A Phenomenological Mathematical Modelling Framework for the Degradation of Bioresorbable Composites

With an ageing population [1] and an increasing rate of sports related injuries [2], the need for a steady and reliable source of good quality materials for orthopaedic applications seems paramount. Currently, the three main commercially available types of orthopaedic implants are: non-degradable implants, biodegradable polymeric implants and bioresorbable composites or biocomposites, that is composites made of biodegradable polymers and calcium-based fillers. Figure 1.1 depicts the different types of interference screws for anterior cruciate ligament (ACL) reconstruction manufactured by Stryker [3].

This chapter briefly discusses relevant literature on the degradation mechanisms of bioresorbable composites and the computational models developed to characterise them. As mentioned in the introductory chapter, the harvest and analysis of published experimental degradation data from bioresorbable composites is one of the main objectives of this thesis. Therefore, a majority of the literature on biocomposite degradation is presented in the following chapters and to avoid repetition, only introductory literature is included here.

This chapter discusses the development of computational degradation models for different bioresorbable composite materials. The models were developed in a two-stage process. Firstly, a general modelling framework was generated and analysed and secondly, this general framework was particularised for specific ceramic fillers yielding the degradation models.

As previously mentioned in the introductory chapter, studying the degradation of biocomposites is a time and resource-consuming process. Therefore it is logical to try and maximise the information that can be extracted from already published experimental data. Although inaccurate and incomplete information in composite characterisation are to be expected, analysing these published degradation data with the computational models obtained from the general modelling framework based on an extended version of Pan et al.’s TCP-polyester composite degradation model [1] and presented in Chap. 3 is, in the author’s opinion, still a worthy approach. By doing so, a global degradation map for biocomposites can be built. This map, albeit incomplete, will aid understanding of the biocomposite degradation mechanisms and highlight areas of particular interest due to their appropriate degradation profiles.

In this chapter, the analysis of the degradation of hydroxyapatite (HA) composites using the HA composites degradation model, described in Sect. 3.​2.​2, is presented. The chapter follows, with minor changes, the structure of Chap. 4. Firstly, in Sect. 5.1, the HA composite degradation data harvested from literature are reported, including the necessary composite degradation input information employed by the computational model. The second section, Sect. 5.2, includes information about the different types of hydroxyapatite (HA) found in the harvested degradation data and their associated values for the ceramic-dependent constants.

This chapter presents the study of the degradation of nanocomposites made of poly(D,L-lactide-co-glycolide) and calcium carbonate. The first section of the chapter describes the materials and methods employed in this work. The second section includes the characterisation of the raw materials followed by the characterisation of the undegraded and degraded composites in the third and fourth sections, respectively. The discussion of the results is reported in the fifth section and lastly, the conclusions in the sixth and final section.

This chapter includes the analysis of the degradation of calcium carbonate (CC) composites employing the CC composites degradation model described in Sect. 3.​2.​3. In addition, it presents a second analysis of the experimental data presented in Chap. 6 using an extended method which takes advantage of the detailed nature of the data. Chapter 7 is the third and last chapter dealing with the use of the ceramic-specific degradation models, derived from the general modelling framework, to analyse the degradation of biocomposites and thus, presents a structure similar to Chaps. 4 and 5. The first section, Sect. 7.1, presents the calcium carbonate composite degradation data harvested from literature. Section 7.2 reports the different types of calcium carbonate encountered in the harvested data and the values of the ceramic-dependent constant for each one of them. Similarly to Chap. 5, the values of the polymer-dependent constants are not included. Those values can be found in Sect. 4.​3. The values at the time origin of the variables employed in the CC composites degradation model are included in Sect. 7.3. The results of the degradation simulations are presented in Sect. 7.4, followed by the discussion in Sect. 7.5. Section 7.6 contains the conclusions derived from the different analyses of the degradation of calcium carbonate composites. The detailed analysis of Chap. 6 data is presented in Sect. 7.7. And lastly, in addition to the calcium carbonate specific conclusions, Sect. 7.8 contains a summary of the core insights derived from the composite degradation analyses carried out in Chaps 4, 5 and 7 with the three ceramic-specific computational models.

In this final chapter, the main conclusions stemming from this research are presented, followed by a series of suggestions for future work.