Modelling Degradation of Bioresorbable Polymeric Medical Devices

Part One: Fundamental methods of modelling degradation of bioresorbable polymeric medical devices

1. Introduction to computer modelling for the design of biodegradable medical devices

• Abstract
• 1.1 Introduction
• 1.2 General modelling techniques useful in studying device degradation
• 1.3 The degradation pathway and models presented in this book
• 1.4 Challenges and unresolved issues
• Acknowledgements

2. Modelling degradation of amorphous biodegradable polyesters: basic model

• Abstract
• 2.1 Introduction
• 2.2 Hydrolysis rate equation
• 2.3 Production of short chains
• 2.4 Master equation for chain scission
• 2.5 Summary of equations and list of symbols
• 2.6 Analytical solutions of the master equation
• 2.7 Numerical solution of the master equation
• 2.8 Concluding remarks

3. Modelling degradation of amorphous biodegradable polyesters: advanced model

• Abstract
• 3.1 Introduction
• 3.2 Partition of carboxylic end groups on long and short chains
• 3.3 Analytical solutions to the master equation
• 3.4 Numerical solution and a parametric study of the model
• 3.5 Separation of end scission from random scission
• 3.6 Contributions from random and end scissions to polymer degradation
• 3.7 Concluding remarks

4. Modelling degradation of semi-crystalline biodegradable polyesters

• Abstract
• 4.1 Introduction
• 4.2 Rate equation for chain scission in semi-crystalline polymers
• 4.3 Actual and extended degrees of crystallinity
• 4.4 Extended degree of crystallinity of chain cleavage-induced crystallisation
• 4.5 Summary of governing equations for simultaneous chain scission and crystallisation
• 4.6 Calculation of number-averaged molecular weight
• 4.7 Comparison between models assuming fast and normal crystallisation
• 4.8 Concluding remarks

5. Modelling biodegradation of composite materials made of biodegradable polyesters and tricalcium phosphates (TCPs)

• Abstract
• 5.1 Introduction
• 5.2 TCP dissolution and buffering reactions
• 5.3 Rate equation for chain scission in presence of buffering reactions
• 5.4 Governing equations for degradation of polyester-TCP composites
• 5.5 Normalised equations
• 5.6 TCP effectiveness map
• 5.7 Concluding remarks

6. Modelling heterogeneous degradation of polymeric devices due to short chain diffusion

• Abstract
• 6.1 Introduction
• 6.2 Scission rate of long chains affected by short chain diffusion
• 6.3 Diffusion equation for short chains
• 6.4 Collection of the governing equations
• 6.5 A numerical study of size effect
• 6.6 Non-dimensionalisation and degradation map
• 6.7 Effect of other factors on the degradation map
• 6.8 Concluding remarks

Part Two: Advanced methods of modelling degradation of bioresorbable polymeric medical devices

7. Finite element analysis (FEA) of biodegradation of polymeric medical devices

• Abstract
• 7.1 Introduction
• 7.2 Case study A: a three-dimensional cube
• 7.3 Case study B: scaffolds in tissue engineering
• 7.4 Case study C: internal bone-fixation screws
• 7.5 Case study D: coronary stents
• 7.6 Conclusions
• Acknowledgement

8. The effective diffusion coefficient of degrading polymers

• Abstract
• 8.1 Introduction
• 8.2 Analytical expressions of the effective diffusion coefficient for a two-phase material
• 8.3 Empirical expressions for the effective diffusion coefficient
• 8.4 Molecular dynamics (MD) and Brownian dynamics (BD)
• 8.5 The direct finite element (DFE) method for effective diffusion coefficients
• 8.6 Summary
• 8.7 Conclusions
• Acknowledgements

9. Mechanical properties of biodegradable polymers for medical applications

• Abstract
• 9.1 Fundamentals of mechanical properties in polymers
• 9.2 Methods of measurement for mechanical properties
• 9.3 Factors that influence the mechanical properties of bioresorbable polymers before degradation
• 9.4 The degradation of mechanical properties
• 9.5 Modelling changes in mechanical properties of degrading polymers
• 9.6 Conclusions

10. Molecular and multi-scale modelling methods of polymer device degradation

• Abstract
• 10.1 Introduction
• 10.2 Mathematical models for polymer chain scission
• 10.3 The Kinetic Monte Carlo (KMC) simulation of hydrolysis reactions
• 10.4 A multi-scale model for device degradations
• 10.5 Conclusions
• Acknowledgement