The artificial intelligence and design of experiment assisted in the development of progesterone-loaded solid-lipid nanoparticles for transdermal drug delivery

The artificial intelligence and design of experiment assisted in the development of progesterone-loaded solid-lipid nanoparticles for transdermal drug delivery


Introduction
Progesterone (PG), the inherent progestin, is a significant gonadal hormone primarily synthesized by the ovary in females and by the testes and adrenal cortex in males (Sato et al. 2021).PG hormones play essential roles in the reproductive system and demonstrate protective effects in various in vivo experimental models that simulate specific pathological aspects observed in age-related neurodegenerative diseases, such as Alzheimer's disease (AD) (Stein 2008;Singh and Su 2013a;Wareham et al. 2022).Because female menopause results in the precipitous decline not only in circulating estrogens but also in circulating PG, it leads to an elevated risk of AD during the postmenopausal period (Singh and Su 2013b;Kim et al. 2021).There are several mechanisms through which PG exhibits neuroprotective effects.For example, the classical genomic mechanism of PG action may be involved in regulating the expression of neurotrophins, potentially promoting cell survival.Major PG metabolites, including allopregnanolone, have been shown to contribute to neuroprotective effects.Another mechanism involves allopregnanolone interacting with membrane-associated receptors linked to ion channels, such as the GABA A receptor system, suggesting a role in mediating protective effects (Guennoun 2020).Alzheimer's disease is a neurodegenerative disorder marked by a gradual decline in cognitive function.The development and advancement of this condition are linked to the accumulation of amyloid-beta (Aβ) protein outside cells and hyperphosphorylated tau protein within cells.PG, which is one of the neurosteroids, can reduce tau hyperphosphorylation and diminish Aβ-induced cytokine production and inflammation in cultured astrocytes (Bassani et al. 2023).
PG belongs to BCS class II, characterized by poor aqueous solubility and labeled as 'practically insoluble' according to the solubility classification adopted by USP and Ph.Eur.PG has a log P value of 3.87.Consequently, the therapeutic use of PG was restricted due to its highly hydrophobic nature as a steroid hormone with very low solubility in water (Suriyaamporn et al. 2024).Additionally, developing a formulated PG for transdermal drug delivery posed challenges because of its solubility (Aumklad et al. 2022).Therefore, solid-lipid nanoparticles (SLN), lipid-based formulations, were developed in this study.In recent years, much attention has been focused on SLN for developing hydrophobic drug formulations to improve transdermal drug delivery (Charoenputtakun et al. 2014;Akombaetwa et al. 2023).SLN are colloid nanocarriers designed to regulate drug delivery systems with an average particle size ranging between 50-1000 nm.SLN have demonstrated various advantages over other colloid nanocarriers, including facilitating controlled drug release, targeting drugs in the CNS, achieving high transdermal bioavailability, enhancing drug stability, enabling the combination of hydrophilic drugs, exhibiting non-toxicity, avoiding the use of organic solvents, and allowing easy large-scale production (Gastaldi et al. 2014;Öztürk et al. 2018).The SLN are easily prepared by ho-mogenizing the liquid mixtures of lipids and emulsifiers with an aqueous phase.However, the components of SLN and the techniques used in the process are important factors that affect SLN properties and stability (Ghasemiyeh and Mohammadi-Samani 2018).
The application of artificial intelligence (AI) and design of experiments (DoE) methods has the potential to revolutionize the way formulation development is designed and optimized (Aksu et al. 2012;Sheetal 2021).DoE is one of the most widely used statistical tools for screening critical quality factors that affect product development.Moreover, it can systematically optimize the entire formulation based on multiple critical quality factor criteria.The utilization of DoE in pharmaceutical development is an appropriate method to establish a connection between formulation and process parameters with the critical quality factors of the pharmaceutical product (Suriyaamporn et al. 2021;Dawoud et al. 2023).This approach facilitates enhanced comprehension of a process, allowing for the definition of its optimal operational conditions.Currently, AI has begun to play a role and is gaining increased attention in various fields, especially in the field of pharmacy.This AI technology can assist in making decisions for complex problems, accelerate the discovery and development of nanomedicines, and also help in predicting satisfactory outcomes (Adir et al. 2020;Figueiró Longo et al. 2023).AI has found application across various domains in nanomedicine, particularly in handling extensive and intricate datasets.In this study, artificial neural networks (ANNs), inspired by biological neurons, are among the most widely used AI techniques.ANNs recognize patterns in a collection of datasets, creating predictive models through a learning or training process (Tan et al. 2023;Habeeb et al. 2024).The development of ANN models capable of forecasting the physicochemical properties of nanocarriers holds the potential to streamline the advancement of nanomedicine.This could result in reduced development time, efficient resource utilization, and expedited production of dependable nanoparticle models for drug delivery (Rebollo et al. 2022;Di Francesco et al. 2023;Skepu et al. 2023).
This study marked the first-time development of PG-SLN for transdermal drug delivery to slow neurodegenerative disorders in postmenopausal women.This study is still a challenge due to the limited number of research initiatives in this area.The objective of this study was to design and develop PG-SLN using AI and DoE techniques to predict the appropriate formulation for transdermal drug delivery in Alzheimer's patients.

The preparation of PG-SLN
PG-SLNs were prepared using the emulsification-ultrasonication method.Briefly, stearic acid was melted in a water bath at 80 °C.Subsequently, medium-chain triglycerides (MCT) and PG were added to the molten solid lipid.The homogeneous lipid phase was slowly dropped and dispersed into the aqueous phase, containing Pluronic F-127, at 80 °C using a probe sonicator (PRO Scientific Inc., VCX 130 PB sonicator and 3 mm microtip, Oxford, USA) at 40 Hz for 20 minutes.The resulting lipid dispersion was cooled down in an ice bath to obtain PG-SLN.Finally, the excess lipid and PG were centrifuged (Eppendorf™ Centrifuge 5810R, Hamburg, Germany) at 12,000 rpm, 4 °C for 10 minutes.Seventy-seven different formulations, guided by DoE, were prepared by varying the critical quality factors, following in Table 1.

The characterization of PG-SLN
The particle size (PS), polydispersity index (PDI), and zeta potential (ZP) of the PG-SLNs were measured using dynamic light scattering (DLS, Zetasizer Nano Series, Malvern Instruments, DTS version 4.10).Before measurement, the PG-SLNs were appropriately diluted with deionized (DI) water and mixed using a vortex mixer to obtain a homogeneous formulation.Subsequently, the formulations were filled into a disposable folded capillary cell and measured.The morphology of PG powder and selected PG-SLN was observed under the scanning electron microscope (SEM, Mira TC, Czech Republic) at a beam voltage of 15.0 kV with 10 kx magnification.The particle size of PG-SLN was measured in diameter and compared with DLS results.

PG content determination using HPLC
The analysis of the PG amount was conducted using HPLC.The PG-SLNs were appropriately diluted with methanol and filtered through a 0.45-µm syringe filter.Chromatographic separation was achieved using a Zorbax Eclipse XDB-C18 column (250×4.6 mm, 5 μm pore size, Agilent, USA), maintained at 30 °C.The mobile phase consisted of 90%v/v methanol and 10%v/v ultrapure water at a flow rate of 1 mL/min, with detection performed at a wavelength of 240 nm.The retention time was approximately 4.4 min [4].The percentage of drug loading (%DL) was calculated from Equation 1.

Amount of PG in PG SLN
Amount of initial PG loading 100 %DL (1)

Design of Experiments for screening critical quality factors
The screening study was conducted to identify critical quality factors.The components of PG-SLNs were the main factors affecting PS, PDI, ZP, and %DL in SLNs.
A central composite design (CCD) with four experimental factors was investigated in Table 1.A total of 77 runs were performed with triplication, randomly selected (Suppl.material 1: table S1).The significant factors were then selected and evaluated for their relationship with outcomes.Based on the results from the screening study, a 3D response surface area (RSA) was used to describe the relationship of these factors.Furthermore, to explore the optimal conditions for the PG-SLNs formulation with the lowest PS, PDI, highest amount of drug, and ZP more than ±30, were determined.The total formulation from optimal conditions and screening study were used as a dataset to generate a prediction model in ANNs.

Artificial Neural Network model and prediction model assessment
According to the DoE analysis, the dataset was used as input factors to generate a prediction model.The PS, PDI, ZP, and %DL were used as output factors.To create a pattern recognition model of the ANN architecture, two hidden layers with 5 and 2 neurons, respectively, were created.Before generating the prediction model, the dataset was appropriately cleaned and normalized to avoid significant biases.Cross-validation was applied to the dataset before training and testing the ANN, with a ratio of 70% for training and 30% for testing.Therefore, the number of data points for training and testing was 54 and 23, respectively.The learning rate was set at 0-1.2, with a momentum of 0.8, and the training cycle was set to 1-1200.These hyperparameters were defined after reaching an R 2 value of over 0.85.To evaluate the prediction model, the 11 experiments of PG-SLNs at various stages in the DoE were applied to the prediction model to generate predicted outputs (Suppl.material 1: table S2).Subsequently, the outcomes of the 11 experiments were formulated and measured.The root mean square error (RMSE) was reported for the accuracy of the prediction model, following Equation 2. The correlation of learning rate and training cycles versus RMSE in ANNs were plotted to explain accuracy when increasing the number of learning rate and

In vitro transdermal drug delivery
The in vitro transdermal drug delivery of PG suspension, optimal PG-SLNs, and optimal PG-SLNs with 2% limonene, each containing an equal drug amount, was conducted using a Franz-diffusion cell.Limonene was employed as a skin enhancer.Neonatal porcine skin was isolated from the subcutaneous layer and cleansed with phosphate buffer saline (PBS, pH 7.4).In the Franz-diffusion cell, the receiver compartment was filled with PBS (pH 7.4) and maintained at a constant temperature of 37±0.5 °C with continuous stirring.The neonatal porcine skin was affixed to the receptor compartment, with the epidermis facing upward toward the donor compartment.Each formulation (1 ml) was added to the donor compartment.Samples (0.5 ml each) were collected from the receptor compartment at predetermined time intervals (0, 0.5, 1, 2, 4, 6, 8, 12, 24, 48 and 120 h) and replaced with an equivalent amount of PBS (pH 7.4) to maintain a sink condition.After transdermal drug delivery, the porcine skin was sliced into small pieces and extracted in 10 ml of methanol using probe sonication (40 Hz).The collected samples were filtered before analysis by HPLC.The percentage of PG permeation versus time and percentage of PG remaining in the skin for each formulation were plotted and reported, respectively.The %PG permeation and % PG remaining in the skin were calculated following Equation 3 and 4, respectively.
%PG permeation Amountof PG in receptor Amountof PG in formulation 100 (3) %PG remaining in the skin Amountof PG in the skin Amountof PG in formulation 100 (4) The skin permeation profiles parameters, which elucidated how PG behaved in delivering across skin tissue.Parameters such as cumulative PG amount over 120 h per area (Q 120 /A), flux (J), lag time (t lag ), diffusion coefficient (K d ), and permeability coefficient (K p ) have been reported.J and t lag can be determined by analyzing the slope and intercept on the time-axis graph of Q 120 /A versus time, respectively.The diffusion coefficient (K d ) and permeability coefficient (K p ) were calculated using equations Equation 5and 6, respectively.
Meanwhile, h represents the thickness of the skin tissue, and C d denotes the concentration of PG in the donor.

In vitro cytotoxicity
The cytotoxicity of PG-suspension, optimal PG-SLNs and PG-SLNs with 2% limonene were determined using an MTT test against SH-SY5Y cells, a human neuroblastoma cell line.The day before the experiment, SH-SY5Y cells were seeded onto 96-well plates at a density of 10,000 cells/ well with Dulbecco's modified Eagle's medium (DMEM) supplemented with 10% fetal bovine serum and grown at 37 °C in a humidified 5% CO 2 incubator.After 24 h of incubation, different concentrations of each formulation were added to each well and incubated for an additional 24 h.Following treatment, the cytotoxicity of all formulations was assessed using MTT solution at a final concentration of 1 mg/mL in each well for 3 h.After removing the media, the formazan crystals in the cells were dissolved by adding 100 µL of dimethyl sulfoxide (DMSO) to each well.The optical density (OD) of each well was measured using an automated microplate reader (Multimode plate reader, Model Victor NivoTM, PerkinElmer, Hamburg, Germany) at 550 nm.The percentages of cell viability of SH-SY5Y cells were calculated using Equation 7. The control group (DI water) was assumed to have 100% cell viability, serving as the baseline.

Statistical analyses
The DoE process for screening critical quality factors was analyzed in Design Expert version 11.The prediction model generated by ANNs was developed using RapidMiner Studio version 10.3 and PyCharm version 2023.3.2, utilizing the scikit-learn library (Pedregosa et al. 2011).The cross-validation process in ANNs was considered successful when the achieved R 2 value exceeded 0.85.To assess the predictive performance of the model, the RMSE was applied.The research was conducted in triplicate, and the outcomes were reported as averages along with standard deviations (SD).For comparing two groups, the two-sided independent t-test was employed.
For multiple groups, one-way ANOVA with a post-hoc test was used.Statistical significance was determined at p-value < 0.05.This investigation utilized SPSS ® software version 19.

Design of Experiments for screening critical quality factors
A screening of critical quality factors was conducted in this study.Based on a previous study, the important factor that mostly affected the physicochemical properties was the component of SLN and drug loading.Seventy-seven combinations of PG-SLN were considered in terms of PS, PDI, ZP, and %DL, generated by DoE software.All factors were significant to the outcome.Fig. 2 shows the relationship between each factor and the outcome, with R 2 greater than 0.7.The 3D-RSA shows that the particle size is in the range of 100 to 500 nm, PDI in the range of 0.01-0.4,ZP in the range of -11 to -38 mV, and %DL in the range of 1.34 to 109.03%.To achieve optimal values for PS, PDI, ZP, and %DL, an additional 10 selected runs from the 3D-RSA were performed to provide more information and a deeper analysis.The 3D-RSA analysis revealed a remarkable impact on the PS and %DL in PG-SLN when the stearic acid concentration increased.In contrast, the decrease in PDI was affected by the increasing stearic acid and low concentration of MCT.Meanwhile, increasing the concentration of Pluronic F127 led to an increase in ZP and %DL.

Artificial Neural Network model and model prediction assessment
Recently, the application of ANN has been employed to perform more intricate analyses and overcome specific constraints associated with the DoE methodology.The PG-SLN was composed of 5% stearic acid + 1.76% MCT + 0.30% Pluronic F-127 + 0.5% PG from predicted model was selected for skin permeation study and neural cell viability.The PS, PDI, ZP, and %DL were 368.01±2.98 nm, 0.22±0.01,-33.73±1.23 and 87.04±17.43%,respectively.The morphology of the selected PG-SLN under SEM revealed a spherical shape, as illustrated in Fig. 5B.The particle size of PG powder was significantly larger than that of SLN-PG, measuring around 10.0±3.21 µm.The particle sizes obtained from both DLS and SEM exhibited non-significant differences.
The skin permeation profile results were presented in Table 3.The values for t lag , J, Q 120 /A, K d , and K p of PG-SLNs with 2% limonene were significantly higher than others.The SLN formulation exhibited a significantly shorter lag time compared to the PG suspension.Therefore, the shorter lag time in SLN formulations resulted in a higher K d .Furthermore, the SLN formulation demonstrated an improvement in the K p of PG into the skin tissue.

In vitro cytotoxicity
The viability results of SH-SY5Y cells treated with PG-suspension, optimal PG-SLNs, PG-SLNs with 2% limonene, and the control were reported in Fig. 7. SH-SY5Y cells were treated at various concentrations (0.1-500 μg/mL) for 24 h.For the PG-suspension, optimal PG-SLNs, and PG-SLNs with 2% limonene, concentrations ranging from 1 to 0.1 μg/mL exhibited over 80% cell viability, with no significant differences observed.The cell viability of all PG formulations showed a slight decline when the concentration exceeded 1 μg/mL, implying a dose-dependent response due to the mild cytotoxicity associated with PG.

Stability
The stability of optimal PG-SLNs and PG-SLNs with 2% limonene was studied for 1, 2, and 3 months at 4, 25, and 40 °C under controlled humidity.The results showed that the physical appearance of both formulations did not change, with no separation or precipitation observed from initiation over the 3-month period.Additionally, PS, PDI, ZP, and drug content were reported as non-significantly changed from 0 to 3 months under every storage condition, as represented in Table 4.

Discussions
This study explored the physicochemical characteristics of PG-SLNs during production, employing an emulsification-ultrasonication process.The objective was to demonstrate the efficacy of this controlled preparation method for advanced experimental designs and data analyses such as DoE and ANN.Critical quality factors included the components of PG-SLN (stearic acid, MCT, and Pluronic F-127) and the amount of PG.DoE was utilized to streamline the experimental setup by screening these critical quality factors.The main factor influencing the physicochemical properties of PG-SLN was the concentration of stearic acid.As a solid lipid with high molecular weight, increasing its concentration led to an increase in PS (Pai and Yeh 1997;Kumar and Randhawa 2015).However, stearic acid contributed to PG solubility through a 'like dissolves like' effect, similar to the role of Pluronic acid as a surfactant, aiding in the reduction of water solubility of the drug (Agafonov et al. 2019).
For optimal conditions and dataset generation for prediction, the PS should range from 20 to 100 nm to enhance drug permeation through the skin (Suriyaamporn et al. 2023a).A PDI below 0.2 indicates homogeneity in PS (Suriyaamporn et al. 2022).A ZP value exceeding ±30 indicated high stability of PG-SLN (Suriyaamporn et al. 2023b).Additionally, the %DL of PG should be maximized.One of the major obstacles in delivering drugs from the blood to the target site in the brain is the bloodbrain barrier (BBB).Several factors play a role in facilitating drug passage through the BBB, such as drug-related factors: molecular weight (below 400 Da), morphology (spherical), size (nanometer range), ionization (at physiological pH), and lipophilicity (log P −0.5 to 6.0) are the primary considerations.The PG-SLN in this study was a potential formulation for delivering therapeutics across the BBB, featuring appropriate spherical shape, particle size in the nanometer range, the lowest polydispersity index (PDI), suitable charge, and high lipophilicity (log P 3.87) (Lo et al. 2021;Satapathy et al. 2021).
Subsequently, 11 different runs were conducted using DoE to compare predicted outcomes, revealing acceptable values for PS, PDI, ZP, and %DL under all tested conditions.The adjustment of the learning rate helps increase the RMSE value; however, when the learning rate is adjusted too high, it may lead to a decrease in RMSE.This is because a higher learning rate causes the model to learn quickly but may skip local minimum points, making the model unstable (Khazaei et al. 2008;Reyad et al. 2023).Additionally, adjusting training cycles involves increas-  (Jia et al. 2021;Rebollo et al. 2022).The use of AI tools has been suggested to develop more effective predictive models, and there is a growing interest in applying these tools in the pharmaceutical and biomedical field in recent years (Moussa et al. 2020).
The selected PG-SLN (5% stearic acid + 1.76% MCT + 0.30% Pluronic F-127 + 0.5% PG) was utilized to assess transdermal drug delivery.The results indicated that PG-SLN exhibited higher permeation compared to PG suspension, attributed to the small PS of the drug that can penetrate through the gap junctions between skin tissues (approximately 50-400 µm) (Aleemardani et al. 2021).However, when loaded with limonene, transdermal drug delivery was further improved.This enhancement may be attributed to limonene's role as a penetration enhancer.Limonene is a well-known permeation enhancer, promoting the absorption of active ingredients through the skin barrier (Chen et al. 2016).The concentration of limonene less than 2% was found to be non-irritating, non-toxic, non-allergenic, and compatible with the drugs (Rangsimawong et al. 2018).Furthermore, limonene was observed to enhance the flexibility of the skin barrier, promoting increased drug permeation and leading to an accumulation of PG in the skin.The skin primarily consists of a lipophilic structure, contributing to the accumulation of PG in the skin (Sakeena et al. 2010;Hmingthansanga et al. 2022).
The neuroprotective effects of PG and its derivative have been demonstrated in various experimental models of neurodegenerative diseases.For instance, in a study involving ovariectomized female 3×Tg-AD mice, which serve as a model for Alzheimer's disease, the administration of PG alone or in combination with estradiol over a period of 3 months specifically mitigated the hyperphosphorylation of Tau (Carroll et al. 2007;Bassani et al. 2023).Moreover, the research team has been extensively focused on the therapeutic development of 3α,5α-THPROG, a derivative of PG, for the treatment of Alzheimer's disease.The results showed that 3α,5α-THPROG enhances neurogenesis, improves cognitive function and memory, and reduces neuroinflammation and beta-amyloid accumulation in 3×TgAD mice.The therapeutic level of PG in mice was in the nano to microgram range to effectively induce neuroprotective effects (Chen et al. 2011;Irwin et al. 2012;Ye et al. 2013;Frye et al. 2020).Currently, clinical trials in phase 1 are recruiting patients with early-stage Alzheimer's disease to determine the effective dosage of the derivative of PG (4-18 mg intramuscular weekly injections for 12 weeks) as a potential regenerative therapy for Alzheimer's disease (Guennoun 2020;ClinicalTrials.gov 2023;Luchetti et al. 2023).Therefore, the PG content in SLN formulations and the PG level in in vitro studies was sufficient to effectively induce neuroprotective effects and slow the progression of neurodegenerative disorders.
In the cytotoxicity assessment of SH-SY5Y cells, a human neuroblastoma cell line, the results indicated that concentrations exceeding 1 μg/mL showed toxicity to SH-SY5Y cells.This outcome could be explained by high concentrations of progesterone potentially inducing off-target effects or interactions with other cellular components, thereby disrupting normal cellular functions and leading to toxicity (Schiffmann et al. 2022).Moreover, elevated levels of progesterone might activate specific metabolic pathways or cellular responses that, beyond a certain point, become detrimental to cell health (Elvia et al. 2019).According to the results, the SLN formulations demonstrated safety for normal neuroblastoma cells at appropriate concentrations, suggesting a favorable outcome in terms of non-cytotoxicity.Furthermore, the stability results suggested that both optimal PG-SLNs and PG-SLNs with 2% limonene remained physically and chemically highly stable under every storage condition throughout the 3-month storage period.
The primary limitation of this study was the relatively small dataset available for training the prediction model.However, this limitation can be addressed through cross-validation to avoid overfitting of the model (Ying 2019).Additionally, the DoE process can enhance the quality of the data through a set of experiments generated by DoE.Therefore, the combination of DoE with ANN will further contribute to the improvement of the model's predictive ability (Rodriguez-Granrose et al. 2021).

Conclusions
This study reported the use of DoE and ANN together to create a predictive model for PG-SLNs formulation, produced through the emulsification-ultrasonication method, intended for transdermal drug delivery to relieve neurodegenerative disorders in postmenopausal women.Critical quality factors included the components of PG-SLN (stearic acid, MCT, and Pluronic F-127) and the amount of PG.DoE streamlined the experimental setup by screening these factors, showing stearic acid concentration as a key influencer of physicochemical properties.For optimal conditions, PS should range from 20 to 100 nm, PDI below 0.2, and ZP exceeding ±30.ANN exhibited high prediction accuracy over RSM, handling multiple outcomes simultaneously, unlike DoE's polynomial models.Despite limitations in dataset size, the study's findings provide valuable insights into optimizing PG-SLNs for enhanced drug delivery and therapeutic efficacy.In comparison to traditional methods, this approach required fewer resources and time, accelerating the production process.The selected PG-SLN (5% stearic acid + 1.76% MCT + 0.30% Pluronic F-127 + 0.5% PG) showed enhanced transdermal drug delivery compared to PG suspension, particularly when loaded with limonene.Limonene improved drug permeation through the skin barrier, with concentrations less than 2% being safe and effective.Consequently, AI enabled the prediction of distinct characteristics and intricate behaviors of nanomaterials.The integration of advanced tools like ANN holds significant promise in advancing the field of nanomedicine, generating new knowledge, and impacting future development.

Figure 1 .
Figure 1.The process of PG-SLNs development using DoE and AI.

Figure 3 .
Figure 3.The correlation of experimental vs predicted values of A. PS; B. PDI; C. ZP; D. %DL from the cross-validation stage.

Figure 4 .
Figure 4.The correlation of learning rate and training cycles versus RMSE in ANNs of A, B. PS; C, D. PDI; E, F. ZP; G, H. %DL, respectively.

Figure 5 .
Figure 5.The morphology of A. the PG at 5 kx magnification; B. the selected PG-SLN at 10 kx magnification under the SEM.

Figure 6 .
Figure 6. A. In vitro transdermal drug delivery of PG formulation; B. %drug remaining in porcine skin.*indicates significantly higher than other formulations.

Table 1 .
Experimental factors and levels' values.
training cycles.Fig.1illustrated the process of PG-SLN development using DoE and AI together.

Table 2 .
Predicted values and experimental results from prediction model of PS, PDI, ZP and %DL.

Table 3 .
Skin permeation profile of PG.
#Skin permeation profile: t lag , lag time; J, flux; Q 120 /A, cumulative amount of PG over 120 h per area; K d , diffusion coefficient; K p , permeability coefficient.*indicates significantly higher than others (p < 0.05).

Table 4 .
The stability results of the optimal PG-SLNs and PG-SLNs with 2% limonene.

Temp (°C) Stability parameters observed PS (nm) PDI ZP (mV) Drug content (%w/w) PG-SLNs PG-SLNs with 2%limonene PG-SLNs PG-SLNs with 2%limonene PG-SLNs PG-SLNs with 2%limonene PG-SLNs PG-SLNs with 2%limonene
(Das et al. 2021;Jierula et al. 2021)fter 24 h treated with PG-suspension, optimal PG-SLNs and PG-SLNs with 2% limonene at concentration of PG equivalent to 0.1-500 μg/mL compared with the control.*indicatessignificantlylowerthancontrol.ing the number of rounds of training data used, which is passed through and updates the model parameters.This results in an improved accuracy of the model.However, an excessive increase in training cycles may lead to a decrease in accuracy, as too many rounds of training may cause the model to overfit the data.This means that the model performs well with the training data but may not predict new, unseen data accurately (AtanganaNjock et al. 2021).Therefore, in this study, the minimum values of learning rate and training cycles that provide the lowest RMSE were reported.Obtaining the minimum learning rate and training cycles can minimize the computational resources required for processing, indicating the precision of the model.The low RMSE values across all tests indicated that the model predictions closely align with the actual values, demonstrating a robust fit of the model to the data(Das et al. 2021;Jierula et al. 2021).Consequently, the ANN model exhibited high prediction accuracy when compared with experimental values from new runs.It is noteworthy that the superiority of ANN over RSM as a predictive tool for PG-SLN was reported in this study.In the prediction phase, the DoE could only offer an isolated analysis for each outcome.Polynomial predictive models are designed to handle only one outcome at a time.Furthermore, the predictive models provided by DoE are built on a foundation of first or second-degree polynomial orders, which are appropriate for linear or quadratic data behaviors