## 3 Results and Discussion
### Measurement of Fatty Acid Composition  
The fatty acid profiles were also identified along with FAME content (mg FAME/g) because they can be used in different biotechnological applications. The FAME content per gram of biomass is listed in Table 2. The range of FAME content was from 0.47 to 8.82 mg/g and Run 10 (30 MPa, 60 \({}^{\circ}\)C, and 8% co-solvent) gave the best results of 8.82 mg/g followed by the central point of the Box-Behnken design with values in the range of 6.87-7.63 mg/g. A summarized polynomial equation was obtained to establish a mathematical model, reach optimum operating conditions, and maximize FAMEs contents from _I. galbana_ by SFE. Equation (9) and data in Table 1 indicate the relevance of the co-solvent factor (\(p<0.05\)) in the FAME quantification under these SFE conditions. \[ \begin{array}{c}\text{FAME}=-39.50\;5-0.30\text{-Cosolvent}+0.0002\text{-P-Cosolvent }+0.03\text{-T-Cosolvent}-\\ 0.10\text{-Cosolvent}^{2}\end{array}  \tag{9}\]  
The optimal value suggested for the response work surface was 8.84 mg/g under the experimental condition of 33.3 MPa, 57 \({}^{\circ}\)C, and 7.9% co-solvent, nearly similar to that observed in our study. These results are presented in Figure 5 (response surface graphic) where at medium pressure, with high temperature and co-solvent, FAME content increased in _I. galbana_ although the co-solvent was the only significant factor in the process. Extractions under increased pressures gave the best results as the solubility of triglycerides could be improved due to an increase in the solvent density. Table 3 presents the profile of primary fatty acids derived from SFE extracts of _I. galbana_. The profile (measured as % area) consists of polyunsaturated fatty acids (PUFAs) in the range of 25.4-95.6%, MUFAs (monounsaturated fatty acids) in the range of 0.0-47.7%, and saturated fatty acids (SFAs) in the range of 4.4-42.1% of total fatty acids. In general, the fatty acid profile was highlighted by linoleic acid (C18:2) followed by linolenic acid (C18:3). Myristic acid (C14:0) and palmitic acid (C16:0) were the main SFAs. The highest recoveries of MUFAs and PUFAs were found under two conditions at 20 MPa, 40 \({}^{\circ}\)C, and 4% co-solvent (Run 12) and 30 MPa, 50 \({}^{\circ}\)C, and 4% ethanol (Run 9), at nearly 47.7 and 95.6%, respectively. SFE is considered an appropriate method for the extraction of fatty acids and lipids or for compounds of low polarity from microalgae because of its non-polar property [50]. It is also a solvent selective for neutral lipids such as triglycerides but does not solubilize phospholipids [51]. Our results corroborate with several reports about the extraction of polar compounds, which could be enhanced by adding of polar co-solvents, such as ethanol [52; 53]. Figure 5: Response surface plot showing combined effects of pressure and temperature on FAMEs content from _I. galbana_. All extractions were done with 8% co-solvent (ethanol, v/v). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c} \hline \hline
**Fully Acid** & **Common Name** & \multicolumn{1}{c}{**1**} & \multicolumn{1}{c}{**2**} & \multicolumn{1}{c}{**3**} & \multicolumn{1}{c}{**4**} & \multicolumn{1}{c}{**5**} & \multicolumn{1}{c}{**6**} & \multicolumn{1}{c}{**7**} & \multicolumn{1}{c}{**8**} & \multicolumn{1}{c}{**9**} & \multicolumn{1  
[PERSON] et al. [54] reported that an increase in the extraction pressure causes intensification in carbon dioxide density and, consequently, an increase in the solvation power for fatty acids. Our results show that under low pressures, more saturated fatty acids are extracted and when the pressure is increased, the proportion of unsaturated fatty acids increases in the extracted phase, an observation also supported by [PERSON] [55]. In general, this indicated that the triglycerides containing the more unsaturated fatty acids could be soluble at higher densities of CO\({}_{2}\) due to increase pressure factor.