## 2 Materials and Methods
### Experimental Set-Up
#### 2.2.3 HS-BA\(\upmu\)E Optimization and Validation Assays  
To optimize the experimental conditions, a one-variable-at-a-time (OVAT) strategy was adopted, which means that while studying the behavior of one parameter, the remaining were kept constant. For HS-BA\(\upmu\)E experimental optimization, the selected parameters were the sorbent coating phase (SX PLUS, R, CN1, CA1, HLB, S-X, S-DVB, and S-CN), the desorption solvent (MeOH, ACN, DCM, \(n\)-C\({}_{6}\), \(n\)-C\({}_{7}\), mixture of \(n\)-C\({}_{6}\) + \(n\)-C\({}_{7}\) (1:1%, \(\
u\)/\(\
u\)), and isooctane), desorption time (15, 30, 45, and 60 min), equilibrium time (1, 2, 3, 6, and 16 h) and temperature (15, 35, and 55 \({}^{\circ}\)C) [7; 13; 14; 15; 16; 17]. For each assay, 100 \(\upmu\)L of a standard mixture solution containing the six selected BVOCs (5.0 mg/L) was spiked at the bottom of a 5 mL vial. The previously prepared BA\(\upmu\)E devices were then inserted into the HS vial and immediately closed and placed into a thermostatic sand bath with controlled temperature for BVOC microextraction. After the enrichment step, the BA\(\upmu\)E devices were removed and transferred into 2 mL vials with inserts followed by 90 \(\upmu\)L of an organic solvent. Then, the 2 mL vials were subjected to ultrasonic treatment (Branson 3510 E-DTH, 42 \(\pm\) 2.5 kHz, 100 W, Zurich, Switzerland) for liquid desorption (LD) of the extracted BVOCs. Next, 10 \(\upmu\)L of the IS solution (20.0 mg/L) was added into each insert and agitated into a vortex (Velp, Italia) for 5 s. Finally, the BA\(\mu\)E devices were removed and the vials were sealed prior to GC-MS analysis. Each assay and blank analysis was performed in triplicate. The data obtained from the HS-BA\(\mu\)E/GC-MS assays were analyzed by comparing the abundance areas with control standard solutions of the target BVOCs. Figure 1 illustrates the experimental setup used.  
In order to validate the proposed methodology under optimized conditions, several parameters were evaluated, including selectivity, sensibility, linearity, and precision, according to previous studies [14; 15; 16; 17], using the same procedure as described above. Initially, selectivity was assessed by verifying the absence of interfering compounds with identical retention times to the target BVOCs, performed using blank assays. Afterward, the sensibility of the HS-BA\(\mu\)E/GC-MS methodology was evaluated through the experimental determination of the limits of detection (LOD) and quantification (LOQ). Then, calibration curves were plotted by analyzing the calibration standards of the six BVOCs ranging from 0.75 mg/L to 6.0 mg/L (15.0 \(\upmu\)g/L to 120.0 \(\upmu\)g/L, respectively). The linearity was assessed using the determination coefficients (\(r^{2}\)), the residual dispersion, and the lack-of-fit test for each calibration plot. The last step of validation assays was dedicated to performing intra- (\(n=6\)) and inter-day (\(n=3\), for 2 days) assays. To perform the precision assays for the HS-BA\(\mu\)E/GC-MS methodology, the IS concentration was maintained at 20.0 mg/L; the low, medium, and high concentrations of the BVOC mixtures corresponded to 1.0, 2.0, and 5.0 mg/L (20.0, 40.0, and 100.0 \(\upmu\)g/L, respectively). The acceptance criterion was the relative standard deviation (RSD), which had to be lower or equal to 30% for all spiking levels [12]. All validation assays were performed in triplicate, except when indicated.  
For comparison with a reference methodology, the validated HS-BA\(\mu\)E/GC-MS was compared with HS-SPME/GC-MS using three BVOCs (\(\alpha\)-pinene, 1.8-cineole, and thymol), following a similar procedure as described in previous work [7]; optimized conditions: PDMS/DVB fiber, HS extraction for 35 min at 35 \({}^{\circ}\)C; however, the IS concentration was maintained at 40.0 mg/L and the BVOC mixture was used in three different concentration levels--low, medium, and high, corresponding to 25.0, 100.0, and 200.0 mg/L (0.3, 2.5 and 5.0 \(\upmu\)g/L, respectively).