*2.2. Methods*

2.2.1. Experimental Design and Optimization of Self-Nanoemulsion Formulations

With reference to this study, the Box–Behnken design (BBD) was pursued to scrutinize the influence of independent variables on dependent ones. Twenty-three formulations were made with the chosen design using Design-Expert Version 13 Software (Stat-Ease, Inc., Minneapolis, MN, USA). The selected statistical design produced various relationships between the independent variables, and they are summarized in Table 1. The three explored factors were the amount of Gr oil in milligrams (A), amount of PV in milligrams (B), and hydrophilic-lipophilic balance (HLB) of the surfactant mixture (Tween80/Span80) (C) in the prepared nanoemulsion. The estimated responses were the globule size of the prepared NEs (Y1) and the mean burn wound diameter (Y2). Preliminary studies were followed to select the factors' levels.

**Table 1.** Independent variables and their levels, along with dependent variables and their constraints, in the BBD of the nanoemulsion formulations.


#### 2.2.2. Gr-PV-NEs Preparation

The production procedure had two steps. The first step was the fabrication of the plain SNEDDS, in which a Gr oil concentration of 10%, 20%, or 30% (according to the design) was blended with 60% of the surfactant mixture with an HLB of 11, 12, or 13 (according to the design) and then brought to 100% by the Transcutol cosurfactant. In the second step, PV was mixed with the plain NEs with the aid of sonication in concentrations of 10, 20, or 40 mg/g of the prepared self-nanoemulsion according to the design, as shown in Table 2.


**Table 2.** BBD and responses of Gr-PV-NEs.

#### 2.2.3. Determination of Globule Size

The droplet size and polydispersity index (PDI) of each of the fabricated Gr-PV-NEs was examined by diluting 100 μL of each formulation with 900 μL of double distilled water in a volumetric flask. Next, the diluted samples were vigorously mixed, and 100 μL of the dispersed sample was withdrawn to determine its droplet size; this was done with a Zeta track particle size analyzer (Microtrac, Inc., Montgomeryville, PA, USA) [38]. Assessment of the sample was carried out in triplicate, and the results were presented as the mean ± standard deviation (SD). PDI is a good tool for evaluating foemulation homogeneity.

#### 2.2.4. Assessment of Wound Healing

#### Animal Handling and Care

The guidelines of the Animal Ethics Committee, Beni Suef Center for Laboratory Animals, Beni Suef, Egypt, were adopted in animal handling and care. Investigators abided by the guidelines articulated in the Declaration of Helsinki and its Guiding Principles in the Care and Use of Animals (NIH Publication No. 85-23, 1985 revision) and adopted the ethical approval of the protocol before experimentation (Approval No. 26/4-21).

The experimental rats were obtained and kept in laboratory cages with free access to food and water. Animals' suffering was minimized according to the guidelines. The animals were kept for a minimum of 14 days prior to the investigation under standard conditions of temperature (25 ± 1 ◦C) and relative humidity (55 ± 5%) with a 12 h light and 12 h dark cycle.

Sixty-nine rats were used in the study; they were divided into 23 groups, with 3 rats per group. Each group was treated with one of the formulations developed by the experimental design. An intraperitoneal dose of thiopental of 15 mg/kg was administered simultaneously with an intramuscular dose of 25 mg/kg of ketamine. The hair on the rat's back was shaved, and the skin was sterilized with an alcohol swab. Following that, burn

wounds were induced on the back skin using 1.5 cm skin biopsy heated bunches. Then, the investigated formulation for each group was applied once daily for a period of 14 days [39].

#### Measurement of Burn Wound Diameter

After the application of each formulation once a day for 14 days, a caliper was used to measure the average diameter of the induced wound lesions in each group to evaluate the second response for each formulation. Measurements were done in triplicate, and the findings were introduced as the mean ± SD.
