Studying permethrin exposure in flight attendants using a physiologically based pharmacokinetic model

Abstract

Assessment of potential health risks to flight attendants from exposure to pyrethroid insecticides, used for aircraft disinsection, is limited because of (a) lack of information on exposures to these insecticides, and (b) lack of tools for linking these exposures to biomarker data. We developed and evaluated a physiologically based pharmacokinetic (PBPK) model to assess the exposure of flight attendants to the pyrethroid insecticide permethrin attributable to aircraft disinsection. The permethrin PBPK model was developed by adapting previous models for pyrethroids, and was parameterized using currently available metabolic parameters for permethrin. The human permethrin model was first evaluated with data from published human studies. Then, it was used to estimate urinary metabolite concentrations of permethrin in flight attendants who worked in aircrafts, which underwent residual and pre-flight spray treatments. The human model was also applied to analyze the toxicokinetics following permethrin exposures attributable to other aircraft disinsection scenarios. Predicted levels of urinary 3-phenoxybenzoic acid (3-PBA), a metabolite of permethrin, following residual disinsection treatment were comparable to the measurements made for flight attendants. Simulations showed that the median contributions of the dermal, oral and inhalation routes to permethrin exposure in flight attendants were 83.5%, 16.1% and 0.4% under residual treatment scenario, respectively, and were 5.3%, 5.0% and 89.7% under pre-flight spray scenario, respectively. The PBPK model provides the capability to simulate the toxicokinetic profiles of permethrin, and can be used in the studies on human exposure to permethrin.

INTRODUCTION

Pyrethroid insecticides account for approximately one-fourth of the worldwide insecticide market. They have been widely used in wood preservation, impregnation of wool carpets and textiles, disinfection and mosquito control.¹ Permethrin is a pyrethroid pesticide that is typically used as an active ingredient to provide a residual effect in aircraft disinsection. Its presence in commercial aircrafts results in potential exposure risks to flight attendants through multiple routes: oral, dermal and inhalation on disinsected aircrafts.^2–5 However, few studies have investigated the permethrin exposure in flight attendants, limiting quantitative information necessary for health risk assessment.

Permethrin exposure routes in flight attendants can be influenced by the disinsection method, which usually depends on the requirements of the destination country. For example, Australia allows for different types of aircraft disinsection, which can be classified into: ground residual treatment and pre-flight spraying using aerosol cans.⁶ Residual treatment is carried out while the aircraft is on the ground, typically, at maintenance areas, with no crews and passengers on the plane. Pre-flight aerosol can spray can be carried out by crewmembers just before the departure of the plane. Overall, the levels of permethrin to which flight attendants are exposed are affected by several factors, including potential variations in spray or application patterns, surface characteristics (e.g., flat, vertical, hard or soft surfaces, etc.) and time since last spray or treatment. In addition, actual concentrations within an aircraft cabin could be either significantly higher or lower than the recommended levels.

Although pyrethroids are reported to be less toxic to mammals compared with other insecticides, people who are temporarily or routinely exposed to pyrethroids could face health risks.^7,8 It has been indicated that pyrethroids may be potential neurotoxicants,^8–10 and may have potential developmental toxicity.^11–13 They can also cause suppressive effects on the immune system.¹⁴ In vitro studies suggested that pyrethroids could have estrogenic activity, and they have been listed as possible endocrine disruptors by the US EPA.^15–18 Symptoms associated with pyrethroids exposure included headache, fatigue, muscle and joint pain, ataxia, skin rash, respiratory difficulties and gastrointestinal disturbances.¹⁹

Pyrethroids can be rapidly metabolized following an exposure. The excretion of pyrethroids largely depends on the administration/ exposure routes and the type of pyrethroid. Metabolism studies suggested that following oral administration, pyrethroids and their metabolites are primarily excreted in the urine, and also can be eliminated by fecal excretion and biliary elimination.^20–23 In a metabolism study of cypermethrin (1:1, cis/trans mixture), the subjects excreted 78% of the trans isomer orally administered dose and 49% of the cis isomer dose in urine as the cyclopropane carboxylic acid metabolite within 24 h.²⁴ Fecal excretion data for deltamethrin suggested that approximately 13–37% of the administered oral dose (0.55–5.5 mg/kg) was directly eliminated in the feces.^25,26 Crawford et al.²² reported that no >2% of cypermethrin was eliminated through biliary elimination. Absorbed pyrethroids can also be exhaled as CO₂ after metabolism. However, <5% of the administered dose was exhaled in the rat study with ⁴C-labeled cypermethrin and fenvalerate.²¹

The biological half-life associated with urinary excretion varied greatly with the metabolites measured and exposure pathways.^27–29 For the dermal studies with cypermethrin and permethrin, the amounts absorbed and circulated systemically following dermal exposure were estimated to be between 27% and 57% of the administered dose, and the elimination half-life was reported to be from 29 to 38 h.^27,28 Oral exposure studies reported half-lives to vary between 4 and 16 h.²⁹ Following inhalation exposure to cyfluthrin at 160 µg/m³ for 10–60 min in male volunteers, 93% of the metabolites were excreted within 24 h.³⁰ Half-lives of 6.4 and 4.2 h were determined for the urinary excretion of the metabolites cis/trans-Cl2CA and trans-chrysanthemumdicarboxylic acid (trans-CDCA), respectively, after oral or inhalation exposure to pyrethroids in volunteers.^29,30

Physiologically based pharmacokinetic models (PBPK) have been widely used to predict target tissue doses of chemicals of interest, as well as to extrapolate animal toxicity data to humans through simulating absorption, distribution, metabolism and elimination of those chemicals.^31–37 Recently, PBPK models have been developed to evaluate the toxicokinetics of deltamethrin, following oral dose administration.^23,38–40 Although these models can be used to study pyrethroid toxicokinetics in humans, they currently do not allow the integration of multiple exposure routes and biomarker measurements in urine, limiting their use in epidemiological studies such as those involving flight attendants.

This study focused on developing and evaluating a PBPK model for the pyrethroid insecticide permethrin that incorporates multiple exposure routes and simulates the permethrin concentrations in different biological tissues and blood, as well as its metabolite concentrations in urine, and also on characterizing the potential variability in the model. The evaluated model was then used to study the toxicokinetics of flight attendants exposed to permethrin in aircrafts that underwent disinsection.

METHODS

Model Description and Parameterization

The permethrin PBPK model was developed based on existing pyrethroid PBPK models developed for rats and adult humans, and included brain, fat, liver, slowly perfused tissues and richly perfused tissues compartments. ^23,38–40 Fat and brain were included in the model because of the highly lipophilic and neurotoxic properties of permethrin. Fat, brain and slowly perfused tissues were described using a diffusion-limited formulation following Tornero-Velez et al.,⁴⁰ while the remaining tissue compartments were described using a flow-limited formulation. Clearance of permethrin in whole blood following the method of Godin et al.,³⁸ rather than the metabolism in plasma and erythrocyte compartments as used in other models Mirfazaelian et al.²³ and Tornero-Velez et al.⁴⁰

Figure 1 presents the model compartments, exposure routes and elimination routes explicitly considered in the PBPK model. As permethrin has low volatility, all inhaled permethrin in both gaseous and particulate phases was assumed to be fully absorbed in lung blood, with no permethrin exhaled. Dermal uptake of permethrin was described using a single compartment for the exposed skin based on data from recent in vitro studies on dermal absorption of permethrin in human skin.^41,42 The cumulative percentage of the dose absorbed dermally was reported to be 1–3%,^{24,27,28,41,42} and the dermal absorption rate was estimated to be the total absorbed amount divided by the exposure time. Urinary elimination of permethrin metabolites was described using a first-order elimination from the liver to the urine compartments.

Figure 1.

Schematic of the physiologically based pharmacokinetic (PBPK) model. Definitions for the abbreviations in the scheme are listed in Table 1.

Table 1 presents the physiological parameters obtained from the literature for the rat and human. Partition coefficients between blood and tissues were from the study by the US EPA.³⁹ Permethrin metabolism parameters for liver and blood clearance were based on the study by Scollon et al.⁴³ and the US EPA,³⁹ respectively. The human model for permethrin was adapted from the animal model by allometric scaling the human physiological and biochemical parameters, and by using human data on metabolism of permethrin from the literature, as shown in Table 1.

Table 1.

Model parameters that describe permethrin in rats and humans.

Parameter	Rat				Human
	Mean	SD	Lower bound	Upper bound	Mean	SD	Lower bound	Upper bound	Distribution
Body weight (BW, kg)
Rat	0.40a	0.080	0.243	0.557
Flight attendant male					78.65b	13.23	52.719	104.581	Normal
Flight attendant female					65.47b	13.77	38.481	92.459	Normal
Cardiac output (QCC, l/h/kg0.75)	14.10a	1.410	11.336	16.864	14.10a	1.410	11.336	16.864	Normal
Alveolar ventilation (QPC, l/h/kg0.75)	24.10c	3.615	17.015	31.185	24.10c	3.615	17.015	31.185	Normal
Fraction of cardiac output
Brain (QBRC)	0.020a	0.006	0.008	0.032	0.114a	0.034	0.047	0.181	Normal
Fat (QFC)	0.070a	0.021	0.029	0.111	0.052a	0.016	0.021	0.083	Normal
Liver (QLC)	0.183a	0.055	0.075	0.291	0.214a	0.064	0.088	0.340	Normal
Skin (QSKC)	0.086d	0.026	0.035	0.137	0.086d	0.026	0.035	0.137	Normal
Slowly perfused tissues (QSC)	0.150e	0.045	0.062	0.238	0.196e	0.059	0.081	0.311	Normal
Rapidly perfused tissues (QRC)	0.491a	0.147	0.202	0.780	0.338a	0.101	0.139	0.537	Normal
Tissue volume (fraction of BW)
Blood (VBLC)	0.070a	0.021	0.029	0.111	0.070a	0.021	0.029	0.111	Normal
Brain (VBRC)	0.005a	0.002	0.002	0.008	0.020a	0.006	0.008	0.032	Normal
Skin (VSKC)	0.051d	0.015	0.021	0.081	0.051d	0.015	0.021	0.081	Normal
Fat (VFC)	0.070a	0.021	0.029	0.111	0.220a	0.066	0.091	0.349	Normal
Liver (VLC)	0.030a	0.009	0.012	0.048	0.030a	0.009	0.012	0.048	Normal
Slowly perfused tissues (VSC)	0.729f	0.073	0.656	0.802	0.569f	0.057	0.512	0.626	Normal
Rapidly perfused tissues (VRC)	0.045a	0.014	0.018	0.072	0.040a	0.012	0.016	0.064	Normal
Partition coefficients
Fat/blood (PF)	48.90g	9.780	22.814	104.813	48.90g	9.780	22.814	104.813	Log-normal
Liver/blood (PL)	0.44g	0.132	0.272	0.713	0.44g	0.132	0.272	0.713	Log-normal
Skin/blood (PSK)	5.60h	1.680	2.034	11.002	5.60h	1.680	2.034	11.002	Log-normal
Brain/blood (PBR)	5.50i	1.650	2.019	10.730	5.50i	1.650	2.019	10.730	Log-normal
Rapidly perfused/blood (PR)	0.44g	0.132	0.272	0.713	0.44g	0.132	0.272	0.713	Log-normal
Slowly perfused/blood (PS)	5.60g	1.680	2.034	11.002	5.60g	1.680	2.034	11.002	Log-normal
Clearance constants (l/h/kg0.75)
Liver metabolic (Kmetl)	21.120j	6.336	11.616	69.819	7.320j	2.196	2.271	15.973	Log-normal
Blood clearance (Kmetb)	0.530g	0.159	0.365	0.770	0.000				Log-normal
Uptake rate constants (h−1)
Gastric absorption rate (Ks)	0.010g	0.003	0.004	0.016	0.010g	0.003	0.004	0.016	Log-normal
Intestinal absorption rate (K1)	0.900g	0.270	0.430	1.860	0.900g	0.270	0.430	1.860	Log-normal
Stomach–intestine transfer (Ksi)	0.700g	0.210	0.340	1.410	0.700g	0.210	0.340	1.410	Log-normal
Elimination rate constant (h−1)
Fecal excretion (Kfec)	0.590a	0.177	0.310	1.180	0.590a	0.177	0.310	1.180	Log-normal
Urinary excretion (Kur)	0.100k	0.030	0.041	0.260	0.100k	0.030	0.041	0.260	Log-normal

^aGodin et al.³⁸ and Clewell et al.⁴⁷

^bUS EPA (Environmental Protection Agency).⁴⁸

^cTimchalk et al.⁴⁹ and Clewell et al.⁵⁰

^dCorley et al.⁵¹

^e0.150 — QSKC (rat); 0.196 — QSKC (human).

^f0.729 — VSKC (rat); 0.62 — VSKC (human).

^gUS EPA.³⁹ Pyrethroid-hydrolyzing activity was not apparent in human serum.³⁸ Therefore, the value was set to 0 in human model.

^hSet to slowly perfused tissue.

ⁱBrain was considered to be a diffusion-limited compartment, and it belongs to the slowly perfused tissues (SPT). It was found that when a value of SPT:blood partition coefficient of 5.6 was used for the brain, the prediction for the time–concentration profile in the brain matched very well with the experimental data (Figure 3). There are potential variability or uncertainties in this estimation, so the simulation was performed following a log-normal distribution for this parameter, with a range from 1.65 to 10.73, which was regarded to include 95% variability in the population.

^jScollon et al.⁴³

^kEstimated.

Model Evaluation and Correlation Analysis

The PBPK model was evaluated by comparing model predictions with experimental data on rats and humans. The rat data set included the permethrin concentrations in the blood and brain collected from 65-day-old male Long–Evan rats at 0.5–24 h following administration of a single oral dose of either 1 and 10 mg/kg of permethrin (cis/trans: 40/60).³⁹

Following the evaluation of the rat PBPK model, the model was then scaled to a human PBPK model using allometric scaling. The human model was evaluated using data from three experiments studying dermal absorption of permethrin.²⁸ In experiment 1, 50 ml of an ethanolic solution containing 215mg permethrin (cis/trans: 25/75) was administered to the hair of six young healthy men for 45 min. In experiments 2 and 3, 60 g of a cream containing 3 g permethrin was administered to the skin of the whole body of another six subjects (test 2: six males; test 3: 3 male/3 female), except the head and genital mucosa, for 12 h, while each subject wore loose clothing. Urine samples in those tests were collected up to 168 h after exposure.

The permethrin PBPK model was evaluated by comparing the predictions with experimental data. Statistical measures such as the square of the correlation coefficient (R²) and root mean squared error (RMSE) were computed based on simulated and measured median values. Correlation coefficient (r) between each two physiological parameters involved in the simulation after 50,000 iterations were also computed and used to ascertain whether any of those parameters were correlated (Appendix Table A1). The criteria for r and R² defined in this study were: if the value is < 0.2, the correlation is regarded to be negligible; a value ranging from 0.2 to 0.35 is considered to represent low or weak correlation; 0.36–0.67 to represent moderate correlation; 0.68–0.9 to represent strong or high correlation; and 0.9–1.0 to represent very strong correlation.^44,45 As only limited samples were collected in experiments, a reliable population distribution from experimental results could not be generated. Therefore, only correlations were evaluated that can reflect whether the simulations captured the shape of the experimental results, and the statistical tests to evaluate the differences between simulated and experimental results were not conducted. RMSE represents the average square root of the variance of the residuals between observed and predicted data points. RMSE values usually are higher in biological measurements, especially when sample size in experiments is small and large interindividual variations exist. However, no common criteria were defined for RMSE in the literature. Generally, a lower value of RMSE indicates a better fit that is useful for prediction. All statistical analyses were performed using the Matlab software.

Table A1.

Correlation coefficient matrix for physiological parameters generated by 50,000 iterations in the Montel Carlo simulation.

	BW	QCC	QPC	VBLC	VFC	VLC	VBrC	VSKC	VSC	VRC	QFC	QLC	QBrC	QSKC
BW	1E + 00
QCC	2E − 03	1E + 00
QPC	4E − 03	7E − 03	1E + 00
VBLC	− 5E − 04	− 2E − 03	− 3E − 03	1 E + 00
VFC	− 2E − 04	2E − 03	− 9E − 04	1E − 04	1E + 00
VLC	2E − 03	1E − 02	1E − 03	− 1E − 03	3E − 03	1E + 00
VBrC	− 6E − 03	3E − 03	− 5E − 03	4E − 03	− 5E − 03	− 3E − 03	1 E + 00
VSKC	− 3E − 03	− 3E − 03	− 5E − 03	− 3E − 03	− 8E − 04	4E − 03	5E − 03	1E + 00
VSC	3E − 03	− 3E − 04	3E − 03	− 2E − 03	− 4E − 04	3E − 03	9E − 04	− 2E − 03	1E + 00
VRC	− 8E − 03	− 4E − 04	7E − 03	− 2E − 03	− 2E − 03	− 2E − 04	6E − 03	OE + 00	− 1 E − 03	1E + 00
QFC	8E − 03	− 4E − 03	6E − 03	− 7E − 03	− 4E − 03	3E − 03	− 2E − 03	1E − 03	− 9E − 04	1E − 04	1E + 00
QLC	− 3E − 03	9E − 03	− 2E − 03	6E − 03	− 6E − 03	− 2E − 03	1 E − 03	− 3E − 03	− 2E − 03	− 4E − 03	− 6E − 03	1E + 00
QBrC	3E − 03	8E − 03	9E − 04	− 4E − 03	− 9E − 03	− 4E − 03	3E − 03	6E − 04	− 9E − 03	− 1E − 02	2E − 03	4E − 03	1E + 00
QSKC	− 2E − 03	4E − 03	4E − 03	− 5E − 04	− 2E − 03	− 1 E − 04	5E − 03	2E − 03	− 3E − 03	− 4E − 03	− 3E − 03	2E − 03	2E − 03	1 E + 00
QSC	− 5E − 03	− 2E − 03	2E − 03	OE + 00	1E − 03	− 3E − 03	− 3E − 03	4E − 03	− 7E − 03	1E − 03	1 E − 03	2E − 03	− 1 E − 03	1 E − 02
QRC	3E − 03	− 6E − 03	− 8E − 03	3E − 03	− 4E − 04	6E − 03	− 1E − 03	2E − 03	− 6E − 03	8E − 03	− 6E − 02	− 3E − 01	− 1 E − 01	− 1E − 01
PF	9E − 03	6E − 03	− 7E − 03	− 3E − 03	4E − 03	− 3E − 03	− 4E − 03	2E − 03	3E − 03	− 7E − 03	− 2E − 03	6E − 03	1E − 03	− 6E − 03
PL	− 5E − 03	− 5E − 03	− 7E − 03	3E − 03	5E − 04	7E − 03	− 4E − 04	1E − 03	2E − 03	− 5E − 03	− 1E − 03	− 3E − 03	− 6E − 03	5E − 03
PBr	7E − 03	4E − 03	− 3E − 03	− 1E − 03	− 7E − 03	− 1 E − 02	− 5E − 04	4E − 04	3E − 03	2E − 03	− 1E − 03	9E − 03	− 2E − 03	2E − 03
PSK	6E − 04	− 1E − 04	1E − 04	5E − 03	2E − 03	2E − 04	− 1E − 03	− 3E − 03	3E − 03	5E − 03	− 9E − 03	8E − 04	− 9E − 04	8E − 03
PS	1E − 02	− 1 E − 03	3E − 03	− 7E − 03	− 2E − 03	− 2E − 03	6E − 03	7E − 04	− 2E − 03	3E − 03	− 1E − 03	− 2E − 03	2E − 03	3E − 04
PR	8E − 03	2E − 03	− 6E − 03	− 9E − 04	3E − 03	7E − 03	− 5E − 03	− 2E − 03	7E − 03	1E − 03	− 4E − 04	2E − 03	3E − 03	− 1E − 03
Ks	1E − 02	− 5E − 03	3E − 03	5E − 04	2E − 03	− 2E − 03	− 3E − 04	− 4E − 03	− 1 E − 03	7E − 03	− 3E − 03	9E − 04	− 4E − 03	4E − 03
Ki	3E − 03	− 9E − 03	7E − 03	3E − 03	9E − 04	5E − 03	− 8E − 04	− 7E − 03	− 2E − 03	1E − 03	− 4E − 03	5E − 03	− 4E − 03	OE + 00
Ksi	5E − 03	− 3E − 03	− 1E − 03	− 1E − 03	− 7E − 03	− 4E − 03	3E − 03	− 2E − 03	6E − 03	− 7E − 04	− 2E − 03	− 3E − 04	− 1 E − 03	1 E − 02
Kfec	2E − 03	− 2E − 04	8E − 04	− 5E − 03	6E − 03	2E − 03	− 4E − 03	− 8E − 03	− 3E − 03	− 4E − 03	− 3E − 03	1E − 04	2E − 03	4E − 03
Kur	4E − 03	2E − 03	6E − 04	2E − 04	− 1E − 03	6E − 03	− 4E − 03	− 6E − 03	− 3E − 03	− 4E − 04	− 6E − 03	− 4E − 03	7E − 04	− 3E − 03
Kmetl	9E − 03	− 5E − 03	OE + 00	2E − 03	7E − 03	− 6E − 03	− 6E − 03	2E − 03	1E − 04	2E − 03	2E − 03	− 6E − 03	8E − 03	8E − 03
	QSC	QRC	PF	PL	PBr	PSK	PS	PR	Ks	Ki	Ksi	Kfec	Kur	Kmetl
QSC	1E + 00
QRC	− 2E − 01	1E + 00
PF	1E − 04	− 4E− 03	1E + 00
PL	1E − 04	6E − 03	− 7E − 03	1E + 00
PBr	6E − 03	7E − 03	6E − 04	− 9E − 02	1E + 00
PSK	1E − 03	− 6E − 03	− 4E − 03	4E − 03	− 2E − 03	1E + 00
PS	− 7E − 03	3E − 03	− 1E − 03	− 2E − 03	2E − 04	9E − 04	1 E + 00
PR	1E − 03	− 4E − 03	− 6E − 03	1 E − 03	6E − 03	5E − 03	3E − 03	1E + 00
Ks	1E − 02	− 4E − 03	− 2E − 03	− 4E − 03	− 5E − 03	− 2E − 03	− 5E − 03	− 6E − 03	1E + 00
Ki	7E − 03	2E − 03	− 3E − 03	6E − 03	− 6E − 03	1E − 03	− 5E − 03	2E − 03	8E − 04	1E + 00
Ksi	− 5E − 03	1E − 03	− 4E − 03	7E − 04	5E − 03	4E − 03	1 E − 02	− 3E − 03	7E − 03	− 1E − 03	1 E + 00
Kfec	− 5E − 03	1E − 02	− 2E − 03	− 3E − 03	− 5E − 03	2E − 04	7E − 03	− 2E − 04	− 2E − 03	− 5E − 03	− 8E − 03	1E + 00
Kur	5E − 04	3E − 03	− 4E − 03	− 2E − 03	− 5E − 03	− 4E − 04	− 2E − 03	− 3E − 03	− 2E − 03	− 3E − 03	8E − 04	− 6E − 03	1E + 00
Kmeti	− 5E − 03	− 2E − 03	2E − 03	− 2E − 03	− 1E − 03	1E − 03	5E − 03	− 1E − 03	8E − 03	− 7E − 03	− 5E − 04	− 3E − 03	− 1E − 03	1 E + 00

Sensitivity Analysis

Sensitivity analysis was performed to identify the model parameters that have the greatest impact on the responses under the specified exposure scenarios. The response variables in the study were the peak concentration of permethrin in blood and the peak hourly urinary excretion rate of 3-phenoxybenzoic acid (3-PBA). The peak hourly urinary excretion rate of 3-PBA was estimated using the assumption that urine can be collected every hour after the exposure. This metric and assumption were hypothetical and were only used for sensitivity analysis purpose. The equation used for the normalized sensitivity coefficient of output i with respect to parameter j (NSC_I,j) was

$$NS{C}_{i,j}=\left(\frac{\mathrm{\Delta }{r}_{i,j}}{r_{i,j}}\right)\times \left(\frac{\mathrm{\Delta }{p}_j}{p_j}\right)$$

where p_j is the nominal value of parameter j, r_i,j is the corresponding model estimate for output i, Δp_j is the change in parameter j (typically 0.1% of p_j) and Δr_i,j is the corresponding change in output i. The NSC values were computed separately under dermal, inhalation and non-intentional oral ingestion exposure scenarios. Specifically, surface loading for dermal exposure and surface–hand–mouth exposure route was 35 µg/cm², and air concentration used for inhalation route was 0.1 mg/m³. Parameters with the absolute NSC values > 0.2 were deemed to have a relative significant impact on the outputs.

Monte Carlo Simulation

Monte Carlo (MC) simulations were performed to provide the distributions of parameters (Table 1). For each exposure scenario, 50,000 iterations were simulated, and within each iteration, the value of each parameter was randomly selected from its generated distribution. To insure consistency between the fractional blood flows and tissue volume percentages, the sum of fractional blood flows and tissue volumes were normalized to 1. To avoid physiologically implausible values for the physiological parameters involved in the simulation, the upper and lower bounds of each distribution were truncated at 1.96 times the standard deviation (STD) above and below the mean, which includes 95% of the total distribution following the methods used by Tan et al.,⁴⁶ except for the volume fraction of slowly perfused tissue (VSC), which was truncated at one STD above and below the mean to exclude unrealistic conditions. Because of large variations and uncertainties associated with the exposure conditions in aircraft disinsection, parameters such as air concentration, surface loading, fingertip area and exposed dermal area, etc., were truncated at three times the STD above and below the mean. Concentration–time profiles for the outputs of interest at 2.5th, 25th, 50th, 75th and 97.5th percentiles were calculated from the MC samples.

Permethrin Exposure Scenarios in Aircraft Cabin Environment

The presence of permethrin in commercial aircrafts results in exposures to flight attendants through multiple routes.^2–5 Eight specific exposure scenarios were simulated in this study, addressing different types of exposures occurring under two major types of disinsection treatments: ground residual treatment and preflight spraying.⁶ Table 2 presents the specific exposure routes considered and the distribution expressions for air concentrations and surface loadings corresponding to each of the eight scenarios. Parameters related to exposure conditions in aircraft are presented in Table 3.

Table 2.

Simulation scenarios for flight attendants working on disinsected aircrafts.

Scenario	RTS			PFS
	Inhalation	Dermal	Oral	Inhalation	Dermal	Orala
A	Dist Ib
B		Dist IIc
C			Dist II
D	Dist I	Dist II	Dist II
E				Phase I:
				Dist IIId
				Phase II:
				Dist IVe
F					Dist Vf
G						Dist V
H				Phase I:
				Dist IIId
				Phase II:	Dist V	Dist V
				Dist IVe

Abbreviations: PFS, pre-flight spray; RST, residual treatment; STD, standard deviation.

^aNon-intentional oral uptake of permethrin attributable to aircraft disinsection was assumed to occur through the surface–hand–mouth route.

^bDist I: log-normal distribution for air concentration (median: 0.05; STD: 0.05; range: 0.0–1.0; unit: mg/cm³).

^cDist II: log-normal distribution for surface loading (median: 35; STD: 35; range: 0.5–140; unit: mg/cm²).

^dDist III: log-normal distribution for air concentration (median: 65; STD: 65; range: 1.0–260; unit: mg/cm³).

^eDist IV: log-normal distribution for air concentration (median: 0.05; STD: 0.05; range: 0.0–1.0; unit: mg/cm³).

^fDist V: log-normal distribution for surface loading (median: 0.58; STD: 0.58; range: 0–2.32; unit: mg/cm²).

Table 3.

Parameters related to exposure conditions in aircraft.

Parameter	Gender	Mean (STD)	Range	Distribution
Exposed dermal area of flight attendant (m2)a	Male	0.999 (0.300)	0.6993–1.499	Log-normal
	Female	0.937 (0.281)	0.6559–1.406	Log-normal
Transferable factor from surface to dermal (%)b	—	—	5–15	Uniform
Cumulative dermal absorption (%)c	—	1.5 (1.5)	0.8–2.0	Log-normal
		None—hair dermal
	—	7.5 (2.25)—scalp	3.0–12	Log-normal
Fingertip area (cm2)d	—	3.5 (0.7)	1.0–5.56	Normal
Transferable factor from hand to mouth (%)e	—	—	10–50	Uniform
Oral absorption (%)f	—	—	40–85	Uniform
Finger number touching mouthg	—	—	1–5	Uniform
Hand–mouth contact frequency (h−1)h	—	—	0–3	Uniform
Exposure duration (h)i	—	—	13–14.5	Uniform

^aUS EPA (Environmental Protection Agency).⁴⁸

^bKeenan et al.⁵² and Williams et al.⁵³

^cEadsforth et al.,²⁴ Hughes et al.,⁴¹ Reifenrath et al.,⁴² Tomalik-Scharte et al.²⁸ and Woolen et al.²⁷

^dEstimated based on the assumption that one fingertip area is ~30% of one finger area, and each finger area is ~10% of the palmar surface of one hand. The average surface area of hands for adult male and female is 0.098 m².⁴⁸

^eEstimated based on studies by Keenan et al.⁵² and Williams et al.⁵³

^fGodin et al.³⁸

^gEstimated assuming one hand was touching the mouth per contact event.

^hEstimated based on the assumption that 1 time per 20 min, which was the most reasonable value for the exposure scenarios in flight attendants.⁵²

ⁱCollected information and adjusted using flight schedule between the United States and Australia.

In the exposure scenarios considered, the required surface loading for residual treatment on an aircraft is 20 µg/cm² for the interior surfaces except floors that have a requirement of 50 µg/cm².⁶ Because of the lack of data from direct measurements of surface loading from aircraft treated by residual method, in the exposure scenarios considered, the surface loading was assumed to follow a log-normal distribution with the median of 35 µg/cm² corresponding to the mean of the two guidance levels. Owing to limited data in the open literature, which cannot allow a calculation for a specific STD for the log-normal distribution used in the simulation, an approximately equaling value of 35 µg/cm² was applied, and the surface loading was truncated to be in the range from 0.5 to 140 µg/cm² (upper level was assumed to be the median value plus three times the STD). The air concentration was assumed to follow a log-normal distribution with a median of 0.5 µg/m³, STD of 0.5 µg/m³ and range from 0.0 to 1.0 µg/m³, based on the rapid decrease of permethrin concentrations in air to below 1.0 µg/m³.^2,3

For pre-flight aerosol can spray scenarios, inhalation exposure to flight attendants was modeled in two stages during a long flight: when the ventilation system is off and when it is turned on. This approach is used because the levels are expected to decrease to low levels after 1–2 h following pre-flight spray.^2,3 In the simulations considered, the first stage was assumed to last 2 h, corresponding to a worst-case scenario. The air concentration during this stage was assumed to be log-normally distributed (median: 65; STD: 65; range: 1.0–260; unit: µg/m³), based on the highest reported mean air concentration of permethrin (65 µg/m³) from different spray tests.² The air concentrations in the second stage were assumed to have the same distribution pattern as in the residual treatment scenario. The surface loadings were assumed to follow a log-normal distribution (median: 0.58; STD: 0.58; range: 0–2.32; unit: µg/cm²), with the median and the STD values corresponding to half of the reported upper range of <2 ng/cm² to 1.16 µg/cm².^2,3

Model outputs considered were cumulative time profiles of urinary metabolite levels of permethrin. The spot urinary concentration was calculated by dividing the mass of permethrin metabolite excreted by the urine volume accumulated during the two excretion time points (Appendix I). The predicted urinary concentrations of permethrin metabolites under the residual treatment scenario were compared with measured values in urine samples collected in post- and 24-h-post-flight samples.⁵ Briefly, those samples were obtained from participants working on flights mostly flying between the United States and Australia with an average flight duration of 14 h. Three urine samples were collected from each participant: one before the boarding for assessing the background levels, a second one after the flight and a third one approximately 24 h later. It should be pointed out that in this study we only simulated the exposures of flight attendants to permethrin attributable to aircraft disinsection, and contributions to the body burden in flight attendants from other sources, for example, dietary, residential pesticide use, etc., were not simulated. Therefore, the simulated permethrin metabolite levels in urine were only compared with the background-subtracted post- and 24-h-post flight urine samples from flight attendants. Finally, contributions of dermal, inhalation and oral exposure routes to permethrin exposure in flight attendants attributable to aircraft disinsection were estimated under both residual treatment and space spraying scenarios.

Software

The PBPK model was implemented in Matlab programming environment. Briefly, the mass balances of chemicals in all compartments comprising the PBPK model were described by a matrix of ordinary differential equations (ODEs), and then they were solved numerically using the stiff ODE solver ode15s in Matlab. The equations associated with the PBPK model are described in Appendix I.

RESULTS AND DISCUSSIONS

Sensitivity Analysis

Sensitivity analysis results for parameters in the model are shown in Figures 2a–c. For the dermal route, the values of NSCs ranged from −0.41 to 0.74 for the peak blood concentration, and from −0.16 to 0.75 for peak hourly urinary excretion rate of 3-PBA. Peak blood concentration was most sensitive to the percentage of cardiac output to liver (QLC), percentage of cardiac output to rapidly perfused tissues (QRC) and partition coefficient between liver and blood (PL). Peak hourly urinary excretion rate of 3-PBA was most sensitive to QRC and partition coefficient between slowly perfused compartment and blood (PS). Further, both output metrics were highly sensitive to exposed dermal area (EXPArea), transferable factor from surface to the dermal (Trans_S_D) and cumulative dermal absorption percentage (DermalABR). Blood concentration was also negatively sensitive to the metabolic constant (K_met) in the liver, while the urinary excretion rate was positively affected by that parameter.

Figure 2.

Normalized sensitivity coefficients (NSC) for the peak blood concentration of permethrin and peak hourly urinary excretion rate of 3-phenoxybenzoic acid (3-PBA). (a and b) Dermal and non-intention oral exposures with the surface loading of 35 µg/cm² for permethrin. (c) Inhalation exposure to 0.1 mg/m³ for permethrin.

For the non-intentional oral ingestion through hand–mouth contact, peak blood concentration was most sensitive to the parameters: fat volume as a fraction of body weight (VFC), slowly perfused volume as a fraction of body weight (VSC), blood volume as a fraction of body weight (VBC), QLC, QRC, PL, gastric absorption rate constant (K_s), intestinal absorption rate constant (K_i), stomach–intestine transfer rate constant (K_si) and fecal excretion rate constant (K_fec). Hourly urinary excretion rate was most sensitive to the parameters: VBC, skin compartment volume as a fraction of body weight (VSKC), VSC, PL, partition coefficient between rapidly perfused compartment and blood (PR) and urinary excretion rate constant (K_ur). Both the peak blood concentration and hourly urinary excretion rate were highly sensitive to the parameters: exposed dermal area, transferable factor from surface to the dermal and dermal absorption rate. Absorption parameters associated with the oral exposure route, for example, K_s, K_i and K_si, were also sensitive to the peak blood concentration and hourly urinary excretion rate, which is consistent with the absorption of permethrin following exposure via oral route mainly occurring in the intestine in the present model. Increases in K_fec were found to decrease the peak blood concentration and hourly urinary excretion rate, while increases in K_ur led to increases in the hourly urinary excretion rate. For the inhalation route, peak blood concentration was most sensitive to the parameters: QLC, QRC and liver metabolic clearance constant (K_metl); hourly urinary excretion rate was most sensitive to the parameters: PL and K_ur. This indicates that the absorbed permethrin following an inhalation exposure is rapidly metabolized in the liver and excreted through urine.

As there are potential statistical correlations between body weight and physiological factors such as fat volume which might affect the performance of the PBPK model, especially when more correlated factors were involved, in this study, the absolute tissue volumes and blood flows to them were not directly involved. Instead, fractional factors were used in the simulation, following common protocols used in PBPK studies.^23,38,40,47 As fractions of body weight and cardiac output were used in the simulation, correlation analysis was conducted and added into the manuscript. Computed correlation coefficients among all but one pair of the physiological parameters (QRC with QLC) involved in the simulation were all <0.2 (Appendix Table A1), which indicates that the investigated parameters were uncorrelated when 50,000 iterations were conducted in the simulation; therefore multicolinearity effects on the output of the model can be neglected. The correlation coefficient for QRC and QLC is 0.28, indicating a weak linear correlation between those two parameters. However, this weak correlation cannot allow a reliable mathematical function to reduce the parameter dimensions in the simulation, and therefore, they cannot be explicitly characterized.

Comparison of Simulated Results with Experimental Data

Figures 3a and b show the comparisons of the experimental and simulated time–concentration profiles in rat brain following oral administration of 1.0 and 10 mg/kg permethrin, respectively. At each dose level, predicted median permethrin concentrations in the brain for the rat captured the shapes of the experimental data over the time range, and fit well to the experimental data (1 mg: R² = 0.78, RMSE = 0.005; and 10 mg: R² = 0.73, RMSE = 0.029). Simulated blood concentration underpredicted the measured data for the two test concentrations (Figures 3c and d). Although the variability in model parameters was expected to be incorporated in the simulation, the discrepancy between the measured and simulated median blood concentrations suggests that other sources of variability were not accounted for within the model itself. It should be pointed out that the interindividual variability was expected to be represented by the distribution for each parameter generated by MCsimulation. Individually, the absolute values for physiological parameters, such as tissue volumes, could be physiologically correlated to the body weight, and therefore these values might be mutually correlated. To account for this correlation, fractional values for parameters as tissue volume and blood flow were utilized rather than absolute physiological parameters in the simulation and the upper and lower bounds of each distribution were truncated at 1.96 times the STD above and below the mean to avoid physiologically implausible values. This approach retained the correlation of the absolute physiological parameters to their body weight for simulated individuals, while allowing for variations to be incorporated in the simulation population distributions and reasonable parameter values being sampled. Thus, the MCsimulation could effectively incorporate interindividual variability for the population studies. However, this approach could result in simultaneously over- or underestimating the values for some physiological parameters for certain individuals in the simulated population, and therefore overestimates the overall variation in the simulation. Several other studies have utilized age-dependent equations to estimate the physiological parameters in deterministic simulations (e.g., Beaudouin et al.³²). However, at each age stage they also observed that physiological parameters, such as body weight, on a population scale were distributed across a wide range. The observed values in the previous studies are comparable to the range we used when our values were truncated at 95% of the total distribution.

Figure 3.

Model predictions and measured time–concentration profiles for permethrin in rats. (a and b) Permethrin concentrations in the brain after 1.0 and 10 mg/kg per os dose, respectively, are displayed. (c and d) Permethrin concentration in the blood after 1.0 and 10 mg/kg per os dose, respectively, is displayed. Circles in the four figures represent the measured data. The line -.-.-. represents a envelope for the 97.5% confidence level, and the line … ‥‥. represents the envelope for the 75% confidence level, and the black solid line represents the median value.

Meanwhile, uncertainty which refers to a different concept from variability, could also exist both in experiment and simulation. Possible sources of uncertainty include: different analytical methodologies that can lead to experimental uncertainties; estimation for some parameter values due to few reported data in the open literature, for example, brain–blood partition coefficient and finger–mouth contact frequency, etc. Additional possible explanation for the lower blood concentration estimates is that the model overestimates the rate of metabolism or the amount absorbed into tissues.

Overestimation or unidentified underestimation of input parameter values could consequently result in overestimation of the variability or uncertainty in the simulation. Several different combinations of parameters involved in the simulation were selected and conducted in a deterministic manner. Different combination did result into different simulated results, for example, a smaller brain volume could significantly increase the brain concentration of permethrin, and a larger blood volume could lead to lower blood concentration of permethrin, which do indicate the importance of the selection of the parameter values. It also indicates the potential variability in the population. However, in this study we can only indicate that there might be a potential overestimation of variability in the simulation, and we are unable to evaluate whether the overestimation of variability exists at the population level or to quantify the magnitude of the potential overestimation. Therefore, further studies should be conducted to address these concerns.

Figures 4a–c display the measured urinary excretion rates from the human experiment²⁸ and the simulated results using the human model extrapolated from the evaluated rat model scaled using human physiological and metabolic parameters (Table 1). R² values between measured median and simulated median values for experiments 1, 2 and 3 were 0.96, 0.91, and 0.87, respectively, and the RMSE values were 3.5, 86.9 and 103.5, respectively. Theoretically, the RMSE value that is close to 0 indicates a better capability for prediction. As there were only six subjects included in each experiment, a reliable distribution to compare with the results from the simulations following 50,000 iterations under each scenario could not be generated from the experimental data. Thus, relatively high RMSE values are possible when significant interindividual variations exist. As can be seen in Figures 4a–c, measured values at the same sampling time were scattered over a wide range, indicating that there were large interindividual variations or uncertainties in the observations. Overall, the high R² values showed that the simulated results captured the shapes for the experimental data, indicating adequate predictability of the human model to simulate the urinary metabolite concentrations of permethrin.

Figure 4.

Modeling total urinary excretion rate of permethrin metabolites, cis/trans-3-(2,2-dichlorovinyl)-2,2-dimethylcyclopropane carboxylic acid (CVA). Test I: 50 ml solution containing 215 mg permethrin (cis/trans: 25/75) was administered onto the wet, washed haired area with shower cap on the heads of six healthy men for 45 min; Tests II and III: 60 g of the cream containing 3 g permethrin (cis/trans: 25/75) was massaged into the showered and dried skin of the whole body except the head and genital mucosa in six men (Test II) and mixed subjects (Test III, male/female: 3/3) for 12 h. Measured data were cited from Tomalik-Scharte et al.²⁸

Prediction of Urinary Metabolite Levels of Permethrin in Flight Attendants

The application of the newly developed PBPK model here marks the first time a human PBPK model was used for studying exposures of flight attendants to permethrin attributable to aircraft disinsection and for interpreting the biomarker data from flight attendants. Figures 5a and b show the predicted urinary levels of 3-PBA attributable to aircraft disinsection under the residual treatment and pre-flight spray scenarios, respectively. The simulated median urinary levels of 3-PBA in the post-flight samples under residual treatment scenario for dermal, oral and inhalation exposure routes were 17.9 (0.63–249.7), 3.85 (0.0–96.2) and 0.25 (0–1.29) µg/l, respectively (Figure 5a). For the 24-h-post flight urine samples, the simulated median 3-PBA levels for dermal and oral exposure routes were 9.77 (0.0–59.6) and 1.35 (0.0–12.5) µg/l, respectively. The median urinary level of 3-PBA attributable to the inhalation route varied from below 0.10 µg/l at the beginning of the exposure to a peak value of 0.76 µg/l. Under the multiple exposure routes, the permethrin exposure in flight attendants under residual treatment scenario resulted in a median of 23.7 µg/l for 3-PBA with a range of 0.63–347 µg/l in post-flight samples, and a median of 13.2 with a range from 0.0 to 75.3 µg/l in 24-h-post flight samples.

Figure 5.

Simulated urinary concentrations for 3-phenoxybenzoic acid (3-PBA) in post- and 24-h-post-flight samples. (a) Simulation under residual treatment scenario; and (b) simulation under preflight spray scenario. The box plot representing the measured data shown in (a) was plotted based on the measured percentiles cited from Wei et al.⁵

Under the pre-spray scenario, simulated urinary levels of 3-PBA in post-flight from dermal, inhalation and oral exposure routes had ranges of 0.0–23.6, 0.82–47.1 and 0–5.44 µg/l with median values of 0.30, 6.23 and 0.18 µg/l, respectively. Altogether, the dermal, inhalation and oral exposure can lead to a median urinary level of 3-PBA in post-flight samples of 8.21 µg/l and a range from 0.81 to 76.0 µg/l. Simulated median urinary levels of 3-PBA in 24-h-post flight samples showed a dramatic decrease from the post-flight levels to 0.56 (0.04–6.33), 0.76 (0.0–7.87), 0.03 (0.0–1.03) and 2.01 (0.05–15.5) µg/l for dermal, inhalation, oral and multiple exposure routes, respectively.

Simulated urinary concentrations of 3-PBA in post-flight and 24-h-post-flight samples under residual treatment scenarios have comparable percentiles to the measured values in the samples from flight attendants working on commercial aircrafts that had been disinsected using a residual treatment with R² values of 0.91 and 0.93 for post-flight and 24-h-post-flight urine samples based on percentiles, respectively (data from Wei et al.⁵), except for the simulated maximum values, which were nearly 2–3 times higher than the measured maximum values. Computed RMSE values were 41.5 and 8.1 for post-flight and 24-h-post flight urine sample, respectively. One possible explanation to this discrepancy is that the measurements were from a limited sample size, and the potential variability was not sampled experimentally, whereas a wide range of variability in the urinary levels can be identified using an MCsimulation of 50,000 iterations. It is also possible that the maximum simulated inputs in the model were overestimated owing to the potential overestimation of values for such factors as hand–mouth contact frequency (h⁻¹), exposed dermal area or cumulative absorption percentage, etc. No direct measured 3-PBA concentrations under pre-flight spray scenarios have been reported in the literature, which can be compared with the simulated results in the study.

Proposed Time–Concentration Profiles in Fat, Brain and Blood in Flight Attendants

The human model was also used to predict the time–concentration profiles for permethrin in fat, brain and blood of flight attendants following multiple exposure routes under residual treatment and pre-flight spray scenarios. As can be seen in Figures 6 a, c and e, proposed median peak concentrations in fat, brain and blood were 19.7 ng/g, 1.6 ng/g and 62.9 ng/ml under the residual scenario, respectively, while those for the pre-spray scenario were 4.01 ng/g, 0.42 ng/g and 0.78 ng/ml, respectively (Figures 6b, d and f).

Figure 6.

Proposed time–concentration profiles for permethrin in fat, brain and blood of flight attendants following multiple exposure routes under residual treatment spray (RTS) (a, c and e) and pre-flight spray (PFS) (b, d and f) scenarios. The line: “-.-.-.” represents an envelope for the 97.5% confidence level, the gray line represents the envelope for the 75% confidence level and the black solid line represents the median value.

Concentrations in fat were predicted to peak between 15 and 30 h in both scenarios, while those in the brain and blood were predicted to peak around 14 and 3 h, respectively. Peak time in specific tissue can be affected by various factors, for example, total exposure duration, exposure time during the entire flight, tissue properties, exposure route type, etc. Fat has the largest partitioning coefficient against blood (median: 48.9) compared with other tissues, which can lead to a slower release of permethrin to blood from fat, while the permethrin in the blood can decrease quickly to relative low levels. Unlike the dermal and oral exposure, which can occur during the entire flight, inhalation exposure in pre-flight scenario mainly occur within the first 2 h at the beginning of the flight based on the aircraft disinsection procedures. This characteristic resulted in the shorter peak time in the brain and blood under pre-spray scenario.

Dermal, Inhalation and Oral Exposure Contributions to Permethrin Exposure Attributable to Aircraft Disinsection in Flight Attendants Under the residual treatment scenario, the dermal exposure route contributed 83.5% (median) ranging from 72.0 to 98.4% to the 3-PBA concentration in the post-flight urine samples (Figure 7), indicating that the dermal exposure was the dominant exposure route for the flight attendants on the residual treated aircrafts. The oral route contributed 16.1% (median) (range: 0.3–27.7%) to the urinary 3-PBA in the post-flight samples, suggesting nonintentional ingestion of permethrin through surface–hand–mouth route cannot be neglected. The median contribution of inhalation exposure route was only 0.4% ranging from 0 to 0.75%, indicating that inhalation was not significant in flight attendants working on aircraft treated by a residual method. The residual treatment scenario used was based on the disinsection practice guideline, which had been carried out by the maintenance personnel on the ground rather than the crews on the planes applying the pesticides, and the air conditioning and recirculation fans were run for at least 1 h to clear the pesticides in the air after residual treatment. If the flight crew enters sooner, inhalation exposure could become an important exposure route.

Figure 7.

Contributions for dermal, oral and inhalation exposure routes to 3-phenoxybenzoic acid (3-PBA) in post-flight urine samples under residual treatment (RTS) and pre-flight spray (PFS) scenarios.

Simulated results under pre-spray scenario show that inhalation had the largest contribution to 3-PBA in the post-flight urine samples of 89.7% (median), ranging from 61.9% to 97.8%, followed by the dermal route with the median contribution of 5.3% (range: 0.70–30.1%), and finally the oral contribution of 5.0% (range: 0.01–7.4%) (Figure 7). Pre-flight spray procedures were assumed to be completed within a maximum of 45 min, and the air concentration was recognized to decrease quickly to lower levels within the first 2 h. Although inhalation mainly occurred during the spraying time period in which the recirculation fans were switched off or set at the lowest flow rate, which represented only a fraction of the entire flight time, the inhalation contribution to the dose was still larger than those from other routes under the pre-spray scenario. This is consistent with the simulated worst-case scenario.

CONCLUSION

In this study, a permethrin PBPK model incorporating three exposure routes was constructed based on previous pyrethroids PBPK models for rats and humans. The PBPK model was evaluated using experimental data, and was used to analyze permethrin exposures and tissue doses under different exposure scenarios. The PBPK model was able to describe adequately 3-PBA concentrations in post- and 24-h-post-urine samples from flight attendants on aircrafts treated with residual disinsection. Dermal exposure was the predominant route to the permethrin exposure under residual treatment scenario, while inhalation was the predominant exposure route under the pre-flight spray scenario. The PBPK model presented here can be applied for additional interpretation of permethrin exposure biomarker data for flight attendants, including reconstruction of exposures from urinary biomarker data.

APPENDIX I

PBPK MODEL EQUATIONS

Abbreviations: Q_c, cardiac output (l/h); Q_p, alveolar ventilation rate (l/h); C_vt, the tissue venous blood concentration (mg/l); AV_i, venous amount in organ i; V_i, Volume of compartment i; A_i, amount of permethrin in the compartment i; Q_i, blood flow to the compartment i; P_i:b, tissue:blood partition coefficient for the compartment i; C_i, concentrations in the compartment i; PVF_i, blood volume fraction of compartment i; PA_i, permeability–surface area product of tissue (l/h); Inhale_Conc, inhaled airborne concentration of permethrin (mg/l); M_BLD, amount of permethrin in blood (mg/h); CA, concentration in blood compartment (mg/l); VB, blood volume; ODRate, oral dose rate (mg/h); Stomach, amount of permethrin in stomach (mg); Intestine, amount of permethrin in intestine (mg); K_s, rate constant of absorption from stomach (h⁻¹); K_i, rate constant of absorption from intestine (h⁻¹); K_si, rate constant of transfer from stomach to intestine (h⁻¹); K_fec, fecal excretion rate constant (h⁻¹).; A_skin, amount of permethrin in the skin compartment; Q_skin, blood flow to the skin compartment; P_skin:b, skin compartment:blood partition coefficient; C_skin, concentrations in skin compartment; derm_rate, dose rate from dermal absorption; SL, surface loading of permethrin (µg/cm²); SA, body surface area in direct contact with surface (cm²); TF, transferable surface residue of permethrin to exposed dermal; CABF, cumulative absorbed dose fraction (%); exp_time, exposure duration (h).; met, amount of metabolized permethrin in excretion compartment (mg); RAM_liver, rate of metabolism in liver (mg/h); RAM_BLD, rate of clearance in blood (mg/h); RAM_i, rate of metabolism from compartment i (mg/h); M_BLD, amount of permethrin in blood (mg); met_exc, amount of excreted permethrin through urine (mg); K_ur, urinary excretion rate constant (h⁻¹)

Model Equations

Rate of change in stomach (mg/h):

$$\frac{\mathit{\text{dStomach}}}{dt}=\mathit{\text{ODRate}}-K_s\times \mathit{\text{Stomach}}-K_{si}\times \mathit{\text{Stomach}}$$

Rate of change in intestine (mg/h):

$$\frac{\mathit{\text{dIntestine}}}{dt}=K_{si}\times \mathit{\text{Stomach}}-K_i\times \mathit{\text{Intestine}}-K_{fec}\times \mathit{\text{Intestine}}$$

Rate of change in blood (mg/h):

$$\frac{d{M}_{BLD}}{dt}=\sum (Q_t\times C_{vt})+Q_p\times \mathit{\text{Inhale}}\_\mathit{\text{Conc}}-Q_c\times CA-RA{M}_{BLD}$$

Rate of clearance in blood (mg/h):

RAM_BLD = K_metb × M_BLD

Permethrin concentration in blood (mg/l):

CA = M_BLD/VB

Distribution in flow-limited tissues (except liver and skin compartments):

$$\frac{d{A}_i}{dt}=Q_i\times \left(CA\frac{C_i}{P_{i:b}}\right)$$

Rate of change in liver compartment:

$$\frac{d{A}_{\mathit{\text{liver}}}}{dt}=Q_{\mathit{\text{liver}}}\times (CA-\frac{C_{\mathit{\text{liver}}}}{P_{\mathit{\text{liver}}:b}})+K_s\times \mathit{\text{Stomach}}-RA{M}_{\mathit{\text{liver}}}$$

Rate of change in skin compartment:

$$\frac{d{A}_{\mathit{\text{skin}}}}{dt}=Q_{\mathit{\text{skin}}}\times (CA-\frac{C_{\mathit{\text{skin}}}}{P_{\mathit{\text{skin}}:b}})+\mathit{\text{derm\_rate}}$$

Dermal absorption rate estimation:

derm_rate = SL × SA × TF × CABF/exp_time

Distribution in diffusion-limited tissues (fat, brain and slow perfused tissues):

$$\frac{dA{V}_i}{dt}=Q_i\times (CA-\frac{A{V}_i}{PV{F}_i\times V_i})+P{A}_i\times (\frac{A_i}{(1-PV{F}_i)\times V_i\times P_{i:b}}-\frac{A{V}_i}{PV{F}_i\times V_i})$$

$$\frac{d{A}_i}{dt}=P{A}_i\times (\frac{A{V}_i}{PV{F}_i\times V_i}-\frac{A_i}{(1-PV{F}_i)\times V_i\times P_{i:b}})$$

Rate of change estimation for metabolized permethrin in excretion compartment (mg/h):

$$\frac{dmet}{dt}=\sum RA{M}_i-K_{ur}\times \mathit{\text{met}}$$

Excretion of metabolized permethrin through urine:

$$\frac{dmet\_exc}{dt}=K_{ur}\times \mathit{\text{met}}$$

Urinary concentration:

$$Conc(\mu g/L)=1000\times \frac{\mathrm{\Delta }Met\_exc}{\mathrm{\Delta }V}$$

where Conc is the urinary concentration for a specific metabolite of permethrin. ΔMet_exc is the cumulative mass of permethrin metabolite during two excretion time points (mg). #x00394;V is the cumulative urine volume at the same duration (l). As for flight attendants, the time duration from the last excretion time to the sampling time point was in the range from 1to 4 h, and the corresponding urine volume was in the range from 0.03 to 0.75 l.