Supplementary Data 

Physiological Parameters

To model human gestation and lactation periods, female specific parameters were used to the 

extent possible for describing the maternal part of the model (Table 1). Human pregnancy duration was 

modeled as 9 months. 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 initial 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 initial 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. 

S1. Calculation of maternal body weight (kg; BWG) and tissue volumes (L) during gestation

BWG = BWi+(VFG-VFi)+VFet+(VMG-VMi)+VPla+(VUtrG-VUtri)+(VBldG-VBldi) (Eq. S1-1)

VMG = BWi*(VMCi+(0.0065*exp(-7.44*(exp(-0.00068*T))))) (Eq. S1-2)

VfG = BWi*(VFCi+(0.09*exp(-12.91*(exp(-0.00080*T))))) (Eq. S1-3)

VUtr = BWi*(VUtrCi+(0.02*exp(-4.72*(exp(-0.00038*T))))) (Eq. S1-4)

, where the subscript i denotes for pre-conception period, i.e., non-pregnant and non-lactating adult 

female stage that was also as GD0 in the current model, while the subscript G represent gestation period 

for the mother. The ‘T’ denotes gestation period as time (hr). The abbreviations for VFG, VFet, VMG, 
VPla, VUtr, and VBldG represent volumes for fat, fetus, mammary gland, placenta, uterus, and blood, 

respectively. The density of the tissue was assumed to be one. 

S2. Calculation of placental volume (L) during gestation in humans

VPla = 0.85*exp(-9.43*(exp(-5.23E-4*T))) (Eq. S2)

S3. Describing maternal cardiac output during pregnancy (L/hr; QCG)

QCG = QCi+(QFG-QFi)+(QMG-QMi)+QPla+(QUtrG-QUtri) (Eq. S3-1)

, where QCi equals QCCi * BWi

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 changes (Gentry et al., 2002). 

QMG = QMi * (VMG/VMi) (Eq. S3-2)

QFG = QFi * (VFG/VFi) (Eq. S3-3)

QUtrG = QUtri * (VUtrG/VUtri) (Eq. S3-4)

S4. Calculating maternal blood volume (L; VBldG) 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 pregestation period (Hytten, 1985). A linear increase in volume during gestation 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. 

VBLDG = VBLDi x(1-HCT)x(1+(0.5*GD)/270) + VBLDi xHCTx(1+(0.18*GD)/270) (Eq. S4)

, where HCT is 0.4, a hematocrit. 

S5. Placental blood flow during pregnancy (L/hr; Qpla) and fetal cardiac output (L/hr; QCF)
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*BWF)/3 (Eq. S5-1)

QCF = (QCI*BWF)*(2/3) (Eq. S5-2)

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

S6. Volume of human fetus (L; BWF)

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). 

BWF = [0.0015*exp{(0.197/0.013)*(1-exp(-0.013*GD))}] 1000 (Eq. S6)

where GD represents gestational age in days. 

S7. Volume of human fetal brain, total volume (L; VBrnF) and fractional volumes for each region 

Fetal brain volume data obtained from ICRP publication 89 (ICRP, 2003) were fitted with a Gompertz 

growth curve using GraphPad Prism (version 4, Graphpad software, Inc., La Jolla, CA). From 8 weeks of 

gestation to birth, VBrnF was expressed using Eq. S7-1. 

VBrnF = (-3.8+1458*exp(-exp((2.72*24.6/1458)*(22.95-GW)+1)))/1000 (Eq. S7-1)

, where GW represent the gestational age in weeks. Before GW8, the fraction of fetal brain volume over 

BWF was assumed to be constant, the fraction being the same as the fraction at GW8 as follows: 

VBrnF = [(VBrnF @GW8)/(BWF @GW8)] * BWF (Eq. S7-2)

Fractional volumes for fetal and neonatal globus pallidus and cerebellum were adapted from the 

information for the earliest age available based on quantitative magnetic resonance imaging of human 

brain development (Giedd et al., 1996). Total brain volume for 5 year old age to convert these regional 
volumes to fractional volumes was adapted from Bjorkman’s study (2005). The fraction of olfactory in 

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

S8. Maternal BWL (kg) during lactation

Maternal BW at term (BWtr) was the BWG at the end of gestation excluding the fetus weight. The 

increment in tissue volumes (as a fraction of BWi) for fat and mammary gland were added to the initial 

BWG at GD0, i.e, BWi to obtain BWtr following Eq. S8-1, the values 0.0836 and 0.0059 were the final 

increment values for fat and mammary gland, respectively. Volumes of fat (VFL) and mammary gland 

(VML) during lactation were calculated using Eqs. S8-2 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 

isopropanol (Gentry, et al., 2002). The increment in the volume of mammary tissue (∆VMC), expressed 

as a fraction of BWi, 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 S2). The mean volume of mammary gland used in 

calculating the fold of increase was 360g in pre-pregnancy period and 1180g during lactation (ICRP, 

2003). The change in fat volume during lactation similarly modeled. The decrement in fat tissue volume, 

∆VFC expressed as a fraction of BWi, was described as a linear decrease from 0.0836 to 0 over the period 

of lactation (TABLE S3). Then, BWL was described by incorporating increases in the mammary gland 

and fat postpartum (Eq. S8-6). 

BWtr = BWi *(1 +(0.0836+0.0059)) (Eq. S8-1)

VMtr = (VMCi + 0.0059)*BWi (Eq. S8-2)

VML = (1 + (∆VMC/VMCi))*(VMCi*BWi) (Eq. S8-3)

VFtr = (VFCi +0.0836)*BWi (Eq. S8-4)

VFL = VFCi*BWi +∆VFC*BWi (Eq. S8-5)

BWL = BWtr+(VML-VMtr) +(VFL-VFtr) (Eq. S8-6)
S9. 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 calculating the BWtr. 

QMtr = QMCi*QCi*(∆VMCtr/VMCi) (Eq. S9-1)

QML = QMtr*(VML*VMtr) (Eq. S9-2)

QFtr = QFCi*QCi*(∆VFCtr/VFCi) (Eq. S9-3)

QFL = QFtr*(VFL/VFtr) (Eq. S9-4)

QCi = QCCi*BWi

0.75 (Eq. S9-5)

QCtr = QCi*(1+(QFC*((∆VFCtr /VFC)-1))+(QMC*((∆VMCtr /VMC)-1))) (Eq. S9-6)

QC = QCtr + (QML - QMtr)+ (QFL - QFtr) (Eq. S9-7)

S10. Describing the neonatal body weight (L; BWN)

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 (BWN0) of the neonate was obtained from 

the current gestation model and was 3.52 kg. 

Age (months) Equation

≤ 40 BWN = (13.64*(1.0-exp(-0.056*months)))+ BWN0 (Eq. S10-1)

40 - 162 BWN = (312.61*(1.0-exp(-0.039*exp(0.0102*months))))-2.22 (Eq. S10-2)

162 - 303 BWN = 2.35*exp(3.53*(1.0-exp(-0.014*months))) (Eq. S10-3)

> 303 BWN = (2.19E-8*months3)-(1.22E-4*months2)+(0.12*months)+50.82 (Eq. S10-4) 

S11. Maternal QPCG (L/hr/kg0.75) during gestation

TABLE S1. 

Gestation 

(weeks)

QPCG

(L/hr/kg0.75)

0 1.0
12 1.5

38 1.5

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

trimester about 50 – 70% (Bonica, 1995). QPG was modeled to achieve about 50% and 70 % greater QP 

values compared to GD0 in the second trimester and at the end of pregnancy, respectively, by varying 

QPCG over the period of gestation. The increase in QP during pregnancy was largely due to an increase in 

the tidal volume and the reduced residual capacity and there seemed to be no significant pregnancyinduced changes in respiratory frequency (Spätling L, 1992). These changes were entered as lung 

parameters in MPPD program to simulate 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 (Spätling 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 

olfactory) and lung were incorporated in the model using TABLE function (TABLE S2). 

TABLE S2. 

Gestation (weeks) FdepLuG FdepNRG FdepNOG

0 0.226 0.334 0.0176

12 0.254 0.353 0.0186

38 0.255 0.371 0.0196

S12. The increment in the volume of the mammary gland as a fraction of BWi during lactation

TABLE S3. 

Lactation (hours) ∆VMC

0 (also at term) 0.0059

336 0.0135

4032 0.0135
S13. The decrement in the volume of the fat as a fraction of BWi during lactation

TABLE S4. 

Lactation (hours) ∆VFC

0 (also at term) 0.0836

4032 0.0

S14. 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 were 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 S5. Neonatal Blood volume (as a fraction of BWN)

Age (Years) Fractional blood volume (VBLDCN)

0 0.083

1 0.053

5 0.079

10 0.078

15 0.086

25 0.077

40 0.077

TABLE S6. Neonatal Liver volume (as a fraction of BWN)

Age (Months) Fractional liver volume (VLivCN)

0 0.037

0.1 0.0445

1 0.0414

2 0.0383

3 0.0363

4 0.0379

5 0.039

 

TABLE S7. Neonatal Brain volume (as a fraction of BWN)
Age (Years) Fractional brain volume (VBrnCN)

0 0.109

0.5 0.093

1 0.092

2 0.089

5 0.069

 

TABLE S8. Neonatal Lung volume (tissue only; as a fraction of BWN)

Age (Years) Fractional lung volume (VLungCN)

0 0.009

1 0.008

5 0.007

TABLE S9. Neonatal Bone volume (as a fraction of BWN)

Age (Years) Fractional lung volume (VBoneCN)

0 0.1

1 0.112

5 0.124

 

S15. Ventilation rates in neonates and children

For neonate and child, recommended pulmonary rates (m3/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 is alveolar ventilation. 

The recommended ventilation values in US EPA (2002) are based on typical activity levels at different 

ages. 

S16. Milk production/suckling rate constant (klacC)

Milk production rate (L/hr) was described as Gentry et al (2003) which adopted Casey et al. (1985)

data (TABLE S10). 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 S10.
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

732 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 zero. 
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