The drug release analysis and optimization for drug-eluting stents in the arterial wall are studied, which involves mechanics, fluid dynamics, and mass transfer processes and design optimization. The Finite Element Method (FEM) is used to analyze the process of drug release in the vessels for drug-eluting stents (DES). Kriging surrogate model is used to build an approximate function relationship between the drug distribution and the coating parameters, replacing the expensive FEM reanalysis of drug release for DES in the optimization process. The diffusion coefficients and the coating thickness are selected as design variables. An adaptive optimization approach based on kriging surrogate model is proposed to optimize the lifetime of the drug in artery wall. The adaptive process is implemented by an infilling sampling criterion named Expected Improvement (EI), which is used to balance local and global search and tends to find the global optimal design. The effect of coating diffusivity and thickness on the drug release process for a typical DES is analyzed by means of FEM. An implementation of the optimization method for the drug release is then discussed. The results demonstrate that the optimized design can efficiently improve the efficacy of drug deposition and penetration into the arterial walls.
Cardiocerebrovascular disease is a serious threat to human health. There are three main treatments for vascular diseases: surgery, coronary angioplasty, and coronary stenting. Coronary stenting is minimally invasive catheter-based interventions. Compared to surgery, the coronary stenting is less invasive, so postoperative recovery is quick. Compared to coronary angioplasty, it can avoid restenosis, efficiently. So coronary stenting has been widely applied to clinical; so far coronary stenting technique has become the most promising treatment for coronary artery diseases; however, the arterial wall damage and restenosis caused by stent have not been completely resolved. This is the main reason that development of stenting is hampered. Fortunately, the coronary stent can carry the drug through drug eluting. The drug-eluting stents (DES) could provide the local high concentration of the drug by local drug delivery system and minimize the systemic side effects. Thereby, the generation of thrombus is suppressed, and the risk of restenosis is reduced [
A few works about DES were reported, Yang and Burt [
The Finite Element Method (FEM) is here used to analyze the process of drug release in the vessels for DES, in which the microstructure of tissue (anisotropic diffusion of the drug, porosity, and retention of the drug protein) and the macrostructure of tissue (thrombus/blood clots) are considered. Based on the FEM analysis, an optimization approach combined with Expected Improvement (EI) function [
The Finite Element Method (FEM) is used to analyze the process of drug release in the vessels for Drug Eluting Stents (DES). As shown in Figure
2D simplified model.
As shown in Figure
At initial time (
The arterial wall is also modeling as porous media. Because the inner and outer walls in the presence of physiological arterial pressure will lead to plasma flow, mass transfer was under diffusion and convection equations [
The control equation of blood flow is the general convection diffusion equation. The control equation and the boundary condition on the interface of artery and coating can be found in reference [
First of all, considering the plasma flow in the arterial wall, the plasma flow velocity in arterial wall, and the pressure difference between inside and outside surfaces determined by the Darcy law, the blood in artery is modeled as incompressible Newtonian Equation. As the drug release in the blood does not affect blood flow, the velocity field can be obtained, and then, with the velocity field as given conditions, the drug concentration distribution at different times can be obtained [
The material properties are the same in reference [
Figure
Drug concentration of the artery wall with different models. (a) Isotropic nonporous medium, (b) isotropic porous media, and (c) anisotropic porous media.
Figure
Influence of coating diffusivity on drug concentration into the artery wall.
As the diffusion coefficient increases, the drug concentration in the artery wall reaches a higher peak with a faster growth. The decay rate of the peak is not proportional to the diffusion coefficient, so the trend of the change of drug concentration is not linear relationship with diffusion coefficient. This conclusion is important, because if we want a longer time drug concentration in the artery wall, it should not increase or decrease the diffusion coefficients of the coating, simply. Therefore, it appears optimal to find an appropriate diffusion coefficient to make the longest time with certain drug concentration. That provides a theoretical basis for DES coating optimization.
Figure
Influence of coating thickness on drug concentration into the artery wall.
The initial concentration of drugs in the coating shifted to a higher level with the decrease of the coating thickness. It is clear that the drug concentration in the artery wall reaches a higher peak with a faster growth. The duration of the drug in the artery wall is not inversely proportional to the coating thickness. So the trend of the change of drug concentration is not linear relationship with the coating thickness. Therefore, it appears optimal to find an appropriate coating thickness.
The two important factors for the distribution of drugs in artery wall are diffusion coefficients and the coating thickness. Therefore, diffusion coefficients and the coating thickness can be chosen as the design variables. An optimization approach based on kriging surrogate model is used to optimize the lifetime of the drug in artery wall. The kriging model was used to build an approximate function relationship between the objective function and design variables (the diffusion coefficients in coating and the thickness of coating), thereby replacing the expensive FEM reanalysis of the objective function value during the optimization. The optimization iterations are based on the approximate relationship for reducing the high computational cost. An adaptive optimization method based on the kriging surrogate model with Latin Hypercube Sampling (LHS) strategy [
The evaluation standard of effect of the drug release on the stent is Mean Residence Time (MRT) [
Samples and responses.
Samples | Taxus diffusivity (m2/s) | Coating thickness (mm) | Response (s) |
---|---|---|---|
1 |
|
0.057 | 4238 |
2 |
|
0.052 | 3658 |
3 |
|
0.073 | 3670 |
4 |
|
0.042 | 3416 |
5 |
|
0.065 | 2928 |
6 |
|
0.031 | 3078 |
7 |
|
0.027 | 3940 |
8 |
|
0.059 | 4104 |
9 |
|
0.072 | 3782 |
10 |
|
0.032 | 3112 |
11 |
|
0.065 | 3862 |
12 |
|
0.046 | 4604 |
13 |
|
0.038 | 4862 |
14 |
|
0.041 | 3984 |
15 |
|
0.062 | 4120 |
As shown in Figure
Iterative optimized process.
Another judge standard is the ratio of mean concentration and initial concentration in the media layer. So the objective function is selected as the drug duration time when
Influence of coating diffusivity on drug concentration into the artery wall.
Influence of coating thickness on drug concentration into the artery wall.
This paper studies the relationship between the properties of the coating and the drug distribution in the arterial wall. The study indicates that diffusion coefficients and the coating thickness are two important factors of the distribution of drugs in artery wall. An optimization approach based on kriging surrogate model is used to optimize the lifetime of the drug in artery wall. The diffusion coefficients and the coating thickness are selected as design variables. The results demonstrate that the optimized design can efficiently control the release of drug in the blood and drug concentration gradient in the blood vessels.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors gratefully acknowledge financial support for this work from the National Natural Science Foundation of China (no. 11072048).