## Supplementary Data

Physiological Parameters To model human gestation and lactation periods, female specific parameters were used to the extent possible for describing the mat ernal part of the model (Table 1 ). Human pregnancy duration was
modeled as 9 m onths. Physiological parameters for non

- pregnant and non

- lactating adult females were used as initial values for pregnant female on gestation day 0 ( GD 0 ) to simulate the gestation period. The parameters for the fetus at the end of gestation were used as i nitial parameter values on postnatal day 0 ( PND 0 ) to simulate neonates. Maternal parameters that are changing during pregnancy and the end of gestation values were either directly used or appropriately adjusted for post

- partum changes and then used
as ini tial values on PND 0 to simulate the lactating mother. Most of the adult female parameters were kept the same in pregnant and lactating females except the parameters changing with time during the respective life stages. Time dependent changes in parameters during gestation and lactation were described using several different growth equations and/or TABLE function in acslX program to interpolate between data points as described below.

S 1. Calculation of maternal body weight (kg; BW G ) and tissue volumes (L) during gestation
BW G = BW i +(VF G - VF i )+VFet+(VM G - VM i )+VPla+(VUtr G - VUtr i )+(VBld G - VBld i ) (Eq. S 1
- 1)
VM G = BW i *(VMC i +(0.0065*exp(

- 7.44*(exp(

- 0.00068*T))))) (Eq. S 1
- 2)
Vf G = BW i *(VFC i +(0.09*exp(

- 12.91*(exp(

- 0.00080*T))))) (Eq. S 1
- 3)
VUtr = BW i *(VUtrC i + (0.02*exp(

- 4.72*(exp(

- 0.00038*T))))) (Eq. S 1
- 4)

, where the subscript i denotes for pre

- conception period, i.e., non

- pregnant and non

- lactating adult female stage that wa s also as GD0 in the current model, while the subscript G represent gestation pe riod for the mother. The ‘T’ denotes gestation period as time (hr). The abbreviations for VF G , VFet, VM G ,VPla, VUtr, and VBld G represent volumes for fat, fetus, mammary gland, placenta, uterus, and blood,

respectively. The density of the tissue was assume d to be one.

S 2. Calculation of placental volume (L) during gestation in humans VPla = 0.85*exp(

- 9.43*(exp(

- 5.23E

- 4*T))) (Eq. S 2)

S 3. Describing maternal cardiac output during pregnancy (L/hr; QC G ) QC G = QC i +(QF G - QF i )+(QM G - QM i )+QPla+(QUtr G - QUtr i ) (Eq. S 3
- 1)

, where QC i equals QCC i * BW i 0.75 and QF, QM, QPla, and QUtr indicate blood flow to fat, mammary gland, and uterus, respectively. It was assumed that the changes in tissue blood flow are proportional to
their volume ch anges (Gentry et al. , 2002)

. QM G = QM i * (VM G

/VM i ) (Eq. S 3
- 2) QF G = QF i * (VF G /VF i ) (Eq. S 3
- 3) QUtr G = QUtr i * (VUtr G /VUtr i ) (Eq. S 3
- 4)

S 4. Calculating maternal blood volume (L; VBl d G ) during pregnancy Blood volume changes during gestation were modeled accounting both for plasma volume expansion and red blood cell (RBC) mass increase in human pregnancy compared to the volume and mass in pre

gestation period (Hytten, 1985) . A linear increase in volume during gestati on was assumed reaching 150 % and 118 % of pre

- conception values for plasma and RBCs, respectively. The hematocrit was
assumed to be 40% of the total blood volume in adult female.
VBLD G = VBLD i x(1

- HCT)x(1+(0.5*GD)/270) + VBLD i xHCTx(1+(0.18*GD)/270) (Eq. S 4)

, where HCT is 0.4, a hematocrit.

S 5. Placental blood flow during pregnancy (L/hr; Qpla) and fetal cardiac output (L/hr; QC F )Total cardiac output in the fetus was calculated using cardiac index (L/hr/kg; QCI) reported in human

fetus (Kiserud et al. , 2006) . They reported that one third of the total cardiac output in fetus distributed to the placenta, while the rest was distributed in the fetus. Hence, QPla = (QCI*BW F )/3 (Eq. S 5
- 1) QC F = (QC I*BW F )*(2/3) (Eq. S 5
- 2)

, where the subscript F indicates the fetus and QCI = 24 L/hr/kg.

S 6. Volume of human fetus (L; BW F ) The volume of human fetus was modeled using a Gompertz equation from Corley et al. (2003) , which was slightly modified to match the birth weight of male infants that was used in the current model (ICRP, 2003)

. BW F = [ 0.0015*exp { ( 0.197/0.013)*(1

- exp(

- 0.013*GD)) }] 1000 (Eq. S 6) where GD represents gestational age in days.

S 7. Volume of human fetal brain , total volume (L; VBrn F ) and f ractional volumes for each region Fetal brain volume data obtained from ICRP publication 89 (ICRP, 2003) were fitted with a Gompertz

g rowth curve using GraphPad Prism (version 4, Graphpad software, Inc., La Jolla, CA). From 8 weeks of gestation to birth, VBrn F was expressed using Eq. S 7

- 1.
VBrn F = (

- 3.8+1458*exp(

- exp((2.72*24.6/1458)*(22.95

- GW)+1)))/1000 (Eq. S 7
- 1)

, where GW repres ent the gestational age in weeks. Before GW8, the fraction of fetal brain volume over
BW F was assumed to be constant, the fraction being the same as the fraction at GW8 as follows:
VBrn F = [(VBrn F @GW8 )/(BW F @GW8 )] * BW F (Eq. S 7
- 2)

Fractional volum es for fetal and neonatal globus pallidus and cerebellum were adapted from the information for the earliest age available based on q uantitative m agnetic r esonance i maging of h uman
b rain d evelopment (Giedd et al. , 19 96) . Total brain volume for 5 year old age to convert these regionalvolumes to fractional volumes was adapted from Bjorkman’s study (2005) . The fraction of olfactory in

the fetus and neonates was assumed to be t he same as that of the adults.

S 8. Maternal BW L (kg) during lactation Maternal BW at term (BW tr ) was the BW G at the end of gestation excluding the fetus weight. The increment in tissue volumes (as a fraction of BW i ) for fat and mammary gland were added t o the initial
BW G at GD0, i.e, BW i to obtain BW tr following Eq. S 8

- 1, the values 0.0836 and 0.0059 were the final increment values for fat and mammary gland, respectively. Volumes of fat (VF L ) and mammary gland (VM L ) during lactation were calculated using Eqs. S 8

- 2 to 5. The increase in mammary tissue volume was calculated as an increase in tissue volume from post

- pregnancy to a peak at 2 weeks postpartum which was maintained to the end of pregnancy as previously described in human pregnancy model for isopr opanol (Gentry , et al. , 2002) . The increment in the volume of mammary tissue (∆VMC), expressed
as a fraction of BW i , at the peak and the term were to obtain the peak 3.2778 fold of increase in mammary tissue volume over the pre

- pregnancy volume (TABLE S 2). The mean volume of mammary g land used in calculating the fold of increase was 360g in pre

- pregnancy period and 1180g during lactation (ICRP, 2003) . The change in f

at volume during lactation similarly modeled. The decrement in fat tissue volume, ∆VFC expressed as a fraction of BW i , was described as a linear decrease from 0.0836 to 0 over the period of lactation (TABLE S 3). Then, BW L was described by incorporating inc reases in the mammary gland and fat postpartum (Eq. S 8

- 6).
BW tr = BW i *(1 +(0.0836+0.0059)) (Eq. S 8
- 1)
VM tr = (VMC i + 0.0059)*BW i (Eq. S 8
- 2)
VM L = (1 + (∆VMC/VMC i ))*(VMC i *BW i ) (Eq. S 8
- 3)
VF tr = (VFC i +0.0836)*BW i (E q. S 8
- 4)
VF L = VFC i *BW i +∆VFC*BW i (Eq. S 8
- 5)
BW L = BW tr +(VM L - VM tr ) +(VF L - VF tr ) (Eq. S 8
- 6)S 9. Calculating maternal tissue blood flows (L/hr) during lactation

The total cardiac output during lactation was modeled as a sum of initial cardiac output at term plus the changes in mammary gland tissue and fat during lactation assuming that the change in blood flow to a tissue is proportional to its volume change during lactation (Gentry et al. , 2003) . Total cardiac output at term was described using the same way as ca lculating the BW tr . QM tr = QMC i *QC i *(∆VMC tr /VMC i ) (Eq. S 9
- 1) QM L = QM tr *(VM L *VM tr ) (Eq. S 9
- 2) QF tr = QFC i *QC i *(∆VFC tr /VFC i ) (Eq. S 9
- 3) QF L = QF tr *(VF L

/VF tr ) (Eq. S 9
- 4) QC i = QCC i *BW i 0.75 (Eq. S 9
- 5) QC tr = QC i *(1+(QFC*((∆VFC tr /VFC)

- 1))+(QMC*((∆VMC tr /VMC)

- 1))) (Eq. S 9
- 6) QC = QC tr + (QM L - QM tr )+ (QF L - QF tr ) (Eq. S 9
- 7)

S 10. Describing the neonatal body weight (L; BW N ) Body weights of the male neonate and child were described using growth equations from the published human lifestage model (Clewell et al. , 2004) . The birth weight (BW N 0) of the neonate was obtained from the current gestation model and was 3.52 kg.
Age (months) Equation ≤ 40 BW N = (13.64*(1.0

- exp(

- 0.056*months)))+ BW N 0 (Eq. S 10
- 1) 40

- 162 BW N = (312.61*(1.0

- exp(

- 0.039*exp(0.0102*months))))

- 2.22 (Eq. S 10
- 2)
162

- 303 BW N = 2.35*exp(3.53*(1.0

- exp(

- 0.014*months))) (Eq. S 10
- 3)
> 303 BW N = (2.19E

- 8*months 3 )

- (1.22E

- 4*months 2 )+(0.12*months)+50.82 (Eq. S 10
- 4)

S 11. Maternal QPC G (L/hr/kg 0.75 ) during gestation
TABLE S 1.

Gestation (we eks) QPC G

(L/hr/kg 0.75 ) 0 1.012 1.5

38 1.5

Alveolar ventilation during human pregnancy is known to be increasing, largely during the 2 nd and third
trimester about 50

– 70% (Bonica, 1995) . QP G was modeled to achieve about 50% and 7 0 % greater QP values compared to GD0 in the second trimester and at the end of pregnancy, respectively, by varying QPC G over the period of gestation. The increase in QP during pregnancy was largely due to an increase in
the tidal volume and the reduced re sidual capacity and there seemed to be no significant pregnancy

induced changes in respiratory frequency (Spätling L, 1992) . These changes were entered as lung parameters in MPPD program to sim ulate the three trimesters during pregnancy as follow: Tidal volume was increased by 15% and 27% of non

- pregnancy value during the second and the third trimesters, respectively (Spätling L, 1992 ) , while the functional residual capacity (FRC) was 20% decreased throughout the pregnancy (Moore, 1994) . This increase in alveolar ventilation returns to non

- pregnant level within two to three months (double check) post

- partum (S pätling L, 1992) . In the current model, QP was assumed to return to preconception value right after delivery, so QP in lactating women was the same as adult female (Table 2). The resulting deposition fractions in nasal (including both respiratory and
olfa ctory) and lung were incorporated in the model using TABLE function (TABLE S 2).
TABLE S 2.
Gestation (weeks) FdepLu G FdepNR G FdepNO G 0 0.226 0.334 0.0176 12 0.254 0.353 0.0186 38 0.255 0.371 0.0196

S 12. The increment in the volume of the mammary gla nd as a fraction of BW i during lactation
TABLE S 3.
Lactation (hours) ∆ VMC 0 (also at term) 0.0059 336 0.0135 4032 0.0135S 13. The decrement in the volume of the fat as a fraction of BW i during lactation
TABLE S 4.
Lactation (hours) ∆ VFC 0 (also at t erm) 0.0836 4032 0.0

S 14. Volume of neonatal tissues Changes in tissue volumes during postnatal growth were described using the data obtained from ICRP publication89 (ICRP, 2003) . For the lung, tissue only values were adopted for incorporation in the model. The bone volume was the sum of total bone, total marrow, and cartilage as reported in ICRP 89. Initial
tissue volumes at birth we re obtained from the current gestation model, the end of gestation values from the fetus. TABLE functions were used to incorporate age

- dependent tissue volumes in neonate and child
in the model.
TABLE S 5. Neonatal Blood volume (as a fraction of BW N ) Age ( Years) Fractional blood volume (VBLDC N ) 0 0.083 1 0.053 5 0.079 10 0.078 15 0.086 25 0.077 40 0.077

TABLE S 6. Neonatal Liver volume (as a fraction of BW N ) Age (Months) Fractional liver volume (VLivC N ) 0 0.037 0.1 0.0445 1 0.0414 2 0.0383 3 0. 0363 4 0.0379 5 0.039

TABLE S 7. Neonatal Brain volume (as a fraction of BW N )Age (Years) Fractional brain volume (VBrnC N )

0 0.109 0.5 0.093 1 0.092 2 0.089 5 0.069

TABLE S 8. Neonatal Lung volume (tissue only; as a fraction of BW N ) Age (Years ) Fractional lung volume (VLungC N ) 0 0.009 1 0.008 5 0.007

TABLE S 9. Neonatal Bone volume (as a fraction of BW N ) Age (Years) Fractional lung volume (VBoneC N ) 0 0.1 1 0.112 5 0.124

S 15. Ventilation rates in neonates and children
For neonate and child, recommended pulmonary rates (m 3 /day) for long term exposure in children provided in US EPA child

- specific exposure factors handbook (2002) were converted to alveolar ventilation rates assuming that approximately two thirds of pulmonary ventilation i s alveolar ventilation. The recommended ventilation values in US EPA (2002) are based on typical activity levels at different

ages.
S 16. Milk production/suckling rate constant (klac C ) Milk production rate (L/hr) was described as Gentry et al (2003) which adopted Cas ey et al. (1985)
data (TABLE S 10). Similar pattern of milk volume changes over the period of lactation in humans was also reported by Dewey and Lonnerdal (1983) . It was assumed that the milk production rate equals to suckling rate.
TABLE S 10

.Age (Hours) Milk production rate (L/hr, kLacC)

0 0.0005 12 0.0005 36 0.0035 50 0.0104 84 0.016 108 0.0192 180 0.0226 324 0.0256 492 0.0266 660 0.0299 73 2 0.03229 4320 0.03229 note: time 0 and 12 hr were both the value for the first day of lactation in Casey et al. (1985) and used in this way to prevent volume 0 at time 0. The volume was used to calculate milk Mn concentration and
volume should not be ze ro.REFERENCES:

Bjorkman, S. (2005). Prediction of drug disposition in infants and children by means of physiologically based pharmacokinetic (pbpk) modelling: Theophylline and midazolam as model drugs. Br J Clin Pharmacol 59 , 691

- 7 04. Bonica, J. J. (1995). Maternal anatomic and physiological alterations during pregnancy and parturition (M. J. Bonica JJ, Ed.^ Eds.), pp. 45

- 83. Williams & Wilkins, Baltimore. Casey, C. E., Hambidge, K. M. and Neville, M. C. (1985). Studies in human lac tation: Zinc, copper, manganese and chromium in human milk in the first month of lactation. Am J Clin Nutr 41 , 1193

- 200. Clewell, H. J., Gentry, P. R., Covington, T. R., Sarangapani, R. and Teeguarden, J. G. (2004). Evaluation of the potential impact of age

- and gender

- specific pharmacokinetic differences on tissue dosimetry. Toxicol Sci 79 , 381

- 93. Corley, R. A., Mast, T. J ., Carney, E. W., Rogers, J. M. and Daston, G. P. (2003). Evaluation of physiologically based models of pregnancy and lactation for their application in children's health risk assessments. Crit Rev Toxicol 33 , 137

- 211. Dewey, K. G. and Lonnerdal, B. (1983) . Milk and nutrient intake of breast

- fed infants from 1 to 6 months: Relation to growth and fatness. J Pediatr Gastroenterol Nutr 2 , 497

- 506. Gentry, P. R., Covington, T. R., Andersen, M. E. and Clewell, H. J., 3rd (2002). Application of a physiologically based pharmacokinetic model for isopropanol in the derivation of a reference dose and reference concentration. Regul Toxicol Pharmacol 36 , 51

- 68. Gentry, P. R., Covington, T. R. and Clewell, H. J., 3rd (2003). Evaluation of the potential impact of pharmaco kinetic differences on tissue dosimetry in offspring during pregnancy and lactation. Regul Toxicol Pharmacol 38 , 1

- 16. Giedd, J. N., Snell, J. W., Lange, N., Rajapakse, J. C., Casey, B. J., Kozuch, P. L., Vaituzis, A. C., Vauss, Y. C., Hamburger, S. D., Ka ysen, D. and Rapoport, J. L. (1996). Quantitative magnetic resonance imaging of human brain development: Ages 4

- 18. Cereb Cortex 6 , 551

- 60. Hytten, F. (1985). Blood volume changes in normal pregnancy. Clin Haematol 14 , 601

- 12. ICRP (2003). Basic anatomical and physiological data for use in radiological protection: Reference values Ed.^ Eds.). The International Commission on Radiological Protection. Kiserud, T., Ebbing, C., Kessler, J. and Rasmussen, S. (2006). Fetal cardiac output, distribution to the place nta and impact of placental compromise. Ultrasound Obstet Gynecol 28 , 126

- 36. Moore, P. J. (1994). Maternal physiology during pregnancy (A. H. a. P. Decherney, M.L. , Ed.^ Eds.), pp. 146

- 154. McGraw

- Hill Companies.Spätling L, F. F., Huch A, Huch R, Rooth G. (1992). The variability of cardiopulmonary adaptation to

pregnancy at rest and during exercise. BJOG: An International Journal of Obstetrics & Gynaecology 99 (Supplement 8) , 10

- 13.