## 3 Results and Discussion
### Determination of Method Operable Design Region
#### 3.3.1 HS-SPME Extraction  
The definition of MODR for HS-SPME(DVB/CAR/PDMS) was performed based on CMAs responses (TPA and IP) from interactions between extracted amines. The CMPs analyzed included NaOH concentration, extraction temperature, extraction time, and ionic strength (salt percentage). Figure S2 (Supplementary Material) shows the Pareto chart analysis of the effects between the studied CMPs on the TPA and IP responses. According to the results, the principal factor affecting TPA is the NaOH concentration, while for IP, it is mainly affected by temperature. Alkalinization of the sample will increase the amines volatility and therefore their concentration in the headspace. This is influenced by the pKa value of the amines (Table 1). The NaOH concentration should raise the pH in two units above the pKa of the analyte [37]. This effect was confirmed by [PERSON] (2016), who verified the appearance of amines after the addition of an alkaline agent [23]. The time of extraction and temperature effects have a role in the development of the equilibrium between the gas phase and the sample. Temperature influences the mass transference kinetics between the sample, headspace, and fiber, and consequently the extraction efficiency and precision [38]. In the case of extraction time, its role is to assure that the amount of the extracted analyte is proportional to the concentration present in the sample [38].  
The effects of all CMPs on TPA and IP, respectively, through the desirability surface contour method, are shown in Figure S3a,b (Supplementary Material). The values chosen for TPA to perform this analysis were defined as the highest desirable (\(3.24\times 10^{8}\)), acceptable mean (\(1.83\times 10^{8}\)), and lowest unacceptable (\(4.23\times 10^{7}\)). In the case of IP, the desirability parameters were defined as the highest desirable (1.5), acceptable mean (6.5), and unacceptable (12). Here, it is possible to see that the regions with higher desirable TPA values are between 10 and 24 M for the NaOH concentration, 20 and 50 min for the extraction time, extraction temperature between 25 and 40 \({}^{\circ}\)C, and NaCl percentage ranging from 15-45%. In the case of IP, for the same interactions, the lowest desirable RSD values are between 1 and 30 min for the extraction time, 6 and 20 M for the NaOH concentration, 25 and 35 \({}^{\circ}\)C for the extraction temperature, and 45% and 55% for the NaCl percentage. Overlaying the CMAs responses (Figure 2a), the desirability plots show a mix between TPA and IP results, resulting in an extended range red area, mostly for the interaction between the NaOH concentration and extraction time. The highest desirability index (dark red zone) is achieved between all CMPs in the following ranges: 10-18 M NaOH concentration; 20-40 min extraction time; 25-35 \({}^{\circ}\)C extraction temperature; and 35-55% NaCl percentage.  
Data verification was performed through the analysis of the agreement between the predicted and the observed values at the optimal condition range, which are described in Supplementary Material Table S5. According to the results, it was found that all the values observed in the experiments were close to the predicted values. However, the results showed slight differences between the observed and predicted values in CMA responses. Such differences might be due to the extended range values for the CMPs and small variations on the optimum point, which produce variability in the CMA responses. Therefore, the parameters at the optimal point were studied through a robustness test (see Section 3.4).