# Modelling the Renal Excretion of the Mycotoxin Deoxynivalenol in Humans in an Everyday Situation

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## Abstract

**:**

_{abs_excr}). F

_{abs_excr}was treated as a random effect variable to address its heterogeneity in the population. The estimated time in which 97.5% of the ingested DON was excreted as DON15GlcA was 12.1 h, the elimination half-life was 4.0 h. Based on the estimated f

_{abs_excr}, the mean reversed dosimetry factor (RDF) of DON15GlcA was 2.28. This RDF can be used to calculate the amount of total DON intake in an everyday situation, based on the excreted amount of DON15GlcA. We show that urine samples collected over 24 h are the optimal design to study DON exposure by HBM.

**Key Contribution:**This study revealed the challenges when analyzing DON intake and excretion data in an everyday situation. Despite a large variability of the absorbed and excreted fraction between individuals; the provided model is in accordance with the results from an experimental setting and can be used in the design of future human biomonitoring studies on DON in order to estimate the DON exposure in humans more accurately.

## 1. Introduction

## 2. Results

_{abs_excr}) and the time from DON intake to DON15GlcA excretion in urine (residence time). The residence time was described using various statistical distributions, namely the gamma distribution, the log-normal distribution, and the exponential distribution, in order to account for the uncertainties related to distribution models. The gamma distribution provided the best fit for the residence time, as indicated by the lowest Akaike Information Criteria (AIC).

#### 2.1. Dietary Intake of DON

#### 2.2. Urinary Excretion of DON

#### 2.3. Model

#### 2.3.1. Residence Time

#### 2.3.2. Reversed Dosimetry Factor

_{abs_excr}) was also assessed using the mathematical model and is shown in Table 2. The mean f

_{abs_excr}was 0.44 using the gamma distribution for the residence time, 0.47 using the log-normal distribution, and 0.44 using the exponential distribution. Based on the f

_{abs_excr}and the identified relative uncertainty in the model, we estimated a reversed dosimetry factor (RDF) for the population mean (with 95% confidence interval) of 2.28 (1.88–2.76), 2.14 (1.74–2.64), and 2.27 (1.84–2.80) using the gamma distribution, the log-normal distribution, and the exponential distribution for the residence time, respectively. The distribution of the individual RDF values (reflecting heterogeneity in the population) ranges from 0.88–5.91 (centered around the population mean value of 2.28) using the gamma distribution. The variation between the individuals was relatively high, compared to the uncertainty of the mean value.

#### 2.3.3. Visualization of Excretion

## 3. Discussion

_{abs_excr}) and the parameters of the distribution of the residence time of DON15GlcA, i.e., the distribution of the time duration between the intake and the excretion in urine. The residence time was best described by the model using the gamma distribution.

## 4. Conclusions

## 5. Materials and Methods

#### 5.1. Participants

#### 5.2. Urinary Analysis

^{−}ions (m/z 341.1497) and using internal calibration with reference to the U-13C-labelled internal standard. DON3GlcA and DON15GlcA were quantified selecting the [M−H]

^{−}ions (m/z 471.1497) and using external calibration based on matrix-matched calibration standards. While DON for chemical analysis was obtained from Romer Labs, DON-glucuronides were available from earlier work [30]. The retention times for DON, DON3GlcA, and DON15GlcA under above conditions were 5.50 min, 5.90 min and 6.20 min, respectively. The apparent recoveries for DON, DON3GlcA, and DON15GlcA in urine samples are shown in Table 3 and extracted ion chromatograms for DON, DON3GlcA, and DON15GlcA are shown in Appendix A. The limits of detection (LOD) and limits of quantification (LOQ) were calculated from calibration curves from the analyses of all urine samples and were defined as 3× and 10× slope/SE of the slope, respectively. Thus, the LOD/LOQ was determined to 1.0/3.4 ng/mL for DON, 4.6/15 ng/mL for DON3GlcA and 2.0/6.8 ng/mL for DON15GlcA. Actual measured concentrations above the LOD were used for the calculations, while concentrations below the LOD were considered zero and not included in the calculations. This increases the uncertainty in the data, but it was decided to not substitute the data <LOD with e.g., ½ LOD as these were samples with (relatively) high volumes. Table 4 shows the number of urine samples that were analyzed above the LOD.

#### 5.3. Dietary Intake

#### 5.4. Statisical Model and Data Eligibility

_{abs_excr}) and the distribution of the residence time, i.e., the time between the DON intake and the excretion of DON15GlcA in urine.

_{abs_excr}-parameter and the parameters of the residence time (average, μ, and variation, σ). This f

_{abs_excr}is the product of the absorbed proportion of DON into the body and the excreted fraction of DON15GlcA into urine. In our previous publication we found that the population cannot be assumed to be homogenous with respect to the absorption of DON [9]. Therefore, we also addressed the heterogeneity in the population by assuming the f

_{abs_excr}-parameter to be random. The data did not allow both parts of the model to be random (data not shown). Therefore, we assumed the residence time distribution as being fixed for all individuals, and only the f

_{abs_excr}as being different. This results in a so-called mixed effects statistical model, of which the details are described in Appendix C. The DON intake and DON15GlcA excretion data were used to fit the model and to estimate the model parameters.

_{abs_excr}, similar to our previously developed biokinetic model on DON [9].

#### 5.5. Validation Steps

_{abs_excr}values and the residuals, respectively. Moreover, we assessed whether the assumption of independently distributed error terms was valid by regressing the residuals to the absolute excretion values and to the time passed since intake (see Appendix E).

#### 5.6. Reversed Dosimetry Factor

_{abs_excr}was used to derive a RDF to estimate future total DON intakes (Appendix F). The f

_{abs_excr}was estimated by the random part of the mixed effects model (see Appendix C). The 95% uncertainty around the population mean RDF was calculated by dividing the RDF by the square of the uncertainty (lower boundary) and multiplying the RDF by the square of the uncertainty (upper boundary).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Extracted ion chromatograms (±3 ppm) from full-scan LC–HRMS for the formate adduct of DON (left) and the deprotonated molecules of DON–glucuronides (right). (

**A**) Negative control urine sample (containing traces of DON15GlcA), (

**B**) urine sample fortified with 20 ng/mL each of DON and DON–glucuronides, (

**C**) urine sample containing 10 ng/mL DON and 13 ng/mL DON15GlcA (DON3GlcA was below the calculated LOD). Chromatograms are on a fixed scale with maximum peak intensities normalized to 2.5 × 106 for DON-formate and 1.5 × 104 for negatively charged DON–glucuronides.

## Appendix B

- CumN
_{excr}(t) - cumulative excretion amount at time t;
- t
_{i} - timepoints of the intake, with t
_{i}< t; - i
- index on the intake;
- N
_{inta}(t_{i}) - intake amount at time t
_{i;} - F (t – t
_{i};μ,σ) - the cumulative distribution function (e.g., gamma, lognormal, or exponential distribution) of the residence time with the to be estimated model parameters μ (average) and σ (variation);
- f
_{abs_excr} - the to be estimated model parameter that describes the proportion of the intake of DON that is excreted as DON15GlcA.

_{j}can then be described by:

- j
- index of the urine voids

## Appendix C

_{abs_excr}, μ and σ). The random part describes the to be estimated distribution of the f

_{abs_excr}parameter as a stochastic variable, with its distributional characteristics to be estimated. The parameters μ and σ are assumed to be fixed.

#### Appendix C.1

_{abs_excr}, μ and σ (see Appendix B).

- f
_{abs_excr,k} - f
_{abs_excr}for individual k; - N
_{inta,k}(t_{i,k}) - intake amount of individual k on time t
_{i,k}; - N
_{excr,k}(t_{j,k}) - excretion amount of individual k on time t
_{j,k}; - t
_{i,k} - intake time points of individual k;
- t
_{j,k} - excretion time points of individual k, t
_{j-1,k}describes the previous excretion time point of individual k (i.e., the excretion between two excretion time points); - F
- the cumulative distribution function of the residence time (e.g., gamma, lognormal, or exponential distribution).

#### Appendix C.2

_{abs_excr}parameter as being log-normally distributed over the population.

_{abs_excr,k}) ~ N(μ

_{fabs_excr}, σ

_{fabs_excr})

- μ
_{fabs_excr}, σ_{fabs_excr} - average and variation of log (f
_{abs_excr}) in the population

_{fabs_excr}, σ

_{fabs_excr}(that describe the distribution of f

_{abs_excr}in the population) and μ, σ (that define the distribution of the time between intake and excretion).

## Appendix D

#### Dealing with Missing Values

- index
- i = 1: DON, i = 2: DON3G;
- n
_{i} - number (moles);
- w
_{i} - molar weight; w
_{1}= 296.3, w_{2}= 458.5.

## Appendix E

_{abs_excr}values, and the fourth graph (4) shows the QQ-plot of the residuals. These graphs show that the assumptions of normally distributed f

_{abs_excr}values and normally distributed error terms are both valid.

**Figure A2.**Validation of the assumptions made. Graph shows the residuals plotted against the fitted values, the second graph shows the residuals plotted against time, the third graph shows the QQ-plot of the calculated individual f

_{abs_excr}values, and the fourth graph shows the QQ-plot of the residuals.

## Appendix F

_{abs_excr}, the fraction of the DON intake excreted as DON15GlcA in urine. As shown in the previously presented formula, the f

_{abs_excr}describes the relation between the intake and (cumulative) excretion when we assume one meal and an infinite t:

_{abs_excr}, i.e., with a population average and an individual variation. In case of the gamma-distributed residence time, the population mean value of the RDF is 2.28 with 95% confidence bounds 2.28/1.10

^{2}= 1.88 and 2.28 × 1.10

^{2}= 2.76 respectively. The individual variation of the RDF is 2.28 with 95% confidence bounds 2.28/1.61

^{2}= 0.88 and 2.28 × 1.61

^{2}= 5.9 respectively.

## Appendix G

**Figure A3.**Dietary DON intake and urinary DON15GlcA excretion for every individual in this study. Solid lines represent the excreted data as analyzed in urine, dashed lines represent the excreted data as fitted by the model. + indicates the dietary intake. Data is shown as nanomoles (nmol) against time in hours during the day (hr).

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**Figure 1.**Frequency of consumed amounts of DON during different parts of the day. The amounts of DON in nanomoles per consumption moment are expressed on the x-axis and the frequency of those consumed amounts are expressed on the y-axis. Different parts of the day are divided in morning (<10:00), midday (between 10:00 and 16:00) and evening (>16:00).

**Figure 2.**Distribution of the weighted time between the estimated DON intake after 16:00 h and the morning urine void the next day. The time between the intake and excretion is plotted against the frequency of that time observed in the individuals.

**Figure 3.**The density function of the statistical model for the excretion of DON15GlcA in a fictional individual, assuming the residence time parameters of the statistical model using the gamma distribution for the residence time. The amount of DON15GlcA excreted in urine is reflected by the area under the curve between two excretion time points (vertical black lines at t = 9, 16, 23, and 31 h). The modeled additional excreted amounts of DON15GlcA are generated at t = 38 and t = 48 h (dashed lines). Intake time points were assumed at t = 8 and t = 18 h (dotted lines). Daily time in hours is expressed at the x-axis. Note that the choice for the residence time is independent from the design of the model, it only affects the visualization.

n | Total 49 | Males 25 | Females 24 |
---|---|---|---|

Average amount DON15GlcA (µg)/24 h (min–max) | 26.1 (0–91.3) | 33.4 (0–91.3) | 18.6 (0–57.2) |

Average concentration DON15GlcA (µg/mL)/24 h (min–max) | 0.02 (0–0.11) | 0.02 (0–0.11) | 0.01(0–0.04) |

Average urine volume in 24 h (mL) (min–max) | 2107 (770–4190) | 2148 (770–4190) | 2064 (950–3845) |

Average urine flow in 24 h (mL/kg bw) (min–max) | 29.1 (9.10–62.0) | 26.6 (9.10–55.1) | 31.8 (13.6–62.0) |

**Table 2.**The modelled residence time and excreted fraction after fitting the data in the model using the different statistical distributions based on 39 individuals in this study.

Gamma | Log-Normal | Exponential | ||
---|---|---|---|---|

Residence time | Mean | 4.70 | 4.15 | 2.89 |

Standard deviation | 2.99 | 2.43 | 2.89 | |

Median | 3.97 | 3.58 | 2.00 | |

97.5% | 12.1 | 10.4 | 10.7 | |

AIC ^{1} | 685 | 739 | 767 | |

F_{abs_excr} | Population mean | 0.44 | 0.47 | 0.44 |

Relative uncertainty ^{2} | 0.10 | 0.11 | 0.11 | |

Relative heterogeneity ^{3} | 0.61 | 0.62 | 0.62 | |

RDF | Population mean (95% confidence interval) | 2.28 (1.88–2.76) | 2.14 (1.74–2.64) | 2.27 (1.84–2.80) |

Population heterogeneity (95% confidence interval) | 2.28 (0.88–5.91) | 2.14 (0.82–5.62) | 2.27 (0.86–5.96) |

^{1}Akaike Information Criterium.

^{2}The relative uncertainty around the F

_{abs_excr}reflects the uncertainty of the F

_{abs_excr}as estimated in the model, see Materials and Methods.

^{3}The relative heterogeneity of the F

_{abs_excr}reflects the variation of the F

_{abs_excr}in the population, see Materials and Methods.

**Table 3.**Apparent recovery for DON, DON3GlcA, and DON15GlcA during the period the urinary analyses were conducted.

Theoretical Concentration (ng/mL) | Mean Apparent Recovery (%) | Standard Deviation (%, n = 15) | |
---|---|---|---|

DON | 20.1 | 99 | 8.7 |

DON3GlcA | 19.8 | 93 | 17 |

DON15GlcA | 20.1 | 86 | 21 |

>LOD | n | % |
---|---|---|

DON | 70/436 | 16 |

DON3GlcA | 76/436 | 17 |

DON15GlcA | 304/436 | 70 |

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## Share and Cite

**MDPI and ACS Style**

van den Brand, A.D.; Hoogenveen, R.; Mengelers, M.J.B.; Zeilmaker, M.; Eriksen, G.S.; Uhlig, S.; Brantsæter, A.L.; Dirven, H.A.A.M.; Husøy, T. Modelling the Renal Excretion of the Mycotoxin Deoxynivalenol in Humans in an Everyday Situation. *Toxins* **2021**, *13*, 675.
https://doi.org/10.3390/toxins13100675

**AMA Style**

van den Brand AD, Hoogenveen R, Mengelers MJB, Zeilmaker M, Eriksen GS, Uhlig S, Brantsæter AL, Dirven HAAM, Husøy T. Modelling the Renal Excretion of the Mycotoxin Deoxynivalenol in Humans in an Everyday Situation. *Toxins*. 2021; 13(10):675.
https://doi.org/10.3390/toxins13100675

**Chicago/Turabian Style**

van den Brand, Annick D., Rudolf Hoogenveen, Marcel J. B. Mengelers, Marco Zeilmaker, Gunnar S. Eriksen, Silvio Uhlig, Anne Lise Brantsæter, Hubert A. A. M. Dirven, and Trine Husøy. 2021. "Modelling the Renal Excretion of the Mycotoxin Deoxynivalenol in Humans in an Everyday Situation" *Toxins* 13, no. 10: 675.
https://doi.org/10.3390/toxins13100675