### 1. Introduction

### 2. Materials and Methods

### 2.1. Operational conditions of the HPLC-MS/MS

^{+}) to 462

*m/z*was monitored for a dwell time of 200 ms. The fragmentor voltage and collision energy were maintained at 100 V and 15 eV, respectively. The mass spectrometer interface in positive mode was operated under conditions of 4,000 V capillary voltage, 300°C drying gas temperature, 7 L/min drying gas, and 40 psi nebulizer pressure.

### 2.2. Experimental Design and Response Surface Analysis

*m/z*and operational conditions of the HPLC-MS/MS. Sensitivity tests were conducted by changing one factor and fixing the other variables, i.e., OFAT analysis, using the conditions described in Table 1. Then, three factors were selected as independent variables for RSA among the seven operational factors: solvent composition, injection volume, nebulizer pressure, drying gas flow rate, drying gas temperature, fragmentor voltage, and collision energy. The experimental conditions for the RSA were identified based on the central composite in cube design (CCD) using a 3 × 2 orthogonal design [30–31]. The conditions of the center point were fixed as close as possible to the best conditions from the OFAT analysis. The center point was replicated five times to calculate the experimental error. This type of design was used to minimize the number of trials needed to obtain statistically relevant results.

##### (1)

$$\eta ={c}_{0}+\sum _{i=1}^{n}{\alpha}_{i}\hspace{0.17em}{x}_{i}+\sum _{i=1}^{n}{\alpha}_{ii}\hspace{0.17em}{x}_{i}^{2}+\sum _{\begin{array}{l}i\\ i<j\end{array}}\sum _{j}{\alpha}_{ij}\hspace{0.17em}{x}_{i}\hspace{0.17em}{x}_{j}$$### 3. Results and Discussion

### 3.1. Selection of Major Factors for Optimization

*m/z*, was tested for the seven factors (Fig. S1). First, solvent composition and injection volume were tested as control factors for the HPLC compartment. The peak area significantly depends on the composition of the acetonitrile in the mobile phase (Fig. S1(a)). The range between 60% and 80% of acetonitrile was optimum. The mechanism for the solvent composition influence on sensitivity is unclear, but a high concentration of acetonitrile in the mobile phase was expected to increase the ionization efficiency by increasing the evaporation capacity of the mobile phase. In Fig. S1(b), the peak area was stable at 2.32 ± 0.40 × 10

^{6}disregarding the injection volume in the range of 2–15 μL. Therefore, only acetonitrile concentration was selected for RSA.

*m/z*. In the sensitivity test shown in Fig. S1(f) for fragmentor voltage, the range between 100 and 150 V was optimum. Generally, a moderate fragmentor voltage in the MRM mode intensifies the ionization of the precursor molecule. However, in this study, a high fragmentor voltage divided the precursor molecule into smaller precursor molecules, including 444 and 462

*m/z,*rather than of 479

*m/z*(data not shown). In this case, the peak intensity for 462

*m/z*obtained in the final detection device was reduced because the first quadrupole only allowed 479

*m/z*to the next step of the collision induced dissociation (CID) to produce 462

*m/z*in the MRM mode.

*m/z*product ion by splitting the 479

*m/z*molecule. An excessively high collision energy splits the 479

*m/z*molecule into product ions smaller than 462

*m/z*in the MRM mode, such as 444 and 154

*m/z*. Using the test presented in Fig. S1(g), 15 eV was identified as the optimum collision energy value for the higher peak area.

### 3.2. Response Surface Analysis and Optimization

*m/z*were chosen as 71.7–128.3 V, 7.9–22.1 eV, and 45.9–74.1% for fragmentor voltage, collision energy, and solvent composition, respectively. An additional trial was undertaken to verify the accuracy of the model prediction by randomly selecting experimental conditions (Trial 16 in Table 2) after obtaining the best model equation that fit the experimental data. The average value of the peak area at the center point was 8.11 ± 0.29 × 10

^{6}and the standard deviation was 3.55%.

*p*value for the lack of fit was significant and the regression coefficient for the peak area was not significant at a 5% α-level. Therefore, an additional six trials (Trials 10 to 15 in Table 2) were utilized to find a more appropriate equation to regress the experimental responses at various conditions with a second or higher order model. The step sizes of the variation were expanded to 28.3 V, 7.1 eV, and 14.1% for fragmentor voltage, collision energy, and solvent composition, respectively.

^{2}value indicates a good explanative power, which is calculated from the ratio of the regression sum of squares to the total sum of squares. In contrast, the adjusted R

^{2}value explains any bias in the R

^{2}value by taking into account the degree of freedom of the independent variables. The R

^{2}and adjusted R

^{2}values for the basic quadratic model (Eq. (2)) were 0.9835 and 0.9650, respectively. The equation was modified to obtain a better quality model, represented by the increased R

^{2}and adjusted R

^{2}values.

##### (2)

$$\begin{array}{l}\eta =-24,899,614+7,066\hspace{0.17em}{\text{X}}_{1}+2,194,213\hspace{0.17em}{\text{X}}_{2}\\ +427,768\hspace{0.17em}{\text{X}}_{3}-48\hspace{0.17em}{{\text{X}}_{1}}^{2}-74,297\hspace{0.17em}{{\text{X}}_{2}}^{2}-3,351\hspace{0.17em}{{\text{X}}_{3}}^{2}\\ -306\hspace{0.17em}{\text{X}}_{1}{\text{X}}_{2}+355\hspace{0.17em}{\text{X}}_{1}{\text{X}}_{3}+1,443\hspace{0.17em}{\text{X}}_{2}{\text{X}}_{3}\end{array}$$##### (3)

$$\begin{array}{l}\eta =6,123,985-46,856\hspace{0.17em}{\text{X}}_{1}-290,998\hspace{0.17em}\hspace{0.17em}{\text{X}}_{2}-442,689\hspace{0.17em}{\text{X}}_{3}\\ -48\hspace{0.17em}{{\text{X}}_{1}}^{2}-48,415\hspace{0.17em}{{\text{X}}_{2}}^{2}+3,903\hspace{0.17em}{{\text{X}}_{3}}^{2}+7,459\hspace{0.17em}{\text{X}}_{1}{\text{X}}_{2}\\ +355\hspace{0.17em}{\text{X}}_{1}{\text{X}}_{3}+59,473\hspace{0.17em}{\text{X}}_{2}{\text{X}}_{3}-259\hspace{0.17em}{\text{X}}_{1}{{\text{X}}_{2}}^{2}-484\hspace{0.17em}{\text{X}}_{2}{{\text{X}}_{3}}^{2}\end{array}$$*η*: the peak areaX

_{1}: fragmentor voltage (V)X

_{2}: collision energy (eV)X

_{3}: solvent composition (%)

^{2}) and (collision energy × solvent composition

^{2}) terms to Eq. (2) increased the R

^{2}and adjusted R

^{2}values to 0.9884 and 0.9673, respectively (Eq. (3)). The

*p*value of the regression was significant at a 0.1% α-level and the lack of fit was not significant at a 5% α-level. These results indicated that the partial cubic model was an accurate representation of the data. The residual plots represent the difference between the experimental and calculated values for the model (Fig. S2), and showed no patterns or trends. Therefore, the model described in Eq. (3) was an adequate approximation for the peak area variance according to the variation in fragmentor voltage, collision energy, and solvent composition (Fig. 2).

^{6}, was observed. The peak area under optimum conditions was estimated as 8.73 × 10

^{6}. In a separate experiment to verify using triplicate analysis of the expected optimum conditions, the 9.18 ± 0.80 × 10

^{6}result showed an insignificant difference from an estimated value of 8.73 × 10

^{6}, i.e., 5.2%. The predictability of the model obtained in this study was also validated using the randomly selected conditions for Trial 16 in Table 2. There was only a 0.56% error between the predicted value from the model, 6.62 × 10

^{6}, and observed value, 6.58 × 10

^{6}. These validations under the optimum and random conditions showed the high accuracy of the model in predicting the response surfaces of the peak area for the target product ion when changing the fragmentor voltage, collision energy, and solvent composition.

^{2}) terms were significant for the peak area at a 0.1% α-level; and (fragmentor) and (solvent composition

^{2}) terms were significant for the peak area at a 5% α-level. However, the (fragmentor voltage × collision energy), (fragmentor voltage × solvent composition), (collision energy × solvent composition), (fragmentor voltage × collision energy

^{2}), and (collision energy × solvent composition

^{2}) two-way interactions were not statistically significant.

^{2}) due to the largest absolute value of the coefficient, 1,857,422. In the same manner, the contributions from terms in Eq. (4) were evaluated. It was considered that interactions had the least influence on the peak area, with rankings of 6 to 10 among the eleven terms. In sum, the interaction between fragmentation voltage, collision energy, and solvent composition had no statistical significance and contribution to variation in the peak area. However, the interaction terms could improve the R

^{2}value, i.e., the predictability of the model.

##### (4)

$$\begin{array}{l}\eta =8,097,587+369,801\hspace{0.17em}{\text{X}}_{1}+267,253\hspace{0.17em}\hspace{0.17em}{\text{X}}_{2}\\ +828,548\hspace{0.17em}{\text{X}}_{3}-19,250\hspace{0.17em}{{\text{X}}_{1}}^{2}-1,857,422\hspace{0.17em}{{\text{X}}_{2}}^{2}\\ -335,072\hspace{0.17em}{{\text{X}}_{3}}^{2}-30,560\hspace{0.17em}{\text{X}}_{1}{\text{X}}_{2}+71,071\hspace{0.17em}{\text{X}}_{1}{\text{X}}_{3}\\ +72,127\hspace{0.17em}{\text{X}}_{2}{\text{X}}_{3}-129,408\hspace{0.17em}{\text{X}}_{1}{{\text{X}}_{2}}^{2}-241,794\hspace{0.17em}{\text{X}}_{2}{{\text{X}}_{3}}^{2}\end{array}$$^{2}). However, the peak area responded with less sensitively to fragmentor voltage and changes in solvent composition.

### 4. Conclusions

*m/z*). The peak area data were collected from conditions designed based on the CCD. The RSA of the collected data resulted in an empirical model that precisely predicted the peak area, with R

^{2}and adjusted R

^{2}values of 0.9984 and 0.9673, respectively. The (solvent composition) and (collision energy

^{2}) terms were the most statistically significant, while the two-way interactions between independent variables were negligible. The optimum conditions for higher sensitivity of the HPLC-MS/MS were 114.9 V, 15.7 eV, and 70.9% for the fragmentor voltage, collision energy, and solvent composition, respectively. Validation under the optimum and random conditions demonstrated the high accuracy of the model in predicting these results. The applied sequential procedure for screening major factors and conducting RSA provided a rapid optimization and comprehensive understanding of the HPLC-MS/MS for analyzing CTC.