A mathematical model for water uptake, degradation, erosion and drug release from degradable polydisperse polymeric networks
Thursday 23rd July 2009
Silva Soares, Joao; Zunino, Paolo
We introduce a general class of mixture models to study water uptake, degradation, erosion, and drug release from degradable polydisperse polymeric matrices. The mathematical model is based on a finite number of constituents describing the polydisperse polymeric system, i.e. each representing collection of chains whose size belongs to a finite interval of degree of polymerization. In order to model water uptake and drug release, two additional constituents (water and drug) constitute the mixture. Constituents diffuse individually accordingly to Fick’s first law and balances of mass of constituents yield partial differential equations that govern the reaction-diffusion system. Hydrolysis, a chemical reaction that breaks down larger chains into smaller ones, is accounted with reactions terms quantifying sources and sinks of polymeric chains and a sink of water. Hydrolysis couples the system of equations and nonlinearities appear through constitutive specification of the diffusivities of constituents on the current network, reaction rates, and boundary conditions. The mathematical model is independent of the number of constituents describing the polydisperse polymeric system and hydrolysis kinetics describe with accuracy the overall decrease in molecular weight distribution and satisfies a monomer conservation principle. A shift between two different types of solutions of the system of partial differential equations, each identified to surface or bulk erosion, is obtained with the variation of a single non-dimensional number, the Thiele modulus, which measures the relative importance of the mechanisms of reaction and diffusion. Results of drug release confirm that drug release from bulk eroding matrices is diffusion-controlled, whereas for surface eroding polymers, drug release is enhanced in an erosion-controlled process.