A multi-scale method for modeling degradation of bioresorbable polyesters.

Unlabelled: A multi-scale model using the cellular automata (CA) and kinetic Monte Carlo (KMC) methods is presented to simulate the degradation process of bioresorbable polyesters such as polylactide (PLA), polyglycolide (PGA) and their copolymers. The model considers the underlying chemical and physical events such as polymer chain scission, oligomer production, crystallization induced by polymer chain scissions, oligomer diffusion and microstructure evolution due to erosion of the small chains. A macroscopic device is discretized into an array of mesoscopic cells. Each cellular lattice is assumed to be made of one polymer chain, which undergoes hydrolysis reaction. The polymer chain scission is modeled using a kinetic Monte Carlo method. Oligomer production, chain crystallization and formation of cavities due to polymer collapse are also modeled on the cellular lattice. Oligomer diffusion is modeled by using Fick's laws at the macroscopic scale. The diffusion coefficient is taken as dependent on the porosity caused by the formation of the cavities. The interactions among the microscopic hydrolysis reaction, mesoscopic formation of cavities and macroscopic diffusion are taken into account. The proposed method forms Multi Scale Cellular Monte Carlo Automata (MS-CMCA). The three-scale approach consists of continuous method and discrete method to deal with certainty problem with underlying stochastic phenomenon. Demonstration examples are provided which show that the model can fit with experimental data in the literature very well.

Statement Of Significance: The original work in this paper is a multi-scale method (including micro scale, mesoscopic scale, macro scale and their coupling) for modeling degradation of bioresorbable polyesters and provides understanding to the process of degradation of biodegradable polymers. The result denotes the solution is reliable. As we know, there have no papers recently to implement three scales modeling and its coupling. There is a two-scale model of amorphous polyester degradation described by Han and Pan (Acta Biomaterialia 2011), our model accounts for effects of re-crystallization to explain the degradation process from three scales and takes into account of copolymers. From our model, the molecular weight distribution with time, chain number with time, degree of crystallinity with time, the evolution of polymer inner shape, weight loss with time (which is found from calculation that both oligomer diffusion and small molecules solution work to the weight loss) can be obtained from the calculation of the three scale model.