# Key Factors for Improving the Carcinogenic Risk Assessment of PAH Inhalation Exposure by Monte Carlo Simulation

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Research Area and Participants

#### 2.2. Sampling and Analytical Methods

#### 2.3. Risk Characterization

_{eq}is the BaP equivalent concentration (BaP

_{eq}) in gaseous phase and particulate phase (ng·m

^{−3}), IR is the inhalation rate (m

^{3}·day

^{−1}), EF is the exposure frequency (365 day·year

^{−1}), ED is exposure duration (53 year), BW is the body weight (kg), and AT is the average time (70 years × 365 day·year

^{−1}). CSF

_{BaP}is the inhalation cancer slope factor for BaP (3.14 per mg·kg

^{−1}·day

^{−1}).

_{eq}and the toxicity equivalency factors (TEFs) were used to express the carcinogenic risk of PAH mixtures. The BaP

_{eq}based on the BaP toxicity was incorporated using Equation (2), where C

_{i}is the concentration of the PAH species in atmospheric samples, and TEF

_{i}is the toxic equivalence factor of the congener of PAH, i. Table S1 lists the PAHs and TEFs used in the calculation associated with the evidence of cancer in PAH-exposed individuals.

#### 2.4. Monte Carlo Simulation

_{eq}concentration, body weight, and inhalation rate were considered as variables. Log-normal distributions were applied to describe variables, because log-normal is the most widely applied model in studies on the exposure parameters [39,40]. Distribution of concentration was obtained by Gaussian fitting of the monitoring data from 25 sampling sites. BW and IR were derived based on the exposure parameter collected from the Exposure Factors Handbook of Chinese Population [41].

## 3. Results and Discussion

#### 3.1. Individual Actual Risks Based on Measured Parameters

^{−7}to 4.67 × 10

^{−5}, with a median of 4.83 × 10

^{−6}. Compared with risks reported from the other cities in China, ILCR in Taiyuan was much higher than that reported in Xingtai, Hebei, with an average ILCR of 3.4 × 10

^{−7}[43]. However, ILCR in Taiyuan was lower than that of people in some typical industrial cities such as Nanchong, Sichuan Province, with a reported value of 1.2 × 10

^{−5}[44] and Changzhou with a value of 3.6 × 10

^{−3}[45].

^{−1}day

^{−1}, which was in the same order of magnitude as the level of particulate PAH

_{15}with a mean value of 21.13 ng kg

^{−1}day

^{−1}. However, it can be seen from Figure 2A that particulate PAHs had a significantly higher BaP

_{eq}contribution and higher risk than did gaseous phase (Kruskal-Wallis test, p < 0.01). Previous research suggested PAHs with higher molecular weight were also more carcinogenic and more easily absorbed onto particles. Our findings are consistent with previous results [46].

^{−6}) was significantly higher than that of urban ones (geomean, 3.4 × 10

^{−6}). Based on the results above, it can be inferred that different exposure levels in urban and rural areas may be more important factors than physiological parameters.

#### 3.2. Population Risk Based on Monte Carlo Simulation

#### 3.2.1. Parameter Distribution Estimation

_{eq}concentration can be described by a log-normal distribution LN(2.21, 1.01). After ranking these data from least to greatest, plotting positions (proportions) for use in a cumulative probability distribution were calculated as:

^{2}= 0.941). In a traditional assessment model, it is difficult to collect the physiological parameters of participants due to the large population and high cost. The development of research on exposure parameters in recent years has provided great convenience to the accurate assessment of health risk through the Monte Carlo method. We obtained quartiles and medians from the Exposure Factors Handbook of Chinese Population. The weight and IR area taken as x values and the corresponding quartiles as y values. The weight and IR distribution of the population were also fitted using a cumulative distribution function of the log-normal model (Figure 3B,C). The fitting parameters describing the curves are shown in Table 2.

#### 3.2.2. Comparison of Risk Distribution between the Two Methods

^{−6}, with a standard deviation of 6.40 × 10

^{−6}. The average risk according to the Monte Carlo simulation was 1.63 × 10

^{−5}with a standard deviation of 2.37 × 10

^{−5}.

#### 3.2.3. Parameter Sensitivity Analysis

_{eq}concentration had the highest parameter sensitivity with Spearman’s r = 0.958. This is consistent with the previous research [47,48]. Exposure concentration was a more sensitive factor than exposure parameters in affecting the accuracy of assessment in this research. The other two parameters, BW and IR, had comparable sensitivity, with r values of −0.185 and 0.182.

#### 3.3. Key Factors for Improving the Monte Carlo Simulation

_{eq}concentration distribution curve was established based on the BaP

_{eq}exposure level of individual participants instead of sampling sites. Thus, the weight of each sample point in the fitting model would be reflected through the number of people near the sites. Second, stratified analysis was used in the population to reduce the difference of physiological parameters in each subgroup. According to the characteristics of exposure parameters, the population was divided into three age groups: 18–44, 45–59, and 60–70 years old. Surrogate samples were generated by MCS. The number of surrogate samples in the age group was determined by the proportion of the age group in the whole population. Finally, the regression relationship between IR and BW was established. IR was replaced by an equation with BW to calculate the carcinogenic risk (Equation (4)). Only the concentration and body weight were used as variables for Monte Carlo simulation. The purpose of the three adjustments was to explore the influence of parameters on the simulation results, increase the accuracy, and reduce the uncertainty of MCS.

#### 3.4. Improved Models

#### 3.4.1. Concentration-Adjusted Monte Carlo

_{eq}concentration in Taiyuan were constructed by ArcGIS software using the inverse distance weighting method (Figure 6A). The participant frequency of each sampling site is illustrated in Figure 6B. From the figure, we can clearly see that the pollution level in the urban area was higher than that in the suburbs. The highest pollution level was found in the north of the city. Jiancaoping District had the highest concentration. Site JCP3 had the greatest BaP

_{eq}concentration of 76.09 ng·m

^{−3}. Fortunately, the participant frequency of four sampling sites in Jiancaoping was relatively low. The residence of only 80 participants was near the sampling site JCP3. The highest frequency was at a sampling site in Xiaodian District, followed by Yingze and Xinghualing.

_{eq}concentrations from each sampling site were replaced by exposure levels of individual participants nearby to build a new BaP

_{eq}concentration distribution. The BaP

_{eq}was also fitted using log-normal distribution LN(2.419,1.317). The risk of the population was estimated by another Monte Carlo simulation. The arithmetic mean of participants was 8.23 × 10

^{−6}, with a standard deviation of 8.48 × 10

^{−6}.

#### 3.4.2. Age-Stratified Monte Carlo

^{−5}, with a standard deviation of 2.4 × 10

^{−5}.

#### 3.4.3. Parameter-Correlation-Adjusted Monte Carlo

^{−6}, with a standard deviation of 1.26 × 10

^{−5}.

#### 3.5. Comparison of Improved Models

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Atmosphere sampling sites in Taiyuan City. Six districts include Jiancaoping (JCP), Xinghualing (XHL), Wanbolin (WBL), Jinyuan (JY), Xiaodian (XD), and Yingze (YZ); four counties include Yangqu (YQ), Loufan (LF), Gujiao (GJ), and Qingxu (QX).

**Figure 2.**Influencing factors of ILCR of participants from Taiyuan. Difference of risk (

**A**) between exposure phrases, (

**B**) between genders, (

**C**) between urban and rural populations, and (

**D**) among age subgroups.

**Figure 3.**Fitting of exposure parameters in the risk assessment (

**A**) BaP

_{eq}concentration, (

**B**) inhalation rate of populations from different age groups, and (

**C**) body weight of populations from different age groups.

**Figure 4.**Risk distribution obtained by (

**A**) individual assessment and (

**B**) traditional assessment model based on MCS.

**Figure 6.**(

**A**) Spatial distribution of BaP

_{eq}concentration in Taiyuan City and (

**B**) participant frequency of each sampling site.

N | Height (cm) | Body Weight (kg) | Inhalation Rate ^{a} (L/min) | ||||
---|---|---|---|---|---|---|---|

Mean | SD | Mean | SD | Mean | SD | ||

SEX | |||||||

Male | 1305 | 171 | 5.41 | 67.7 | 8.8 | 14.04 | 0.73 |

Female | 1435 | 160 | 5.80 | 56.9 | 10.1 | 11.07 | 1.17 |

AREA | |||||||

Urban | 1382 | 166 | 7.53 | 63.0 | 11.0 | 12.51 | 1.83 |

Rural | 1358 | 164 | 7.84 | 60.6 | 10.6 | 12.30 | 1.71 |

Age group | |||||||

16 ~< 25 years | 450 | 166 | 8.06 | 57.4 | 10.7 | 12.17 | 2.03 |

26 ~< 35 years | 626 | 166 | 7.48 | 61.3 | 10.8 | 12.48 | 1.87 |

36 ~< 45 years | 737 | 164 | 7.34 | 62.9 | 10.5 | 12.47 | 1.67 |

46 ~< 55 years | 618 | 165 | 7.67 | 63.7 | 10.8 | 12.56 | 1.64 |

56 ~< 65 years | 303 | 163 | 8.31 | 63.0 | 11.0 | 12.14 | 1.66 |

66 ~< 75 years | 6 | 171 | 10.89 | 70.5 | 12.0 | 11.68 | 1.60 |

^{a}Inhalation rates were estimated based on the basal metabolic rate (BMR), the estimation method is provided in Supplementary Materials, Text S1.

Age Subgroup (Years) | BW (kg) | IR (m^{3}·day^{−1}) | ||||
---|---|---|---|---|---|---|

a | b | R^{2} | a | b | R^{2} | |

18–44 | 4.169 | 0.225 | 0.991 | 2.823 | 0.175 | 0.944 |

45–59 | 4.192 | 0.204 | 0.991 | 2.816 | 0.150 | 0.986 |

60–70 | 4.142 | 0.216 | 0.993 | 2.660 | 0.157 | 0.988 |

Whole population | 4.169 | 0.218 | 0.992 | 2.788 | 0.195 | 0.995 |

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**MDPI and ACS Style**

Qin, N.; Tuerxunbieke, A.; Wang, Q.; Chen, X.; Hou, R.; Xu, X.; Liu, Y.; Xu, D.; Tao, S.; Duan, X.
Key Factors for Improving the Carcinogenic Risk Assessment of PAH Inhalation Exposure by Monte Carlo Simulation. *Int. J. Environ. Res. Public Health* **2021**, *18*, 11106.
https://doi.org/10.3390/ijerph182111106

**AMA Style**

Qin N, Tuerxunbieke A, Wang Q, Chen X, Hou R, Xu X, Liu Y, Xu D, Tao S, Duan X.
Key Factors for Improving the Carcinogenic Risk Assessment of PAH Inhalation Exposure by Monte Carlo Simulation. *International Journal of Environmental Research and Public Health*. 2021; 18(21):11106.
https://doi.org/10.3390/ijerph182111106

**Chicago/Turabian Style**

Qin, Ning, Ayibota Tuerxunbieke, Qin Wang, Xing Chen, Rong Hou, Xiangyu Xu, Yunwei Liu, Dongqun Xu, Shu Tao, and Xiaoli Duan.
2021. "Key Factors for Improving the Carcinogenic Risk Assessment of PAH Inhalation Exposure by Monte Carlo Simulation" *International Journal of Environmental Research and Public Health* 18, no. 21: 11106.
https://doi.org/10.3390/ijerph182111106