(569a) A Unified Mathematical Model for Predicting Controlled Release from Surface and Bulk Eroding Matrices without Regression

The development of polymeric matrices to control the release of small molecules, peptides and proteins has created an industry valued at over $110 billion dollars. Spurred by a desire to explain how agent egress occurs, many attempts have been made to model drug release based on the physical properties of the matrix, drug, and polymer. Over time, these models have progressed from empirical equations that provide descriptive insights into more mechanistic forms capable of predicting release data in specific matrix systems, such as small molecules encapsulated in PLGA microspheres or polyanhydride implants.

We have recently published the first, broadly applicable, predictive model for the most widely used polymers in bulk-eroding biodegradable matrices (e.g. polyester formulations such as Lupron Depot®). We have also recently extended this model to traditionally surface eroding systems, such as polyanhydride implants (e.g. Gliadel wafer®). In its new form, the model considers two phases (solid and aqueous) of the encapsulated agent to account for dissolution kinetics. Accounting for these kinetics is essential, as many polyanhydride matrices, being too small to prolong release via surface erosion, extend release based solely upon solubility limitations. Diffusion reaction equations were also added to account for matrix hydration kinetics, which can have a significant duration over an implant's lifetime. Accounting for the hydration kinetics allows the calculation of the critical length where a system transitions from surface to bulk erosion. Unlike prior methods of calculating this critical length, the current model uses a mechanistically relevant second order degradation rate expression, which also accounts for changes in the polymer's initial molecular weight.

This extended form of the model can now be used to predict release data without regression for both bulk and surface eroding systems. Further, the plasticity of the model's framework allows modeling of systems that noticeably transition from surface to bulk erosion. To test the model regression free predictions were compared to published data from all three types of systems. Theoretical predictions from this model also indicate that properly sized implants, composed of common biodegradable polymers with specific molecular weights, can prolong the duration of release for hydrophilic agents to at least one month by transitioning between erosion schemes.

In conclusion, extending our published model to account for dissolution and hydration kinetics allows it to accurately describe a broader range of systems. Accounting for the hydration kinetics also enabled the calculation of a critical length which hints at a transitioning erosion scheme for many systems originally thought to be dominated by surface erosion. With this increased understanding of biodegradable matrix controlled release, therapeutics design may be improved based on model predictions and new materials may be targeted based on their potential to control release.