Modeling and simulation of drug release from multi-layer biodegradable polymer microstructure in three dimensions

doi:10.1016/j.simpat.2007.09.008

Simulation Modelling Practice and Theory

Volume 16, Issue 1, January 2008, Pages 15-25

https://doi.org/10.1016/j.simpat.2007.09.008 Get rights and content

Abstract

Multi-layer biodegradable polymer drug delivery microstructures with micro-chambers have many exceptional advantages in a long-term controlled drug delivery. In this paper, a mathematical model for the drug release from this type of three-dimensional (3D) drug delivery microstructures is presented by using 3D cellular automata and discrete iterations. The validity of the model is proved by comparing with the Gőpferich’s simulated profiles for the same composite polymer cylinder matrices. Based on this model, furthermore, the simulations are done to describe the dynamic behavior of drug release from this type of microstructures. The simulation results show that this 3D mathematical model can describe accurately the drug release behavior and therefore can provide a new optimal design tool for this kind of multi-layer biodegradable polymer drug delivery microstructure.

Introduction

Biodegradable polymers have many applications in different areas. Especially, they have attracted great interests in drug delivery for targeting or prolonging implantable drug release because of many excellent characteristics, such as unnecessary surgical removal of the spent devices, free from the toxicological problems, and degradable in biological fluids with tunable release rate to produce biocompatible or nontoxic products, etc. For examples, polyanhydrides (CPP–SA) have been applied in the treatment of brain cancer using disc-shaped implants loaded with antineoplastic agents [1]; poly lactic acid (PLA), poly glycolic acid (PGA), and their copolymers (PLGA) have been applied in various drug delivery devices due to their excellent biocompatibility and biodegradability [2], [3].

Generally, the process by which biodegradable polymer hydrolyzes and disappears into their environments is often called erosion. According to how the hydrolysis takes place, there are two different erosion mechanisms, termed as surface erosion (heterogeneous erosion) and bulk erosion (homogeneous erosion). A number of studies have been developed to investigate these mechanisms and model the erosion process. Moreover, many mathematical models have been reported to describe the drug release from biodegradable polymer drug delivery system [4], [5], [6], [7]. For example, Gőpferich et al. [8], [9], [10], [11], [12] investigated the degradation and erosion mechanisms of polymer and developed Monte Carlo-based model to simulate the erosion process and the drug release from polymer matrices. Zygourakis et al. [13], [14], [15] proposed a cellular automata (CA) model to simulate the drug release process from surface eroding polymer matrices. Couarraze et al. [16] presented a mathematical model to quantify the drug release from bulk eroding polymer films, in which the polymer degradation and drug diffusion are considered simultaneously.

Recently, due to the development of microelectromechanical systems (MEMS) technique, many efforts have been made to develop the biodegradable drug delivery microstructure with micro-chambers [17], [18], [19] by utilizing the microfabrication technologies. Fig. 1 shows two Polyanhydride (P(SA–RA 70:30)) microstructures with different micro-chamber shapes fabricated in our laboratory using UV–LIGA and micro-molding technique. The schematic design diagram for the biodegradable polymer drug delivery system with micro-chambers is shown in Fig. 2, in which the micro-chambers are served as the drug carriers. A multi-layer structure with micro-chambers can then be obtained by gluing each layer of the microstructure filled with the drugs together, as shown in Fig. 2. The multi-layer drug delivery microstructure allows the enclosed drugs to release in a controlled fashion that depends on the erosion characteristics of the biodegradable polymer inside the human body. During the release, the micro-chambers degrade gradually along the periphery under the interactions of water and bioenzyme in body tissues.

In comparison with the reported implantable drug delivery systems, this type of drug delivery system has some exceptional advantages in the long-term controlled drug delivery. For instance, the flexibility of the multi-layer and large array of micro-chambers makes it possible for the long-term simultaneous delivery of multiple drugs. Additionally, it can be used to intelligently obtain a linear delivery of drugs by the optimal designs of the micro-chambers and their distributions. Up to today, however, little effort has been devoted to the modeling of the drug release from the multi-layer biodegradable polymer drug delivery microstructure. Therefore, to characterize the drug release mechanism, it is necessary to develop the three-dimensional (3D) theoretical model of the drug release from the multi-layer biodegradable polymer drug delivery microstructure, in which the effects of structural parameters and physical/chemical properties of the polymer device as well as the biochemical properties of the drugs are required to be taken into account.

In this paper, a 3D mathematical model is presented to describe the dynamic behavior of the drug release from the multi-layer biodegradable polymer drug delivery microstructure with micro-chambers using cellular automata (CA) and discrete iterations. And then, the model is applied to the optimal design of the micro-chambers and their distributions of this type of drug delivery microstructure with a linear delivery of drugs.

Section snippets

CA-based model of biodegradable polymer drug delivery system in three dimensions

In the late 90’s, Gőpferich et al. developed a Monte Carlo-based model to simulate the erosion of three-dimensional rotationally symmetric polymer matrices [11] and to predict drug release from such composite devices [12]. In their model, the cylinder cross section is represented by a two-dimensional computational grid. The grid divides the cross section into individual polymer pixels of the same volume. This is achieved by decreasing the step-size in radial direction with the root of the

Simulation results and discussion

Based on the above CA-based 3D drug release model, programs for simulation are coded in MATLAB, and run on a Dell Dimension 4600 Personal computer (Pentium (R) 4 CPU 2.66 GHz, 512 MB memory). Generally, the computation times depend on the intrinsic dissolution rates of the solid components that determine the number of iterations needed to completely dissolve a model microstructure.

Conclusions

The multi-layer biodegradable polymer drug delivery microstructure with micro-chambers fabricated by using the UV–LIGA and Micro-molding technique has many exceptional advantages in long-term controlled drug delivery. To characterize the drug release mechanism, it is necessary to develop the three-dimensional (3D) theoretical model for this kind of drug delivery microstructure.

In this study, a CA-based 3D mathematical model is presented which can describe the dynamic behavior of the drug

Acknowledgements

This work was supported by the Natural Science Foundation of China (NSFC) (No. 50375116) and the National High Technology Research and Development Program of China (863 Program) (No. 2003AA404170).

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Modeling and simulation of drug release from multi-layer biodegradable polymer microstructure in three dimensions

Abstract

Introduction

Section snippets

CA-based model of biodegradable polymer drug delivery system in three dimensions

Simulation results and discussion

Conclusions

Acknowledgements

Adv. Drug Deliver. Rev.

J. Control. Release

Biomaterials

Biomaterials

J. Control. Release

Chem. Eng. Sci.

Biomaterials

Int. J. Pharm.

Biomaterials

Sens. Actuat. B: Chem.

Theor. Comput. Sci.

Theor. Comput. Sci.