ABSTRACT
We establish a novel mathematical model to describe and analyze pH levels in the vicinity of poly(N-vinylcaprolactam-co-acetoacetoxyethyl methacrylate-co-N-vinylimidazole) (VCL/AAEM/VIm) microgel-functionalized polymers during biodegradation. Biodegradable polymers, especially aliphatic polyesters (polylactide/polyglycolide/polycaprolactone homo- and copolymers), have a large range of medical applications including delivery systems, scaffolds, or stents for the treatment of cardiovascular diseases. Most of those applications are limited by the inherent drop of pH level during the degradation process. The combination of polymers with VCL/AAEM/VIm-microgels, which aims at stabilizing pH levels, is innovative and requires new mathematical models for the prediction of pH level evaluation. The mathematical model consists of a diffusion-reaction PDE system for the degradation including reaction rate equations and diffusion of acidic degradation products into the vicinity. A system of algebraic equations is coupled to the degradation model in order to describe the buffering action of the microgel. The model is validated against the experimental pH-monitored biodegradation of microgel-functionalized polymer foils and is available for the design of microgel-functionalized polymer components.
Subject(s)
Hydrogen-Ion Concentration , Models, Theoretical , Polyesters/chemistry , Polymers/chemistry , Biocompatible MaterialsABSTRACT
We establish a novel mathematical model to describe and analyze pH levels in the vicinity of poly(N-vinylcaprolactam-co-acetoacetoxyethyl methacrylate-co-N-vinylimidazole) (VCL/AAEM/VIm) microgel-functionalized polymers during biodegradation. Biodegradable polymers, especially aliphatic polyesters (polylactide/polyglycolide/polycaprolactone homo- and copolymers), have a large range of medical applications including delivery systems, scaffolds, or stents for the treatment of cardiovascular diseases. Most of those applications are limited by the inherent drop of pH level during the degradation process. The combination of polymers with VCL/AAEM/VIm-microgels, which aims at stabilizing pH levels, is innovative and requires new mathematical models for the prediction of pH level evaluation. The mathematical model consists of a diffusion-reaction PDE system for the degradation including reaction rate equations and diffusion of acidic degradation products into the vicinity. A system of algebraic equations is coupled to the degradation model in order to describe the buffering action of the microgel. The model is validated against the experimental pH-monitored biodegradation of microgel-functionalized polymer foils and is available for the design of microgel-functionalized polymer components.
ABSTRACT
Antimicrobial photodynamic therapy (aPDT) is a promising method to treat local bacterial infections. The therapy is painless and does not cause bacterial resistances. However, there are gaps in understanding the dynamics of the processes, especially in periodontal treatment. This work describes the advances in fundamental physical and mathematical modeling of aPDT used for interpretation of experimental evidence. The result is a two-dimensional model of aPDT in a dental pocket phantom model. In this model, the propagation of laser light and the kinetics of the chemical reactions are described as coupled processes. The laser light induces the chemical processes depending on its intensity. As a consequence of the chemical processes, the local optical properties and distribution of laser light change as well as the reaction rates. The mathematical description of these coupled processes will help to develop treatment protocols and is the first step toward an inline feedback system for aPDT users.
