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Article

Application of All-Ages Lead Model Based on Monte Carlo Simulation of Preschool Children’s Exposure to Lead in Guangdong Province, China

by
Jing Hu
1,†,
Zhengbao Zhang
2,†,
Senwei Lin
3,†,
Qiuhuan Zhang
4,
Guoxia Du
1,
Ruishan Zhou
1,
Xiaohan Qu
1,
Guojiang Xu
3,
Ying Yang
2,* and
Yongming Cai
5,6,7,*
1
School of Public Health, Guangdong Pharmaceutical University, Guangzhou 510006, China
2
Guangdong Province Center for Disease Control and Prevention, Guangzhou 511430, China
3
Source of Wisdom Co., Ltd., Guangzhou 510091, China
4
Guangdong Institute of Public Health, Guangzhou 511430, China
5
College of Medical Information and Engineering, Guangdong Pharmaceutical University, Guangzhou 510006, China
6
Guangdong Provincial Traditional Chinese Medicine Precision Medicine Big Data Engineering Technology Research Center, Guangzhou 510006, China
7
Cloud-Based Computing Precision Medical Big Data Engineering Technology Research Center of Guangdong Universities, Guangzhou 510006, China
*
Authors to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Sustainability 2023, 15(2), 1068; https://doi.org/10.3390/su15021068
Submission received: 19 November 2022 / Revised: 25 December 2022 / Accepted: 29 December 2022 / Published: 6 January 2023
Browse Figures
Versions Notes

Abstract

:
Introduction: Lead (Pb) poisoning in children is a major public health issue worldwide. The physiologically based pharmacokinetic model (PBPK model) has been extensively utilized in Pb exposure risk assessment and can connect external exposure with biological monitoring data. This study aimed to combine a Monte Carlo simulation with the all-ages lead model (ALLM) to quantify the heterogeneity and uncertainty of certain parameters in the population. The parameters of the all-ages lead model based on Monte Carlo simulation (ALLM + MC) were localized in Guangdong Province. Our study discusses the practicability of the application of the localized ALLM + MC in Guangdong Province. Methods: A local sensitivity analysis was used to assess the impact of pharmacokinetic parameters on the prediction of blood lead level (BLL). Environmental Pb concentration, exposure parameters, and sensitive parameters were included in the ALLM + MC, and the differences between the ALLM- and the ALLM + MC-predicted values were compared. Additionally, we localized the exposure parameters in the ALLM + MC and used them to evaluate BLL in preschool children from Guangdong Province. Finally, we compared the predictive values to those observed in the literature. Results: The predictive values of ALLM and ALLM + MC had a significant correlation (r = 0.969, p < 0.001). The predictive value of ALLM was included in the ALLM + MC prediction range. Moreover, there were no significant differences between the predictive and the observed values of preschool children from Guangdong Province (z = −0.319, p = 0.749). Except for children aged 5–6, the difference between the predictive and the observed values was less than 1 μg/dL. The root mean square error (RMSE) and the mean deviation (RMD) of ALLM and ALLM + MC were reduced by 24.73% and 32.83%, respectively. Conclusions: The localized ALLM + MC is more suitable for predicting the BLL of preschool children in Guangdong Province, which can be used to explain the heterogeneity and uncertainty of parameters in the population. The ALLM + MC has fewer time, space, and financial restrictions, making it more appropriate for determining the BLLs in large populations. The use of ALLM + MC would improve the feasibility of regular and long-term blood Pb detection.

1. Introduction

Pb is abundant in the living environment and preschool children (less than 7 years old) are the most vulnerable at-risk group for adverse effects of Pb poisoning [1]. Infants, toddlers, and children are at risk for lead poisoning from food sources as well [2]. Children who are exposed to Pb may suffer major health consequences in terms of their nerve development, immune suppression, reproductive function, cognitive function, growth and development, intelligence [1,3,4,5,6,7,8,9,10,11,12], etc. Pb can damage human health in a variety of ways, including air, soil, indoor dust, diet, and drinking water. Connecting external exposure with biological monitoring data is crucial for effectively assessing the risk of Pb exposure. In Europe and America, the PBPK model has been widely used for health-risk assessment of Pb exposure, formulation of environmental safety limits, and the evaluation of the effect of pollution control measures [13,14,15]. The PBPK model, which is made up of corresponding compartments of various tissues and organs connected by blood circulation, is based on anatomical, physiological, and biochemical characteristics. According to the principle of mass balance, it establishes a set of differential equations and represents the process of drug absorption, distribution, metabolism, and excretion (ADME) in the body [16,17,18]. The PBPK model can not only predict Pb concentration in blood, tissues, and even organs after exposure in various environmental media but also connect the external exposure to biological monitoring data, making data interpretation easier. The Environmental Protection Agency (EPA) of the United States of America developed the all-ages lead model (ALLM) and the integrated exposure uptake bio-kinetic (IEUBK) model to thoroughly assess and predict multimedia Pb exposure [19,20]. The IEUBK model is useful for predicting BLLs in preschool children [20,21], while ALLM is a model structure extension based on IEUBK that combines the modeling structure and growth equation of other models. In addition to predicting BLLs in Pb-exposed people of all ages, ALLM can also forecast Pb levels in tissues, organs, and excretion. Furthermore, ALLM considers gender in Pb dynamics and has a more comprehensive model structure, which helps include multiple exposure sources and media.
ALLM consists of two parts: the exposure and biokinetic models. Based on input exposure concentrations in air, indoor dust, soil, diet, and drinking water (g/day). The bio-kinetic model receives daily Pb intake from the exposure model and simulates (a) Pb absorption into the diffusible plasma of the gastrointestinal and respiratory tracts, (b) Pb transfer into various tissues and organs, and (c) Pb excretion through urine, sweat, hair, nails, and peeled skin. In general, ALLM can predict Pb concentrations in blood, tissues, and organs, as well as in excretion after Pb exposure, based on Pb concentration input from various environmental sources. In particular, the population’s BLLs is frequently used as an indicator in health risk assessment of Pb exposure [22,23,24,25]. The ALLM output is greatly influenced by the heterogeneity and uncertainty of Pb concentrations from external environments, and exposure and pharmacokinetic parameters in the population [26]. As a result, the individual values generated by the ALLM may not accurately reflect the population’s average level.
The Monte Carlo simulation is a vital statistical analysis technique. It is useful to quantify the population’s heterogeneity and uncertainty [27] and to demonstrate the uncertainty of a known probability distribution by establishing a mathematical model based on probability distribution [28,29]. Barbara et al. developed a model based on Monte Carlo simulation and accurately predicted the BLLs of children in the area [30]. Furthermore, Zhong et al. evaluated the effect of parameter uncertainty on the uncertainty of BLLs output using the Monte Carlo simulation in conjunction with the IEUBK model [26]. The findings showed an improved model that could be used to assess the BLLs of Chinese preschool children. As a result, by combining the Monte Carlo simulation and ALLM to obtain the population BLLs and error range, the prediction effect of the population BLLs is improved, and the heterogeneity and uncertainty of each parameter in the population can be quantified.
With the implementation of the Pb control policy, child BLLs in China have decreased significantly [31]. However, the BLL of children in Guangdong Province is 5 μg/L~327 μg/L, the median is 59.66 μg/L [32], which is still very high. Because of the irreversibility, accumulative character, and latency of Pb poisoning [33], it is critical to measure the dose in tissues when assessing the risk of Pb exposure. Only epidemiological study has been carried out on the risk assessment of environmental Pb exposure in Guangdong Province [34,35,36], large-scale BLL measurements are typically laborious and require considerable amounts of supplies [37]. These issues can be effectively solved by implementing the ALLM + MC. However, ALLM was founded upon a large number of American population studies. Since American children’s dietary habits and behavioral patterns differ significantly from those of Guangdong Province, China, poor prediction results would arise from the direct use of American parameters [38,39]. Through the database retrieval, literature review and sorting, it is found that the environmental medium lead concentration and biological monitoring data in Guangdong Province are relatively rich. To enable the local application of the ALLM + MC, Guangdong Province has been used in this paper as an example to localize the exposure parameters in ALLM.
This study applied ALLM + MC for the first time to explain the heterogeneity and uncertainty of parameters in preschool children. Based on this, the ALLM + MC parameters were localized for Guangdong Province, and the feasibility of applying ALLM + MC to the province’s preschoolers was assessed. The PBPK model of Pb has not before been used in research to predict the BLLs of children in Guangdong Province. For this purpose, we first constructed the ALLM using the Monte Carlo simulation. On this basis, the model’s exposure parameters were localized and used to predict BLLs in preschool children. To assess the model’s predictive ability, the obtained predictive values were compared to those observed.

2. Materials and Methods

2.1. Construction of the ALLM + MC

2.1.1. Improvement of the ALLM

Pb intake (g/day) through food was directly entered into ALLM. We took the IEUBK model’s formula as a reference to calculate daily dietary Pb intake based on the inputted Pb concentration in food and amount of daily intake [40]. Consequently, the heterogeneity of dietary Pb concentrations and dietary daily food intake within the population could be quantified and future changes be facilitated. The daily dietary Pb intake was considered equal to the amount of each food type’s intake and the dietary Pb concentration. The modified dietary Pb exposure model’s equation is shown below:
I N f o o d t o t a l = ∑ i = 1 3 f o o d i * I R f o o d i
where INfoodtotal (g/day) represents the total dietary Pb intake; foodi (mg/kg), the Pb concentration from three dietary sources; and IRfoodi (g/day), the food daily intake amount.

2.1.2. Sensitivity Analysis of Pharmacokinetic Parameters

Sensitivity analysis is used to quantify the effect of parameter changes on results [41,42,43]. In this study, we propose running a sensitivity analysis of the model in R to investigate the effect of pharmacokinetic parameters (rate of transfer between tissues and organs, etc.) on predicted BLLs. Sensitivity analysis was performed for 30 pharmacokinetic parameters with a parameter variation range of 1%, and sensitivity coefficients were calculated for each preschool age group using the formula [44]:
s = ( f ( x + △ × x , Φ ) − f ( x , Φ ) ) / f ( x , Φ ) △
where x is the default value of the target parameter; △ is the range of variation of the target function, which is set to 1% in this case based on previous studies; Φ is the other parameters in the model with default values; and f is ALLM. Sensitive parameters have sensitivity coefficients greater than 0.1, indicating that a 1% change in the sensitive parameter has a 0.1% effect on blood Pb.

2.1.3. Construction of the ALLM + MC

Children’s exposure parameters, environmental medium Pb concentration and sensitive parameters are included in the ALLM + MC (Figure 1) to quantify the impact of these parameters on predicting BLLs. On the other hand, we assumed that the Pb contents in each environmental medium followed a log-normal distribution since it is the typical distribution of environmental concentration data [45,46,47,48]. In each age group, the daily intake of grains, vegetables, and dust followed a log-normal distribution, the daily water intake followed a triangular distribution, and the ventilation rate followed a normal distribution [26,49]. Sensitive pharmacokinetic parameters were set to default values and normal distributions were assumed. All of the parameters listed above were within the 95% confidence interval.
To compare the difference between ALLM and ALLM + MC in predicting BLLs, we entered values into the two models. Preschool children were divided into 0–1, 1–2, 2–3, 3–4, 4–5, 5–6, 6–7 age groups. The concentration of air, indoor dust, drinking water, ventilation rate, and daily intake of dust and drinking water were taken as the recommended input values of the ALLM model [19]. In the case of the dietary Pb exposure route, we only considered grain and vegetable intake temporarily. Dietary Pb intake was calculated by the sum of the amount of daily intake and Pb concentration. Grain Pb concentration and vegetable Pb concentration data were obtained from the U.S. Food and Drud Administration 2018–2020 total digital study (TDS) elements report [50]. Additionally, the daily intake of grain and vegetables were both taken from the Exposure Factors Handbook: 2011 Edition [51]. In the ALLM + MC, the environmental medium Pb concentration, and the exposure and sensitive parameters were randomly selected from the defined distribution as the simulated blood Pb values of preschool children (see Supplementary Tables S1 and S2). To ensure the stability of the results, data of children (per gender) were run 10,000 times using the models based on the Monte Carlo simulation. The total blood Pb value consisted of the average of BLLs for each gender.

2.2. Localization and Application of the Improved Model

2.2.1. Localization of Model Exposure Parameters

Exposure parameters are critical in human health risk assessment, and their accuracy levels scientifically validate the whole procedure [52]. Therefore, we localized the exposure parameters of the present model.
Previous research has shown that the Pb isotope ratio of Chinese children’s blood Pb is close to that of food, drinking water and air [53]. In the Pearl River Delta region of Guangdong, residential dust may be the main source of children’s Pb exposure at present [54]. Therefore, we focused on the four Pb exposure pathways (air, indoor dust, diet, and drinking water). Since the third total diet study in China shows that grains and vegetables provide 72.2% of dietary Pb sources for children aged 2–7 years [55], only vegetables and grains were considered in this study. Values of daily ventilation rate, indoor dust, drinking water, and grain and vegetable intake in the study population referred to the Exposure Factors Handbook of Chinese Population (Children Volume) [56]. In particular, the vegetable intake of children aged 2–3 referred to the average level of Chinese children.
Since the geometric standard deviation (GSD) of grain and vegetable intake and indoor dust intake of children from Guangdong Province were not present in the revised literature, GSD values of Japan were used instead [57,58]. The GSD of Japan was formerly used in Chinese preschool children studies with good fitting [26,49]. Previously, the U.S. GSD had been used, fitted among Chinese preschool children [26,49]. Two articles of IEUBK were taken as references for the coefficient of variation of ventilation rate, with a rate of 20% [26,49].

2.2.2. Application of the Model

To evaluate the applicability of ALLM + MC, we collected environmental Pb concentration data and biological monitoring data of cities from Guangdong Province and combined them with weights to represent the average level of Guangdong Province. The combined environmental Pb concentration was used as the input for fitting. Then, the predicted BLLs were compared with the observed BLLs.
The epidemiological research literature on BLLs of the study population, published in 2003, was retrieved from the China National Knowledge Infrastructure (CNKI), the Wanfang Data Knowledge Service Platform, PUBMED, Web of Science, and Elsevier ScienceDirect. During this research, the subject words in the Chinese database were “blood lead” and “children”, and the subject words in the English database were “blood lead level”, “China”, and “Children”. The publication period of choice was from 1 January 2003 to 31 December 2021. The inclusion criteria comprised: (1) as subjects, preschool children without obvious Pb exposure, as long as there was clear information about sampling location, sampling year, age, etc.; (2) BLLs expressed as mean (M), standard deviation (SD), geometric mean (GM), or geometric standard deviation (GSD), as long as there was a relationship between age and BLLs; (3) the types of blood sampled could be venous blood or peripheral blood. It has been reported that there is no difference between venous blood Pb and peripheral blood Pb [59]; (4) the sample size was greater than 500; (5) the monitoring method of blood Pb was atomic absorption spectrometry or electron-coupled plasma mass spectrometry, as there is no difference according to the previous articles [60]; (6) if multiple articles used research objects in the same area, only the literature with the largest sample size could be included in this research.
The published blood lead literature corresponding to the urban environmental Pb concentration literature was retrieved from the five abovementioned public databases. The inclusion criteria for environmental Pb concentration in the literature were similar to those of the biological monitoring literature and had to be in the same period as that of the biological monitoring data or as close as possible. Since it was impossible to find the Pb concentration of indoor dust from various regions of the Guangdong Province in the existing literature, we assumed that it was the same as that of overall Chinese indoor dust, with a GM of 162.90 mg/kg and a GSD of 2.15 mg/kg [61]. Since it was also impossible to find the Pb concentration in drinking water in literature of the area, it was defined to be the same as that of overall China, with a GM of 0.054 μg/L and a GSD of 2.05 μg/L [49].
Finally, we collected data on preschool children’s BLLs and their corresponding Pb concentrations in air, vegetables, and grains in 5 cities in Guangdong Province (displayed in Supplementary Tables S3–S6). We weighted and combined the biological monitoring data of each subgroup into the BLLs of the subjects according to the sample size (see Supplementary file for the formula and Table S3). Moreover, we combined the environmental Pb concentration data of many cities into the data representing Guangdong Province according to the formula (see Supplementary Materials for details).
The sensitivity analysis showed that the maternal blood Pb concentration was sensitive to the BLLs of children aged 0–1. Therefore, maternal blood Pb concentration was also included in the Monte Carlo simulation (data shown in Supplementary Table S7). To compare the predictive results of ALLM and ALLM + MC, we used the two models to fit and calculate the corresponding evaluation indicators of BLLs in the subjects. In ALLM, the mean or GM of environmental Pb concentration, exposure and sensitive parameters were used as inputs for the prediction (see Supplementary Table S8). In ALLM + MC, the environmental medium Pb concentration, exposure, and sensitive parameters randomly selected from the defined distribution were used as inputs to simulate blood Pb value. To ensure the stability of the results, data of children (according to gender) were run 10,000 times using the ALLM + MC. The total blood Pb value consisted of the average of BLLs.
In this study, root mean square error (RMSE) and mean deviation (RMD) were selected to evaluate the model validation results [62,63]. RMSE evaluates the consistency between the predicted and the observed value, while RMD is used to assess the systematic bias of the model, as shown below:
R M S E = 100 O ∑ i = 1 n ( P i − O i ) 2 n
R M D = 100 O ∑ i = 1 n P i − O i n
where Pi is the predicted value, Oi is the observed value, O is the mean of the observed value, and n is the sample size. The closer RMSE and RMD are to 0, the better the simulation effect is [64].

2.3. Statistical Analysis

The R 3.6.3 was used for the sensitivity analysis and the establishment of ALLM + MC. Microsoft Office 2021 software was used to calculate RMSE and RMD, and Matlab 9.11 was the tool to draw a scatter plot of preschool children’s BLLs. SPSS 19.0 was used for statistical analysis. In particular, the Pearson correlation analysis evaluated a possible correlation between the predicted value of ALLM and that of ALLM + MC. Finally, the Mann–Whitney U test was employed to analyze the difference between the predicted and the observed value at a significance level of p < 0.05.

3. Results

3.1. Construction of ALLM + MC

3.1.1. Results of the Sensitivity Analysis

Table 1 shows the sensitive parameters and sensitivity coefficients for children aged 1–7 years. The results of other pharmacokinetic sensitivity analyses are shown in Supplementary Table S9. Of the 30 pharmacokinetic parameters, 5 had sensitivity coefficients greater than 0.1. In 1-year-old children, another crucial factor is the coefficient on the rate of Pb transfer from the surface or non-exchangeable bone volume to exchangeable (cortical or trabecular) bone volume. Except for children of age 0 to 1, the rate of Pb transfer from red blood cells to diffusible plasma is sensitive. At that age, their BLLs are responsive to maternal blood Pb concentration. Our findings revealed that their BLL was primarily influenced by the rate of Pb transfer to the bone compartment and the rate of red blood cell transfer to diffusible plasma.

3.1.2. Construction of ALLM + MC

We included the default value of environmental Pb concentration, and default values of exposure and sensitive parameters in the ALLM + MC (refer to the USA Exposure Factors Handbook: 2011 Edition). Table 2 shows the differences in BLLs predicted by ALLM and ALLM + MC according to gender and age. ALLM point estimates were included in the range of ALLM + MC prediction. The predicted BLLs of ALLM significantly correlated with the predicted BLLs of ALLM + MC (r = 0.969, p < 0.001).

3.2. Localization and Application of the Model

Table 3 compares exposure parameters in Guangdong Province to those in the U.S. We found significant differences in grain, vegetable, and drinking water and ventilation rate. Thus, the BLLs may be predicted erroneously if the U.S. exposure parameters were used to evaluate preschool children in Guangdong Province.
Table 4 displays the observed values of preschool children in the Guangdong Province, as well as the predicted values of the two models. There was a statistically significant difference between the predicted and observed values of ALLM (Z = −2.747, p < 0.05). The difference between those values in ALLM + MC was not statistically significant (Z = −0.319, p = 0.749). The RMSE and RMD in the predicted values of ALLM + MC were lower when compared to ALLM, showing that the model’s random and systematic errors were smaller and had a better effect than ALLM.
Figure 2 shows a comparison between the predicted and observed mean BLLs in the study subjects. Predicted values of both ALLM and the ALLM + MC fell within the M ± SD of the observed values; however, the ALLM + MC predictions were closer to the observed values. The range of error between predicted and observed values for children of all ages is shown in Figure 2. Except for children aged 5~6, there was a disparity between the predicted and observed values of less than 1 μg/dL in all age groups. Considering the variability of Pb concentration, and the exposure and pharmacokinetic parameters in the environmental media, the results showed that ALLM + MC was more suitable than ALLM for predicting BLLs in this population. Therefore, in the present context, the application of a localized ALLM + MC seemed valid.

4. Discussion

The present study applied the Monte Carlo simulation to ALLM to consider the heterogeneity and uncertainty of environmental Pb concentration, and the exposure and pharmacokinetic parameters in preschool children from the Guangdong province. On this basis, the exposure parameters of the model were localized and used to predict BLLs and the practicability of the model in the analyzed population. The results showed that ALLM + MC had not only a better fitting effect than ALLM, but also predicted BLLs values that were closer to the observed values.
As shown in Table 1, the output of ALLM is a point estimate of BLLs for each age group, which may or may not represent the population’s average level and its error. We used the Monte Carlo simulation to establish ALLM with the aim of more accurately describing the BLLs of preschool children and quantifying relevant parameters. The Monte Carlo simulation is essentially a statistical method based on random numbers [65]. The mathematical model of the probability distribution is established in Monte Carlo simulation, and the uncertainty is represented by random sampling from the known probability distribution [66]. The process of random sampling is then repeated indefinitely. The simulated value can be infinitely close to the real situation as the number of repetitions increases. Therefore, we repeated the process 10,000 times and determined the type of probability distribution of the external exposure Pb concentration, the exposure, and pharmacokinetic parameters. Then, we performed random draws to estimate the BLLs point value and its error margin. According to Table 2, ALLM + MC had better results at predicting the mean and error range of BLLs across all age groups compared to ALLM. Because ALLM + MC can reflect the variation in BLLs in the population, it may be more appropriate for determining the corresponding BLLs. When ALLM + MC was used to assess the BLLs, its model-fitting effect was better than ALLM, as shown in Table 4. Conversely, the point estimate of BLLs in ALLM may not take into account the population’s heterogeneity, which makes it unsuitable for determining BLLs in the general population.
Except for children aged 0~1 years, the predicted value of ALLM in other age groups was much lower than the observed value, as shown in Figure 2. The BLLs of preschool children would be underestimated with serious consequences if the individually predicted values of the ALLM were utilized to assess it. Monte Carlo simulation has been widely used in the risk assessment of Pb exposure with results that agree with ours, indicating that Monte Carlo can effectively account for population heterogeneity and be used to assess population BLLs. For example, Zhong et al. evaluated the influence of parameter uncertainty on the uncertainty of output BLLs using Monte Carlo simulation combined with the IEUBK model, and the predicted and observed values fit well [30]. Moreover, Barbara et al. used Monte Carlo simulation to create a model that accurately predicted the BLLs of children in the district [14]. It is worth noting that among the predicted values of ALLM + MC, the predicted value of BLLs in children aged 4–7 years is lower than the observed value. On the one hand, children get better at excreting Pb as they get older. In children, the urinary pathway is the primary route for excretion. RBLAD is the model parameter that affects urinary excretion (rate coefficient of lead transfer from bladder to urine). RBLAD is equal to 12 d−1 at 0–1 years old, 15 d−1 at 1–4 years old, and 11 d−1 at 5–7 years old. Children’s lead excretion times get stronger after age 5–7, which could account for why the measured value for ages 4 to 7 is lower. On the other hand, due to the lack of relevant literature and data on lead absorption and metabolism parameters of children in Guangdong Province, we used the pharmacokinetic parameters recommended by EPA for calculation in this study. The pharmacokinetic parameters of children in Guangdong Province and those in Europe and the U.S. may differ, and as a result, this discrepancy may be due to that fact. Children in Guangdong Province may not have the same lead metabolism characteristics as children in Europe and the U.S.
Lead PBPK models are currently based on European and American populations and are widely used there and in other countries. According to earlier studies, predicted values fit well with observed values in Europe and America [67,68]. Chinese researchers have previously implemented the default values of the model for exposure parameters to assess the risk of Pb exposure in Chinese children, but the model fit was poor [38,39]. As a result, we compared exposure parameters between children in Guangdong Province and children in the United States and detected a significant difference between grain and vegetable intake. In China, former research has found that the most common source of Pb exposure in preschool children is food [26,49]. If the dietary intake of American children and other factors were used to conduct a risk assessment of children’s Pb exposure in the Guangdong Province, significant inaccuracies could arise and impact the efficiency and objectivity of risk decision-making.
To apply the ALLM + MC in our study population, we localized the exposure parameters. The obtained predicted value is very close to the observed value and its error range, as shown in Figure 2. When making predictions, ALLM + MC was more accurate than ALLM because its predicted value was more closely aligned with the observed value. Therefore, the application of the localized ALLM + MC to preschool children from the Guangdong Province seems feasible, reliable, and necessary. The use of ALLM + MC would improve the feasibility of regular and long-term blood Pb detection. The localized ALLM + MC has fewer time and space restrictions than the conventional epidemiological survey, and it also allows the reduction of manpower, material resources, and financial resources, making it more appropriate for determining the BLLs in large populations.
According to the third China Total Diet Study, grains and vegetables provide 72.2% of the dietary Pb sources for children aged 2–7 years [55]; thus, grains and vegetables were used as the primary sources of dietary Pb in this study. However, it should be considered that meat and milk can provide 5% of a child’s dietary Pb source and may account for the little difference between predicted and observed values. On the other hand, we directly cited in the model the default pharmacokinetic parameter values suggested by EPA, which were obtained from studies based on American and European populations. The latter may also result in a slight discrepancy between the projected and observed results. The pharmacokinetic parameters must then be further optimized to increase the model’s prediction accuracy. Finally, in the future, we plan to include more subjects in the development of ALLM + MC for assessing the risk of Pb exposure in Chinese preschool children.

5. Conclusions

This study established ALLM + MC, which can be used to explain the heterogeneity and uncertainty of parameters in the population. The localized ALLM + MC applied to preschool children in Guangdong Province demonstrated good predictive ability. The ALLM + MC has fewer time, space and financial restrictions, making it more appropriate for determining the BLLs in large populations. The use of ALLM + MC would improve the feasibility of regular and long-term blood Pb detection.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/su15021068/s1, Figure S1: Map of study areas in Guangdong Province; Table S1: Exposure parameters input and references of ALLM based on Monte Carlo simulation; Table S2: External exposure Pb concentration parameters input and references of ALLM based on Monte Carlo simulation; Table S3: References of biomonitoring data in Guangdong Province, China (unit: μg/dL); Table S4: Pb concentrations in air (unit: μg/m3); Table S5: Pb concentrations in vegetables (unit: mg/kg); Table S6: Pb concentrations in grain (unit: mg/kg); Table S7: Pb concentration in maternal blood in Guangdong Province (unit: μg/dL); Table S8: Exposure parameters input and references of ALLM based on Monte Carlo simulation in Guangdong Province, China; Table S9: List of ALLM model parameters for sensitivity analysis. References [19,26,49,50,51,56,57,58,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95] are cited in the supplementary materials.

Author Contributions

All authors contributed to study conception and design. The literature was collected by J.H., R.Z., G.D., X.Q., and Q.Z.; S.L. and G.X. were responsible for writing and running the code. The manuscript was written by J.H., Z.Z., and Y.Y., and Y.Y. and Y.C. were responsible for revising the manuscript. All authors have read and agreed to the published version of the manuscript.

Funding

This project was sponsored by Key-Area Research and Development Program of Guangdong Province (No.2019B020210003), Research on Prediction Trend of Population Infected with COVID-19 Based on Big Data (NO.2020KZDZX1126), Natural Science Foundation of Guangdong Province (No.2020A1515010783, No. 2020A1515010861), National Natural Science Foundation of China Youth Fund (No. 81903286).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The environmental lead concentration data and exposure parameter data of Guangdong Province used in this study are shown in Supplementary Tables S3–S8. The values of pharmacokinetic parameters refer to the technical support documents published by the U.S. EPA (https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=P1012GIX.txt, accessed on 1 January 2023).

Acknowledgments

The authors thanks experts from Guangdong Province CDC for their guidance on the relevant professional knowledge of this research.

Conflicts of Interest

The authors declare no conflict of interest.

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Sustainability 15 01068 g001 550
Figure 1. Schematic description of the ALLM + MC.
Figure 1. Schematic description of the ALLM + MC.
Sustainability 15 01068 g001
Sustainability 15 01068 g002 550
Figure 2. Comparison of predicted and observed BLLss in Guangdong Province.
Figure 2. Comparison of predicted and observed BLLss in Guangdong Province.
Sustainability 15 01068 g002
Table
Table 1. Sensitivity coefficient of ALLM pharmacokinetics parameters.
Table 1. Sensitivity coefficient of ALLM pharmacokinetics parameters.
ParameterDescription0~11~22~33~44~55~66~7
ARCORTRate coefficient for Pb transfer from nonexchangeable cortical bone to diffusible plasma.00.180.190.160.130.110.09
ARRBCRate coefficient for Pb transfer from RBC to diffusible plasma.−0.05−0.98−0.98−0.98−0.98−0.98−0.98
ARCS2DFRate coefficient for Pb transfer from the cortical bone surface to exchangeable cortical bone volume.0−0.28−0.19−0.14−0.09−0.06−0.06
RDIFFRate coefficient for Pb transfer from exchangeable bone (cortical or trabecular) volume to surface or non-exchangeable bone volume.00.130.080.050.020.0010.00
BLDMOTMaternal blood Pb concentration.0.990.030.010.010.010.010.01
Table
Table 2. Comparison between BLLs predicted by ALLM or ALLM + MC.
Table 2. Comparison between BLLs predicted by ALLM or ALLM + MC.
Age Group (Years)BLLs Predicted by ALLM, μg/dLBLLs Predicted by ALLM + MC (M ± SD), μg/dL
MaleFemaleTotalMaleFemaleTotal
0~10.610.620.610.58 ± 0.300.59 ± 0.300.58 ± 0.30
1~21.371.411.390.91 ± 1.090.93 ± 1.120.92 ± 1.11
2~31.321.361.340.88 ± 1.040.91 ± 1.070.89 ± 1.06
3~41.211.251.230.82 ± 0.930.84 ± 0.960.83 ± 0.95
4~51.081.111.100.74 ± 0.820.76 ± 0.840.75 ± 0.83
5~60.930.960.950.65 ± 0.710.67 ± 0.730.66 ± 0.72
6~70.840.850.850.59 ± 0.620.60 ± 0.630.59 ± 0.63
Table
Table 3. Comparison of localized and American exposure parameters (AM).
Table 3. Comparison of localized and American exposure parameters (AM).
Age Group 0~11~22~33~44~55~66~7
Grain (g/day)Guangdong a24.779.1143.6156.4166.1171.4186.0
U.S. b33.066.081.0101.0101.0101.0119.0
Vegetable (g/day)Guangdong a49.596.4194.5170.6159.7149.0232.2
U.S. b91.0120.0145.0170.0170.0170.0210.0
Dust (g/day)Guangdong a0.030.060.060.040.040.040.10
U.S. b0.030.060.060.060.060.060.06
Water (L/day)Guangdong a0.590.910.810.860.850.861.19
U.S. b0.360.270.320.330.330.330.41
Ventilation rate (m3/day)Guangdong a5.05.25.87.78.08.39.4
U.S. b5.48.08.910.110.110.112.0
a Refer to the Exposure Factors Handbook of Chinese Population (Children Volume). b Refer to the Exposure Factors Handbook: 2011 Edition.
Table
Table 4. Comparison of localized model validations.
Table 4. Comparison of localized model validations.
Age Groups (Year)BLLs Predicted by ALLM (μg/dL)BLLs Predicted by ALLM + MC (μg/dL)Observed BLLs (μg/dL)
0~14.184.554.07
1~23.345.064.72
2~34.296.005.19
3~44.406.245.85
4~53.845.956.34
5~63.485.456.74
6~73.835.516.05
0~73.915.545.13
RMSE38.0313.30
RMD−32.31−0.52
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MDPI and ACS Style

Hu, J.; Zhang, Z.; Lin, S.; Zhang, Q.; Du, G.; Zhou, R.; Qu, X.; Xu, G.; Yang, Y.; Cai, Y. Application of All-Ages Lead Model Based on Monte Carlo Simulation of Preschool Children’s Exposure to Lead in Guangdong Province, China. Sustainability 2023, 15, 1068. https://doi.org/10.3390/su15021068

AMA Style

Hu J, Zhang Z, Lin S, Zhang Q, Du G, Zhou R, Qu X, Xu G, Yang Y, Cai Y. Application of All-Ages Lead Model Based on Monte Carlo Simulation of Preschool Children’s Exposure to Lead in Guangdong Province, China. Sustainability. 2023; 15(2):1068. https://doi.org/10.3390/su15021068

Chicago/Turabian Style

Hu, Jing, Zhengbao Zhang, Senwei Lin, Qiuhuan Zhang, Guoxia Du, Ruishan Zhou, Xiaohan Qu, Guojiang Xu, Ying Yang, and Yongming Cai. 2023. "Application of All-Ages Lead Model Based on Monte Carlo Simulation of Preschool Children’s Exposure to Lead in Guangdong Province, China" Sustainability 15, no. 2: 1068. https://doi.org/10.3390/su15021068

APA Style

Hu, J., Zhang, Z., Lin, S., Zhang, Q., Du, G., Zhou, R., Qu, X., Xu, G., Yang, Y., & Cai, Y. (2023). Application of All-Ages Lead Model Based on Monte Carlo Simulation of Preschool Children’s Exposure to Lead in Guangdong Province, China. Sustainability, 15(2), 1068. https://doi.org/10.3390/su15021068

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