## 3 Results and Discussion
### Effects of Different Parameters on the Extraction Yield and Total Carotenoids Content and Recovery
Generally, conventional methods are applied to extract bioactive compounds (especially from carotenoids family) using organic solvents [31] achieving better extraction yield although they are often required large volumes, making the method expensive and environmentally unfriendly [32]. For instance, [PERSON] et al. [20] used different solvents and extraction time to improve the fucoxanthin recovery and were able to obtain 20.87 mg/g of fucoxanthin from dry biomass of marine microalga _I. aff. galbana_ (CCMP1324) using acetone. These results are better than total carotenoids rich in fucoxanthin extracted by SFE in our study, which may be due to an increase in solvent density and swelling of the matrix because of co-solvent addition. Total Phenolic Content and Antioxidant Response in Isochrysis galbana by Supercritical Fluid Extraction  
Table 2 presents the results of total phenolic content (TPC) and TEAC method as an antioxidant response. The estimated response surfaces are described in Figure 4A based on the parameters for TPC, which was complemented with a summarized second-order polynomial Equation (7) as a mathematical model to find the optimum conditions that maximize TPC as follows:  
\[\text{TPC}=-619.40+2.38\cdot\text{P}-0.0045\cdot\text{P}^{2}+0.0029\cdot\text {P}\cdot\text{T}+0.077\cdot\text{P}\text{-Co-solvent} \tag{7}\]  
This quadratic interaction of the pressure factor was significant for this response variable (TPC) as is evident in Table 1. The optimal condition was determined to be 34.8 MPa, 48 \({}^{\circ}\)C, and 8% co-solvent with an optimal yield of 133.9 mg GAE/g biomass. These results are better than those reported in other studies using _I. galbana_ as natural biomass rich in bioactive compounds through conventional methods of extraction [33; 34]. For example, [PERSON] et al. [33] and [PERSON] et al. [35] reported yields from _I. galbana_ clone Tahiti, and _I. galbana_ to be nearly 17.79 mg GAE/g and 12.24 mg GAE/g, respectively. Many reports compare SFE with conventional processes because they have advantages and disadvantages in both cases. In particular, fluids under supercritical condition reducing process time and enhancing the extraction yield. Parameters as temperature or pressure ease selectivity, effective penetrating the biomass and better mass transfer between phases versus conventional methods [18; 36]. The results mentioned in Table 2 indicate enhanced TPC content with an increase in the percentage of co-solvent (8% under optimal condition). In algae, the use of co-solvent such as ethanol increases the polarity of SFE and with it, the phenolic compounds, antioxidant activity, and fucoxanthin recovery are expected to increase [25; 37; 38]. _Sargassum muticum_ is a brown alga rich in fucoxanthin, fatty acids and phenolic compounds described by [PERSON] et al. [25]. They demonstrated that an increase in the ethanol concentration strongly improved variables such as total yield, radical scavenging capacity, and the fucoxanthin extraction yield. However, due to the lower process selectivity, the phenolic content using maximum co-solvent (10% ethanol) was moderately higher than with pure CO\({}_{2}\). Other reports of TPC extraction from conventional methods include studies by [PERSON] et al. [39] on _Isochrysis_ ISO-T and _Isochrysis_ sp. giving yields of 2.67 and 4.57 mg GAE/g, respectively, which are relatively low. In a study performed by [PERSON] et al. [40], 23 microalgae were evaluated using sequential organic solvent extraction and it was observed that _Nostoc ellipsosporum_ CCAP 1453/17 had a TPC of \(60.35\pm 2.27\) mg GAE/g. The antioxidants, such as fucoxanthin and phenolic compound in _Isochrysis_ sp., have been prescribed for the prevention of the age-related changes in the central nervous system as they scavenge free radicals and reactive oxygen species (ROS) [41]. The use of ABTS in the radical scavenging assay is a popular indirect method for determining the antioxidant capacity of bioactive compounds [42; 43]. The antioxidant response was determined by TEAC method.