## 1 Introduction  
Headspace solid-phase microextraction (HS-SPME) is a convenient and solvent-free sample preparation technique that enables the extraction of analytes with minimal matrix interference. This technique works by exposing a coated fiber to the headspace of the sample of interest and allowing the volatile compounds to adsorb or absorb onto the fiber coating. The fiber is then thermally desorbed into an analytical instrument, such as gas chromatography-mass spectrometry (GC-MS), for further analysis. HS-SPME is based on the partitioning of the analyte between the fiber coating, the sample headspace, and the sample itself [1, 2]. The process is influenced by multiple parameters, e.g., fiber type, incubation time, headspace-to-sample phase volume ratio, extraction time and temperature, agitation type and speed, matrix pH, and ionic strength. Optimizing the most influential and/or most practical parameters for specific sample types is essential for obtaining a higher extraction efficiency [3, 4, 5, 6].  
HS-SPME has been used in various fields, such as environmental sciences [7, 8], food sciences [9, 10], and metabolomics [11, 12, 13], highlighting its efficacy and advantages in sample preparation. HS-SPME is also considered one of the \"greenest\" methodologies as the thermal desorption process is solvent-free, thereby enhancing the eco-sustainability of the method [1; 14; 15]. Validomics is a sub-field of metabolomics that studies the thousands of volatile compounds (VCs) emitted from a biological system [16], including the human body [17; 18; 19; 20]. These compounds encompass a wide range of chemical classes, including hydrocarbons, aldehydes, ketones, alcohols, nitrogen-containing, sulfur-containing compounds, and others [21]. The analysis of these compounds provides information associated with specific diseases [20], e.g., respiratory diseases [22; 23], gastrointestinal diseases [24; 25], diabetes [26; 27], and lung cancer [28; 29]. Moreover, profiling VCs can reveal information on other physiological statuses of an individual, such as diet and lifestyle [30] and environmental exposure [31].  
Sample preparation and extraction play a pivotal role in VC profiling. HS-SPME has been widely used for the extraction of VCs from biofluid samples such as blood [32; 33; 34], urine [35; 36], sputum [37; 38], and bronchoalveolar lavage fluid (BALF) [39; 40; 41; 42]. With specific regards to BALF, the matrix of interest for our study, HS-SPME has been used in previous studies for the extraction of VCs to diagnose infections in people with cystic fibrosis (CF) [39], evaluate primary graft dysfunction post-lung transplantation [43], and investigate associations with CF lung microbiome [40]. Despite its research importance, we found no published work specifically focusing on the optimization of HS-SPME for extracting VCs from BALF samples.  
GC-MS has been utilized for analyzing compounds extracted by HS-SPME. However, conventional GC-MS can cause co-elution of compounds from complex matrices. Therefore, our study employed a comprehensive two-dimensional gas chromatography (GC\(\times\)GC) coupled with a time-of-flight mass spectrometry (Tof MS) for VC analysis. GC\(\times\)GC has been an important technique to couple with HS-SPME, which significantly enhances the sensitivity and selectivity compared to the conventional GC-MS system, providing three- to ten-fold more peaks [44; 45; 46].  
For advancements in volatolomics research, it is important to extract and identify as many features as possible. Hence, here, we aimed to partially optimize the HS-SPME method to maximize both the number and intensity of VCs extracted from BALF samples. This optimization work will aid in the discovery of volatile biomarkers with potential diagnostic capability.