## 1 Introduction
RSM describes the relationship between the experimental factors studied and the process response (for example, the efficiency of the main product or the antioxidant activity of the fermented plant extract), where the response surface is approximated by mathematical functions (for example, polynomials) that allow prediction of response values for different combinations of factors. The RSM technique offers numerous advantages for optimising the fermentation process to obtain fermented plant extracts (FPEs) with the highest values of the process parameters tested while reducing the number of experiments required [22; 23]. _Syzygium aromaticum_ L. belongs to the _Mytaceae_ family, which includes more than 3000 species and about 150 genera, such as the myrtle, eucalyptus, clove, and guava families. Clove essential oil is obtained by distilling the flowers, stems, and leaves of _Syzygium aromaticum_ L. _Mytaceae_. Clove comprises approximately 15-20% of CEO, which contains a high amount of phenolic compounds with several biological activities, includingantibacterial, antifungal, insecticidal, and antioxidant properties. At least 30 chemicals have been discovered in CEO, with eugenol accounting for at least 50%. The remaining 10-40% contains eugenyl acetate, \(\beta\)-caryophyllene, and \(\alpha\)-humulene. Minor or trace components (less than 10%) include diethyl phthalate, caryophyllene oxide, cadinene, \(\alpha\)-copaene, 4-(2-propenyl)-phenol, clavicol, and \(\alpha\)-cubebene. The Food and Drug Administration (FDA) classifies CEO as generally recognised as safe (GRAS); for this reason, it is used in perfumes, cosmetics, sanitary products, medicines, and foods. CEO was recently recognised as an effective anaesthetic for sedating fish. This essential oil has also shown anti-inflammatory effects in meat and cheese. Due to its properties, the oil finds numerous applications, especially in the pharmaceutical industry (as an ingredient in warming and analgesic ointments) and in dentistry (as an ingredient in analgesic preparations, tooth cavity fillings, mouth and gum rinses, and toothpastes). Cosmetic formulas for acne skin care recommend eugenol because it improves the complexion of people with acne and psoriasis, reducing the appearance of lesions and accelerating their healing. Eugenol, a pale yellow liquid, is classified as an absorption promoter, which is characterised by high antimicrobial activity as well as antioxidant activity. It is a very interesting compound, considering not only its applications in medicine (an antiseptic in dental and medical practice) and cosmetics but also in organic synthesis and polymerisation processes (for example, it is used as an antioxidant for plastics and rubber). In addition, eugenol is widely used as a flavouring agent in food, beverages, candy, and frozen products. It is also present in many other aromatic plants, such as basil, cinnamon, and bay leaves [24; 25; 26; 27; 28; 29; 30]. In our previous study, the non-fermented and fermented extracts were obtained from the ground and defatted seeds of spotted thistle _Silbyum marimum_. Their antioxidant activity was evaluated using DPPH, ABTS, and FRAP techniques, while total polyphen content was measured using the Folin-Ciochateu method. High antioxidant activity was found for both the extract (0.91 mmol \(\mathrm{Trolox}/\mathrm{L}\)\(\pm\) 0.2) and the bio-ferment (1.19 mmol \(\mathrm{Trolox}/\mathrm{L}\)\(\pm\) 0.2), which was evaluated by the DPPH technique, so the resulting cosmetic raw materials were incorporated into hydrogel (H) and organogel (O) vehicles to obtain cosmetic formulations with antioxidant activity. We then evaluated the in vitro permeation through porcine skin of the main components contained in the obtained cosmetic raw materials, such as silibinin and taxifolin, which are part of the silymarin complex. For comparison, we also used pure silymarin (S).