Degradation, Erosion, and Drug Release Kinetics

Modeling Degradation, Erosion, and Drug Release Kinetics 

Modeling the behavior of bioerodible polyanhydrides is complicated by the many phenomena contributing to release profiles described in the previous section. The degradation kinetics may be coupled to other processes, such as diffusion and dissolution, and the overall erosion kinetics represent the sum of all of these multiple processes (Goepferich, 1996a). 

The simplest model for pure erosion control with kinetics dominated by a single rate constant and uniformly distributed drugs was described by Hopfenberg (1976). This model says nothing about the various physical phenomena that contribute to erosion, and therefore fails to describe drug release profiles from many poly anhydride systems. Below we classify some of the models that can be found in the literature. 

The broadest class of models, phenomenological models, account explicitly for individual phenomena such as swelling, diffusion, and degradation by incorporation of the requisite transport, continuity, and reaction equations. This class of models is useful only if it can be accurately parameterized. As phenomena are added to the model, the number of parameters increases, hopefully improving the model s accuracy, but also requiring additional experiments to determine the additional parameters. These models are also typically characterized by implicit mean-field approximations in most cases, and model equations are usually formulated such that explicit solutions may be obtained. Examples from the literature are briefly outlined below. 

Zygourakis (1990 Zygourakis and Markenscoff, 1996) developed a discretized model in which cells are assigned a degradation time, upon exposure to solvent, based on their identity as either drug, polymer, solvent, or void. The initial distribution of cells can be modeled after the microstructure of the polymer matrix and multiple phases are explicitly accounted for. The solution is found numerically. 

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Whether in copolymers or blends, inhomogeneous erosion has a nontrivial effect on drug release kinetics as will be shown later. Leong et al. (1985) demonstrated that the pH of the degradation media also has a dramatic effect on the erosion rate, which increases with increasing pH. The acceleration of degradation of polyanhydrides with increase in pH is widely reported and has been used to speed up experiments (Shakesheff et al., 1994). 

To provide better control of polymer matrix erosion, a more orderly degradation and erosion process is needed. In an effort to achieve this goal, materials that erode heterogeneously have been produced. In particular, for materials that erode from the surface only, the kinetics of dissolution and the release of incorporated drugs can be precisely controlled. The first surface-eroding bio-erodible polymer formulation was produced at Alza Corp. in the 1970s it was a copolymer of methyl vinyl ether and maleic anhydride [20] ... 

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