A Statistical Kinetic Model for the Bulk Degradation of PLA-b-PEG-b-PLA Hydrogel Networks Andrew T. Metters, Christopher N. Bowman, and Kristi S. Anseth* Department of Chemical Engineering, UniVersity of Colorado at Boulder, Boulder, Colorado 80309-0424 ReceiVed: February 9, 2000; In Final Form: May 22, 2000 A theoretical model has been developed to describe the bulk-degradation behavior of model PEG-b-PLA hydrogels. Utilizing a statistical approach to predict the cleavage of cross-links within these networks, the model accounts for both structural and kinetic issues during the degradation and, from direct comparison, can accurately predict the complex erosion profiles of the cross-linked hydrogels. The mass loss profiles of the cross-linked networks are shown to depend on parameters such as the order of the hydrolysis reaction, the value of the kinetic rate constant, the number of cross-links per backbone chain, and the mass fraction of network contained in the backbone as opposed to the rest of the network. Such an accurate degradation model based on fundamental parameters allows a greater understanding of the bulk-degradation process and its controlling factors. Introduction Researchers have recently begun experimenting with a new class of degradable, polymeric hydrogels. Traditional synthetic hydrogels are generally insoluble, yet water-swellable, cross- linked polymer networks that have long histories of proven application as contact lenses, super-absorbent materials, drug delivery vehicles, and adhesives. 1 Their combined hydrophilic and cross-linked nature provides a unique combination of mechanical strength and high water content which can be matched by few materials. Degradable networks offer the same advantages as normal hydrogels, but also contain bonds that can be cleaved hydrolytically or enzymatically. Applications for these degradable, cross-linked networks include improved drug delivery devices, tissue adhesives, orthopedic implants, and adhesion barriers. 2-5 For many specialized uses, including tissue- engineering applications, the ability to use a degradable hydro- gel, as opposed to a material that remains in the body indefinitely, is very attractive. To function most effectively in any application, the degrada- tion behavior of the hydrogels must be predictable and well understood under a wide variety of conditions. The relationships between this behavior and other macroscopic properties must also be known. Unfortunately, the correlations among a bio- degradable hydrogel’s design, composition, and ultimate func- tion are not well understood. No theoretical models currently exist to describe the important features of their degradation be- havior, and even experimental characterization of their degrada- tion is limited. Thus, this work aims to provide a general framework for the bulk-degradation process of cross-linked gels. A more complete understanding of the controlling factors behind the degradation phenomenon and the relationships between the microscopic chemical structure of the hydrogels and their macroscopic performance during degradation will allow greater functional design of the network. Background Although polymers degrade through several mechanisms, hydrogels that degrade chemically, via hydrolysis of the cross- links, are the focus of this investigation. Hydrolytically labile polymers such as polyesters and polyanhydrides have found uses both inside and outside the human body. 6 Both classes of polymer undergo hydrolytic bond cleavage to form water-soluble degradation products, resulting in polymer erosion. In this context, the term “degradation” refers to the actual bond cleavage reaction, whereas “erosion” refers to the depletion of mass from the device or implant. While the degradation of many polymers follows first-order or pseudo first-order kinetics, their erosion, which is gauged by mass loss, is generally much more complicated. Hydrolytic degradation occurs whenever degradable polymer segments (e.g., esters or anhydride linkages) come into contact with water. If water diffusion into a sample is slow compared to the hydrolysis reaction, then the water will be consumed on the surface by hydrolysis before it can penetrate into the bulk of the sample. Many polyanhydrides and poly(ortho esters) fall into this category and are designated as surface-eroding polymers. Bulk erosion, on the other hand, occurs when diffusion of water into the sample is much faster than the hydrolysis reaction. This type of mechanism occurs in linear polymers such as PLA and other, more hydrophilic polymer networks such as hydrogels. This contribution examines the behavior of degradable, chemically cross-linked hydrogels, particularly those synthesized from macromers of poly(lactic acid)-poly(ethylene glycol)-poly- (lactic acid) copolymer (PLA-b-PEG-b-PLA) as a model system. Sawhney et al. 7 originally described the synthesis of a triblock PLA-b-PEG-b-PLA copolymer with acrylate end groups (See Figure 1). Since that time, Hubbell and others have proven the usefulness of gels constructed from these macromers in a number of biomedical applications. 2-5 While the degradation behavior of these hydrogels has also been examined experi- mentally, 8 the fundamentals behind this behavior have not been thoroughly investigated nor are the complexities of the process well understood. Currently, no theoretical models exist in the literature to explain the unique bulk-degradation and erosion behavior of cross-linked hydrogel systems. Predicting such behavior would allow the current materials to be strategically optimized. 9 In addition, an accurate degradation model based on fundamental * To whom correspondence should be addressed. E-mail: Kristi.Anseth@ colorado.edu. Fax: (303) 492-4341. 7043 J. Phys. Chem. B 2000, 104, 7043-7049 10.1021/jp000523t CCC: $19.00 © 2000 American Chemical Society Published on Web 07/12/2000