Derivation of an Analytical Solution to a Reaction-Diffusion Model for Autocatalytic Degradation and Erosion in Polymer Microspheres.
A mathematical reaction-diffusion model is defined to describe the gradual decomposition of polymer microspheres composed of poly(D,L-lactic-co-glycolic acid) (PLGA) that are used for pharmaceutical drug delivery over extended periods of time. The partial differential equation (PDE) model treats simultaneous first-order generation due to chemical reaction and diffusion of reaction products in spherical geometry to capture the microsphere-size-dependent effects of autocatalysis on PLGA erosion that occurs when the microspheres are exposed to aqueous media such as biological fluids. The model is solved analytically for the concentration of the autocatalytic carboxylic acid end groups of the polymer chains that comprise the microspheres as a function of radial position and time. The analytical solution for the reaction and transport of the autocatalytic chemical species is useful for predicting the conditions under which drug release from PLGA microspheres transitions from diffusion-controlled to erosion-controlled release, for understanding the dynamic coupling between the PLGA degradation and erosion mechanisms, and for designing drug release particles. The model is the first to provide an analytical prediction for the dynamics and spatial heterogeneities of PLGA degradation and erosion within a spherical particle. The analytical solution is applicable to other spherical systems with simultaneous diffusive transport and first-order generation by reaction.
Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, United States of America; Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America.
Ashlee N
AN
Ford Versypt
Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, United States of America.
Paul D
PD
Arendt
Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, United States of America; Department of Chemical and Materials Engineering, University of Kentucky, Lexington, Kentucky, United States of America; Department of Pharmaceutical Sciences, University of Kentucky, Lexington, Kentucky, United States of America.
Daniel W
DW
Pack
Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, United States of America; Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America.
Richard D
RD
Braatz
D002384:Catalysis; D004337:Drug Carriers / Q000737:chemistry*; D016503:Drug Delivery Systems; D019344:Lactic Acid / Q000737:chemistry*; D008863:Microspheres; D008962:Models, Theoretical; D011100:Polyglycolic Acid / Q000737:chemistry*; D000077182:Polylactic Acid-Polyglycolic Acid Copolymer
D004337:Drug Carriers; D000077182:Polylactic Acid-Polyglycolic Acid Copolymer; D011100:Polyglycolic Acid; D019344:Lactic Acid