Abstract
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.
Highlights
Poly(D,L-lactic-co-glycolic acid) (PLGA) microspheres are biodegradable polymeric devices that are widely studied for controlled-release drug delivery [1,2,3,4]
PLGA erosion is treated by assuming that all carboxylic acid end groups have a uniform constant diffusion coefficient D independent of the length of the polymer chain to which they are attached; with this assumption, diffusion of degradation products can be included in the analytical expression for autocatalyst concentration
The expression differs from the common reaction-diffusion case treated in the spherical catalyst literature as we treat a generation rather than consumption reaction term. This is the first application of such an analytical expression for the reaction-diffusion equation to PLGA microspheres to model degradation and erosion of the polymer
Summary
Poly(D,L-lactic-co-glycolic acid) (PLGA) microspheres are biodegradable polymeric devices that are widely studied for controlled-release drug delivery [1,2,3,4]. Drug molecules dispersed in the bulk polymer are released by diffusion by two main pathways: through the nondegraded polymer bulk and through aqueous pores that form in the polymer bulk as the polymer undergoes hydrolysis. Between microsphere size range extremes, drug release may transition from the diffusion-controlled regime (diffusive release through the nondegraded polymer bulk is faster through smaller microspheres that have shorter diffusion lengths than in larger microspheres) to the erosion-controlled regime (diffusive release through aqueous pores is faster through larger microspheres that have eroded porous interiors than in smaller microspheres). Poorly water-soluble molecules are known to diffuse more through the nondegraded polymer bulk so are released more quickly in the diffusion-controlled regime [5, 6]. Small, highly water-soluble molecules and macromolecules are known to diffuse more through aqueous pores so are released more quickly in the erosion-controlled regime [7]. To describe the development of the pore structure in the microspheres, it is first necessary to consider how the polymer reacts and forms pores
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