# Estimation of Oral Exposure of Dairy Cows to the Mycotoxin Deoxynivalenol (DON) through Toxin Residues in Blood and Other Physiological Matrices with a Special Focus on Sampling Size for Future Predictions

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## Abstract

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## 1. Introduction

**DON**) is a common Fusarium sp.-derived contaminant of feedstuffs for cows [1,2,3]. In particular, maize-originating feedstuffs, such as maize grain and maize silage, are significant sources of exposure for dairy cows [4,5]. Moreover, distillers grains and solubles (DDGS) might further contribute to DON exposure, as ethanol production is known to concentrate mycotoxins in the by-product DDGS [6]. Ruminants, in general, and dairy cows, in particular, are regarded as quite resistant to the toxic effects of DON due to ruminal metabolism of the toxicologically less active derivative DOM-1 [7]. However, an efficient inactivation requires a functioning rumen, a situation that might be disturbed due to inadequate feeding strategies, leading to ruminal acidosis, or as a consequence of poor feeding hygiene, resulting in ruminal dysbiosis. Furthermore, high levels of feed intake of cows increase the ruminal passage rate of ingesta and decrease the time available for rumen metabolism, including that of mycotoxins [8]. All these conditions might become even more relevant when the DON content of the diet is increased. To avoid adverse effects of DON, a guidance value of 5 mg DON/kg diet at a reference dry matter (DM) content of 88% must not be exceeded [9].

**ZEN**), another Fusarium toxin often co-occurring with DON, linear relationships between ZEN residues in physiological specimens and oral ZEN exposure, expressed in µg/kg body weight (

**BW**) and d, have been suggested to be useful for the prediction of oral ZEN exposure based on the determination of ZEN residues in physiological specimens of individual cows [10].

## 2. Materials and Methods

#### 2.1. Description of Data

#### 2.1.1. Data for the Derivation of Prediction Equations and Internal Validation

#### 2.1.2. Data for External Validation

#### 2.2. Calculations and Statistics

#### 2.2.1. Calculations

**DON residues**= DON + DOM-1 + conjugates (glucuronidated and sulfated DON and DOM-1)

#### 2.2.2. Statistics

**RStudio**,

**R version 4.2.1**[17]. Graphic presentations were prepared using the package

**ggplot2**[18].

#### Development of Prediction Equations

**lm**function of the package

**stats**[17]. Prediction intervals were extracted from the regression results by the function

**predict.lm**of the same package.

**OLS**) fitting is vulnerable to extreme observations, a robust fitting was additionally conducted by iterated re-weighted least squares (

**IWLS**) using the

**rlm**function of the

**MASS**package [19]. The robust linear fitting puts less weights on influential observations, making regression results more robust compared with OLS estimations. In the next step, the validity of the regression coefficients obtained from the

**lm**and

**rlm**procedures was evaluated through the bootstrapping method. As a re-sampling method, bootstrapping does not rely on a known probability distribution; instead, it estimates the sampling distribution from which the means and standard errors are derived by the percentile method [20]. Regression coefficients were estimated from 2000 bootstrap replications; most researchers use this number, which is based on a sufficient accuracy to investigate regressions [21,22] and to ensure comparability in methodology. Distributions of regression coefficients were plotted as histograms for visual inspection, and mean values and standard errors were derived using the

**bootstraps**procedure of the package

**rsample**[23].

**raintest**function, which performs the rainbow test and is implemented in the package

**lmtest**[24].

**lm**procedure.

**augment.lm**function of package

**broom**[25].

#### Internal and External Validation of Prediction Equations for DON Residues in Blood

**tobit**function of the package

**AER**was used for this purpose [26].

**CCC**function of the package

**DescTools**[27]. Furthermore, concordance between the two methods was visually evaluated by the Bland–Altman method plotting the difference of corresponding data pairs, i.e., measured and estimated DON exposure, against their means [28]. The scatter of these data pairs was descriptively evaluated with the aid of horizontal helper lines, indicating the mean of the difference covered by the range limited by the ±1.96 standard deviation of that differences [28].

#### Estimation of Sample Size for Future Predictions

**N**. The width of the confidence interval of an arithmetic mean $\overline{\mathit{y}}$ depends on the variability of the trait expressed as the residual standard deviation ${\mathit{s}}_{\mathit{e}}$, sample size

**n**, and the t-quantile for a given confidence level

**P**= 1 −

**α**:

**d**is given as:

**n**when the standard error ${\mathit{s}}_{\overline{\mathit{y}}}$ is expressed through the ratio of the corresponding residual standard deviation ${\mathit{s}}_{\mathit{e}}$ and the square root of

**n**:

**N**is that the standard deviation and, thus, the standard error of the mean for infinite populations are modified to:

**N**, the sampling size can be derived through rearranging the half interval width

**d**as [29]:

**n**.

## 3. Results

^{2}since the latter is not applicable for robust regressions.

#### 3.1. Prediction Equations

#### 3.1.1. Blood

**rlm**function were performed in a similar way as described for the linear models employing the procedure

**lm**. In general, robust regressions resulted in substantially lower RSE and correspondingly tighter prediction intervals and lower exposure thresholds. Moreover, slopes were steeper, and intercepts were estimated to be located closer to the origin (Figure A2 and Figure A3, Table 2).

**lm**procedures were tested (Figure A4 and Figure A5, Table 2).

#### 3.1.2. Urine, Bile, and Milk

**lm**and

**rlm**were tested exclusively for these matrices (Figure A6, Figure A7, Figure A8, Figure A9, Figure A10 and Figure A11, Table 2). In general, for models with intercepts, those were significantly higher than zero, except for the

**rlm**for bile. As for the blood models described, the slopes increased when the intercepts were omitted both for

**lm**and

**rlm**, albeit at a higher level for the latter. Although the bootstrapping means for intercepts and slopes matched those estimated from the original regressions for all three matrices both for

**lm**and

**rlm**, the histograms and qq-plots suggested departures from symmetry depending on the matrix and estimation procedure. While for urine and milk the

**lm**procedure appeared to be superior to

**rlm**, the opposite was noticed for bile.

#### 3.2. Influential Statistics

**lm**models without an intercept for the combined blood dataset (Figure 2) and the other matrices (data not shown). Hat scores for blood increased with distance from the centroid in the direction of the abscissa up to 0.11. A larger portion of the data of Experiment 1 were characterized by larger positive Studentized regression residuals compared with those with negative residuals. Only three observations located in the right part of the scatter showed larger Cook’s distances. Combining all 3 measures in 1 plot revealed that a total of 18 suspicious observations were identified, characterized by Studentized residuals that were either greater than 2; less than −2; had hat scores greater than the value represented by the mean of the hat scores plus the twofold standard deviation of the hat scores; or had a Cook’s distance larger than 1. Applying the same three filtering conditions to urine, bile, and milk revealed nine, four, and eight suspicious data points, respectively. In particular, hat scores varied from 0.01 to 0.18, 0.01 to 0.4, and 0.009 to 0.09; Studentized residuals ranged from −2.21 to 3.36, −3.17 to 3.39, and −2.55 and 3.73; and Cook’s distances ranged from ~0.0 to 0.54, ~0.0 to 7.07, and ~0.0 to 0.39 for urine, bile, and milk, respectively.

#### 3.3. Internal and External Validation of Prediction Equations for DON Residues in Blood

#### 3.4. Estimation of Sampling Size for Future Predictions

## 4. Discussion

#### 4.1. Toxicokinetic Aspects of DON as a Basis for Regressive Evaluation of the Data for Diagnostic Purposes

#### 4.2. Handling of Influential Observations and Fitting Methods

**rainbow test**, particularly when the combined dataset of DON residue levels in blood from Experiments 1 and 2 was used for the regression. However, the apparent departures from linearity observed for some regression equations are likely caused by the discussed noise in the region of the origin and by the fact that lower toxin concentrations both in the diets and the physiological specimens are associated with larger unavoidable errors, according to the rules of Horwitz [40]. While linearity can be assumed for DON residues in blood on the basis of toxicokinetic backgrounds, the situation for the other specimens appears to be more complex. Urine, bile, and milk are the main excretory routes for DON residue elimination but are excreted irregularly (bile and urine) or with an artificial pattern (milk). Thus, DON residues are more or less concentrated in these matrices depending on the magnitude of influx from the blood, which, in turn, depends on the time elapsed since the last meal and its size. Although these factors contribute to the variation, linearity was also confirmed for the regression equations estimated for urine and milk, while DON residue levels in bile obviously did not follow a linear pattern, according to the

**rainbow test**. A closer look at the scatter of bile residues revealed that two observations in particular that were located in the right lower quadrant were flagged as influential. In fact, the maximum DON residue concentration in bile was the only observation amongst all matrices that exceeded a Cook’s distance of 1 and reached a value of 7.07. Bootstrapping of the linear models resulted in two-peaked slope distributions and substantial deviations from linearity in the qq-plots. In this situation, bootstrapping of the robust linear regression largely overcame these problems, leading to a symmetrical slope distribution, particularly when estimated without an intercept. Moreover, the differences in the slopes estimated through linear and robust linear regression were larger for bile than for the other matrices. Larger differences in regression results obtained from OLS fitting vs. IWLS, as observed for bile, provided a practical diagnostic warning that outliers may be influencing the OLS results [41]. That this was observed only for bile, although even more individual observations were flagged as apparently influential in other matrices, might be due to the fact that extreme values occurred both in the direction of the abscissa and the ordinate, which was not the case for bile. This might also be the reason why the robust fitting of milk DON residues using bootstrapping even deteriorated the symmetry of slope distribution and the corresponding qq-plot. The same phenomenon was observed for blood DON residues, where OLS was found to be superior compared with IWLS. A similar trend was noticed for urine.

#### 4.3. Comparative Aspects on Suitability of Various Matrices as Predictors

#### 4.4. Internal and External Validation of Prediction Equations for DON Residues in Blood

^{2}of a corresponding linear regression are unsuited to confirm the concordance, defined as the degree of agreement, between two methods, as they can still deviate systematically from each other [22,42]. Pearson’s r just reflects the precision component of the linear relationship and is a measure of how far the observations are located from the best-fit line, while accuracy considers how far the best-fit line deviates from the 45° line [43]. Precision and accuracy are combined in the CCC as proposed by Lin [43]. Furthermore, it is strongly recommended to estimate the intercept in addition to the slope of the regression line as an essential part of an overall (fully quantifying) calibration as a regressive form of validation of the known (measured) DON exposure. Thus, the calibration curves for internal and external validation were estimated with intercepts. The intercept for the internal calibration line did not significantly differ from zero, while the slope suggested that the predicted DON exposure was 0.23 µg/kg BW/d lower per each 1.0 µg/kg BW/d increase in observed DON exposure, which is equivalent to a 23% underestimation. The smaller location shift compared with the larger scale shift further substantiated the systematic deviation of the regression line from the 90° angle bisector. The closer both shifts are to zero, the more closely the regression line will match the 45° line and CCC will reach 1.0 when both shifts are equal to zero [44]. Compared with the internal calibration, both shifts were higher for the external calibration, whereby the slope nearly reached that estimated for the internal calibration curve, resulting in an underestimation of 26%. For a number of observations (n = 80) of the dataset used for external validation (Experiment 3), the predicted DON exposure was zero, although a positive DON exposure was noticed at the same time, which likely resulted from the more than tenfold higher LODs for DON residues in blood compared with Experiments 1 and 2. OLS fitting does not provide the best estimates for regression coefficients when dependent observations are equal to zero, for example, such as when they are left-censored, while Tobit regression uses a modified likelihood function in such a way that it mirrors the unequal sampling probability for non-censored and censored observations [45]. Applying this method to Experiment 3 increased the slope from 0.77 when estimated using OLS to 0.87 when using Tobit regression. At the same time, the intercept on the ordinate decreased markedly to a value −29 µg DON/kg BW/d and, consequently, had a more pronounced location shift. Moreover, the RSE was higher compared with OLS fitting. On the basis of this and for a better comparability with the internal validation, the results of the OLS were preferred.

#### 4.5. Recommendations for Appropriate Sampling Sizes for Future Predictions

## 5. Conclusions

**rlm**models) generally resulted in lower RSEs and tighter prediction intervals through the outweighing of apparent outliers. However, on the basis of toxicokinetic considerations, these outliers were identified as valid observations. Together with the overall variability in the data, OLS-fitted models (ordinary linear regressions,

**lm**models) were considered as more appropriate. The associated wider prediction intervals appeared to reflect the practical situation more reliably. Furthermore, bootstrapping of IWLS and OLS models was used to avoid having to rely on the assumptions that usually have to be fulfilled for regressions. Results showed that OLS fitting was superior compared with the corresponding IWLS fittings, except for the case of bile. On the basis of the limited data situation for bile, the derived equations should only be used with caution.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Linear regression (method

**lm**) of deoxynivalenol (DON) residues in

**blood**on DON exposure with ((

**A**,

**B**) for zooming in the lower concentration range) and without intercept ((

**C**,

**D**) for zooming in the lower concentration range) separately for Experiments 1 and 2 (n = 116 and n = 121, respectively). Red and blue solid lines denote the linear regressions, and dashed red and blue lines limit the prediction intervals at a 0.95 confidence level for future predictions for Experiments 1 and 2, respectively. Red and blue filled dots show the corresponding measured data pairs. Blue open circles lying on the red solid line represent the predicted values of Experiment 2 when regression of Experiment 1 is used as prediction equation.

**Figure A2.**Linear regression (method

**rlm**) of deoxynivalenol (DON) residues in

**blood**on DON exposure with ((

**A**,

**B**) for zooming in the lower concentration range) and without intercept ((

**C**,

**D**) for zooming in the lower concentration range) separately for Experiments 1 and 2 (n = 116 and n = 121, respectively). Red and blue solid lines denote the linear regressions, and dashed red and blue lines limit the prediction intervals at a 0.95 confidence level for future predictions for Experiments 1 and 2, respectively. Red and blue filled dots show the corresponding measured data pairs. Blue open circles lying on the red solid line represent the predicted values of Experiment 2 when regression of Experiment 1 is used as prediction equation.

**Figure A3.**Linear regression (method

**rlm**) of deoxynivalenol (DON) residues in

**blood**on DON exposure with (

**A**) and without intercept (

**C**) using the original dataset pooled over Experiments 1 and 2 (n = 237). Red solid lines denote the linear regression, and dashed red lines limit the prediction intervals at a 0.95 confidence level for future predictions. Red dots show the measured data pairs. Blue solid lines represent 200 bootstrap regressions randomly selected from a total of 2000 bootstraps. Intercept and slopes generated by bootstrapping (n = 2000) using the original dataset were used for validation and are presented as density distributions (solid red vertical lines show the mean value of the regression coefficients, and dashed blue vertical lines include the 0.95 confidence interval) and qq-plots (with intercept (

**B**) and without intercept (

**D**)).

**Figure A4.**Linear regression (method

**lm**) of deoxynivalenol (DON) residues in

**blood**on DON concentration in feed with ((

**A**,

**B**) for zooming in the lower concentration range) and without intercept ((

**C**,

**D**) for zooming in the lower concentration range) separately for Experiments 1 and 2 (n = 116 and n = 121, respectively). Red and blue solid lines denote the linear regressions, and dashed red and blue lines limit the prediction intervals at a 0.95 confidence level for future predictions for Experiments 1 and 2, respectively. Red and blue filled dots show the corresponding measured data pairs. Blue open circles lying on the red solid line represent the predicted values of Experiment 2 when regression of Experiment 1 is used as prediction equation.

**Figure A5.**Linear regression (method

**lm**) of deoxynivalenol (DON) residues in

**blood**on DON concentration in feed with (

**A**) and without intercept (

**C**) using the original dataset pooled over Experiments 1 and 2 (n = 237). Red solid lines denote the linear regression, and dashed red lines limit the prediction intervals at a 0.95 confidence level for future predictions. Red dots show the measured data pairs. Blue solid lines represent 200 bootstrap regressions randomly selected from a total of 2000 bootstraps. Intercept and slopes generated by bootstrapping (n = 2000) using the original dataset were used for validation and are presented as density distributions (solid red vertical lines show the mean value of the regression coefficients, and dashed blue vertical lines include the 0.95 confidence interval) and qq-plots (with intercept (

**B**) and without intercept (

**D**)).

**Figure A6.**Linear regression (method

**lm**) of deoxynivalenol (DON) residues in

**urine**on DON exposure with (

**A**) and without intercept (

**C**). Red solid lines denote the linear regression using the original dataset of Experiment 1, n = 99, and dashed red lines limit the prediction intervals at a 0.95 confidence level for future predictions. Red dots show the measured data pairs. Blue solid lines represent 200 bootstrap regressions randomly selected from a total of 2000 bootstraps. Intercept and slopes generated by bootstrapping (n = 2000) using the original dataset were used for validation and are presented as density distributions (solid red vertical lines show the mean value of the regression coefficients, and dashed blue vertical lines include the 0.95 confidence interval) and qq-plots (with intercept (

**B**) and without intercept (

**D**)).

**Figure A7.**Linear regression (method

**rlm**) of deoxynivalenol (DON) residues in

**urine**on DON exposure with (

**A**) and without intercept (

**C**). Red solid lines denote the linear regression using the original dataset of Experiment 1, n = 99, and dashed red lines limit the prediction intervals at a 0.95 confidence level for future predictions. Red dots show the measured data pairs. Blue solid lines represent 200 bootstrap regressions randomly selected from a total of 2000 bootstraps. Intercept and slopes generated by bootstrapping (n = 2000) using the original dataset were used for validation and are presented as density distributions (solid red vertical lines show the mean value of the regression coefficients, and dashed blue vertical lines include the 0.95 confidence interval) and qq-plots (with intercept (

**B**) and without intercept (

**D**)).

**Figure A8.**Linear regression (method

**lm**) of deoxynivalenol (DON) residues in

**bile**on DON exposure with (

**A**) and without intercept (

**C**). Red solid lines denote the linear regression using the original dataset of Experiment 1, n = 85, and dashed red lines limit the prediction intervals at a 0.95 confidence level for future predictions. Red dots show the measured data pairs. Blue solid lines represent 200 bootstrap regressions randomly selected from a total of 2000 bootstraps. Intercept and slopes generated by bootstrapping (n = 2000) using the original dataset were used for validation and are presented as density distributions (solid red vertical lines show the mean value of the regression coefficients and dashed blue vertical lines include the 0.95 confidence interval) and qq-plots (with intercept (

**B**) and without intercept (

**D**)).

**Figure A9.**Linear regression (method

**rlm**) of deoxynivalenol (DON) residues in

**bile**on DON exposure with (

**A**) and without intercept (

**C**). Red solid lines denote the linear regression using the original dataset of Experiment 1, n = 85, and dashed red lines limit the prediction intervals at a 0.95 confidence level for future predictions. Red dots show the measured data pairs. Blue solid lines represent 200 bootstrap regressions randomly selected from a total of 2000 bootstraps. Intercept and slopes generated by bootstrapping (n = 2000) using the original dataset were used for validation and are presented as density distributions (solid red vertical lines show the mean value of the regression coefficients and dashed blue vertical lines include the 0.95 confidence interval) and qq-plots (with intercept (

**B**) and without intercept (

**D**)).

**Figure A10.**Linear regression (method

**lm**) of deoxynivalenol (DON) residues in

**milk**on DON exposure with (

**A**) and without intercept (

**C**). Red solid lines denote the linear regression using the original dataset of Experiment 1, n = 109, and dashed red lines limit the prediction intervals at a 0.95 confidence level for future predictions. Red dots show the measured data pairs. Blue solid lines represent 200 bootstrap regressions randomly selected from a total of 2000 bootstraps. Intercept and slopes generated by bootstrapping (n = 2000) using the original dataset were used for validation and are presented as density distributions (solid red vertical lines show the mean value of the regression coefficients and dashed blue vertical lines include the 0.95 confidence interval) and qq-plots (with intercept (

**B**) and without intercept (

**D**)).

**Figure A11.**Linear regression (method

**rlm**) of deoxynivalenol (DON) residues in

**milk**on DON exposure with (

**A**) and without intercept (

**C**). Red solid lines denote the linear regression using the original dataset of Experiment 1, n = 109, and dashed red lines limit the prediction intervals at a 0.95 confidence level for future predictions. Red dots show the measured data pairs. Blue solid lines represent 200 bootstrap regressions randomly selected from a total of 2000 bootstraps. Intercept and slopes generated by bootstrapping (n = 2000) using the original dataset were used for validation and are presented as density distributions (solid red vertical lines show the mean value of the regression coefficients and dashed blue vertical lines include the 0.95 confidence interval) and qq-plots (with intercept (

**B**) and without intercept (

**D**)).

**Table A1.**Summary of limits of detection (

**LOD**) and of quantification (

**LOQ**) in feed and various physiological matrices for deoxynivalenol (DON) and DOM-1 applied for Experiments 1 to 3.

Experiment | Matrix | Toxin | LOD (ng/mL) | LOQ (ng/mL) | Sample Clean-Up | Detection Method | Reference |
---|---|---|---|---|---|---|---|

1 | Feed | DON | 0.03 mg/kg | IAC | HPLC-DAD | [48] | |

Blood plasma | DON | 0.19 | 0.65 | SPE | HPLC-MS/MS | [11] | |

DOM-1 | 0.09 | 0.31 | SPE | HPLC-MS/MS | |||

Urine | DON | 0.25 | 0.80 | SPE | HPLC-MS/MS | [13] | |

DOM-1 | 0.25 | 0.85 | SPE | HPLC-MS/MS | |||

Milk | DON | 0.31 | 1.03 | SPE | HPLC-MS/MS | [14] | |

DOM-1 | 0.17 | 0.58 | SPE | HPLC-MS/MS | |||

Bile | DON | 0.16 | 0.53 | IAC | HPLC-MS/MS | [12] | |

DOM-1 | 0.04 | 0.13 | IAC | HPLC-MS/MS | |||

2 | Feed | DON | 0.03 mg/kg | IAC | HPLC-DAD | [48] | |

Blood plasma | DON | 0.22 | 0.72 | SPE | HPLC-MS/MS | [34] | |

DOM-1 | 0.16 | 0.55 | SPE | HPLC-MS/MS | |||

3 | Feed | DON | 0.03 mg/kg | IAC | HPLC-DAD | [48] | |

Blood serum | DON | 2.0 | IAC | HPLC-UVD | [16] | ||

DOM-1 | 2.0 | IAC | HPLC-UVD |

**Table A2.**Sample size

**n**to be collected dependent on half width of the confidence interval (

**hw_CI**) as a fraction of the standard deviation (

**fr_SD**) for different herd sizes (

**N**). Standard deviation of DON residues in blood was obtained from the pooled dataset of Experiments 1 and 2 (see Table 1).

fr_SD | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1 |

hw_CI | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |

N | ||||||||||

25 | 24 | 20 | 17 | 14 | 11 | 9 | 8 | 7 | 6 | 6 |

50 | 45 | 34 | 24 | 18 | 14 | 11 | 9 | 8 | 7 | 6 |

75 | 63 | 43 | 29 | 20 | 15 | 12 | 9 | 8 | 7 | 6 |

100 | 80 | 50 | 32 | 21 | 15 | 12 | 10 | 8 | 7 | 6 |

125 | 95 | 56 | 34 | 22 | 16 | 12 | 10 | 8 | 7 | 6 |

150 | 109 | 60 | 35 | 23 | 16 | 12 | 10 | 8 | 7 | 6 |

175 | 121 | 64 | 36 | 23 | 16 | 12 | 10 | 8 | 7 | 6 |

200 | 132 | 67 | 37 | 24 | 17 | 12 | 10 | 8 | 7 | 6 |

225 | 143 | 69 | 38 | 24 | 17 | 13 | 10 | 8 | 7 | 6 |

250 | 152 | 71 | 39 | 24 | 17 | 13 | 10 | 8 | 7 | 6 |

275 | 161 | 73 | 39 | 24 | 17 | 13 | 10 | 8 | 7 | 6 |

300 | 170 | 75 | 40 | 25 | 17 | 13 | 10 | 8 | 7 | 6 |

325 | 177 | 76 | 40 | 25 | 17 | 13 | 10 | 8 | 7 | 6 |

350 | 184 | 77 | 40 | 25 | 17 | 13 | 10 | 8 | 7 | 6 |

375 | 191 | 78 | 41 | 25 | 17 | 13 | 10 | 8 | 7 | 6 |

400 | 197 | 79 | 41 | 25 | 17 | 13 | 10 | 8 | 7 | 6 |

425 | 203 | 80 | 41 | 25 | 17 | 13 | 10 | 8 | 7 | 6 |

450 | 209 | 81 | 41 | 25 | 17 | 13 | 10 | 8 | 7 | 6 |

475 | 214 | 82 | 41 | 25 | 17 | 13 | 10 | 8 | 7 | 6 |

500 | 219 | 83 | 42 | 25 | 17 | 13 | 10 | 8 | 7 | 6 |

625 | 239 | 85 | 42 | 25 | 17 | 13 | 10 | 8 | 7 | 6 |

750 | 256 | 87 | 43 | 26 | 17 | 13 | 10 | 8 | 7 | 6 |

875 | 269 | 89 | 43 | 26 | 18 | 13 | 10 | 8 | 7 | 6 |

1000 | 279 | 90 | 43 | 26 | 18 | 13 | 10 | 8 | 7 | 6 |

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**Figure 1.**Linear regression (method

**lm**) of deoxynivalenol (DON) residues in

**blood**on DON exposure with (

**A**) and without intercept (

**C**) using the original dataset pooled over Experiments 1 and 2 (n = 237). Red solid lines denote the linear regression, and dashed red lines limit the prediction intervals at a 0.95 confidence level for future predictions. Red dots show the measured data pairs. Blue solid lines represent 200 bootstrap regressions randomly selected from a total of 2000 bootstrap replications. Intercept and slopes generated by bootstrapping (n = 2000) using the original dataset were used for validation and presented as density distributions (solid red vertical lines show the mean value of the regression coefficients, and dashed blue vertical lines include the 0.95 confidence interval) and qq-plots (with intercept (

**B**) and without intercept (

**D**)).

**Figure 2.**Influential statistics for the linear regression (method

**lm**) of deoxynivalenol (DON) residues in

**blood**on DON exposure without intercept (black crosses mark the centroid of the scatter; red and blue filled dots represent data from Experiments 1 and 2, respectively): Hat scores (

**A**) (scores increase from smallest to largest dot size from 0.004 to 0.11); Studentized residuals (

**B**) (residuals increase from smallest to largest dot size from −3.62 to 7.01); Cook’s distance (

**C**) (distances increase from smallest to largest dot size from ~0.0 to 0.8); plot of Studentized residuals against hat scores with Cook’s distances indicated by dot size (

**D**) (distances increase from smallest to largest dot size from ~0.0 to 0.8); blue vertical lines indicate the mean value of hat score plus the two- and threefold standard deviation of hat score. Blue horizontal lines show −2 and +2 Studentized residuals. Observations that were either greater than 2, less than −2 Studentized residuals, had values larger than the mean value of hat scores plus the two- and threefold standard deviation of hat scores, or had a Cook’s distance greater than 1 are circled in black. Red solid lines denote the linear regression, and dashed red lines limit the prediction intervals at a 0.95 confidence level for future predictions. Red dots show the measured data pairs.

**Figure 3.**Internal (

**A**,

**B**) and external (

**C**,

**D**) validation of prediction equation for DON residues in blood (Equation 6) using the data from which the regression was estimated (combined dataset of Experiments 1 and 2) and data from an independent study (Experiment 3), respectively. Results of the linear regressions of the DON exposure as predicted by Equation 6 on observed DON exposure are shown as regression lines along with the 90° angle bisector (dotted lines) in (

**A**,

**C**) and as Bland–Altman plots in (

**B**,

**D**) for internal and external validation, respectively. (

**A**) y = 2.12 + 0.77x, n = 237, RSE = 27.3 µg/kg BW/d for solid line; Lin’s concordance correlation coefficient (CCC) = 0.83, Pearson’s correlation coefficient (r) = 0.84. (

**B**) Mean difference of 6.4 (red solid line) ± 1.96·30.2 (standard deviation of difference, blue dashed lines) µg/kg BW/d. (

**C**) y = −29.06 + 0.87x, n = 267, left-censored n = 80, residual standard error (RSE) = 38.2 µg/kg BW/d for the Tobit regression (dashed line), and y = −6.28 + 0.74x, n = 267, RSE = 31.1 µg/kg BW/d for the ordinary linear regression (solid line); Lin’s CCC = 0.79, Pearson’s r = 0.87. (

**D**) Mean difference of −29.4 (red solid line) ± 1.96·36.8 (standard deviation of difference, blue dashed lines) µg/kg BW/d. Red, blue, and green dots represent data from Experiments 1, 2, and 3, respectively, in (

**A**,

**C**); orange dots indicate the addition of the left-censored data from Experiment 3.

**Figure 4.**(

**A**) Sample size to be collected dependent on herd size as a fraction of standard deviation (std) for different half widths of the confidence interval (CI;

**green**: 0.6 × std;

**blue**: 0.5 × std;

**red**: 0.4 × std) (

**B**) Sample size to be collected dependent on half width of the confidence interval (CI) as a percent fraction of standard deviation (std) for different herd sizes (N;

**green**: N = 100;

**blue**: N = 50;

**red**: N = 10).

**Figure 5.**Theoretical toxicokinetic profiles of deoxynivalenol (

**DON**) residue concentrations in blood for 3 exposure levels (blue—low, green—medium, and red—high) (

**A**) as a basis for linear relationships between DON concentration in blood and diet (

**B**) or exposure (

**C**): (

**A**) After feeding the DON-contaminated diets for the first time, the (mean) DON concentration in blood increases until a mean steady state is reached (filled circles, dashed line). This scenario applies for ad libitum fed animals consuming contaminated meals several times per day. The magnitude of oscillation of DON concentrations in blood depends mainly on the half-lives of DON in blood, meal frequency, and on meal size. (

**B**) Based on (

**A**), plotting of mean steady state DON residues (filled circles) or individual DON residues (unfilled circles) versus the DON concentration of the underlying DON-containing diets results in linear dose–response relationships. Variation of individual values at comparable exposure levels occurs in the direction of the abscissa only and represents variation in time of blood sampling relative to the last meal and is further modified by the meal size. (

**C**) Compared with (

**B**), variation additionally occurs in the direction of the ordinate, as individual DON exposure varies at similar dietary DON concentrations due to differences in body weight (

**BW**) and DON intake as the product of dry matter intake and DON concentration of the diet. This individuality may result in overlapping between different exposure levels and an overall increased dispersion of observations over the entire observation range. Black unfilled circles and squares represent possible scenarios observable at dietary DON background contamination. In addition to non-detection in blood (unfilled squares that intercept the ordinate), the DON exposure might become virtually zero when dietary DON concentrations remain lower than LOD/LOQ. In this situation, DON residues in blood might still be detectable (unfilled black squares that intercepts the abscissa), owing to sensitivity differences of analytical methods for feed and blood.

**Figure 6.**Ultrasound-guided localization and puncturing of the gall bladder (photographs by Alexander Starke).

**Figure 7.**Exemplarily demonstration of the consequences of setting different half interval widths of the confidence interval (CI) as a fraction of standard deviation (SD = 20 ng/mL blood, see Table 1, combined dataset for Exps. 1 and 2) as an indicator of the precision of the estimation of the mean value at the predictor (DON residues in blood) and, consequently, at the response variable (DON exposure).

**Table 1.**Descriptive statistics for deoxynivalenol (DON) exposure and DON residue levels in blood and other specimens for Experiments 1 and 2 used for deriving prediction equations and for Experiment 3 used for external validation.

DON (mg/kg Diet, 88% DM) | N | Mean | Standard Deviation | Median | Minimum | Maximum | |
---|---|---|---|---|---|---|---|

Experiment 1 | |||||||

DON exposure (µg/kg BW/d) | 0.06–4.61 | 116 | 64.3 | 69.0 | 61.5 | 0.8 | 213.3 |

0.06 | 56 | 1.7 | 0.6 | 1.6 | 0.8 | 3.0 | |

2.31 | 30 | 83.5 | 16.3 | 82.0 | 56.2 | 120.2 | |

4.61 | 30 | 161.7 | 29.5 | 158.8 | 111.8 | 213.3 | |

DON residue levels (ng/mL) | |||||||

Blood plasma | 0.06–4.61 | 116 | 21.7 | 25.2 | 9.5 | 1.0 | 112.3 |

0.06 | 56 | 4.8 | 3.0 | 4.5 | 1.0 | 18.0 | |

2.31 | 30 | 20.9 | 10.1 | 18.8 | 2.5 | 48.0 | |

4.61 | 30 | 53.9 | 27.6 | 54.6 | 4.8 | 112.3 | |

Urine | 0.06–4.61 | 99 | 1914.3 | 2839.6 | 609.5 | 39.9 | 13,555.0 |

0.06 | 44 | 184.7 | 147.3 | 121.0 | 39.9 | 664.5 | |

2.31 | 29 | 1772.5 | 1182.1 | 1690.0 | 422.7 | 5587.5 | |

4.61 | 26 | 4999.3 | 3849.6 | 4108.8 | 271.2 | 13,555.0 | |

Bile | 0.06–4.61 | 85 | 22.5 | 32.2 | 9.1 | 0.3 | 207.0 |

0.06 | 45 | 3.2 | 2.9 | 2.5 | 0.3 | 11.0 | |

2.31 | 20 | 27.7 | 17.9 | 23.6 | 7.3 | 65.5 | |

4.61 | 20 | 61.0 | 42.3 | 56.3 | 9.9 | 207.0 | |

Milk | 0.06–4.61 | 109 | 1.1 | 1.5 | 0.5 | 0 | 5.7 |

0.06 | 49 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |

2.31 | 30 | 1.1 | 0.7 | 1.0 | 0.0 | 2.8 | |

4.61 | 30 | 3.0 | 1.4 | 3.3 | 0.5 | 5.7 | |

Experiment 2 | |||||||

DON exposure (µg/kg BW/d) | 0.14–0.2 | 121 | 9.8 | 4.5 | 10.1 | 2.8 | 18.4 |

DON residue levels (ng/mL) | |||||||

Blood plasma | 0.14–0.2 | 121 | 2.7 | 1.6 | 2.6 | 0.0 | 8.0 |

Experiments 1 and 2 | |||||||

DON exposure (µg/kg BW/d) | 0.06–4.61 | 237 | 36.5 | 55.5 | 10.6 | 0.8 | 213.3 |

DON residue levels (ng/mL) | |||||||

Blood plasma | 0.06–4.61 | 237 | 11.9 | 20.0 | 3.7 | 0.0 | 112.3 |

Experiment 3 | |||||||

DON exposure (µg/kg BW/d) | 0.35–4.66 | 267 | 88.2 | 75.4 | 34.8 | 3.8 | 224.5 |

DON residue levels (ng/mL) | |||||||

Blood serum | 0.35–4.66 | 267 | 23.3 | 25.2 | 12.0 | 0.0 | 127.0 |

**Table 2.**Parameter estimates for different regression models relating deoxynivalenol (DON) exposure (=y, µg/kg BW/d) or dietary DON concentrations (=y, mg/kg diet at 88% DM) to DON residues (sum of all detected metabolites) in various specimens from cows (ng/mL) (=x) based on linear regression (b = slope) with and without an intercept (a) using either a linear model (

**lm**) or a robust linear model (

**rlm**) for estimation of regression coefficients, which are presented with standard errors (SE) and p-values. The ultimately recommended prediction equations (6 for blood, 20 for urine, and 28 for milk) are printed in red; for details, please see text.

Speci-men | Me-thod | Experiment | y | a p-Value | SE | b p-Value | SE | Rainbow Test (p-Value) | RSE (µg/kg BW/d) | N | Exposure Threshold ^{1} (ng/mL) | Figure Equation |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Blood | lm | 1 | DON exposure | 17.36 | 5.157 | 2.17 | 0.156 | 0.012 | 42.1 | 116 | Figure A1A,B | |

0.001 | <0.001 | 1 | ||||||||||

Blood | lm | 2 | DON exposure | 4.98 | 0.598 | 1.81 | 0.191 | 0.122 | 3.4 | 121 | Figure A1A,B | |

<0.001 | <0.001 | 2 | ||||||||||

Blood | lm | 1 | DON exposure | 2.52 | 0.123 | 0.039 | 44.0 | 116 | Figure A1C,D | |||

<0.001 | 3 | |||||||||||

Blood | lm | 2 | DON exposure | 3.17 | 0.125 | 0.043 | 4.3 | 121 | Figure A1C,D | |||

<0.001 | 4 | |||||||||||

Blood | lm | 1 and 2 | DON exposure | 8.68 | 2.272 | 2.33 | 0.098 | 1.000 | 30.0 | 137 | 21.8 | Figure 1A |

<0.001 | <0.001 | 5 | ||||||||||

Blood | lm | 1 and 2 | DON exposure | 2.52 | 0.086 | 1.000 | 30.9 | 137 | 24.3 | Figure 1C | ||

<0.001 | 6 | |||||||||||

Blood | rlm | 1 | DON exposure | 7.61 | 4.107 | 2.50 | 0.124 | 0.012 | 30.6 | 116 | Figure A2A,B | |

0.068 | <0.001 | 7 | ||||||||||

Blood | rlm | 2 | DON exposure | 4.83 | 0.671 | 1.89 | 0.215 | 0.122 | 3.1 | 121 | Figure A2A,B | |

<0.001 | <0.001 | 8 | ||||||||||

Blood | rlm | 1 | DON exposure | 2.67 | 0.090 | 0.039 | 27.8 | 116 | Figure A2C,D | |||

<0.001 | 9 | |||||||||||

Blood | rlm | 2 | DON exposure | 3.20 | 0.131 | 0.043 | 4.6 | 121 | Figure A2C,D | |||

<0.001 | 10 | |||||||||||

Blood | rlm | 1 and 2 | DON exposure | 1.65 | 0.926 | 2.60 | 0.040 | 1.000 | 8.7 | 137 | 6.0 | Figure A3A |

0.066 | <0.001 | 11 | ||||||||||

Blood | rlm | 1 and 2 | DON exposure | 2.67 | 0.034 | 1.000 | 9.4 | 137 | 6.9 | Figure A3C | ||

<0.001 | 12 | |||||||||||

Blood | lm | 1 | DON diet | 0.52 | 0.143 | 0.06 | 0.004 | <0.001 | 1.16 | 116 | Figure A4A,B | |

<0.001 | <0.001 | 13 | ||||||||||

Blood | lm | 2 | DON diet | 0.15 | 0.003 | 0.01 | 0.001 | 0.012 | 0.02 | 121 | Figure A4A,B | |

<0.001 | <0.001 | 14 | ||||||||||

Blood | lm | 1 | DON diet | 0.07 | 0.003 | <0.001 | 1.22 | 116 | Figure A4C,D | |||

<0.001 | 15 | |||||||||||

Blood | lm | 2 | DON diet | 0.05 | 0.002 | 0.176 | 0.08 | 121 | Figure A4C,D | |||

<0.001 | 16 | |||||||||||

Blood | lm | 1 and 2 | DON diet | 0.19 | 0.064 | 0.07 | 0.003 | 1.000 | 0.84 | 137 | 22.5 | Figure A5A |

<0.001 | <0.001 | 17 | ||||||||||

Blood | lm | 1 and 2 | DON diet | 0.07 | 0.002 | 1.000 | 0.86 | 137 | 24.3 | Figure A5C | ||

<0.001 | 18 | |||||||||||

Urine | lm | 1 | DON exposure | 35.67 | 6.249 | 0.017 | 0.002 | 0.937 | 51.5 | 99 | 4021 | Figure A6A |

<0.001 | <0.001 | 19 | ||||||||||

Urine | lm | 1 | DON exposure | 0.022 | 0.002 | 0.468 | 59.2 | 99 | 5237 | Figure A6C | ||

<0.001 | 20 | |||||||||||

Urine | rlm | 1 | DON exposure | 26.59 | 5.21 | 0.018 | 0.00 | 0.937 | 42.57 | 99 | 3083 | Figure A7A |

<0.001 | <0.001 | 21 | ||||||||||

Urine | rlm | 1 | DON exposure | 0.023 | 0.00 | 0.468 | 26.42 | 99 | 2179 | Figure A7C | ||

0.00 | 22 | |||||||||||

Bile | lm | 1 | DON exposure | 27.71 | 7.00 | 1.59 | 0.18 | 0.026 | 52.82 | 85 | 50.1 | Figure A8A |

<0.001 | <0.001 | 23 | ||||||||||

Bile | lm | 1 | DON exposure | 2.00 | 0.16 | 0.003 | 57.24 | 85 | 58.2 | Figure A8C | ||

0.00 | 24 | |||||||||||

Bile | rlm | 1 | DON exposure | 7.62 | 4.46 | 2.24 | 0.11 | 0.026 | 25.53 | 85 | 19.2 | Figure A9A |

0.098 | <0.001 | 25 | ||||||||||

Bile | rlm | 1 | DON exposure | 2.38 | 0.08 | 0.003 | 22.16 | 85 | 18.3 | Figure A9C | ||

0.00 | 26 | |||||||||||

Milk | lm | 1 | DON exposure | 27.46 | 5.30 | 35.40 | 2.79 | 0.576 | 43.99 | 109 | 1.7 | Figure A10A |

<0.001 | <0.001 | 27 | ||||||||||

Milk | lm | 1 | DON exposure | 44.17 | 2.47 | 0.300 | 48.97 | 109 | 2.2 | Figure A10C | ||

0.00 | 28 | |||||||||||

Milk | rlm | 1 | DON exposure | 15.40 | 3.72 | 39.02 | 1.96 | 0.576 | 21.11 | 109 | 0.67 | Figure A11A |

<0.001 | <0.001 | 29 | ||||||||||

Milk | rlm | 1 | DON exposure | 43.39 | 1.16 | 0.300 | 13.57 | 109 | 0.61 | Figure A11C | ||

<0.001 | 30 |

^{1}The exposure thresholds were derived from the intercepts of the lower limit of the prediction interval from linear regressions of DON residue levels in physiological specimens on DON exposure on abscissa. Abbreviations: DM, dry matter; BW, body weight; RSE, residual standard error of regression.

**Table 3.**Comparative aspects regarding the usefulness of various specimens from cows for estimation of exposure to deoxynivalenol (DON).

Specimen | Urine | Blood | Bile | Milk |
---|---|---|---|---|

Expected DON residue levels | very high | low | low | very low |

Specimen collection | non-invasive | minimally invasive | minimally invasive | non-invasive |

Closeness to the inner (systemic) exposure | reasonable | good | poor | reasonable |

Relationship to dietary exposure ^{1} | linear | linear | weakly linear | linear |

^{1}at steady state.

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**MDPI and ACS Style**

Dänicke, S.; Kersten, S.; Billenkamp, F.; Spilke, J.; Starke, A.; Saltzmann, J.
Estimation of Oral Exposure of Dairy Cows to the Mycotoxin Deoxynivalenol (DON) through Toxin Residues in Blood and Other Physiological Matrices with a Special Focus on Sampling Size for Future Predictions. *Dairy* **2023**, *4*, 360-391.
https://doi.org/10.3390/dairy4020024

**AMA Style**

Dänicke S, Kersten S, Billenkamp F, Spilke J, Starke A, Saltzmann J.
Estimation of Oral Exposure of Dairy Cows to the Mycotoxin Deoxynivalenol (DON) through Toxin Residues in Blood and Other Physiological Matrices with a Special Focus on Sampling Size for Future Predictions. *Dairy*. 2023; 4(2):360-391.
https://doi.org/10.3390/dairy4020024

**Chicago/Turabian Style**

Dänicke, Sven, Susanne Kersten, Fabian Billenkamp, Joachim Spilke, Alexander Starke, and Janine Saltzmann.
2023. "Estimation of Oral Exposure of Dairy Cows to the Mycotoxin Deoxynivalenol (DON) through Toxin Residues in Blood and Other Physiological Matrices with a Special Focus on Sampling Size for Future Predictions" *Dairy* 4, no. 2: 360-391.
https://doi.org/10.3390/dairy4020024