Computer simulation of polymer chain scission in biodegradable polymers

Biodegradable polymers degrade due to the hydrolysis (chain scission) of the polymer chains. Two theories of hydrolysis are that 1) scissions occur randomly at any bond in chains, and 2) scissions occur in the final bond at chain ends. In this study, a simulation tool was developed to simulate both random chain scission and chain end scission. The effect of each type of scission was analysed. Random scissions were found to have over 1000 time’s greater impact on molecular weight reduction than end scissions. For the degradation of poly lactic acid by random scission, it was found that Mn must reduce to <5000 g/mol in order for a polymer to exhibit significant mass loss due to the diffusion of water-soluble short chains. In contrast, end scission was able to produce a significant fraction of water-soluble chains with little or no effect on Mn. The production rate of water-soluble chains was linearly related to end scission but increase in an accelerated manner due to random scission. Molecular weight distributions were fitted to experimental data for the degradation of poly D-lactic acid

An atomic finite element model for biodegradable polymers. Part 2. A model for change in Young’s modulus due to polymer chain scission

Atomic simulations were undertaken to analyse the effect of polymer chain scission on amorphous poly(lactide) during degradation. Many experimental studies have analysed mechanical properties degradation but relatively few computation studies have been conducted. Such studies are valuable for supporting the design of bioresorbable medical devices. Hence in this paper, an Effective Cavity Theory for the degradation of Young's modulus was developed. Atomic simulations indicated that a volume of reduced-stiffness polymer may exist around chain scissions. In the Effective Cavity Theory, each chain scission is considered to instantiate an effective cavity. Finite Element Analysis simulations were conducted to model the effect of the cavities on Young's modulus. Since polymer crystallinity affects mechanical properties, the effect of increases in crystallinity during degradation on Young's modulus is also considered. To demonstrate the ability of the Effective Cavity Theory, it was fitted to several sets of experimental data for Young's modulus in the literature

Degradation mechanisms of bioresorbable polyesters. Part 2, Effects of initial molecular weight and residual monomer

This paper presents an understanding of how initial molecular weight and initial monomer fraction affect the degradation of bioresorbable polymers in terms of the underlying hydrolysis mechanisms. A mathematical model was used to analyse the effects of initial molecular weight for various hydrolysis mechanisms including noncatalytic random scission, autocatalytic random scission, noncatalytic end scission or autocatalytic end scission. Different behaviours were identified to relate initial molecular weight to the molecular weight half-life and to the time until the onset of mass loss. The behaviours were validated by fitting the model to experimental data for molecular weight reduction and mass loss of samples with different initial molecular weights. Several publications that consider initial molecular weight were reviewed. The effect of residual monomer on degradation was also analysed, and shown to accelerate the reduction of molecular weight and mass loss. An inverse square root law relationship was found between molecular weight half-life and initial monomer fraction for autocatalytic hydrolysis. The relationship was tested by fitting the model to experimental data with various residual monomer contents

A Mechanistic Model for Acidic Drug Release Using Microspheres Made of PLGA 50:50

Polyester microspheres are extensively studied for controlled release drug delivery devices, and many models have been developed to describe drug release from the bulk polymer. However, the interaction between drugs and polymers is ignored in most of the existing mathematical models. This paper presents a mechanistic model which captures the interplay between acidic drugs and bioresorbable polyesters. The model considers the autocatalytic effect on polymer degradation arising from carboxylic acid end groups of oligomers and drug molecules. Hence, the enhancing effect of acidic drug on the rate of degradation was fully considered. On the other hand the drug release from polyester microspheres is controlled by drug diffusion from polymer matrix. The drug diffusion coefficient depends strongly on the level of degradation of the polymer. This effect is also included in the model. It is shown that the model can effectively predict experimental data in the literature for both polymer degradation and drug release. Furthermore, the model is used to design different systems of microspheres which release drugs with either a zero order profile or burst followed by zero order release profile

A Model for Simultaneous Crystallisation and Biodegradation of Biodegradable Polymers.

This paper completes the model of biodegradation for biodegradable polymers that was previously developed by Wang et al. (Wang Y, Pan J, Han X, Sinka, Ding L. A phenomenological model for the degradation of biodegradable polymers. Biomaterials 2008;29:3393-3401). Crystallisation during biodegradation was not considered in the previous work which is the topic of the current paper. For many commonly used biodegradable polymers, there is a strong interplay between crystallisation and hydrolysis reaction during biodegradation – the chain cleavage caused by the hydrolysis reaction provides an extra mobility for the polymer chains to crystallise and the resulting crystalline phase becomes more resistant to further hydrolysis reaction. This paper presents a complete theory to describe this interplay. The fundamental equations in the Avrami’s theory for crystallisation are modified and coupled to the diffusion-reaction equations that were developed in our previous work. The mathematical equations are then applied to three biodegradable polymers for which long term degradation data are available in the literature. It is shown that the model can capture the behaviour of the major biodegradable polymers very well

Effects of Surface Diffusion and Heating Rate on First-Stage Sintering That Densifies by Grain-Boundary Diffusion

This paper presents a computational study of the role played by surface diffusion on first-stage sintering of powders that densify by grain-boundary diffusion. Coupled grain-boundary and surface diffusion is considered as the mechanism for matter redistribution. By using several novel approaches of presentation of the numerical data, it is shown that the assumption of fast surface diffusion is invalid for typical sintering conditions and materials in first stage of sintering. The study reveals a simple explanation for the role played by surface diffusion in matter redistribution of combined grain-boundary and surface diffusion—surface diffusion changes direction from moving atoms away from a contact neck to depositing atoms onto it as the rate of surface diffusion increases. The reverse surface diffusion blunts the neck and retards densification. It is shown that this mechanism is significant not only for free sintering but also for pressure assisted sintering. It is further confirmed that the widely observed beneficial effect of spark plasma sintering on densification can be, at least partially, attributed to its fast heating rate, which quickly passes through sintering at low temperatures where surface diffusion dominates

Multi-scale modelling of sintering

Multi-scale modelling of sinterin

Multi-Scale Modelling of Sintering

Multi-scale modelling of sinterin

Detection of degradation in polyester implants by analysing mode shapes of structure vibration

This paper presents a numerical study on using vibration analysis to detect degradation in degrading polyesters. A numerical model of a degrading plate sample is considered. The plate is assumed to degrade following the typical behaviour of amorphous copolymers of polylactide and polyglycolide. Due to the well-known autocatalytic effect in the degradation of these polyesters, the inner core of the plate degrades faster than outer surface region, forming layers of materials with varying Young׳s modulus. Firstly the change in molecular weight and corresponding change in Young׳s modulus at different times are calculated using the mathematical models developed in our previous work. Secondly the first four mode shapes of transverse vibration of the plate are calculated using the finite element method. Finally the curvature of the mode shapes are calculated and related to the spatial distribution of the polymer degradation. It is shown that the curvature of the mode shapes can be used to detect the onset and distribution of polymer degradation. The level of measurement accuracy required in an experiment is presented to guide practical applications of the method. At the end of this paper a demonstration case of coronary stent is presented showing how the method can be used to detect degradation in an implant of sophisticated structure

A model for hydrolytic degradation and erosion of biodegradable polymers.

For aliphatic polyesters such as PLAs and PGAs, there is a strong interplay between the hydrolytic degradation and erosion - degradation leads to a critically low molecular weight at which erosion starts. This paper considers the underlying physical and chemical processes of hydrolytic degradation and erosion. Several kinetic mechanisms are incorporated into a mathematical model in an attempt to explain different behaviours of mass loss observed in experiments. In the combined model, autocatalytic hydrolysis, oligomer production and their diffusion are considered together with surface and interior erosion using a set of differential equations and Monte Carlo technique. Oligomer and drug diffusion are modelled using Fick's law with the diffusion coefficients dependent on porosity. The porosity is due to the formation of cavities which are a result of polymer erosion. The model can follow mass loss and drug release up to 100%, which cannot be explained using a simple reaction-diffusion. The model is applied to two case studies from the literature to demonstrate its validity. The case studies show that a critical molecular weight for the onset of polymer erosion and an incubation period for the polymer dissolution are two critical factors that need to be considered when predicting mass loss and drug release. STATEMENT OF SIGNIFICANCE: In order to design bioresorbable implants, it is important to have a mathematical model to predict polymer degradation and corresponding drug release. However, very different behaviours of polymer degradation have been observed and there is no single model that can capture all these behaviours. For the first time, the model presented in this paper is capable of capture all these observed behaviours by switching on and off different underlying mechanisms. Unlike the existing reaction-diffusion models, the model presented here can follow the degradation and drug release all the way to the full disappearance of an implant