# Insights from a Box–Behnken Optimization Study of Microemulsions with Salicylic Acid for Acne Therapy

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## Abstract

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^{3}fractional factorial design was selected. The effect of independent variables namely X1: Tween 80/PG (%), X2: Lecithin (%), X3: Oil phase (%) was analyzed considering their impact upon the internal structure and evaluated parameters chosen as dependent factors: viscosity, mean droplet size, and work of adhesion. A high viscosity, a low droplet size, an adequate wettability—with a reduced mechanical work—and clarity were considered as desirable for the optimal systems. It was found that the optimal microemulsion which complied with the established conditions was based on: Tween 80/PG 40%, lecithin 0.3%, oat oil 2%, salicylic acid 0.5%, hyaluronic acid 1%, and water 56.2%. The response surface methodology was considered an appropriate tool to explain the impact of formulation factors on the physical properties of microemulsions, offering a complex pattern in the assessment of stability and quality attributes for the optimized formulation.

## 1. Introduction

_{1}: viscosity (cP), Y

_{2}: mean droplet size (nm), and Y

_{3}: work of adhesion (mN/m).

## 2. Materials and Methods

#### 2.1. Materials

^{®}Direct 8 Water Purification System (Merck Millipore, Bedford, MA, USA), and used as aqueous phase.

#### 2.2. Preparation of Salicylic Acid-Based Microemulsions

^{3}fractional factorial design. The systems were formulated by applying the water titration method, under continuous stirring at 70 °C. The use of heat at the moment of preparation was considered favorable to assure the homogenization of microemulsions. Initially, calculated amounts of lecithin were weighed and placed in a melting pot, on a hotplate stirrer (DLAB MS-H380-Pro, DLAB Scientific, Beijing, China). Based on the affinity of lecithin for the oil phase, at the melting point of lecithin, the proper amount of oat oil was added, resulting in an orange-like lipophilic mixture. Tween 80 and PG were separately mixed to solubilize salicylic acid, and finally added drop by drop into the lipophilic phase by stirring. In the last step, hyaluronic acid was solubilized in 8 mL of distilled water and then embedded in the above-mentioned mixture of lipophilic phase and surfactants. After a proper homogenization, the water titration method was initiated, keeping operational conditions constant, for up to 2 h. Heating was gradually reduced to avoid evaporation. Clear or almost translucent microemulsions were obtained and placed into equilibration in a calm environment.

_{18}-monooleate chain responsible for interaction with lipophilic entities [61]. In association with a medium-chain alcohol, in our case, propylene glycol is formed as a binary mixture [74] with a powerful solubilization effect for the oil phase and lipophilic API. It is well known that Tween 80 and propylene glycol are implied in penetration activity at the level of stratum corneum, ensuring the diffusion of the API through deeper layers of the skin [36,75,76]. Several studies have concentrated on this phenomenon, and proposed Tween 80/PG tensioactive blend to sustain O/W microemulsion generation [46,77,78].

_{ME}) were calculated. The HLB

_{ME}required was considered, taking into consideration the HLB

_{Tween 80}= 15 and HLB

_{Lecithin}= 5. The following formula (Equation (1)), proposed by de Melo Cotrim A.C. et al. was applied [84]:

#### 2.3. Organoleptic Analysis

#### 2.4. pH Determination

#### 2.5. Conductivity Analysis

#### 2.6. Refractive Index Determination

#### 2.7. Rheological Evaluation

^{−1}.

#### 2.8. Droplet Size and Zeta Potential Analysis

#### 2.9. Superficial Analysis

#### 2.10. Data Analysis and Optimization of Microemulsions Using Box–Behnken Design

_{1}), lecithin concentration (X

_{2}), and oat oil concentration (X

_{3}), at three levels of variation, coded as follows: low (−1), medium (0) and high (+1). A 3

^{3}fractional factorial design was generated using Minitab software (Minitab-Trial version, LLC, State College, PA, USA). Overall, 13 formulations equivalent to 13 runs with one center point without replication were generated, developed, and evaluated, choosing several responses as dependent variables, coded as Y: viscosity (Y

_{1}), mean droplet size (Y

_{2}), and work of adhesion (Y

_{3}).

_{1}, X

_{2}, and X

_{3}) was represented using a quadratic model quantified by the following fit of second order polynomial equation (Equation (5)), generated by software:

## 3. Results

#### 3.1. Formulation Design

^{3}fractional factorial plan, using three formulation factors as independent variables, and implementing a proper preparation protocol based on water titration. In this way, three independent variables, denoted as X

_{1}, X

_{2}, and X

_{3,}are presented in Table 2, considering three levels of variation: Low (−1), Medium (0), and High (+1). Table 3 provides the experimental matrix generated from the software.

_{ME}. The values were close to the HLB

_{Tween 80}value, which signifies that the designed mixture promoted stability for the microemulsion-based samples.

Formulation | Run Order | ^{1} Clarity | Tween 80/PG | Lecithin | Oil | HLB_{ME} |
---|---|---|---|---|---|---|

MELSA 1 | 1 | ++ | −1 | −1 | 0 | 14.90 |

MELSA 2 | 2 | +++ | +1 | −1 | 0 | 14.46 |

MELSA 3 | 3 | ++ | −1 | +1 | 0 | 14.62 |

MELSA 4 | 4 | +++ | +1 | +1 | 0 | 14.80 |

MELSA 5 | 5 | +++ | −1 | 0 | −1 | 14.75 |

MELSA 6 | 6 | +++ | +1 | 0 | −1 | 14.87 |

MELSA 7 | 7 | + | −1 | 0 | +1 | 14.75 |

MELSA 8 | 8 | +++ | +1 | 0 | +1 | 14.87 |

MELSA 9 | 9 | +++ | 0 | −1 | −1 | 14.93 |

MELSA 10 | 10 | +++ | 0 | +1 | −1 | 14.72 |

MELSA 11 | 11 | + | 0 | −1 | +1 | 14.93 |

MELSA 12 | 12 | + | 0 | +1 | +1 | 14.72 |

MELSA 13 | 13 | +++ | 0 | 0 | 0 | 14.85 |

^{1}Notation of clarity parameters: “+” was attributed for an opalescent system, “++”—for a low clarity system, and “+++”—for a high clarity system.

#### 3.2. pH Determination

#### 3.3. Conductivity Analysis

#### 3.4. Refractive Index Determination

#### 3.5. Rheological Evaluation

^{2}= 0.9992–0.9999) showed a good fit for the model of viscosity. Consequently, in Figure 5, cumulative rheological plots of shear stress (Pa) as a function of shear rate (s

^{−1}) were provided to sustain Newtonian behavior of microemulsions tested at 25 ± 0.5 °C. For a better visualization, rheological profiles were divided in three groups depending on Tween 80/PG concentration and denoted as (a) microemulsions with low viscosity (formulated with Tween 80/PG 20%), (b) microemulsions with high viscosity (formulated with Tween 80/PG 40%), and (c) microemulsions with intermediate viscosity (formulated with Tween 80/PG 30%). As suggested by the rheological profiles, viscosity was expressed in Pa∙s and then converted into cP. The final results reported in Table 4 were used for interpretation and optimization of viscosity as a critical quality attribute.

#### 3.6. Droplet Size and Zeta Potential Analysis

#### 3.7. Superficial Analysis

_{LG}), contact angle (CA), and work of adhesion (W), which can be visualized in Table 5. Their quantification was performed by applying a Young equation, which was fitted with two models of study: the pendant drop model and the contact angle model.

_{LG}), before the drops fell on the glass slide under gravitational force. Figure 8 visually represents images of each drop from MELSA 1–MELSA 13 systems, which were released from a Hamilton syringe and subjected to measurements. Superficial tension varied between 32.57 ± 0.34 mN/m and 37.36 ± 0.16 mN/m and was significantly influenced by Tween 80/PG (%) (p < 0.05). The minimum value corresponded to MELSA 2, while the maximum value was depicted for MELSA 5. It can be observed that the higher values of superficial tension were specific for microemulsions with Tween 80/PG of 20%, and consequently higher concentrations of water. Related results were obtained in the group of systems with the medium level of Tween 80/PG of 30%. The differences between the two groups regarding the superficial tension values were not significant. Considering the last group, the influence of Tween 80/PG at the maximum level of 40% had a high persistence among γ

_{LG}values. The impact of lecithin as a second surfactant was quite significant, the values being placed between 32.57 ± 0.34–33.73 ± 0.24 mN/m.

_{LG}represents the result of the forces that will oppose a complete wetting phenomenon, determining interactions between adhesion and cohesion forces, and formation of various angles between 40.74 ± 0.70–57.91 ± 0.38°, which describe a moderate wettability. Complementary to this, the values of γ

_{LG}varied between 33.38 ± 0.46–52.90 ± 1.82 mN/m, promoting a variation in the work of adhesion on a larger domain of 52.72 ± 1.44–81.00 ± 2.49 mN/m. The values of γ

_{LG}were significantly influenced by Tween 80/PG (%) and the oat oil (%) (p < 0.05). Lecithin (%) offered a supplementary significant effect on the work of adhesion (p < 0.05). Thereby, for microemulsions with a minimum level of Tween 80/PG of 20%, modification in lecithin concentration slightly influenced the values of γ

_{LG}. In the case of MELSA 1 and MELSA 3, the elevation of γ

_{LG}with 1 mN/m produced an insignificant increase in contact angle, and consequently in the work of adhesion. Decreasing the level of lecithin to 0.3% in the case of MELSA 7, and adding 2% oil phase, will determine the action of a low γ

_{LG}, and formation of a contact angle of 43.27°, promoting a proper adhesion defined by a work of adhesion of 58.64 mN/m. On the other hand, in the case of MELSA 5, the hydrophilic effect of water at the maximum amount of 77.2%, influenced γ

_{LG}to reach 41.31 mN/m. The forces implied in the mechanical work were powerful, so the work of adhesion had a higher value, determining a display of drops with the smallest medium angle of 40.73°. From this group, a good work of adhesion was obtained for MELSA 7 with Tween 80/PG 20%, lecithin 0.3%, and oat oil 2%.

_{LG}of 37.63 mN/m, promotion of an angle of 51.93°, and a medium work of adhesion of 60.80 mN/m. This profile can be compared with that of MELSA 3. The increase in viscosity was favorable for the angle elevation, and consequently for the work of adhesion. Hereinafter, in MELSA 10 case, γ

_{LG}increased proportionally with the use of the maximum level of lecithin and influences the formation of drops of 54.04° and the highest work of adhesion from this group. In this case, cohesion forces opposed to the wettability of the surface. Following the case of MELSA 11, the adhesion was more favorable, even if the angle was comparable with the anterior one. With a γ

_{LG}of 33.38 mN/m, work of adhesion was proper at a minimum level of lecithin, and a maximum level of oil. Maintaining oat oil concentration at constant level, and increasing lecithin at 0.5%, γ

_{LG}facilitated a displaying of drops with a smaller angle, but under the effect of higher forces implied in adhesion. Similarly, it can be observed in the last case, for MELSA 13. From this group, a better adhesion was obtained for MELSA 11 with Tween 80/PG 30%, lecithin 0.1%, and oat oil 2%. To conclude this series, a short brief point considering the influence of lecithin and oil phases on the dynamic of microemulsions at the contact with a surface can be made. By reference to the four microemulsions (MELSA 9, MELSA 10, MELSA 11, and MELSA12) the following were emphasized:

- Between MELSA 9 and MELSA 10, the variation of lecithin through a higher concentration, determined an increase in the angle and the work of adhesion.
- Between MELSA 9 and MELSA 11, the variation of oil through a higher concentration, determined an increase in angle, but a decrease in the work of adhesion. In this case, a wettability phenomenon is expected to occur.
- Between MELSA 11 and MELSA 12, the variation of lecithin, keeping constant the maximum amount of oil, determined an increase in the work of adhesion, but a decrease in the contact angle. The oil phase improved the wettability of the surface.
- Between MELSA 10 and MELSA 12, the variation of oil, keeping constant the maximum amount of lecithin, determined a decrease in the contact angle, and a decrease in the work of adhesion. The oil phase improved the wettability at the level of the surface.

_{LG}. Consequently, the work of adhesion increased from 67.52 mN/m up to 76.91 mN/m, without modification in the contact angle value. As with the previously discussed series, lecithin had an additional impact on the induction of a higher work of adhesion, limiting the wettability of surface. In the case of MELSA 6 and MELSA 8, an increase in the contact angle can be observed. The maximum value of 57.91° was reached, with a work of adhesion of 81 mN/m at a minimum level of oil of 1%, and lecithin 0.3%. At a maximum level of oil of 2%, the drop adhered much better to the surface, keeping a similar angle. Weaker mechanical forces contributed to a good wettability in the last case. It can be seen that a better adhesion was obtained for MELSA 8 with Tween 80/PG 40%, lecithin 0.3%, and oat oil 2%.

#### 3.8. Optimization of Critical Quality Attributes for Microemulsions Using Box–Behnken Design

^{3}fractional factorial design characterized by 13 experimental runs in the Minitab software. The analysis of responses namely Y

_{1}: viscosity (cP), Y

_{2}: mean droplet size (MPS)—Ds (nm), Y

_{3}: work of adhesion—W (mN/m), as a function of formulation factors defined as X

_{1}: Tween 80/PG (%), X

_{2}: lecithin (%), and X

_{3}: oat oil (%), was conducted by applying the response surface methodology (RSM). Accordingly, the following were considered as valuable for this stage: the response surface regression accompanied by a statistical interpretation for each response, and the highlights of contour plots and response surfaces. Subsequently, Pareto charts were considered representative plans that can emphasize the significance of independent variables, and interactions that can influence the response. Associated with the experimental responses, predicted values were determined based on the fitted model of the second order polynomial equations.

#### 3.8.1. Optimization of Viscosity

_{1}) (p < 0.05). The second order polynomial equation (Equation (6)) that fitted the response (Y

_{1}) was proposed hereinafter:

_{1}), a group with the highest levels of 188.17–292.69 cP was outlined, determining a decrease in fluidity and a better stability. The variation of X

_{2}, and X

_{3}was not of significance in this case (p > 0.05), as well as their squares and interactions. To exemplify this, ANOVA analysis results are shown in Table 8. Only one square defined as ${\mathrm{X}}_{1}^{2}$ was of significance, having a positive effect for the Y

_{3}response.

_{1}response were projected, which are shown in Figure 12 and Figure 13.

_{1}and X

_{2}factors was considered representative to explain viscosity variation in low, medium, and high levels of Tween 80/PG (%). It can be observed that the response is specifically sensitive for X

_{1}variation. By reference to Y axis, flat lines signified the negligible effect of lecithin for Y

_{1}response.

_{1}and X

_{3}factors in the case (b). The increase of Tween 80/PG (%) from 20% up to 40%, determined the elevation of viscosity, attaining the maximum value over 250 cP, but in an independent manner. That is why the flat lines target the X axis, without determining a significant effect for the Y axis variable.

_{1}variation as a function of Tween 80/PG (%) and lecithin (%) was chosen and projected as a surface in gradient color—case (a), and wireframe plot—case (b). In the first case, a proportional elevation of viscosity with the increase of Tween 80/PG (%) is observed from a lighter blue tone through to a darker shade at any level of lecithin. In addition, the embossed surface emphasizes the maximum points which were related with the optimal expected results. Thereby, it can be appreciated that valuable viscosity responses which can be relevant for a therapeutic purpose regarding parameters such as—clarity, spreadability, stability—were obtained at the highest level of Tween 80/PG of 40%. The systems were MELSA 2, MELSA 4, MELSA 6, and MELSA 8.

_{1}) was completed after representation of factorial plots and prediction of optimal viscosity, taking into consideration the aforementioned criteria. On this path, the main effects plot for viscosity, shown in Figure 14, represents the final evidence whereby the Tween 80/PG (%) factor critically influenced viscosity, while the rest of the terms (lecithin (%) and oat oil (%)) had a non-significant effect on viscosity. Keeping X

_{1}as the main factor, in the interval 20–30% a lower effect on viscosity was observed, with a minor decrease, followed by an elevation, attaining a significant effect of over 30%.

_{3}variable, by setting a high level of 2% as desired. The obtained solution indicated a system with X

_{1}: 40%, X

_{2}: 0.1%, and X

_{3}: 2% as the best fit to obtain a high response. Predicted viscosity was 263.83 cP, and the composite desirability was 0.8953. The solution of predictive response is presented in Table 9.

#### 3.8.2. Optimization of Mean Droplet Size (Ds)

_{1}term, oat oil (%)—X

_{3}term, and the two-way interaction between the two terms: X

_{1}X

_{3}(p < 0.05). Thus, the quadratic polynomial equation (Equation (7)) that fitted the response (Y

_{2}) is presented below:

_{1}term had a negative effect on Ds in the sense of minimization. By contrast, the X

_{3}term had a positive coefficient, including a positive effect on Ds elevation. Considering the interaction of the two variables, the X

_{1}X

_{3}term had a negative coefficient, associated with a negative effect directed through a minimization of Ds as a desirable consequence.

_{2}response presented in Figure 17, the two representative cases that explain particle dispersion in the domain of 1–40 nm, taking into consideration the significance of formulation variables, can be observed. In the first representation—case (a), the response is shown in gradient color signifying the variation of Ds from high dimension particles (dark blue color), through to small particles (red and orange colors), as a function of X

_{1}factor and X

_{2}factor. The response is specifically sensitive to the X

_{1}variation, and it can be deduced that this is due to the presence of curvature lines directed through the X axis specific to the Tween 80/PG variation. Additionally of note is the narrowing of an extremely small particle domain, associated with the selection of Tween 80/PG at the maximum level of 40%. A wider domain of particles around 4–8 nm was marked at the medium level of Tween 80/PG of 30%. An increase in droplet size was determined by decreasing in Tween 80/PG level to the inferior limit. On the other hand, the effect of lecithin was not significant for the response. Particles in the fixed domain can be formed either at low or high levels of lecithin.

_{1}factor and X

_{3}factor. Assuming the aforementioned considerations concerning X

_{1}X

_{3}interactions deduced from the regression equation, the Ds response is specifically sensitive to both variables. The highest sensitivity is attributed to the X

_{3}variable, and the contour lines oriented through the Y axis can be observed. Therefore, a red domain is specific for particles with a diameter under 5 nm, which can be formed when X

_{1}is settled to a low level and associated with a low level of X

_{3}. In the same manner, at a maximum level of X

_{1}, small particles were formed when X

_{3}was settled at any of the three levels of variation. Finally, setting up the X

_{1}and X

_{3}parameters at a medium level is favorable to attain small particles. An increase of X

_{3}to the maximum level, using medium levels of X

_{1}, will sustain the obtaining of particles in a larger domain of up to 40 nm. To conclude, concentrations of Tween 80/PG of 40% are required in order to attain small particles, if the oil phase is considered to be 2%, as well as in the case when the system contains a medium concentration of stabilizer mixture of 30%, prepared with small, medium, or a maximum level of oil phase.

_{2}variation as a function of Tween 80/PG (%) and lecithin (%), a surface in gradient color—case (a), and a wireframe plot—case (b) was projected. On the surface plot can be seen a 3D variation of Ds as function of Tween 80/PG (%), in the sense of minimization from a lighter green shade to a darker tone on the X axis direction, without significant influence of the lecithin level. Moreover, the wireframe model interprets these effects due to the embossed view presented with maximum and minimum points.

_{2}variation as a function of Tween 80/PG (%) and oat oil (%), a surface projected in gradient color—case (c), and the associated wireframe plot—case (d) can be seen. The surface plot shows the variation of Ds in the sense of minimization from a lighter blue color to a darker green tone with respect to the oil phase amount. The area of small Ds is attributed to the use of medium to high levels of Tween 80/PG at any concentration of oil phase. In addition, the points of maximum and minimum targeting of the Ds response are shown on the wireframe in case (d).

_{2}) required the study of variables’ main effects using factorial plots, the prediction of an optimal system, and its corroboration with experimental results. Thus, the main effects plot for Ds presented in Figure 19 represents a cumulative analysis which proves the impact of Tween 80/PG and oat oil factors as critical attributes for the droplet size of microemulsions, as earlier explained. These two factors are graphically presented in an opposite manner. A decrease in droplet size through the expected domain can be described, along with the increase in Tween 80/PG level and the minimization of oil level. Lecithin exerted a lesser effect on Ds with an isolated response observed at 0.5% in the direction of particle enlargement, but cannot be considered significant for the model.

_{1}: 35%, X

_{2}; 0.2214%, X

_{3}: 2%, with a composite desirability of 1.0000. The solution of predicted response is shown in Table 11.

#### 3.8.3. Optimization of Work of Adhesion

_{3}using a reduced second order polynomial equation, as a cause of the lack of significance for the model sustained by a full quadratic equation (p > 0.05). In this way, the regression equation (Equation (8)) is presented as follows:

_{3}) was significantly influenced by four terms presented in the regression equation, in particular: Tween 80/PG (%)—X

_{1}term, lecithin (%)—X

_{2}term, oat oil (%)—X

_{3}term, and a squared term ${\mathrm{X}}_{1}^{2}$, with p < 0.05 according to ANOVA analysis. It can be appreciated that Tween 80/PG (%) had a negative effect on the work of adhesion, along with oat oil (%), in the direction of response minimization. On the other hand, lecithin (%) was considered favorable to increase the response, along with the squared term attributed to Tween 80/PG (%).

_{3}response is further presented in Figure 21 as a Pareto chart, taking into consideration the main terms of impact for the work of adhesion of microemulsions to a solid surface. Thus, the main effect on the work of adhesion was considered to be produced by oat oil, followed by the stabilizer mixture of Tween 80/PG and its squared term, and lecithin as a lipophilic surfactant. The other squared terms implied in the model were insignificant.

_{3}response are presented in Figure 22 and bring out the main effects of the three formulation factors, highlighting three cases of interdependence, denoted (a), (b), and (c).

_{1}and X

_{3}factors can be observed. It is important to mention that the X

_{3}factor namely oat oil (%) prevails as the main ingredient in the modulation of adhesion. Both factors had a significant sensitivity for response assessment, being described by well-defined curved lines that were projected on the Y axis and the X axis. Following the gradient colors exposed below, it can be seen that at high levels of Tween 80/PG and low levels of oat oil, the work of adhesion had a maximum value of 81.00 mN/m. By increasing oil concentration, the work of adhesion slightly decreased to over 70 mN/m, then reaching over 60 mN at the maximum level of oil. In a similar fashion, at medium and minimum levels of Tween 80/PG and lower oil levels, the work of adhesion remained in the middle green area, around 65 mN/m. The increase in the oil phase level involved a decrease in the work of adhesion, described by extended yellow and orange-like patterns. The minimum W value was attributed to a small red domain, associated with the selection of Tween 80/PG (%) at medium level, and the oil phase at maximum level.

_{1}and the X

_{2}factor. In this situation, lecithin exerted a small effect on W, being considered a factor that was implied in the minimization of response on the entire domain of Tween 80/PG variation. This fact is justified by the presence of larger red and orange like areas related to W responses under 65 mN/m. The narrowed domain of response over 65 mN/m was determined by the X

_{1}factor. Hence, the contour lines are directed through abscissa, increasing the sensitivity response for Tween 80/PG.

_{3}response as a function of the X

_{2}and X

_{3}terms. Observed on the plot are a different allure of contour lines which are directed onto the ordinate, and to a lesser extent, through the abscissa, which is related to the sensitivity of the oil phase effect on the work of adhesion. The area related to a high response of over 60 mN/m is represented by the two green tone domains for systems with low or medium levels of oil associated with low or medium amounts of lecithin. An isolated case of high W over 65 mN/m is depicted on the blue area and is specific to the maximum level of lecithin and low oil concentrations. By contrast, variation in the work of adhesion in the opposite sense is associated with the increase of oil content, but independent of lecithin.

_{3}response in a 3D manner as a function of Tween 80/PG (%) and oat oil (%) in (a) and (b) cases. It can be observed the minimized effect of response in low levels of Tween 80/PG and high levels of oil phase, from lighter green through darker green-like zones. Points of maximum and minimum are better distinguished on the wireframe representation.

_{1}factor in the work of adhesion modulation, but without a significant effect on the X

_{2}term. The embossed appearance of the wireframe model shows maximum points related with high W values, when Tween 80/PG (%) was set at 40%, and medium or minimum points corresponding with the use of lower levels of the stabilizer.

_{3}response was determined in relationship with the X

_{2}and X

_{3}factors. On the surface plot, it can be seen that better results in the matter of adhesion were obtained with high levels of oil phase and low levels of lecithin, being marked by the lighter green tones. The results were well defined on the wireframe plot. The decrease in oil concentration and the increase in lecithin level assured intermediate and high responses for Y

_{3}.

_{3}), included as in the previous cases, and the main effects of variables are represented using factorial plotting. Thus, Figure 24 presents the main effects of the analyzed factors on the Y

_{3}response which are related with our previous findings. It can be observed that the X

_{1}and X

_{3}terms had a critical influence on the response: firstly, X

_{1}can, in a first phase, induce a decrease in the work of adhesion over a variation from low to medium levels (from 20% to 30%) and continue with a considerable increase in response (at 40%); secondly, the oil phase had an opposite behavior explained by the minimization of adhesion in high concentrations of 2%. Separately, lecithin had a diminished effect on adhesion in the selected domain of concentration and it was proportional to the X

_{1}effect in the limited domain of 30–40%, but not as powerful.

_{3}value of 60 mN/m, and then compare them with experimental versions. In this case, optimization parameters were configured in the sense of minimizing Y

_{3}, and resulted in two cases presented in Table 13. In the first case, constraints were imposed only on the oil variable as maximized. X

_{1}and X

_{3}variables had no constraints. The fitted solution proposed the following composition: X

_{1}: 33.53%, X

_{2}: 0.5%, X

_{3}: 2%, with a composite desirability of 1.0000. A second run was also deemed to be valuable. Constraints were imposed on both the X

_{1}and X

_{3}variables in order to be maximized. The solution was based on the following formula: X

_{1}: 40%, X

_{2}: 0.107%, X

_{3}: 2%, with a composite desirability of 1.0000.

_{3}response is marked by a blue intermittent line in all three cases. A red perpendicular line marks the optimized level of the variable. At their intersection, a gray line passes in the sense of response minimization as was previously pointed out.

## 4. Discussion

_{1}: 35%, X

_{2}: 0.2214%, X

_{3}: 2%, with a Ds of 5 nm. From the experimental results, two systems were in immediate area of response, specifically MELSA 8 and MELSA 11. It was admitted that only one system with the maximum level of X

_{1}and X

_{3}factors was declared as optimal, with respect to desired quality parameters, namely MELSA 8, with a Ds of 2.17 nm.

_{L/G}. Subsequently, the study of contact angle—CA at the contact with planar surfaces constitutes a method to evaluate the wettability of a system, particularly hydrophilicity or hydrophobicity nature, as it was reported in the study of Popa L. et al. [85]. Goniometry was rarely applied in the research of microemulsions, and it was considered that their behavior at the contact with surfaces is not fully unveiled [100]. Although, Butt U. et al. studied some topical microemulsions for ophthalmic delivery which were characterized as hydrophilic systems after the evaluation of contact angle. The values of contact angle varied between 12.2–25.2° at the contact with a hydrophilic surface, and 25.9–43.8° at the contact with a hydrophobic surface, which were chosen as models to explain the wetting behavior of microemulsions at corneal level [61]. Similarly, in topical delivery, skin is considered a low hydrophobic surface [101], and for this reason the analysis of drops was performed on glass slide. It was considered that contact angle rely on three properties: the surface tension of liquid (γ

_{L/G}), surface free energy and interaction forces at liquid-solid surface [61].

_{L/G}and CA parameters, were considered two key factors in the assessment of work of adhesion which was considered relevant for the optimization of microemulsions. In pendant drop model, γ

_{L/G}varied between 32.57–37.36 mN/m, describing stability of the systems characterized by low superficial tensions, and consequently low interfacial tensions between oil and water phases. In the study of Yati K. et al., the values of γ

_{L/G}reported after applying De Nouy ring method for microemulsions stabilized with Tween 80 and sorbitol, were placed between 39.76–43.4 mN/m [95]. Likewise, in CA model γ

_{L/G}was evaluated as a parameter implied in drop dynamics, succeeding adhesion promotion. It was observed that Tween 80/PG (%) had a powerful effect in the angle generation. Microemulsions had a hydrophilic character, with angles under 90°, placed between 40.74–57.91° and supported the wetting of the planar surface.

_{L/G}and enhance interactions with the surface. During the response surface analysis, it was revealed in this case the impact of all three formulation factors (X

_{1}, X

_{2}, X

_{3}) in modulation of adhesion, where oat oil exerted an important action on wettability behavior, in two opposite directions.

_{1}: 33.53%, X

_{2}: 0.5%, X

_{3}: 2%, and X

_{1}: 40%, X

_{2}: 0.107%, X

_{3}: 2%. For these solutions, two formulations from the experimental domain were proposed. MELSA 12 complied with the first run, but MELSA 8 was the most reliable model, due to the fact that MELSA 12 did not accomplish the requirements in the matter of clarity and viscosity. It can be appreciated that a higher level of oil, not only has the role of lipophilic carrier for an API, but also determines an affinity for the surface, specifically an intimate contact with lipidic structures of the skin membrane.

## 5. Conclusions

_{1}: Tween 80/PG (%), X

_{2}: Lecithin (%), and X

_{3}: Oat oil (%), as independent variables. Viscosity (Y

_{1}), mean droplet size (Y

_{2}) and work of adhesion (Y

_{3}) were analyzed as dependent parameters influenced by X

_{1}, X

_{2}and X

_{3}, by applying a response surface methodology.

_{1}factor highly influenced viscosity parameter. In high concentrations of 40%, viscous fluids with Newtonian behavior were formed, being defined by an adequate spreadability on surfaces which sustain their topical application. Based on the value of predicted viscosity of 263.83 cP, two systems were selected as optimal microemulsions, specifically MELSA 6 (287.77 cP) and MELSA 8 (217.73 cP). MELSA 8 was considered to be a model system due to the presence of 2% oil phase, as was proposed in the predictive analysis step.

_{1}and X

_{3}factors, in an opposite manner. Thus, increasing concentration of the X

_{1}factor through to the maximum level determined a decrease in droplet size, while the maximum level of X

_{3}was a priority for particle growing. The possibility to obtain a reduced droplet size by keeping X

_{1}and X

_{3}at the maximum level was studied. Throughout the optimization process, MELSA 8 and MELSA 11 were found to comply with a predicted response of droplet size of 5 nm, keeping the oil phase level at 2%. MELSA 8 had the highest level of Tween 80/PG of 40%, while MELSA 11 contained an intermediate level of the stabilizer. If the clarity parameter is considered, MELSA 8 remained the first choice among the group of microemulsions.

_{1}, X

_{2}and X

_{3}modulated the response in a different manner. X

_{3}was the key factor that supported adhesion at maximum level of the oil phase, increasing the contact with the surface. In this case, the maximum level of oil phase at 2% was maintained over the predictive analysis. Two responses were generated, emphasizing two microemulsions with Tween 80/PG 33.53% and 40% that can sustain wettability and adhesion with a work of adhesion of 60 mN/m. As a result, MELSA 12 with a medium level of Tween 80/PG was considered to be one of the optimal systems, with a response of 59.79 mN/m, but without respecting clarity criterion. By contrast, MELSA 8 exerted a work of adhesion of 62.13 mN/m, being related to the second predicted response.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Critical steps performed in the preparation process of microemulsions with salicylic acid.

**Figure 2.**Photo capture of MELSA 1–MELSA 13 microemulsions at one day after preparation—case (

**a**), and after one month—case (

**b**), visualized at room temperature, 25 ± 0.5 °C.

**Figure 3.**Graphical representation of conductivity values for microemulsions, dividing them as systems with (

**a**) High conductivity, (

**b**) Low conductivity, and (

**c**) Medium conductivity, depending on Tween 80/PG concentration.

**Figure 4.**Graphical representation of refractive index variation for microemulsions, considering three cases: (

**a**) systems with low RI values, (

**b**) systems with high RI values, and (

**c**) systems with medium RI values, depending on Tween 80/PG concentration.

**Figure 5.**Rheological profiles expressed as shear stress as a function of shear rate for MELSA 1–MELSA 13 microemulsions, tested at 25 ± 0.5 °C, proving their Newtonian behavior, divided in three groups: (

**a**) microemulsions with low viscosity, (

**b**) microemulsions with high viscosity, and (

**c**) microemulsions with intermediate viscosity.

**Figure 6.**Cumulant profiles of scattering intensity as function of droplet size for the most representative systems emphasized in optimization process: (

**a**) MELSA 6, (

**b**) MELSA 8, (

**c**) MELSA 11 and (

**d**) MELSA 12.

**Figure 7.**Representation of dynamic light scattering for the optimized microemulsion MELSA 8, using the in-situ head of ViscoKin particle analyzer, and five steps that are followed to assess the response related with the Cumulant algorithm.

**Figure 8.**Captures for microemulsion drops (1–13) in pendant drop model study, evaluating γ

_{LG}at 25 ± 0.5 °C.

**Figure 9.**Representation of contact angle, superficial tension and work of adhesion and their variation, for each microemulsion (1–13) in a comparative manner, after the contact angle model study.

**Figure 10.**Captures for microemulsion drops (1–13), placed on the glass slide, in contact angle model study, evaluating γ

_{LG}and CA at 25 ± 0.5 °C.

**Figure 11.**Pareto chart of standardized effects for viscosity response, emphasizing main factors implied in modulation of response, namely A: Tween 80/PG, and AA: Tween 80/PG × Tween 80/PG as squared term, where the factors AB: Tween 80/PG × Lecithin, B: Lecithin, AC: Tween 80/PG × Oat oil, C: Oat oil, BB: Lecithin × Lecithin, CC: Oat oil × Oat oil, and BC: Lecithin × Oat oil were insignificant.

**Figure 12.**Contour plots representing viscosity response (Y

_{1}) as function of (

**a**) Tween 80/PG (%), Lecithin (%), and (

**b**) Tween 80 (%), Oat oil (%).

**Figure 13.**Surface plots representing viscosity response (Y

_{1}) as a function of Tween 80/PG (%) and Lecithin (%): (

**a**) Surface representation in gradient color, and (

**b**) Wireframe model.

**Figure 14.**Main effects plot for viscosity response (Y

_{1}), considering individual effect of each independent variable.

**Figure 15.**Predictive optimization plot for viscosity response as function of three setting parameters: X

_{1}—maximized, X

_{2}—no constraints, and X

_{3}—maximized, with a composite desirability of 0.8953.

**Figure 16.**Pareto Chart of standardized effects for Ds response, emphasizing main factors implied in the definition of response, namely A: Tween 80/PG (%), C: Oat oil (%), and AC: Tween 80/PG (%) × Oat oil (%) as interaction term, where the factors B: Lecithin, BC: Lecithin × Oat oil, CC: Oat oil × Oat oil, AA: Tween 80/PG × Tween 80/PG, BB: Lecithin × Lecithin, and AB: Tween 80/PG × Lecithin were insignificant.

**Figure 17.**Contour plots representing Ds response (Y

_{2}) variation as function of: (

**a**) Tween 80/PG (%), Lecithin (%), and (

**b**) Tween 80/PG (%), Oat oil (%).

**Figure 18.**Surface plots representing: Ds response (Y

_{2}) as a function of Tween 80/PG (%) and lecithin (%) in two cases—(

**a**) Surface representation in gradient color; (

**b**) Wireframe model, and Ds response (Y

_{2}) as function of Tween 80/PG (%) and Oat oil (%) in two cases—(

**c**) Surface representation in gradient color; (

**d**) Wireframe model.

**Figure 19.**Main effects plot for Ds response (Y

_{2}), considering individual effect of each independent variable.

**Figure 20.**Predictive optimization plot for Ds response as function of three setting parameters: X

_{1}—kept between 30–40%, X

_{2}—without constraints, X

_{3}—maximized, with a composite desirability of 1.000.

**Figure 21.**Pareto Chart of standardized effect for W response, emphasizing the main factors implied in the definition of response, namely C: Oat oil (%), A: Tween 80/PG (%), AA: Tween 80/PG (%) × Tween 80/PG (%) as squared term, and B: Lecithin (%), where the factors CC: Oat oil × Oat oil and BB: Lecithin × Lecithin were insignificant.

**Figure 22.**Contour plots representing W response (Y

_{3}) variation as a function of: (

**a**) Tween 80/PG (%), Oat oil (%), (

**b**) Tween 80/PG (%), Lecithin (%), and (

**c**) Oat oil (%), Lecithin (%).

**Figure 23.**Surface plots representing: W response (Y

_{3}) as a function of Tween 80/PG (%) and Oat oil (%), in two cases—(

**a**) Surface representation in gradient color, (

**b**) Wireframe model; W response (Y

_{3}) as function of Tween 80/PG (%) and Lecithin (%), in two cases—(

**c**) Surface representation in gradient color, (

**d**) Wireframe model; W response (Y

_{3}) as function of Oat oil (%) and Lecithin (%) in two cases—(

**e**) Surface representation in gradient color, and (

**f**) Wireframe model.

**Figure 24.**Main effects plot for W response (Y

_{3}), considering individual effect of each independent variable.

**Figure 25.**Predicted optimization plots for W response (Y

_{3}) as function of three setting parameters: X

_{1}—without constraints, X

_{2}—without constraints, and X

_{3}—maximized, with a composite desirability of 1.0000.

**Figure 26.**Predicted optimization plots for W response (Y

_{3}) as function of three setting parameters: X

_{1}—maximized, X

_{2}—without constraints, and X

_{3}—maximized, with a composite desirability of 1.0000.

Formulation | ^{1} Tween 80/^{2} PG (2:1)(X _{1}) | ^{1} Lecithin(X _{2}) | ^{1} Oil(X _{3}) | ^{1,3} HA | ^{1,4} SA | ^{1} Water |
---|---|---|---|---|---|---|

MELSA 1 | 20 | 0.1 | 1.5 | 1 | 0.5 | 76.9 |

MELSA 2 | 40 | 0.1 | 1.5 | 1 | 0.5 | 56.9 |

MELSA 3 | 20 | 0.5 | 1.5 | 1 | 0.5 | 76.5 |

MELSA 4 | 40 | 0.5 | 1.5 | 1 | 0.5 | 56.5 |

MELSA 5 | 20 | 0.3 | 1 | 1 | 0.5 | 77.2 |

MELSA 6 | 40 | 0.3 | 1 | 1 | 0.5 | 57.2 |

MELSA 7 | 20 | 0.3 | 2 | 1 | 0.5 | 76.2 |

MELSA 8 | 40 | 0.3 | 2 | 1 | 0.5 | 56.2 |

MELSA 9 | 30 | 0.1 | 1 | 1 | 0.5 | 67.4 |

MELSA 10 | 30 | 0.5 | 1 | 1 | 0.5 | 67 |

MELSA 11 | 30 | 0.1 | 2 | 1 | 0.5 | 66.4 |

MELSA 12 | 30 | 0.5 | 2 | 1 | 0.5 | 66 |

MELSA 13 | 30 | 0.3 | 1.5 | 1 | 0.5 | 66.7 |

^{1}The values presented in the table for each component are expressed as percentage (%), and calculated for 20 mL of microemulsion;

^{2}PG—propylene glycol;

^{3}HA—Hyaluronic acid;

^{4}SA—Salicylic acid.

**Table 2.**Factorial plan for microemulsions with three independent variables and three levels of variation, coded for each factor; and dependent variables for study of the optimization process.

Factor | Variable | Low (−1) | Medium (0) | High (+1) |
---|---|---|---|---|

X_{1} | Tween 80/PG (%) | 20 | 30 | 40 |

X_{2} | Lecithin (%) | 0.1 | 0.3 | 0.5 |

X_{3} | Oil (%) | 1 | 1.5 | 2 |

**Table 4.**Results of pH, conductivity, refractive index, viscosity, and particle characteristics determined at 25 ± 0.5 °C, which describe the physical character of MELSA 1–MELSA 13 microemulsions.

Code | pH | Conductivity (μS/cm) | Refractive Index | Viscosity (cP) | Droplet Size (nm) | PDI | Zeta Potential (mV) |
---|---|---|---|---|---|---|---|

1 | 3.50 ± 0.01 | 1042.7 ± 1.2 | 1.3610 ± 0.0001 | 20.65 ± 2.05 | 11.35 ± 1.05 | 0.268 ± 0.011 | −1.98 ± 0.02 |

2 | 3.71 ± 0.01 | 506.0 ± 3.0 | 1.3874 ± 0.0001 | 292.69 ± 4.18 | 3.32 ± 1.85 | 0.091 ± 0.010 | −2.78 ± 0.05 |

3 | 3.49 ± 0.01 | 1088.0 ± 1.7 | 1.3624 ± 0.0001 | 27.89 ± 2.63 | 21.88 ± 1.25 | 0.039 ± 0.017 | −3.78 ± 0.05 |

4 | 3.70 ± 0.01 | 621.3 ± 0.6 | 1.3860 ± 0.0001 | 188.17 ± 3.03 | 5.88 ± 1.16 | 0.070 ± 0.010 | −2.14 ± 0.05 |

5 | 3.49 ± 0.01 | 1065.0 ± 1.0 | 1.3610 ± 0.0001 | 24.33 ± 1.15 | 3.43 ± 1.73 | 0.297 ± 0.075 | −3.83 ± 0.01 |

6 | 3.63 ± 0.02 | 524.3 ± 0.6 | 1.3863 ± 0.0001 | 287.77 ± 4.30 | 1.58 ± 0.20 | 0.119 ± 0.023 | −3.16 ± 0.06 |

7 | 3.48 ± 0.01 | 986.3 ± 1.5 | 1.3617 ± 0.0000 | 16.94 ± 2.16 | 37.72 ± 4.55 | 0.250 ± 0.025 | −2.80 ± 0.02 |

8 | 3.71 ± 0.01 | 542.3 ± 0.6 | 1.3880 ± 0.0001 | 217.73 ± 3.54 | 2.17 ± 1.54 | 0.352 ± 0.027 | −1.72 ± 0.03 |

9 | 3.54 ± 0.01 | 772.0 ± 1.0 | 1.3728 ± 0.0001 | 48.47 ± 3.06 | 5.14 ± 2.15 | 0.134 ± 0.018 | −1.43 ± 0.03 |

10 | 3.54 ± 0.01 | 728.7 ± 1.5 | 1.3729 ± 0.0001 | 34.82 ± 1.05 | 5.30 ± 2.53 | 0.218 ± 0.037 | −2.33 ± 0.05 |

11 | 3.53 ± 0.01 | 717.3 ± 1.5 | 1.3764 ± 0.0001 | 51.23 ± 3.33 | 6.45 ± 2.55 | 0.202 ± 0.011 | −2.38 ± 0.03 |

12 | 3.59 ± 0.01 | 786.0 ± 0.0 | 1.3735 ± 0.0001 | 39.29 ± 2.08 | 26.02 ± 3.78 | 0.557 ± 0.038 | −1.38 ± 0.05 |

13 | 3.56 ± 0.01 | 661.3 ± 1.5 | 1.3768 ± 0.0001 | 45.84 ± 2.67 | 4.11 ± 1.65 | 0.240 ± 0.021 | −2.38 ± 0.02 |

**Table 5.**Superficial parameters of microemulsions, explored during goniometric analysis at 25 ± 0.5 °C.

Code | Models Applied in Goniometric Study | |||||
---|---|---|---|---|---|---|

Pendant Drop | Contact Angle Model | |||||

Vol (μL) | γ_{LG} (mN/m) | Vol (μL) | γ_{LG} (mN/m) | CA (°) | W (mN/m) | |

1 | 6.56 ± 0.04 | 34.80 ± 0.35 | 5.30 ± 0.17 | 35.78 ± 1.96 | 45.51 ± 3.06 | 60.71 ± 1.96 |

2 | 6.53 ± 0.10 | 32.57 ± 0.34 | 6.53 ± 1.27 | 41.23 ± 1.89 | 50.27 ± 0.76 | 67.52 ± 2.99 |

3 | 6.65 ± 0.02 | 35.55 ± 0.03 | 5.00 ± 0.48 | 36.78 ± 0.72 | 46.59 ± 1.44 | 62.04 ± 0.53 |

4 | 6.56 ± 0.05 | 33.36 ± 0.16 | 6.17 ± 0.30 | 45.59 ± 1.50 | 49.01 ± 2.40 | 76.91 ± 2.90 |

5 | 7.15 ± 0.02 | 37.36 ± 0.16 | 6.95 ± 0.13 | 41.31 ± 1.67 | 40.74 ± 0.70 | 72.61 ± 3.08 |

6 | 6.47 ± 0.12 | 33.69 ± 0.24 | 6.58 ± 0.43 | 52.90 ± 1.82 | 57.91 ± 0.38 | 81.00 ± 2.49 |

7 | 6.84 ± 0.07 | 36.25 ± 0.21 | 6.94 ± 0.35 | 33.93 ± 0.70 | 43.27 ± 1.29 | 58.64 ± 1.25 |

8 | 6.72 ± 0.17 | 33.73 ± 0.24 | 6.49 ± 0.14 | 40.14 ± 0.86 | 56.78 ± 2.30 | 62.13 ± 1.66 |

9 | 6.36 ± 0.09 | 33.61 ± 0.10 | 5.79 ± 0.15 | 37.63 ± 1.81 | 51.93 ± 1.62 | 60.80 ± 2.38 |

10 | 7.10 ± 0.21 | 35.85 ± 0.29 | 6.23 ± 0.67 | 42.87 ± 3.95 | 54.04 ± 2.61 | 68.14 ± 7.88 |

11 | 6.76 ± 0.18 | 35.37 ± 0.85 | 6.94 ± 0.21 | 33.38 ± 0.46 | 54.59 ± 1.86 | 52.72 ± 1.44 |

12 | 7.05 ± 0.11 | 36.12 ± 0.35 | 7.11 ± 0.70 | 35.98 ± 0.99 | 48.50 ± 2.49 | 59.79 ± 1.39 |

13 | 6.52 ± 0.08 | 34.11 ± 0.08 | 7.70 ± 0.44 | 35.42 ± 0.29 | 46.75 ± 4.14 | 59.64 ± 1.62 |

**Table 6.**Results of ANOVA-Single factor test, emphasizing the variance of γ

_{LG}in the two groups: γ

_{LG}determined in pendant drop model, and γ

_{LG}determined in contact angle model study at 25 ± 0.5 °C.

SUMMARY | ||||||
---|---|---|---|---|---|---|

Groups | Count | Sum | Average | Variance | ||

Column 1 | 13 | 452.37 | 34.798 | 1.9753 | ||

Column 2 | 13 | 512.94 | 39.457 | 29.74 | ||

ANOVA | ||||||

Source of Variation | Sum of Squares | df | Mean of Squares | F | p-Value | F Crit |

Between Groups | 141.10 | 1 | 141.10 | 8.8975 | 0.0065 | 4.2596 |

Within Groups | 380.61 | 24 | 15.86 | |||

Total | 521.72 | 25 |

**Table 7.**Optimization parameters presented as function of independent variables analyzed using response surface methodology for microemulsions MELSA 1–MELSA 13.

Variable | Independent Variables | Dependent Variables | |||||
---|---|---|---|---|---|---|---|

X_{1} | X_{2} | X_{3} | Y_{1} | Y_{2} | Y_{3} | ||

Formulation | Tween 80/PG (%) | Lecithin (%) | Oil (%) | ^{1} Clarity | Viscosity (cP) | Droplet Size (nm) | Adhesion Work (mN/m) |

MELSA 1 | 20 | 0.1 | 1.5 | ++ | 20.65 ± 2.05 | 11.35 ± 1.05 | 60.71 ± 1.96 |

MELSA 2 | 40 | 0.1 | 1.5 | +++ | 292.69 ± 4.18 | 3.32 ± 1.85 | 67.52 ± 2.99 |

MELSA 3 | 20 | 0.5 | 1.5 | ++ | 27.89 ± 2.63 | 21.88 ± 1.25 | 62.04 ± 0.53 |

MELSA 4 | 40 | 0.5 | 1.5 | +++ | 188.17 ± 3.03 | 5.88 ± 1.16 | 76.91 ± 2.90 |

MELSA 5 | 20 | 0.3 | 1 | +++ | 24.33 ± 1.15 | 3.43 ± 1.73 | 72.61 ± 3.08 |

MELSA 6 | 40 | 0.3 | 1 | +++ | 287.77 ± 4.30 | 1.58 ± 0.20 | 81.00 ± 2.49 |

MELSA 7 | 20 | 0.3 | 2 | + | 16.94 ± 2.16 | 37.72 ± 4.55 | 58.64 ± 1.25 |

MELSA 8 | 40 | 0.3 | 2 | +++ | 217.73 ± 3.54 | 2.17 ± 1.54 | 62.13 ± 1.66 |

MELSA 9 | 30 | 0.1 | 1 | +++ | 48.47 ± 3.06 | 5.14 ± 2.15 | 60.80 ± 2.38 |

MELSA 10 | 30 | 0.5 | 1 | +++ | 34.82 ± 1.06 | 5.30 ± 2.53 | 68.14 ± 7.88 |

MELSA 11 | 30 | 0.1 | 2 | + | 51.23 ± 3.33 | 6.45 ± 2.55 | 52.72 ± 1.44 |

MELSA 12 | 30 | 0.5 | 2 | + | 39.29 ± 2.08 | 26.02 ± 3.78 | 59.79 ± 1.39 |

MELSA 13 | 30 | 0.3 | 1.5 | +++ | 45.84 ± 2.67 | 4.11 ± 1.65 | 59.64 ± 1.62 |

^{1}Notation of clarity parameters: “+” was attributed for an opalescent system, “++”—for a low clarity system, and “+++”—for a high clarity system.

Source | DF | Sum of Squares | Mean of Squares | F-Value | p-Value |
---|---|---|---|---|---|

Model | 9 | 132,377 | 14,709 | 26.49 | 0.010 |

Linear | 3 | 102,978 | 34,326 | 61.83 | 0.003 |

X_{1} | 1 | 100,475 | 100,475 | 180.97 | 0.001 |

X_{2} | 1 | 1887 | 1887 | 3.40 | 0.162 |

X_{3} | 1 | 616 | 616 | 1.11 | 0.370 |

Square | 3 | 25,294 | 8431 | 15.19 | 0.026 |

${\mathrm{X}}_{1}^{2}$ | 1 | 18,463 | 18,463 | 33.25 | 0.010 |

${\mathrm{X}}_{2}^{2}$ | 1 | 26 | 26 | 0.05 | 0.843 |

${\mathrm{X}}_{3}^{2}$ | 1 | 2 | 2 | 0.00 | 0.954 |

2-Way Interaction | 3 | 4105 | 1368 | 2.46 | 0.239 |

X_{1}X_{2} | 1 | 3123 | 3123 | 5.62 | 0.098 |

X_{1}X_{3} | 1 | 981 | 981 | 1.77 | 0.276 |

X_{2}X_{3} | 1 | 1 | 1 | 0.0 | 0.973 |

Error | 3 | 1666 | 555 | ||

Total | 12 | 134,042 |

**Table 9.**Response optimization for viscosity by maximizing the response and keeping X

_{3}at maximum level.

Solution | X_{1} | X_{2} | X_{3} | Y_{1} | 95% Confidence Interval | Composite Desirability |
---|---|---|---|---|---|---|

Tween 80/PG (%) | Lecithin (%) | Oat Oil (%) | Viscosity (cP) | |||

1 | 40 | 0.1 | 2 | 263.83 | (170.1, 357.6) | 0.8953 |

Source | DF | Sum of Squares | Mean of Squares | F-Value | p-Value |
---|---|---|---|---|---|

Model | 9 | 1448.02 | 160.89 | 9.95 | 0.042 |

Linear | 3 | 1011.19 | 337.06 | 20.85 | 0.016 |

X_{1} | 1 | 471.71 | 471.71 | 29.18 | 0.012 |

X_{2} | 1 | 134.64 | 134.64 | 8.33 | 0.063 |

X_{3} | 1 | 404.84 | 404.84 | 25.04 | 0.015 |

Square | 3 | 42.83 | 14.28 | 0.88 | 0.539 |

${\mathrm{X}}_{1}^{2}$ | 1 | 27.96 | 27.96 | 1.73 | 0.280 |

${\mathrm{X}}_{2}^{2}$ | 1 | 20.57 | 20.57 | 1.27 | 0.341 |

${\mathrm{X}}_{3}^{2}$ | 1 | 29.91 | 29.91 | 1.85 | 0.267 |

2-Way Interaction | 3 | 393.99 | 131.33 | 8.12 | 0.060 |

X_{1}X_{2} | 1 | 15.88 | 15.88 | 0.98 | 0.395 |

X_{1}X_{3} | 1 | 283.92 | 283.92 | 17.56 | 0.025 |

X_{2}X_{3} | 1 | 94.19 | 94.19 | 5.83 | 0.095 |

Error | 3 | 48.50 | 16.17 | ||

Total | 12 | 134,042 |

**Table 11.**Response optimization for mean droplet size (Ds) by minimizing the response and keeping X

_{3}at maximum level.

Solution | X_{1} | X_{2} | X_{3} | Y_{2} | 95% Upper Confidence interval | Composite Desirability |
---|---|---|---|---|---|---|

Tween 80/PG (%) | Lecithin (%) | Oat Oil (%) | Ds (nm) | |||

1 | 35.0 | 0.2214 | 2 | 5 | (11.84) | 1.0000 |

Source | DF | Sum of Squares | Mean of Squares | F-Value | p-Value |
---|---|---|---|---|---|

Model | 6 | 702.080 | 117.013 | 10.08 | 0.006 |

Linear | 3 | 523.165 | 174.388 | 15.03 | 0.003 |

X_{1} | 1 | 140.784 | 140.784 | 12.3 | 0.013 |

X_{2} | 1 | 78.940 | 78.940 | 6.80 | 0.040 |

X_{3} | 1 | 303.442 | 303.442 | 26.15 | 0.002 |

Square | 3 | 178.915 | 59.638 | 5.14 | 0.043 |

${\mathrm{X}}_{1}^{2}$ | 1 | 135.300 | 135.300 | 11.66 | 0.014 |

${\mathrm{X}}_{2}^{2}$ | 1 | 0.663 | 0.663 | 0.06 | 0.819 |

${\mathrm{X}}_{3}^{2}$ | 1 | 3.636 | 3.636 | 0.31 | 0.596 |

Error | 6 | 69.630 | 11.605 | ||

Total | 12 | 771.710 |

**Table 13.**Response optimization for work of adhesion (W), with two possible solutions, by minimizing the response to 60 mN/m.

Solution | X_{1} | X_{2} | X_{3} | Y_{3} | 95% Confidence Interval | Composite Desirability |
---|---|---|---|---|---|---|

Tween 80/PG (%) | Lecithin (%) | Oat Oil (%) | W (mN/m) | |||

1 | 33.53 | 0.5 | 2 | 60.00 | (48.66, 71.34) | 1.0000 |

2 | 40 | 0.107 | 2 | 60.00 | (44.63, 75.37) | 1.0000 |

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Anicescu, M.-C.; Dinu-Pîrvu, C.-E.; Talianu, M.-T.; Ghica, M.V.; Anuța, V.; Prisada, R.-M.; Nicoară, A.C.; Popa, L.
Insights from a Box–Behnken Optimization Study of Microemulsions with Salicylic Acid for Acne Therapy. *Pharmaceutics* **2022**, *14*, 174.
https://doi.org/10.3390/pharmaceutics14010174

**AMA Style**

Anicescu M-C, Dinu-Pîrvu C-E, Talianu M-T, Ghica MV, Anuța V, Prisada R-M, Nicoară AC, Popa L.
Insights from a Box–Behnken Optimization Study of Microemulsions with Salicylic Acid for Acne Therapy. *Pharmaceutics*. 2022; 14(1):174.
https://doi.org/10.3390/pharmaceutics14010174

**Chicago/Turabian Style**

Anicescu, Maria-Cristina, Cristina-Elena Dinu-Pîrvu, Marina-Theodora Talianu, Mihaela Violeta Ghica, Valentina Anuța, Răzvan-Mihai Prisada, Anca Cecilia Nicoară, and Lăcrămioara Popa.
2022. "Insights from a Box–Behnken Optimization Study of Microemulsions with Salicylic Acid for Acne Therapy" *Pharmaceutics* 14, no. 1: 174.
https://doi.org/10.3390/pharmaceutics14010174