Mathematical modeling of bioerodible, polymeric drug delivery systems

The aim of this article is to give an introduction into mathematical modeling approaches of bioerodible controlled drug delivery systems and to present the most important erosion theories reported in the literature. First, important parameters such as degradation and erosion are defined and physicochemical methods for their investigation are briefly presented. Then, phenomenological empirical models as well as models based on diffusion and chemical reaction theory are discussed. Due to the significant chemical and physicochemical differences among individual bioerodible polymers used for controlled drug delivery systems, various mathematical models have been developed to describe the chemical reactions and physical mass transport processes involved in erosion-controlled drug release. Various examples of practical applications of these models to experimental drug release data are given. For those involved in the design and development of biodegradable drug delivery systems this will help to choose the appropriate mathematical model for a specific drug release problem. Important selection criteria such as the desired predictive power and precision, but also the effort required to apply a model to a particular system will be discussed. Furthermore, before models can be used for drug release predictions certain parameters such as drug dissolution or polymer degradation rate constants, have to be known. The number of parameters to be determined significantly differs between the models. The practical benefit of carefully choosing the right model is that effects of composition and device geometry on the drug release kinetics can be predicted which can reduce laborious formulation studies to a minimum.