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Back to Journal »International Journal of Nanomedicine» Volume 15

Finite element analysis of skin pharmacokinetic prediction of nano-transdermal drug delivery system based on multi-layer geometric model

Authors: Gu Ying, Gu Kun, Yang Kun, Yang Ming, Wang Sheng, Liu Jie 

The 2020 volume will be published on August 12, 2020: 15 pages 6007-6018

DOI https://doi.org/10.2147/IJN.S261386

Single anonymous peer review

Editor who approved for publication: Dr. Linlin Sun

Yongwei Gu,1–3,*Qing Gu,4,*Qing Yang,1,2 Meng Yang,3Shengzhang Wang,5 Jiyong Liu1–3 1 Department of Pharmacy, Shanghai Cancer Center, Fudan University, Shanghai 200032; 2 Oncology, Shanghai Medical College, Fudan University Teaching and Research Section, Shanghai 200032; 3 Department of Pharmacy, Changhai Hospital, Second Military Medical University, Shanghai 200433; 4 Department of Pharmacy, Zhabei Central Hospital, Jing'an District, Shanghai 200070; 5 Institute of Biomechanics, Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433 Corresponding author: Wang Shengzhang, Department of Aeronautics and Astronautics, Institute of Biomechanics, Fudan University, Shanghai 200433 Tel/Fax +86-21-65647825 Email [email protected] Jiyong Liu, Department of Pharmacy, Shanghai Cancer Center, Fudan University, Shanghai 200032, People’s Republic of China ; Department of Oncology, Shanghai Medical College, Fudan University, Shanghai 200032, Tel/Fax +86-21-64175590 Email [email protected] Background: Skin pharmacokinetics is an indispensable indicator of drug fate after transdermal delivery System (TDDS). However, the heterogeneity and complex skin composed of the stratum corneum, living epidermis, dermis and subcutaneous tissue inevitably lead to the change of the drug diffusion coefficient (Kp) according to the skin depth, which severely limits the pharmacokinetics of TDDS in the whole layer. Development in the skin. Methods: The multi-layer geometric skin model was established, and the Kp of the drug in the SC, living epidermis and dermis were obtained by molecular dynamics simulation, in vitro penetration experiment and in vivo microdialysis technology. In addition, finite element analysis (FEA) based on drug Kps in different skin layers was applied to two-dimensional and three-dimensional simulations of the percutaneous dynamic penetration process of paeonol nanoemulsions (PAE-NEs). In addition, the simulated skin pharmacokinetic characteristics of PAE-NEs were verified by in vivo experiments. Results: The molecular dynamics simulation of coarse-grained modeling was successful, and the Kp of PAE in SC was 2.00×10−6 cm2/h. The Kp of PAE-NE in live epidermis and dermis detected by penetration test and microdialysis probe technology were 1.58×10-5 cm2/h and 3.20×10-5 cm2/h, respectively. In addition, the verification results show that the simulated skin pharmacokinetic characteristics of PAE-NEs are consistent with in vivo experiments. Discussion: This study shows that the multi-layer geometric skin model established by the combination of FEA can accurately predict the skin pharmacokinetics of TDDS. Keywords: Nano transdermal drug delivery system, skin pharmacokinetics, finite element analysis, multilayer geometric model, diffusion coefficient, paeonol nanoemulsion

Transdermal Drug Delivery System (TDDS) is interested in drug delivery systems or skin-targeted drugs that can produce a strong first pass effect. 1 Skin pharmacokinetics, a monitor that detects the fate of TDDS in the body, can directly reflect the change of drug concentration, the strength of the drug at the target site, the dose-effect relationship, and the absorption and metabolism of the drug in the skin. However, there are few studies on the skin pharmacokinetics of TDDS in the whole skin.

SC is considered to be the main obstacle to the transdermal absorption of drugs. Therefore, skin pharmacokinetics, referred to as the pharmacokinetics of TDDS in SC, is widely used to study drug metabolism in the skin. 2 However, the heterogeneous structure of the skin can be divided into the stratum corneum (SC), living epidermis, dermis, and subcutaneous tissue from a macro perspective: SC, a solid model, is a strong barrier to absorb drugs through the skin; living epidermis composed of living cells There are inherent obstacles to the diffusion of TDDS; the dermis has a certain influence on the penetration depth of TDDS and the depth of the skin. 3 The penetration process of TDDS includes overcoming the SC barrier, penetrating into the viable epidermis and dermis, and then being absorbed by capillaries. Therefore, skin pharmacokinetics may not fully explain the skin pharmacokinetics of drugs. In addition, the pharmacokinetics of TDDS can also be determined by measuring changes in blood drug concentration over time4 or drug retention in skin tissues after subcutaneous administration5 or a combination of both. The retention of drugs throughout the skin and the skin does not provide insight into the drug transport properties of different skin layers. In order to more accurately explore the dynamic distribution of TDDS in each layer of the skin, the drug transport properties of different layers of the skin need to be studied more systematically, especially for drugs in specific skin layers.

The mathematical model of the skin has attracted more and more attention in predicting the permeability of transdermal drug delivery. The mathematical model of skin penetration prediction has evolved from steady-state models (quantitative structural penetration relationship models, structure-based models, and porous pathway models) to time-dependent transient models (including basic models, compartment models, and complex models), as well as SC The slow binding/distribution kinetics), where the compartment model, also known as the PK model, can be used to track the fate of the drug after it penetrates the skin. 7 McCarley et al. 8 described the representation of SC/living epidermis to predict drug absorption into and through the skin. Unfortunately, the one/two compartment model cannot completely accurately reflect the diffusion process of the drug throughout the skin. (Before, we also used the two-compartment model to study the transdermal process of the drug. However, the in vivo skin pharmacokinetic results are significantly different from the simulation results (P<0.01), as shown in the supplementary data). Therefore, a multi-chamber model should be established to simulate the entire skin and drug penetration process. However, due to the complex skin structure and limited experimental equipment, the drug permeability of different skin layers cannot be obtained through experiments. In recent years, a mathematical method has been reported to calculate the penetration of drugs in time and space. 9

FEA provides approximate numerical solutions of partial differential equations. The main basis of FEA is to deal with domains with polygonal meshes (elements) and boundaries. These domains can be discrete continuous domains. For example, the skin can be dispersed into connected subdomains. According to reports, the two-dimensional (2D) FEA model is used to study the diffusion of lipophilic solutes in SC. 10 Rim et al.11 developed an FEA model to simulate the diffusion of compounds into two isotropic materials through the skin, respecting the vehicle and the skin. According to reports, 2D FEA is used to simulate the dynamic water diffusion in SC and the penetration of macromolecules in the epidermis. 12,13 However, the simulation of drug diffusion in the skin over time is limited to the study of SC or the drug diffusion in the skin is described as homogeneous, and the simulation results are rarely verified by experiments. In order to detect drug absorption and metabolism over time and space (three-dimensional, 3D) in the entire skin with different layer structures, the multi-layer geometric structures of TDDS, SC, living epidermis, and dermis should be meshed with different polygons and densities in FEA Divide. In addition, the FEA simulation is performed with the input Kps, including the Kp of the drug from the carrier to the SC, from the SC to the live epidermis, and from the live epidermis to the dermis.

Paeonol (PAE, 2ʹ-hydroxy-4ʹ-methoxyphenyl), extracted from the traditional Chinese medicine Mudan Cortex and Witch Hazel, is widely used as an anti-inflammatory and anti-allergic. 14 In addition, PAE loaded in nanoemulsion can be improved. 15 Therefore, PAE-NEs was selected as a model nano-transdermal drug to study skin pharmacokinetics. In this study, we established a multi-layer geometric model and obtained Kps of PAE-NEs in SC, live epidermis and dermis through MD simulation, in vitro penetration experiment and in vivo skin microdialysis probe technology. In addition, the finite element analysis method is used to predict the fate of PAE-NEs in the skin based on input parameters. Finally, the feasibility of using FEA to simulate the skin pharmacokinetics of drugs was verified through in vivo experiments. The development combination of multi-layer geometric model, numerical simulation and experiment is a powerful tool to promote the development of TDDS skin pharmacokinetics.

Lecithin E200 was purchased from Degussa (Germany). Isopropyl myristate (IPM) was purchased from China Pharmaceutical Chemical Reagent Co., Ltd. Alkyl polyglycoside (APG) was purchased from China Research Institute of Daily Use Chemical Industry. The purity of paeonol is not less than 98.0% and is provided by the State Food and Drug Administration (Beijing, China). Methanol was purchased from Sigma-Aldrich (HPLC grade). All other reagents are AR grade.

SPF-grade male SD rats, weighing 200±20g and about 1.5 months old, were purchased from the Second Military Medical University. All animal experiment protocols comply with the international ethics guidelines and the National Institutes of Health guidelines for the care and use of laboratory animals, and were approved by the Biomedical Ethics Committee of the Second Military Medical University; the approval number is PREC2017-073.

PAE-NEs are prepared using emulsification technology. In short, PAE (1%) dissolved in IPM (12%) is combined with alkyl polyglycoside (APG, surfactant, 12%), lecithin (surfactant, 6%) and 1, 2 -Propylene glycol (co-surfactant, 9%). Then, while stirring at a speed of 300 rpm, an aqueous solution (60%) was added dropwise to the mixture at room temperature until the system was clear.

The drug delivery system consists of TDDS and skin (Figure 1). Due to the heterogeneity of the skin, the permeability of the drug in the skin depends on the depth of penetration. The fate of the drug exposed to the skin is to diffuse to the SC, penetrate or metabolize to the viable epidermis and dermis, and be absorbed by the system or combined with tissues. 16 Therefore, the multi-layer structure model of the complete drug delivery system is divided into TDDS and the skin is composed of SC, living epidermis and dermis, as shown in Figure 1A and B. Figure 1 Multi-layer geometric model of the drug delivery system: carrier, SC, living epidermis, and dermis. (A) 3D schematic diagram of the vehicle and skin texture. (B) A 2D schematic diagram of the drug penetration process from the carrier to the subcutaneous tissue and the prominent pathways marked with diffusion coefficients (Dm, Ds, De, and Dd).

Figure 1 Multi-layer geometric model of the drug delivery system: carrier, SC, living epidermis, and dermis. (A) 3D schematic diagram of the vehicle and skin texture. (B) A 2D schematic diagram of the drug penetration process from the carrier to the subcutaneous tissue and the prominent pathways marked with diffusion coefficients (Dm, Ds, De, and Dd).

Through the Fick diffusion equation, the drug permeability curve of the drug delivery system as a function of time (t) and depth (x), through the Fick diffusion equation in the carrier, skin and capillaries, is shown as the following equation (Equations 1-4)17, 20 The initial conditions are as follows (Equations 5-8): (1) (2) (3) (4)

Among them, Cm, Cs, Ce, Cd; Dm, Ds, De, Dd; Lm, Ls, Le, Ld represent drug concentration; drug Kp; are the thickness and thickness of carrier, SC, epidermis and dermis, respectively. (5) (6) (7) (8)

Among them, Cm0, Cs0, Ce0 and Cd0 represent the initial drug concentration in the carrier, SC, live epidermis, and dermis, respectively, for the first application.

For boundary conditions, there is no drug exchange between the drug delivery system and the surrounding environment (Equation 9). Equation (10) shows the balance condition of the vehicle/skin surface (SC). Equations (11-13) represent the continuity of flux through the carrier/SC, SC/live epidermis, and live epidermis/dermis, respectively. In addition, the equation. (14) describes drugs absorbed and eliminated by capillaries. (9) (10) (11) (12) (13) (14)

In the formula, Cm, Cs, Ce, and Cd represent the drug concentration in the excipient, SC, live epidermis, and dermis, respectively, Km represents the isolation factor between the excipient and the skin interface, and kcl represents the drug that clears capillaries.

The Kps parameters of the different layers of the multi-layer structure model are the key points of the numerical simulation. In this work, Kps of different skin layers were performed by different methods, including MD simulation, in vitro penetration test and in vivo skin microdialysis probe technology. The drug Kp is calculated according to Fick's law, as shown in Equation 1. (15): (15)

Where D (cm2/h) is the drug Kp, J (μg/cm2/h) is the permeation flux of each layer, C (μg/cm3) is the initial interface drug concentration, and x (cm) is the thickness model layer.

Coarse-grained (CG) MD simulation technology is used to simulate the diffusion process of drugs in the skin SC. In the simulation, GROMACS V4.5.1 and Van der Waals (VMD) software were used to construct dimyristoyl-sn-glycero-3-phosphocholine (DMPC) as a double monolayer system that simulates SC. 21,23 In addition, TIP3P was constructed to simulate the water in the initial system. 24,25

The parameters of CG DMPC and hydraulic field are set according to the theory of Marrink et al. 26 The simulated environment is room temperature and atmospheric pressure. Under the LINCS algorithm, the atomic bond length is kept within the equilibrium distance, and the electrostatic interaction is calculated using the Particle-Mesh-Ewald (PME) algorithm. In addition, the descent algorithm and the conjugate gradient algorithm are used to minimize the system energy. The drug molecules were then placed on the upper surface of the phospholipid bilayer to simulate the membrane permeation process and kinetic diffusion of 100 ns at 310.15 K. Calculate the Kp of drug molecules passing SC according to Einstein's relationship: (16)

Where D represents the drug Kp, r(t) represents the proton coordinate at time t, and represents the mean square displacement (MSD) calculated from the initial time t0.

Franz diffusion cell was used to study the Kp of PAE-NEs in living epidermis. In short, the rat's abdominal hair was removed with electric clippers, the skin without subcutaneous tissue was harvested, and then the skin was peeled off with tape. 2 Skin samples were treated with 1 M NaBr solution for 4 hours, and then with 27. Then the epidermal tissue was installed between the donor and recipient compartments and treated with 0.5 g of PAE-NE. The receptor compartment is filled with receptor medium (physiological saline) and stirred at a speed of 300 rpm at 32±0.5°C. 28,29 Periodically (0.5, 1, 2, 4, 6, 8, 10, and 12 hours), take out 1 mL of receiving medium for analysis, and refill the receiving chamber with fresh medium. Detect cumulative permeability and use permeability profile and equation to fit Kp. (15), (17) and (18): 29,30 (17) (18)

Where Qn (μg/cm2) is the accumulated transdermal permeability in vitro, Cn is the drug concentration of the extracted sample, V0 and Vi are the receiving medium and the volume of the extracted sample, Ci is the drug concentration of the i-th extracted sample, and S is the effective penetration rate. The penetration area, J (μg/cm2/h) is the slope of the penetration profile of PAE-NEs.

The Kp of PAE-NEs in the dermis of the skin was obtained by using the skin microdialysis probe technology combined with MATLAB software. Rats anesthetized with 25% carbamate (0.4 mL/100 g) were fixed on a warming pad to maintain body temperature. Then, under 3D computer tomography (CT) monitoring, the skin microdialysis probe is implanted in the dermis and guided with an 18 G puncture needle. Then, the probe implanted in the abdominal skin was equilibrated with perfusion fluid (PBS solution) at a flow rate of 5 μL/min for 1 hour. The dialysis solution was sampled and analyzed by LC-MS every 20 minutes (100 μL) for 12 hours. Calculate the drug concentration in the dermis according to the established microdialysis method, as shown in the supplementary data. Then, Fourier series fitting was performed on the concentration-time curve of the drug in the dermis using MATLAB software. In addition, the concentration-time curve is integrated to obtain the total drug flux. The Kp of PAE-NE in the dermis is calculated using Fick's law (Equation 15).

The mapping grid is used to digitize the multiple layers of the drug delivery system, where the thickness of the carrier, SC, live epidermis, and dermis are 0.1 cm, 0.02 cm, 0.02 cm, and 0.16 cm, respectively. The 31,32 element meshes are divided and optimized using the meshing tool provided by the PDE tool software in Matlab 12.0. The initial drug concentration in the simulation is 0.2 g/cm3, and the initial drug concentration in the skin is 0 g/cm3. In the entire skin layer, the horizontal (expansion direction) size is much larger than the vertical (depth direction) size, which satisfies the boundary conditions of the numerical multi-layer geometric model. The time step and convergence criteria are set to 1 and 0.0001, respectively.

The multi-layer geometric model and input parameters (respectively the Kps of the dermis detected by the drug in SC, live epidermis and MD simulation detection, in vitro penetration test and in vivo microdialysis probe technology) simulate the transport process of PAE-NEs in the skin. Using the FEA method to assist the PDE tool in Matlab12.0, the 2D dynamic diffusion process of PAE-NE and the change of 3D drug concentration in the entire skin over time and space within a period of time in the digital multi-layer model.

The experimental and simulated drug concentration-time curve results were compared to verify the feasibility of the FEA method to predict TDDS skin pharmacokinetics. In the experiment, the skin microdialysis probe technology was used to obtain the drug concentration in the dermis layer over time, and the depth of the probe in the skin was monitored by CT. Correspondingly, the single line of the simulated curve (drug concentration-time curve) is separated from the 3D dynamic process of PAE-NEs obtained using FEA, where the depth is the same as the probe in the dermis.

The data are shown as mean ± SD. PK parameters were analyzed with Kinetica 5.0 software. P values ​​less than 5% are considered significant.

The study of drug penetration process in SC is limited by traditional methods, and MD simulation is a powerful tool that can intuitively study the process of drug delivery over time and skin depth. 33,34 In MD simulations, coarse-grained (CG) modeling allows long-term and larger length-scale simulations compared to traditional atomic models. 22,35 Considering that the main permeation barrier in SC is located in lipids, and the phospholipid molecules of DMPC are considered to be similar to lipid membrane structures, DMPC chose to construct SC phospholipid bilayers, as shown in Figure 2A and B. 22,36. The simulation system constructed by DMPC, water (grey) and PAE (blue) is shown in Figure 2C. As shown in Figure 2D-F, the dynamic diffusion process of PAE in the skin shows that as the simulation time increases, the drug gradually approaches DMPC. Figure 2 MD simulation of PAE dynamic penetration in SC. (A) Two-dimensional schematic diagram of SC phospholipid bilayer structure; (B) 3D structure of phospholipid molecule modeled by van der Waals sphere model. Carbon atom: dark gray; oxygen atom: red; nitrogen atom: blue; hydrogen atom: light gray; and phosphorus atom: gold; (C) simulation system, the hydrophobic part of DMPC is modeled by van der Waals model: blue, red and Gold marks the nitrogen, oxygen and phosphorus atoms respectively. The hydrophilic tail carbon chain is modeled by the current model, and the carbon atoms are gray. In addition, the gray shaded double molecules are on both sides of water molecules; (DF) the dynamic process of PAE in SC, the coordinates of (DF) are (35.758, 29.998, 23.602), (40.145, 25.609, 24.273) and (33.722, 21.450) , 31.273); 305 (G) the change of the thickness of the phospholipid double layer; (H) the diffusion trajectory of drug molecules (n=6).

Figure 2 MD simulation of PAE dynamic penetration in SC. (A) Two-dimensional schematic diagram of SC phospholipid bilayer structure; (B) 3D structure of phospholipid molecule modeled by van der Waals sphere model. Carbon atom: dark gray; oxygen atom: red; nitrogen atom: blue; hydrogen atom: light gray; and phosphorus atom: gold; (C) simulation system, the hydrophobic part of DMPC is modeled by van der Waals model: blue, red and Gold marks the nitrogen, oxygen and phosphorus atoms respectively. The hydrophilic tail carbon chain is modeled by the current model, and the carbon atoms are gray. In addition, the gray shaded double molecules are on both sides of water molecules; (DF) the dynamic process of PAE in SC, the coordinates of (DF) are (35.758, 29.998, 23.602), (40.145, 25.609, 24.273) and (33.722, 21.450) , 31.273); 305 (G) the change of the thickness of the phospholipid double layer; (H) the diffusion trajectory of drug molecules (n=6).

As shown in Figure 2G, the thickness of the phospholipid bilayer remains within a reasonable and stable range within the simulated 100 ns, indicating that the parameters, settings, and simulation system are stable. In the analysis of drug diffusion trajectory (n=6, Figure 2H), random initial conditions (the relative position of the drug and DMPC) resulted in an incomplete match of the drug molecular trajectory. In addition, the mean square displacement (MSD) (Figure 2H) is combined with the equation. (16) Kp used to fit the PAE in SC, calculated Kp is about 2.00×10-6 cm2/h. However, the MD simulation of PAE-NEs penetration in SC or skin epidermis and dermis needs further study.

The penetration curve of PAE-NEs in the living epidermis is shown in Figure 3. (17) and (18) (Qn=103.03 t+66.86, R2=0.996), equations. (15) And the thickness of the live epidermis (0.20 mm), the Kp of 36 PAE-NEs in the live epidermis is 1.58×10−5 cm2/h. In addition, the 12-hour cumulative permeability reached 75.82±2.85%. Generally speaking, tape stripping is a minimally invasive method to obtain the SC layer, which is used to measure the drug concentration in the SC. 2 In the study, the tape stripping method was used to remove SC. In vitro penetration testing is a broad alternative method and a useful tool for studying the pharmacokinetics of TDDS. 37,38 Therefore, the in vitro permeability of PAE-NEs in living epidermis can be calculated based on the in vitro permeability curve. The Kp of PAE-NEs in the living epidermis is slightly different from previous reports, which may be due to the Kp of the drug that varies with drug molecules and skin types. 13,39 Figure 3 In vitro penetration curve of PAE-NE. The red solid line represents the cumulative transdermal permeability, and the blue solid line represents the cumulative permeability (n=5).

Figure 3 In vitro penetration curve of PAE-NEs. The red solid line represents the cumulative transdermal permeability, and the blue solid line represents the cumulative permeability (n=5).

The microdialysis probe technology used to detect the pharmacokinetics of TDDS is frequently reported. 29,40,41 In our research, we creatively applied this technology to detect the Kp of drugs in the dermis. The depth of the microdialysis probe implanted in the dermis, shown and located by CT, is 1.36 mm. The Fourier series curve of PAE-NEs concentration-time in the dermis was fitted with MATLAB, as shown in Figure 4. According to Fick's law, the Kp of PAE-NEs is 3.20×10−5 cm2/h. The results of the drug Kp in SC, live epidermis and dermis showed that the permeability of PAE-NEs gradually increased with the depth of the skin, and the permeability in the dermis was about twice that in the live epidermis, which was consistent with previous reports. 13, 39, 42 Figure 4 The concentration-time curve (solid line) of PAE-NE in the skin probe microdialysis solution located at 0.136 cm of the skin and the Fourier series fitting curve (solid line) of the drug concentration over time.

Figure 4 The concentration-time curve (solid line) of PAE-NEs in the skin probe microdialysis solution located at 0.136 cm of the skin and the Fourier series fitting curve (solid line) of the drug concentration over time.

FEA is a powerful grid-based method for numerically solving partial differential equations of dynamic drug penetration in the skin. 13,23 The spatial domain interconnected by nodes is divided into basic shapes, which can be triangles, quadrilaterals and polygons. The density of nodes in the domain is different, and each point and node has unique attributes. Figure 5 shows the meshing of the multi-layer domain, the diffusion rate and the internal boundary conditions of the skin multi-layer model. The time domain is 10 hours, the time step = 0.001 hours = 0.06 minutes, and the convergence is 0.001. Figure 5 The finite element mesh of the finite element solution (A) and the multilayer geometry of the drug delivery system (B). Dm, Ds and De are the drug from the carrier to the SC, from the SC to the live epidermis, and from the Kp epidermis of the live epidermis To the dermis, respectively.

Figure 5 The finite element mesh of the finite element solution (A) and the multilayer geometry of the drug delivery system (B). Dm, Ds, and De are the drug from the carrier to the SC, from the SC to the live epidermis, and from the Kp epidermis of the live epidermis To the dermis, respectively.

The two-dimensional dynamic penetration process of PAE-NEs in the drug delivery system at different simulation times is shown in Figure 6A-D. The results show that drug penetration is time-dependent: initially, there is no drug penetration at simulation time = 0. And with the extension of the simulation time, the drug penetrated from the carrier to the SC, living epidermis and dermis. In addition, as shown in Figure 6E, the 3D schematic diagram of PAE-NEs drug concentration over time and skin depth based on the four-layer model simulates the entire dynamic process from drug administration to skin metabolism. Figure 6 The drug concentration of PAE-NEs changes with time and skin depth. (AD) 2D drug penetration process and drug concentration when FEA simulation time is 0, 100, 200, and 300 minutes; (E) 3D schematic diagram of drug concentration-time-skin depth simulated by FEA.

Figure 6 The drug concentration of PAE-NEs changes with time and skin depth. (AD) 2D drug penetration process and drug concentration when FEA simulation time is 0, 100, 200, and 300 minutes; (E) 3D schematic diagram of drug concentration-time-skin depth simulated by FEA.

In the verification experiment, the depth of the implanted lined microdialysis probe was 1.68 mm. The drug concentration-time curve is shown as the green dashed line in Figure 7. The drug concentration-time curve at a skin depth of 1.68 mm measured by the in vivo skin microdialysis probe technology is compared with the numerical simulation curve extracted by FEA simulation. The drug concentration-time-skin curve at a depth of 1.68 cm is drawn in the same coordinate system. As shown in Figure 7: The green dashed line and the blue dashed line represent experimental results and numerical simulation results, respectively. The comparison results show that FEA can best fit the overall skin pharmacokinetics. The small errors between the experimental and simulation results indicate that the FEA method combined with the multi-layer geometric model is an accurate method to study the pharmacokinetics of PAE-NE skin. Figure 7 Comparison of experimental data of skin pharmacokinetics and FEA simulation results. The green dashed line represents the experimental result, and the blue dashed line represents the numerical simulation result.

Figure 7 Comparison of experimental data of skin pharmacokinetics and FEA simulation results. The green dashed line represents the experimental result, and the blue dashed line represents the numerical simulation result.

In the research of FEA method based on drug Kps to simulate TDDS skin pharmacokinetics in multi-layer geometric model, the limitation lies in whether the Kps of drugs in SC, live epidermis and dermis can be accurately determined. The Kp of the PAE molecule in SC simulated by MD simulation is an approximate value. And with the development of computing power, the Kp of formulations (PAE-NEs) using MD simulation models need to be further studied. In addition, the permeability of PAE-NEs in the living epidermis using exfoliated skin may be different from that in the body. In fact, the skin inevitably undergoes elastic deformation during the preparation process, which may affect transdermal penetration. 13,40 As for the permeability of PAE-NEs in the dermis, the flux J is fitted with a Fourier series, which cannot completely match the experimental concentration-time curve. It is important to realize that more complex models and techniques should be developed to obtain more accurate input parameters to use FEA to predict skin pharmacokinetics.

This is the first study to study the skin pharmacokinetics of TDDS in combination with the FEA simulation method based on the mathematical multilayer geometry of the drug delivery system. We used coarse-grained MD simulations to simulate the Kp in SC, and explored the interaction between PAE and SC at the molecular level. In addition, an in vitro penetration experiment of PAE-NEs in foreign skin was also carried out to obtain Kp in vigorous epidermis. In addition, the Kp of PAE-NEs in the dermis was obtained by in vivo skin microdialysis probe technology combined with Fourier series fitting. What is exciting is that the PAE-NEs skin pharmacokinetic curve and input parameters simulated by the FEA method show very consistent with the actual in vivo performance. It can be concluded that the FEA method based on the multilayer geometric model is a promising strategy for predicting the skin pharmacokinetics of TDDS.

This work was awarded by the National Natural Science Foundation of China (81873011, 81573613), Shanghai Municipal Science and Technology Commission (18401931500), Shanghai Municipal Health and Family Planning Commission Excellent Talents Program (2018BR27), and Shanghai Navigation Plan (20YF1412100).

The authors report no conflicts of interest in this work.

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