## 3 Results and Discussion
### HS-SPME Method Optimization
#### 3.1.3 Optimization of Extraction Time and Temperature  
We hypothesized that an optimum combination of extraction temperature and extraction time would yield the highest total peak area and total peak number. We observed that the highest total peak area was achieved using an extraction temperature of 50 \({}^{\circ}\)C and an extraction time of 50 min. In contrast, the highest total peak number was obtained with the same extraction time but at a slightly lower temperature of 45 \({}^{\circ}\)C. The total peak area extracted by these two conditions was 2.25 \(\times\) 10\({}^{7}\) and 2.31 \(\times\) 10\({}^{7}\), respectively, showing a 2.7% difference. The total peak numbers extracted were 291 and 285, respectively, indicating a 2.1% difference (Figure 3). As these two differences were minor and not statistically different, 45 \({}^{\circ}\)C and 50 min were selected as a compromise for high-throughput analysis. The analysis of variance results revealed a lack-of-fit \(p\)-value of 0.003 for the total peak area and 0.001 for the total peak number, respectively. The output table and Pareto Chart for the CCD are attached in the supplementary file (Figure S1, Table S3). Six replicates of the center point sample showed low relative standard deviation and high reproducibility (Supplementary Figure S3; Table S4).  
Figure 2: (**a,b**) The comparison of the total peak area and total peak number extracted from non-diluted and diluted samples. The \(p\)-value was calculated based on the student \(t\)-test. * \(p\)-value < 0.05; *** \(p\)-value < 0.001. The shape of the points represents different vial size: round dot—10 mL vial; square—20 mL vial.  
In a prior HS-SPME optimization work on a cell culture infected with respiratory syncytial virus, the authors evaluated optimization parameters using 12 compounds, targeting a broad spectrum of major chemical classes [48]. Inspired by this approach, we similarly tested our hypothesis by examining 41 compounds (Supplementary, Table S2) from different chemical classes. These compounds meet one of these two criteria [48]: (1) they have a mass spectral similarity score greater than 850, and (2) the difference between the calculated retention index (RI) and the RI in the library is less than 30. After conducting a response surface analysis on these 41 compounds, we observed that none exhibited an optimum plateau in the perspective plot within the specified extraction temperature and time range (Supplementary Figure S1).  
Extraction time is a critical parameter of the HS-SPME method, determining whether the system reaches equilibrium across the headspace, sample, and fiber phases. The duration required for a system to reach equilibrium depends on various factors, such as extraction temperature, sample matrix, and the nature of the analytes. For example, the equilibrium in HS-SPME of plasma samples at 37 \({}^{\circ}\)C is reached approximately after 90 min [58]. Extraction temperature can influence the equilibrium time, meaning that increasing temperature may shorten the time required for reaching equilibrium [3].  
We suspect that our system did not achieve equilibrium under the designated conditions, as indicated by the continuously rising total peak area and total peak number within the given without reaching a maximum value. We believe this could be due to the insufficient extraction time and the relatively low extraction temperature.