Modelling Degradation of Bioresorbable Polymeric Medical Devices.

Cover -- Modelling Degradation of Bioresorbable Polymeric Medical Devices -- Copyright -- Contents -- List of contributors -- Woodhead Publishing Series in Biomaterials -- Part One Fundamental methods of modelling degradation of bioresorbable polymeric medical devices -- 1 Introduction to computer modelling for the design of biodegradable medical devices -- 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 -- References -- 2 Modelling degradation of amorphous biodegradable polyesters: basic model -- 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 -- References -- 3 Modelling degradation of amorphous biodegradable polyesters: advanced model -- 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 -- References -- 4 Modelling degradation of semi-crystalline biodegradable polyesters -- 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 -- References -- 5 Modelling biodegradation of composite materials made of biodegradable polyesters and tricalcium phosphates (TCPs) -- 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 -- References -- 6 Modelling heterogeneous degradation of polymeric devices due to short chain diffusion -- 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 -- References -- Part Two Advanced methods of modelling degradation of bioresorbable polymeric medical devices -- 7 Finite element analysis (FEA) of biodegradation of polymeric medical devices -- 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 -- References -- 8 The effective diffusion coefficient of degrading polymers -- 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.

References -- 9 Mechanical properties of biodegradable polymers for medical applications -- 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 -- References -- 10 Molecular and multi-scale modelling methods of polymer device degradation -- 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 -- References -- Index.

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