Modelling degradation of medical implants made of biodegradable polymers

Bioresorbable polymer is widely used inside the human body as resorbable medical devices such as fixation screws, plates, sutures, and tissue engineering scaffolds. The most important feature for such devices is that they ‘disappear’ after serving the temporary function that is surgically required. The current design for these devices is still based on trial and error. The degrading process is complex and many factors were involved. This makes the design optimisation very hard. The degradation rate for such devices varies from months to years, making the experimental work expensive and time-consuming. Mathematical modelling could be used in the early stages of designing, and would give an indication of certain degradation behaviours without doing experiments first. The existing mathematical models developed by the Leicester group were used to successfully capture the trend of average molecular weight, degree of crystallisation, and Young’s modulus. However, the previous models still have many gaps to fully capture the underlying chemistry and physics of polymer degradation. Some of the models are also over-complicated to be used in practical designs. This thesis presents several new developments and simplifications to the previous models. These include the separation of long and short polymer chains in the rate equation for polymer chain scission, adding the effect of water diffusion and providing a list of analytical solutions for simple but commonly used situations. A complete set of governing equations are provided by integrating the new rate equation with previously developed equations for crystallization, oligomer diffusion and short chain diffusion. A major issue in the development of biodegradable devices is that it is extremely time consuming and expensive to obtain experimental data for degradation rate because the degradation can take up to several years. The thesis presents a demonstration on how the mathematical model, together with the finite element method, can be used to project degradation rate from one device, for which experimental data are available, to another which is under design. Finally the effective cavity theory for change in Young's modulus and degradation detection using mode analysis, previously developed by the Leicester group, are simplified to make them much more straightforward to use by end users.