弱聚电解质水凝胶溶胀释药的数值模拟

doi:10.7503/cjcu20170541

摘要/Abstract

摘要：

在三相模型的基础上, 结合Langmuir等温吸附方程和药物释放方程, 建立了弱聚电解质水凝胶溶胀释药的数学模型; 运用有限元方法, 研究了药物在弱聚电解质水凝胶内均匀分布时凝胶体系的材料参数对溶胀及释药性能的影响; 分析了水凝胶在不同阶段的释药机理; 比较了药物在载药基体内的均匀分布和不均匀分布模式对凝胶释药性能的影响, 当药物在载药基体内正弦分布时呈现零级释药动力学特点; 对比分析了模拟结果与实验结果, 验证了弱聚电解质水凝胶溶胀释药模型的准确性.

关键词: 弱聚电解质水凝胶, 溶胀, 药物释放, 数学模型, 有限元模拟

Abstract:

Based on the three-phase model, a mathematical model of swelling and drug release for weak polyelectrolyte hydrogels was established by combination of Langmuir isothermal adsorption equation and drug release equation; the finite element method was adopted to investigate the influence of the material parameters on swelling and drug release in the case of drugs were distributed within the weak polyelectrolyte hydrogels homogeneously; the mechanism of drugs released from weak polyelectrolyte hydrogels in different moments was analyzed as well; then the impacts of drug distribution conditions within the hydrogels which consist of homogeneous distribution and inhomogeneous distribution on swelling and drug release were compared comprehensively, and it has been found that drug release process is consistent with zero order release kinetics when drugs presented the sine distribution in the hydrogels; finally, the simulated results were comparatively compared with Beebe’s experimental results to validate the accuracy of this simulation.

Key words: Weak polyelectrolyte hydrogel, Swelling, Drug release, Mathematical model, Finite element simulation

TrendMD:

叶慧, 刘亚博, 贾玉玺. 弱聚电解质水凝胶溶胀释药的数值模拟. 高等学校化学学报, 2018, 39(4): 817.

YE Hui, LIU Yabo, JIA Yuxi. Numerical Simulation of Swelling and Drug Release Processes for Weak Polyelectrolyte Hydrogels^†. Chem. J. Chinese Universities, 2018, 39(4): 817.

图/表 10

Table 1 Material parameters and values

Reference object	Parameter	Value
Free ions	Diffusion coefficient, D_i/(m²·s^-1)	1×1 $0 - 9 27$
Drugs	Initial concentration, c_d0/(kg·m^-3)	1.264
Solution	Viscosity, η/(Pa·s)	1×10^-3
	Fluid pressure, p₀	0
	Electric potential, ψ₀	0
Polymer network	Initial volume fraction of water, ϕ_w0	0.8
	Initial concentration of fixed charge, c_f0/(mmol·L^-1)	2.12

Table 1 Material parameters and values

Reference object	Parameter	Value
Free ions	Diffusion coefficient, D_i/(m²·s^-1)	1×1 $0 - 9 27$
Drugs	Initial concentration, c_d0/(kg·m^-3)	1.264
Solution	Viscosity, η/(Pa·s)	1×10^-3
	Fluid pressure, p₀	0
	Electric potential, ψ₀	0
Polymer network	Initial volume fraction of water, ϕ_w0	0.8
	Initial concentration of fixed charge, c_f0/(mmol·L^-1)	2.12

Fig.1 Change of swelling degree with time for different ƒsp ƒsp: a. 1×1013; b. 3×1013; c. 5×1013; d. 7×1013.

Fig.2 Change of drug release amount with time for different ƒspƒsp: a. 1×1013; b. 3×1013; c. 5×1013; d. 7×1013.

Fig.3 Change of swelling degree with time for different polymer density Polymer density/(kg·m-3): a. 1200; b. 1500;c. 1600.

Fig.4 Change of drug release amount with time for different polymer densityPolymer density/(kg·m-3): a. 1200; b. 1500;c. 1600.

Table 2 Exponential relation of drug release ratio to time

Diffusive type	n	Control step of drug release
Case Ⅰ diffusion(Fickian diffusion)	0.45	Drug diffusion
Case Ⅱ diffusion(Relaxation diffusion)	0.89	Polymer relaxation
Case Ⅲ diffusion(Anomalous diffusion)	0.45-0.89	Drug diffusion and polymer relaxation

Fig.5 Logarithmic diagram of drug release ratio to time for different data fitting models

Fig.6 Radial distribution of drug concentration for c0=3.5sin(r×π/4)(A) and c0=3.5[1-sin(r×π/4)](B)

Fig.7 Change of drug release amount with time for 3.5(a), 3.5[1-sin(r×π/4)](b) and 3.5sin(r×π/4)(c)

Fig.8 Change of swelling degree with pH valuesa. Simulated data; b. experimental data.

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