In order to determine the most effective factors in measuring Histamine, the design of a partial factorial experiment of 5 factors with two replications using Minitab software was used. Table 3 shows the factorial design matrix and the sub-peak chromatogram values (responses) for Histamine.
P value: This part was used to check the accuracy of the model. To determine the effectiveness of the factors with 95% confidence level, P˂0.05 was considered as the limit point. As a result, factors with a value less than 0.05, factors affecting the process and factors with a value greater than 0.05 are considered as ineffective factors. According to the value of P, the factors affecting the response are of triethylamine, phenyl isothiocyanate and pH of acetate buffer.
Figure 3 is the residual diagrams used to evaluate the adequacy of the model. In Fig. 3, using the Normal probability diagram, the normality of the data can be detected. In this method, by specifying the data on the graph and passing the best line through the data, the normalcy of the data can be realized.
Figure 3 shows the Versus fits diagram for constant data variance. Residual changes should not have a specific structure and be scattered. Figure 3 Histogram If the remaining changes are gaussian, the data can be said to have a normal population and according to the figure, we can say that the data are normal.
The Residual observation order diagram in Fig. 3 examines the independence of the data with respect to time and the independence of the data with respect to the mean and variance. Also, this diagram should not show a specific structure. In this experiment, the horizontal axis shows the order of 32 experiments that were performed randomly.
Figure 4 shows the diagrams of the interaction between the factors. When the lines between the invoices are parallel, there is no interaction between the invoices. If the lines related to the factors are non-parallel, the greater the angle between the lines, the greater the intensity of the interaction. The lowest interaction between factors is between TEA-pH, PITC-pH, Time- pH and Temperature - pH and the highest interaction is between PITC- pH.
In Fig. 5, the Main Effects diagrams of the vertical axis are the average response, and the larger the angle between the factor lines and the horizontal line of the response axis, the more effective that factor is. According to the figure, we conclude that when the factors are at their highest level, we will have the highest response.
3.1. Optimization of factors affecting Histamine measurement
Based on the results of the screening stage, important and effective factors on Histamine measurement were selected and the optimal values of these important factors were determined by central composite design. In all experiments performed on the central composite design, ineffective factors were considered constant. The values of these factors were selected according to their coefficients shown in Table 4. Thus, the variables that had positive coefficients used its upper level and the variables that had negative coefficients used its low level in the optimization stage. Table 5 shows the central composite design matrix and the sub-peak chromatogram values for Histamine.
The experimental results of the designed experiments were analyzed by ANOVA method. In order to obtain an experimental model for predicting the response, the results of the analysis are shown in Table 6.
Using Table 6, the simplest model for measuring Histamine is suggested as follows:
Response = 2453899 + 29056 X1 + 64170 X2 + 154626 X3–31463 X12–75842 X32
R2 = 96.42% R2adj = 92.84%
Table 5
Central composite design matrix and results obtained
Run | X1 | X2 | X5 | Rep. |
18 | - | - | - | 2075259 |
19 | + | - | - | 2190332 |
20 | - | + | - | 2200121 |
21 | + | + | - | 2283971 |
22 | - | - | + | 2365552 |
23 | + | - | + | 2399868 |
24 | - | + | + | 2465012 |
25 | + | + | + | 2636967 |
26 | α- | 0 | 0 | 2302695 |
27 | +α | 0 | 0 | 2332546 |
28 | 0 | α- | 0 | Not Detection |
29 | 0 | +α | 0 | 2441860 |
30 | 0 | 0 | α- | 1801031 |
31 | 0 | 0 | +α | 2479179 |
32 | 0 | 0 | 0 | 2495904 |
33 | 0 | 0 | 0 | 2469746 |
34 | 0 | 0 | 0 | 2458286 |
35 | 0 | 0 | 0 | 2398801 |
36 | 0 | 0 | 0 | 2429029 |
37 | 0 | 0 | 0 | 2450778 |
A time-lapse model shows that it fails to adequately represent the relationship between factors and response variables. To determine if the model fits the data correctly, we consider the p-value. If its value is more than 0.05, it can be said that the model fits the data well. The amount of lack of fit in this study was 0.092, which is more than 0.05. As a result, it can be said that the model fits the data correctly.
Table 6
Statistical parameters for central composite design performed for Histamine measurement response
Source of variation | DF | F-Value | P-Value | (F-Value/Total F-Value) |
Model | 9 | 26.94 | 0.000 | 0.08 |
Linear | 3 | 58.41 | 0.000 | 0.16 |
TEA | 1 | 5.47 | 0.044 | 0.02 |
PITC | 1 | 14.93 | 0.004 | 0.04 |
pH | 1 | 154.83 | 0.000 | 0.43 |
Square | 3 | 20.75 | 0.000 | 0.06 |
TEA*TEA | 1 | 9.97 | 0.012 | 0.03 |
PITC*PITC | 1 | 4.50 | 0.063 | 0.01 |
pH*pH | 1 | 57.94 | 0.000 | 0.16 |
2-Way Interaction | 3 | 0.43 | 0.739 | 0.00 |
TEA*PITC | 1 | 0.57 | 0.468 | 0.00 |
TEA*pH | 1 | 0.00 | 0.959 | 0.00 |
PITC*pH | 1 | 0.71 | 0.423 | 0.00 |
Error | 9 | | | 0.00 |
Lack-of-Fit | 4 | 3.69 | 0.092 | 0.01 |
Pure Error | 5 | | | |
Total | 18 | | | |
Two-dimensional and three-dimensional diagrams resulting from central composite design
Using two-dimensional and three-dimensional diagrams, the relationship between response and factors can be shown. In the 3D diagrams in Fig. 6, one factor is considered at a fixed midpoint and the effect of the other two factors is investigated.
In addition, by drawing two-dimensional diagrams or contours, simultaneous examination of the factors can be done. According to the guide next to the chart, the answers change as the colors change. In fact, contour charts are the top view of 3D charts.
According to the guide provided in Fig. 7, as the green color is highlighted, the response will increased.. According to the diagram shown, by keeping TEA constant in its medium value, we increase it by increasing the pH and PITC to a high level. By keeping the pH constant at its medium value, we increase it by increasing the TEA and PITC to a high level. We also have an increase in PITC and TEA at a high level by keeping the pH constant at its medium value.
3.2. Achieving the optimal end point
After modeling and checking the accuracy and adequacy of the model and reviewing the relevant diagrams, optimization was performed to obtain the maximum response. According to the Optimization Plot diagram (Fig. 8) optimal points was determined. According to the obtained optimum point, the optimized values of triethylamine, phenyl isothiocyanate and buffer pH were 28 µl, 35 µl and 6.9, respectively.
Furthermore, Fig. 9 showed the chromatogram of the control sample and the chromatogram of the Histamine sample. For further evaluation of the method developed, Fig. 9 shows the black chromatogram corresponds to the blank sample and the blue chromatogram corresponds to the standard 1.0 mg. L− 1.
3.3. Method validation
The optimized analytical method was validated in terms of recovery, Standard deviation of reproducibility, Relative Standard deviation of reproducibility, Deviation from the standard of Reproducibility and Relative standard deviation of Reproducibility and recorded in Table 7. Spike solutions were prepared and studied at concentrations of 1.0, 2.5, 5.0, 10.0, 50.0 and 100.0 mg/L. Also, by drawing the calibration curve, the obtained coefficient of determination was 0.9994. LOD method was obtained for histamine 1.19 µg.ml− 1and LOQ was 0.36 µg.ml− 1.
Table 7
Results of the method study for Histamine
Spike level (µg.ml− 1) | Mean of recovery | Standard deviation of reproducibility | Relative standard deviation of reproducibility | Deviation from the standard of Reproducibility | Relative standard deviation of Reproducibility |
1.00 | 90.88 | 0.02 | 1.99 | 0.01 | 1.41 |
2.50 | 103.80 | 0.05 | 2.06 | 0.04 | 1.69 |
5.00 | 95.80 | 0.09 | 1.80 | 0.06 | 1.22 |
10.00 | 96.06 | 0.21 | 2.21 | 0.23 | 2.44 |
50.00 | 101.23 | 0.90 | 1.78 | 0.38 | 0.74 |
100.00 | 97.47 | 0.03 | 1.06 | 0.29 | 0.30 |