## 3 Results and Discussion  
### Investigation of the Chromatographic Method  
In the present analytical method, special attention had to be paid to the chromatographic separations and column cleanup due to the wide range of lipophilicity of the analytes (LogP values) as well as the complex fatty substrate. More specifically, FERA has an intermediate polarity (LogP = 1.5), in contrast to \(\alpha\)-TOC, which is extremely lipophilic (LogP = 10.5). On the other hand, FERA (LogP = 1.5), QR (LogP = 2.2), and RSV (LogP = 3.4) are likely to present separation problems due to their similar polarity. To determine the appropriate chromatographic conditions, a series of experiments were conducted regarding the choice of the stationary phase and its temperature, the composition of the mobile phase and its flow rate, as well as the sample diluent. Given the circumstances, and with the aim of creating a non-time-consuming analytical method that could be used in routine analyses, it was obvious that the mobile phase had to be with gradient elution. Therefore, a simplified mobile phase with gradient elution (and buffers) was initially used, which was subsequently modified. Regarding the stationary phase, an ACE\({}^{\circledgtrgtr}\) phenyl (Avantor\({}^{\circledgtr}\), Radnor, PA, USA; 150 mm \(\times\) 4.6 mm, 5 \(\upmu\)m) and C\({}_{18}\) columns of different dimensions and particles size (a) Merck (Merck KGaA, Darmstadt, Germany; 125 mm \(\times\) 4.6 mm, 5 \(\upmu\)m) (b) MZ\({}^{\circledgtr}\) (MZAnalysentechnik, Mainz, Germany; 150 \(\times\) 4.6 mm), 3 \(\upmu\)m (c) Aqua Evosphere Fortis(r) (Fortis Technologies, Neston, UK; 250 mm \(\times\) 4.6 mm, 5 \(\upmu\)m) and (d) HS, Discovery(r) Supelco (Supelco, Bellefonte, PA, USA; 250 mm \(\times\) 4.6 mm, 5 \(\upmu\)m), were tested under the same analytical conditions. After investigation, phenyl was discarded because the peaks of RSV and QR were not sufficiently separated (Supplementary Figure S1A). Among the C\({}_{18}\) columns, only the two (Discovery and Aqua Evosphere) with the largest dimensions (25 cm \(\times\) 4.6 mm) exhibited the best behavior. Between them, the C\({}_{18}\) Discovery was chosen, and the mobile phase was further studied using acetonitrile as the organic solvent (A: acetonitrile with 0.2% formic acid and B: H\({}_{2}\)O with 0.2% formic acid). The case of replacing acetonitrile with methanol was rejected from the beginning mainly because the total run time would increase significantly. Another issue that had to be addressed was that the gradient elution program should be as smooth as possible in order to minimize baseline noise. The one chosen, for sufficient peak separation in a short period of time, included the following steps: Initially and up to the first four minutes, the % content of phase B was 20%. Then from 4 to 9 min it went linearly to 100%, where it was maintained until 17 min. Then in the next 3 min the system returned to 20% of phase B, where it remained until 25 min, where the injection was completed (total run). Given the presence of acetonitrile in the mobile phase in high concentration, an inorganic salt could not be used as a buffer solution because it would create precipitation problems. Thus, the performance of the proposed mobile phase was tested after the addition of three different acids (at their optimal concentrations): 0.2% formic acid (FA), 0.1% trifluoroacetic acid (TFA), and 0.2% acetic acid (ACA). Of these, 0.2% formic acid showed the best separation (Supplementary Figure S2). Last but not least, the flow rate of the mobile phase and the column temperature should be determined to ensure short elution times of the analytes at relatively low pressures. Thus, three flow rates (0.8, 1.0, and 1.5 mL-min\({}^{-1}\)) were investigated at temperatures from 25-40 \({}^{\circ}\)C. A flow rate of 1.5 mL-min\({}^{-1}\) and a column temperature of 40 \({}^{\circ}\)C were finally selected.