

BINDCpCpC,

,,, 145.055.0

QCQCQCQCQCQ

C BOvenBOSLvenSLRAvenRAKIvenKILIvenLIven

,,,.,

QCQAQCC inhALUven

art

Partitioning between tissue and plasmaPartitioning between tissue and plasma

Conc. in venousConc. in venousblood of eachblood of eachorganorgan

Model ParametersModel Parameters

Absorption through Inhalation Exposure (AAbsorption through Inhalation Exposure (ALULU)) 30 – 50% (adults)30 – 50% (adults)

Absorption through Gastrointestinal Tract (AAbsorption through Gastrointestinal Tract (AGIGI)) 8 -11% (adults)8 -11% (adults) 40 – 50% (children)40 – 50% (children)

Metabolic Constants (KEMetabolic Constants (KELILI and KE and KEKIKI)) 30% (liver)30% (liver) 70% (kidney)70% (kidney)

Uncertainty and Variability in PBPK modelsUncertainty and Variability in PBPK models

Model errors and data gapsModel errors and data gaps Uncertainty in extrapolating animal data to the case of Uncertainty in extrapolating animal data to the case of

humans (especially metabolic parameters)humans (especially metabolic parameters) Measurement errors and analytical uncertaintiesMeasurement errors and analytical uncertainties Uncertainty in exposure levels and parameter valuesUncertainty in exposure levels and parameter values

Inter-or-intra species variability in kinetics may be due to Inter-or-intra species variability in kinetics may be due to differences in:differences in:

• Physiology (body weight, %body fat, Organ sizes, Physiology (body weight, %body fat, Organ sizes, shapes)shapes)

• Variation (e.g. genetic) in metabolism and biochemistryVariation (e.g. genetic) in metabolism and biochemistry• Co-exposure to other chemicalsCo-exposure to other chemicals• Disease statesDisease states

Methodology of the StudyMethodology of the Study

Selection ofSelection ofSampling locationSampling location

Collection ofCollection ofSamplesSamples Food ItemsFood Items

LaboratoryLaboratoryAnalysisAnalysis

SampleSampleProcessingProcessing DigestionDigestion AnalysisAnalysis

on AASon AAS

Interpretation Interpretation of Dataof Data

Water SamplesWater Samples Air samples

FiltrationFiltration

Urine samples

Blood samples

Parameter Estimation and Risk characterization

Sampling LocationSampling Location

Sample CollectionSample Collection

Air Sample CollectionAir Sample Collection

Food Sample CollectionFood Sample Collection

Blood Sample CollectionBlood Sample Collection

Urine Sample CollectionUrine Sample Collection

GroupsGroups Food ItemsFood ItemsNon-Leafy Non-Leafy VegetablesVegetables

Potato, Brinjal, Tomato, Ladyfinger, Pumpkin, Beans, Potato, Brinjal, Tomato, Ladyfinger, Pumpkin, Beans, Cauliflower, Cucumber, Onion, Gourd, CabbageCauliflower, Cucumber, Onion, Gourd, Cabbage, , Carrot, Radish, Bottle GourdCarrot, Radish, Bottle Gourd

Leafy VegetablesLeafy Vegetables Spinach, Fenugreek, CorianderSpinach, Fenugreek, Coriander

FruitsFruits Banana, Orange, Papaya, Grapes, AppleBanana, Orange, Papaya, Grapes, Apple, Guava, Guava

CerealsCereals Wheat, RiceWheat, Rice

PulsesPulses Moong, Masoor, Arhar, Urad (Green), Urad (Black), Moong, Masoor, Arhar, Urad (Green), Urad (Black), Chana, RajmaChana, Rajma, Chole, Chole

MilkMilk Cow Milk, Buffalo MilkCow Milk, Buffalo Milk

Collection of Food SamplesCollection of Food SamplesCollected using Market Basket methodCollected using Market Basket method

SiteSiteFood GroupFood Group

SinghpurSinghpur BhitoorBhitoor FieldsFields

Non-Leafy VegetablesNon-Leafy Vegetables 2828 2626 1212Leafy VegetablesLeafy Vegetables 66 66 33FruitsFruits 1212 1212 22CerealsCereals 66 66 --PulsesPulses 2424 2424 --

No. of Food Samples Collected for StudyNo. of Food Samples Collected for Study

Collection of Food SamplesCollection of Food Samples

Food Sample CollectionFood Sample CollectionDuplicate Diet Survey

Blood Sample collectionBlood Sample collection

Sample AnalysisSample Analysis

Air Sample AnalysisAir Sample Analysis

Food Sample AnalysisFood Sample Analysis

• Filter Paper ConditioningFilter Paper Conditioning• Sample ExtractionSample Extraction• Instrumentation and AnalysisInstrumentation and Analysis

•Sample ProcessingSample Processing•Sample ExtractionSample Extraction•Instrumentation and AnalysisInstrumentation and Analysis

Sample AnalysisSample Analysis

Blood Sample AnalysisBlood Sample Analysis

Urine Sample AnalysisUrine Sample Analysis

• Sample ExtractionSample Extraction

• Instrumentation and AnalysisInstrumentation and Analysis

• Sample ExtractionSample Extraction

• Instrumentation and AnalysisInstrumentation and Analysis

Sample ExtractionSample Extraction

Temperature Profile used in Digestion

0

50

100

150

200

0 5 10 15Time (minutes)

Tem

pera

ture

(0 C

)

Microwave Digestion System (Ethos Ez Labsatation, Milestone, Italy)

Extraction of PbExtraction of Pb

Sample Analysis: GFAAS (GBC Avanta Sigma)Sample Analysis: GFAAS (GBC Avanta Sigma)

CalibrationCalibration

Working StandardsWorking StandardsWavelength: 283.3 nmWavelength: 283.3 nmVolume injected: 20 Volume injected: 20 LL

Final TemperatureFinal Temperature Ramp TimeRamp Time Hold TimeHold Time Gas TypeGas Type

4040 2.02.0 1.01.0 InertInert

9090 5.05.0 5.05.0 InertInert

120120 10.010.0 5.05.0 InertInert

400400 10.010.0 5.05.0 InertInert

400400 1.01.0 1.01.0 NoneNone

21002100 1.51.5 2.02.0 NoneNone

23002300 1.01.0 1.01.0 InertInert

Graphite Furnace ProgramGraphite Furnace Program

Sample AnalysisSample Analysis

MDL: 0.8 ppbMDL: 0.8 ppb

Recovery Recovery Food Samples: 94-95%Food Samples: 94-95%Blood Samples: 89%Blood Samples: 89%

Risk CharacterizationRisk Characterization

Non-LeafyNon-LeafyVegetablesVegetables WaterWater

LeafyLeafyVegetablesVegetables MilkMilk

FruitsFruits PulsesPulsesCerealsCereals

Monte Carlo SimulationMonte Carlo Simulation

Examine Probability Distribution of lead levels of Food Items and

Quantity of Food Consumed

PBPK Model

Dietary Lead Dietary Lead IntakeIntake

ExposureExposurethrough Airthrough Air

PbBPbB

Risk CharacterizationRisk Characterization

1010g/dLg/dL

RiskRisk

Quantity of Food Consumed Pb Levels in Food Items

Results and DiscussionResults and DiscussionAverage lead levels in food itemsAverage lead levels in food items

22Sharma Sharma et alet al. (2005); . (2005); 33-ATSDR (1999); -ATSDR (1999); 44-Tripathi -Tripathi et al.et al. (1997); (1997); 55-Zhang -Zhang et al.et al. (1998); (1998); 66-Ysart -Ysart et al.et al. (1999); (1999); 77-Urieta -Urieta et al.et al. (1996); (1996); 8**8**-Cuadrado -Cuadrado et al.et al. (1995), only data of Madrid are taken. (1995), only data of Madrid are taken. 9 9*-Krishnamurti *-Krishnamurti and Vishwanathan (1991), only data of Uttar Pradesh are taken.and Vishwanathan (1991), only data of Uttar Pradesh are taken.

Food GroupPresent Study at

Pratap Pur Hari (1)

Urban area,Kanpur (2)

US cities(3)

Bombay(4)

China(5)

Britain(6)

Basque(7)

Madrid(8)**

IEPHM(9)*

Cereals 106.3880.12(25.93–207.01)

n = 6

119.9982.13(28.97–223.90)

n = 8(2–136) 18.2

n = 15

56.4±100.0

(4–616)n = 59

2033

(10–65)n = 12

3041132 170

Pulses 220.80116.47(43.60–405.36)

n = 48

283.28118.42(65.23–415.98)

n = 21

253.3n = 13

33.0±25.6(4–143)n = 34

10(<5–30) 22.43.0 350

Leafy vegeta

bles

317.6861.80(191.68–437.53)

n=15

325.6074.06(181.56–541.61)

n = 32

100.4n = 11 10 430

Non-leafy vegeta

bles

101.9752.80(36.17–243.70)

n = 66

121.9158.29(24.84–279.29)

n = 114(5–649) 4.1

n = 32 2023

(5–45)n = 12

1826 360

Fruits 5.651.77(1.05–17.35)

n = 18

7.326.1(2.22–17.60)

n = 10(5–223) 7.4

n = 7 <1015

(<5–25)n = 10

18119

Milk 0.460.19(ND–0.65)

n = 6

4.082.78(0.4–7.79)

n = 8(3–83) 1.6

n = 4 <109

(<5–20)n = 4

34.91.8 50

Water 3.960.86(3.16–5.25)

n = 6

8.433.99(4.5–16.04)

n = 11< 5 1.2

n = 13 111

Conclusions: Pb concentrations in food items in Kanpur city are high compared to other cities. High in leafy vegetables. Concentration in food items from rural area is somewhat less to urban samples.

Probability Distribution Plots Probability Distribution Plots – Pb Levels in Food Items– Pb Levels in Food Items

Leafy Vegetables

Perc

ent

500450400350300250200

99

9590

80706050403020

105

1

Mean

>0.150

317.7StDev 61.80N 15KS 0.139P-Value

Probability Plot of Leafy VegetablesNormal

Pulses

Perc

ent

5004003002001000

99

9590

80706050403020

105

1

Mean

0.039

220.8StDev 116.5N 24KS 0.186P-Value

Probability Plot of PulsesNormal

Milk

Perc

ent

0.70.60.50.40.30.20.10.0-0.1-0.2

99

9590

80706050403020

105

1

Mean

>0.150

0.2645StDev 0.1936N 4KS 0.182P-Value

Probability Plot of MilkNormal

Non Leafy Vegetables

Perc

ent

3002001000-100

99.9

99

959080706050403020105

1

0.1

Mean

<0.010

102.0StDev 52.81N 66KS 0.146P-Value

Probability Plot of Non Leafy VegetablesNormal

Cereals

Perc

ent

3002001000-100

99

9590

80706050403020

10

5

1

Mean

0.110

106.4StDev 80.12N 6KS 0.291P-Value

Probability Plot of CerealsNormal

Fruits

Perc

ent

20151050-5

99

9590

80706050403020

105

1

Mean

0.048

5.652StDev 4.107N 20KS 0.194P-Value

Probability Plot of FruitsNormal

Conclusion: Except for non leafy vegetables and pulses Pb levels in all food items are normally distributed at 95% confidence.

Probability Distribution Plots Probability Distribution Plots – Food Intake– Food Intake

Non Leafy Vegetables

Perc

ent

1751501251007550

99.9

99

959080706050403020105

1

0.1

Mean

>0.150

117.8StDev 18.19N 68KS 0.056P-Value

Probability Plot of Non Leafy VegetablesNormal

Pulses

Perc

ent

807060504030

99.9

99

959080706050403020105

1

0.1

Mean

>0.150

53.60StDev 7.523N 68KS 0.038P-Value

Probability Plot of PulsesNormal

Milk

Perc

ent

5004003002001000

99.9

99

959080706050403020105

1

0.1

Mean

>0.150

227.9StDev 56.24N 68KS 0.031P-Value

Probability Plot of MilkNormal

Cereals

Perc

ent

700600500400300200

99.9

99

959080706050403020105

1

0.1

Mean

>0.150

439.0StDev 66.83N 68KS 0.025P-Value

Probability Plot of CerealsNormal

Leafy Vegetables

Perc

ent

70605040302010

99.9

99

959080706050403020105

1

0.1

Mean

>0.150

46.10StDev 8.234N 68KS 0.031P-Value

Probability Plot of Leafy VegetablesNormal

Fruits

Perc

ent

6050403020100

99.9

99

959080706050403020105

1

0.1

Mean

>0.150

31.32StDev 8.358N 68KS 0.052P-Value

Probability Plot of FruitsNormal

Conclusion:Food intake for all food items are normally distributed at 95% confidence

• Lead intake through IngestionLead intake through IngestionDiet consumption patternDiet consumption pattern

Food ItemFood Item Food Intake (g/day)Food Intake (g/day)Adult Veg dietAdult Veg dietaa Adult veg dietAdult veg dietbb

CerealsCereals 500500 4394396767PulsesPulses 5757 545488Leafy VegetableLeafy Vegetable 2121 464688Non-Leafy VegetableNon-Leafy Vegetable 113113 1181181818FruitsFruits 1818 313188MilkMilk 163163 22822855WaterWater 2 L2 L 220.50.5

a Source: Planning Commission, India (2002)a Source: Planning Commission, India (2002)b Source: Survey Conducted at Pratap Pur Harib Source: Survey Conducted at Pratap Pur Hari

Lead intakeLead intake• Lead intake through Inhalation Lead intake through Inhalation • Rural – 0.28 Rural – 0.28 µg/m3µg/m3• Urban – 0.66 Urban – 0.66 µg/m3 (Maloo, 2003)µg/m3 (Maloo, 2003)

Pictorial Depiction of Probability exposure Pictorial Depiction of Probability exposure assessmentassessment

x +

Exposure I1 C1I2 C2

= x + x

Exposure I1 I2C1 C2

Exposure using Planning Commission data

Exposure using Field data

=

I = Food intake C = Concentration of Pb in food items

Comparison of Dietary Intake Values obtained Comparison of Dietary Intake Values obtained using Field data and Planning Commission datausing Field data and Planning Commission data

Dietary Lead Intake (microgram/ day)

Freq

uenc

y

450375300225150750

80

70

60

50

40

30

20

10

0

Mean StDev N97.90 53.01 30187.34 40.45 300

VariableField dataPlanning commission data

Normal Probability Density Function

Conclusion:To address the variability/uncertainty actual measurements of dietary Intake should be taken rather than going by fixed food consumption pattern

Blood and Urine Pb LevelsBlood and Urine Pb Levels

Obse

rved

PbB

(m

icro

gram

/dL)

14

13

12

11

10

9

8

7

6

5

Boxplot of Observed PbB

PbB (microgram/ dL)

Freq

uenc

y

13.512.010.59.07.56.04.53.0

30

25

20

15

10

5

0

Mean 8.260StDev 2.006N 300

Normal Probability Distribution Plot for PbB (microgram/ dL)

PbU

(mic

rogr

am/d

L)

14

12

10

8

6

4

2

Boxplot of PbU

PbU (microgram/ day)

Freq

uenc

y

13.512.010.59.07.56.04.53.0

35

30

25

20

15

10

5

0

Mean 8.222StDev 1.936N 300

Normal Probability Distribution Plot for PbU (microgram/ day)

Mean=8.34SD=1.94

Mean=8.37SD=2.02

Comparison of Present Study PbB Levels with Comparison of Present Study PbB Levels with Other StudiesOther Studies

Area No. of Samples

Geometric mean concentration

(μg/dL)Deonar (suburban Bombay)a

28 8.9(2.9-31.2)

Parel (central Bombay)a

60 11.5(2.9-47.7)

Byculla (central

Bombay)a

94 11.9(1.1-35.3)

Greater Bombaya

77 14.4(2.9-41.2)

Kanpurb 24 18(ND-140)

Present study 68 8.34(4.56-13.59)

Source a : R. N. Khandekar et at, (1987) Source b: Seth (2000)

Conclusion:PbB observed in present study are comparable to that of Deonar Study Study by Seth (2000) shows higher levels as data reported is for year 1996 when leaded gasoline was used

PbB and PbU LevelsPbB and PbU LevelsArea Survey

SiteNumber of

SubjectsAge PbB

(µg/L)PbU (µg/L) Correlation

CoefficientsReferences

Bangkok 52 19-57 32.3 (1.37) 2.35 (1.70) 0.31a Zhang etal._1998a.

Kuala Lumpur 47 21-47 65.4 (1.4) 4.74 (1.79) 0.43b Moon et al._1996.

Manila 45 21-64 37 (1.36) 3.64(1.82) 0.08 Zhang et al._1998b.

Tainan 51 22-66 33.9 (1.26) 1.54 (1.99) 0.12 Ikeda et al._1996.

Beijing 50 20-62 43.4(1.38) 5.73(1.69) 0.31a Zhang et al._1997.

Jinan 50 21-55 35.3(1.44) 2.16(1.55) 0.27 Ibid.

Nanning 50 23-57 54.5(1.42) 1.57(1.99) 0.38b Ibid.

Shanghai 50 23-58 55.4(1.47) 1.81(1.8) 0.45b Ibid.

Xian 50 24-58 43.4(1.32) 3.34(2.14) 0.02 Kae Higashikawa et al., 2000

Tokyo Kyoto 61 40-68 37.7(1.7) 1.74(2.63) 0.63b Shimbo et al._1999.

Seoul Pusan 55 31-49 47.2(1.27) 3.11(2.02) 0.11 Moon et al._1995.

--- 84 --- 300 21.33 0.9a Gross, 1979

Pratap Pur Hari

35 20-45 82.3(16.1) 5.58(1.34) 0.82a The present study

Numbers in the parentheses show standard deviation a. P < 0.05b. P < 0.01

Conclusions: High correlation between PbB and PbU was observed in present study, Study by Gross (1979) and Shimbo et al. (1999). If PbB levels are high, kidney enhances its performance in terms of getting toxic metals out of system

Relationship of Urinary Lead Excretion rate and Blood Lead Concentration

56789

1011121314

5 6 7 8 9 10 11 12 13 14 15Blood Levels (microgram/dL)

Urin

ary

Lead

Exc

retio

n (m

icro

gram

/day

)Relationship of Urinary Lead Excretion Rate and PbB

Present Study

Gross, 1979

Conclusions: Trend is comparable with that of Gross, 1979 KEKI may be variable from one person to another

Validation of PBPK ModelValidation of PBPK Model

Morisawa Morisawa et al.et al. (2001) examined for reliability of PBPK model by (2001) examined for reliability of PBPK model bycomparing simulated results with experimental datacomparing simulated results with experimental data

Same exercise performed in present study on same data using Same exercise performed in present study on same data using Mathematica program for confidence on model performanceMathematica program for confidence on model performance

Experiment I (Rabinowitz Experiment I (Rabinowitz et al.et al. (1976)) (1976))

SubjectSubject Dose patternDose pattern Body Weight Body Weight (kg)(kg)

Dose Rate Dose Rate ((g/day)g/day)

Dose period Dose period (days)(days)

AA DietaryDietary 7070 204204 104104

Subject A

Time (day)0 100 200 300

Blo

od le

ad le

vel (

mic

rogr

am/d

L)

0

2

4

6

8ObservedEstimated

Validation of PBPK ModelValidation of PBPK Model

Dots represent experimental dataSolid line output by Mathematica program

Conclusion:The output from Mathematica program matches with experimental data

Performance of PBPK ModelPerformance of PBPK Model

Measured and Modeled PbB levels for age group 30-40 yrs

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20 25 30 35

Subject

PbB

leve

ls (m

icro

gram

/dL)

Conclusion:In no case PbB level for an individual was outside the model computed range of his/her interval estimate of PbB.

Parameters (KEParameters (KELILI, KE, KEKIKI) Estimation) Estimation Steady state PBPK Model

,( ) 0LI art ven LI GI GI LI LI LIQ C C A D KE C V

0, KIKIKIKIvenartKI VCKECCQ

Cart = Cven, RA

Cart = Cven, SL

Cart = Cven, BO

……….(2)

……(1)

……………………………………………(3)

……………………………………………(4)

……………………………………………(5)

i

iiven P

CCp ,

iveniveniveniven CpKBIND

BINDCpCpC,

,,, 145.055.0

Cart = Cven

QCQCQCQCQCQ

C venBOvenSLvenRAKIvenKILIvenLIven

,,

Let us take,

MUout = KEKICKIVKI (mass/day)

MUout = Mass of lead excreted in urine (mass/day)

Cont……………………………………………………….(6)

…………….(7)

……..(9)

……………………………………………………(8)

MUout = PbU x Urine dischargeFrom eq. (2),

KI

outartKIven Q

MUCC ,

Recall Cart = Measured PbB from subjects, Cven,KI for all subjects calculated from eq (10)

…………………………………….(10)

Rewriting eq (9) to obtain Cven,LI

LI

venBOBOSLvenSLRAvenRAKIvenKIvenLIven Q

CQCQCQCQQCC

)( ,,,,

……(11)

Cont……

RHS of eq (11) is known

Calculate Cven,LI and Cven,KI Corresponding CPi forLiver and kidney

CPi Ci

Concentration of Pb in organ/tissue is known

Recall,

MUout = KEKICKIVKI…………………………………(12)

In eq (12) all variables known, KEKI can be estimated

In eq (1) all variables known, KELI can be estimated

Cont……

Variation In KE_LI Value

0

0.05

0.1

0.15

0.2

0.25

0.3

0 5 10 15 20 25 30 35 40

Subject

KE_L

I (1/

day)

KE_LI (1/ day)

Freq

uenc

y

0.240.210.180.150.120.09

40

30

20

10

0

Mean 0.1602StDev 0.03225N 300

Normal Probability Distribution Plot for KE_LI

KE_LI

Perc

ent

0.250.200.150.100.05

99

9590

80706050403020

105

1

Mean

0.140

0.1585StDev 0.03372N 35KS 0.129P-Value

Probability Plot of KE_LINormal

KELI

Mean = 0.16SD = 0.03

Variation in KE_KI Value

00.10.20.30.40.50.60.70.80.9

0 5 10 15 20 25 30 35 40

Subject

KE_K

I (1/

day)

KE_KI (1/ day)

Freq

uenc

y

0.90.80.70.60.50.40.3

60

50

40

30

20

10

0

Mean 0.6643StDev 0.1095N 300

Normal Prbability Distribution Plot for KE_KI

KE_KI

Perc

ent

1.00.90.80.70.60.50.4

99

9590

80706050403020

105

1

Mean

>0.150

0.6554StDev 0.1117N 35KS 0.106P-Value

Probability Plot of KE_KINormal

KEKI

Mean = 0.66SD = 0.11

Conclusion: Metabolic parameters (KELI and KEKI) show substantial variation and one should take these parameters as random variables in model to fully reflect the uncertainties caused due to variability in KELI and KEKI

Group Philadelphia Cab-

drivers

StarkeFL

BarksdaleWI

Los AngelesCab-drivers

Los AnglesOffice workers

Present Study

PbA (μg/m3) 2.62 0.81 1.01 6.10 3.06 0.28

PbB (μg/dl) 21.6 15 12.9 23.7 18.9 8.23

PbU(μg/day) 22.7 15.2 18.2 26.4 20 8.37

RenalClearance

(kg/day)

0.104 0.095 0.135 0.11 0.103 0.101±

0.015

Lead in air, blood and urine (Azar et al., 1975)

Conclusions: Average value of clearance is close to the value reported in other studies through renal clearance. This study additionally provides information on associated uncertainties in renal clearance.

Parameter SensitivityParameter Sensitivity

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1

KE_KI(1/day)

PbB(

mic

rogr

am/d

L)

0

2

4

6

8

10

12

14

0 0.05 0.1 0.15 0.2 0.25

KE_LI(1/day)

PbB(

mic

rogr

am/d

L)

Conclusions:Varied in range – 0.43 0.54 0.66 0.87

Unit change in KEKI – PbB inc/dec by 6 µg/dL

In plausible range of KEKI – error in PbB estimate can be ±15%

Conclusions:Varied in range – 0.09 0.12 0.16 0.19

Unit change in KELI – PbB inc/dec by 34 µg/dL

In plausible range of KELI – error in PbB estimate can be ±23%

Probabilistic Risk Characterization: ImprovementsProbabilistic Risk Characterization: Improvements

=

PbBParameters (KELI, KEKI)

(fixed)

Food Intake (variable)

Pb Concentration

in Food (Variable)

=

PbB

Parameters (KELI, KEKI)

(fixed)

Food Intake (fixed)

Pb Concentration in Food (Variable)

=

PbBParameters (KELI, KEKI) (variable)

Food Intake (variable)

Pb Concentration in Food (Variable)

Case1: Variability only in Pb concentration in food intake

Case2: Variability in food consumption and concentration

Case3: Variability in food consumption, concentration and parameters (KELI, KEKI)

PbB (microgram/ dL)

Freq

uenc

y

121086420

18

16

14

12

10

8

6

4

2

0

Mean

5.043 1.432 100

StDev N4.580 1.161 1004.856 1.367 100

VariableCase1Case2Case3

Normal Probability Distribution Plot Case1, Case2, Case3

8.9x10-5

5.4x10-4

9.3x10-3

Case 1

Case 2

Case 3

Risk Estimation

Conclusions:The results suggest that by not considering the uncertainties, the error in risk characterization will be underestimated and risk engineers will err on side of false protection.Therefore it is important to address/include the uncertainties in risk Characterization.

8.9x10-5

Case 1

Case 2

ConclusionsConclusions

The PBPK model parameters (food intake, Pb The PBPK model parameters (food intake, Pb concentration food items, KEconcentration food items, KEKIKI and KE and KELILI) vary from person ) vary from person to person to a large extent and thus they should be to person to a large extent and thus they should be considered as random variables. considered as random variables.

Parameter values (KEParameter values (KEKIKI and KE and KELILI) were found sensitive to ) were found sensitive to model output (PbB). In the plausible range of KEmodel output (PbB). In the plausible range of KEKIKI and and KEKELILI, the error in PbB estimates can be ±15% and ±23% , the error in PbB estimates can be ±15% and ±23% respectively.respectively.

Overall risk characterization was done by considering Overall risk characterization was done by considering these parameters as variables.these parameters as variables.

ConclusionsConclusions The results suggest that by not considering the The results suggest that by not considering the

uncertainties, the error in risk characterization will be uncertainties, the error in risk characterization will be underestimated as given below:underestimated as given below:

Variability only in Pb concentration in food Variability only in Pb concentration in food intakeintake

8.98 x 108.98 x 10-5-5

Variability in food consumption and Variability in food consumption and concentration concentration

5.43 x 105.43 x 10-4 -4

Variability in food consumption, Variability in food consumption, concentration and parameters (KEconcentration and parameters (KEKI KI and and KEKELILI) )

9.34 x 109.34 x 10-3-3

ConclusionsConclusions

It can be concluded that by not considering the uncertainties, the error in risk characterization will be underestimated. While wishing to remain conservative in the quantification of risk to err on the side of protection of humans and the environment, an underestimated uncertainty (e.g., food intake, Pb concentration food items, KELI and KEKI) may eclipse safety and may result in a false sense of protection.