A phenomenological mathematical modelling framework for the degradation of bioresorbable composites
Creators: name: Moreno-Gomez, Ismael
Publisher: name: Apollo - University of Cambridge Repository
Year: 2018
Subjects: modelling
bioresorbable
composite
polymeric matrix
ceramic filler
tricalcium phosphate
hydroxyapatite
calcium carbonate
polylactide
polyglycolide
degradation

description: Understanding, and ultimately, predicting the degradation of bioresorbable composites made of biodegradable polyesters and calcium-based ceramics is paramount in order to fully unlock the potential of these materials, which are heavily used in orthopaedic applications and also being considered for stents. A modelling framework which characterises the degradation of bioresorbable composites was generated by generalising a computational model previously reported in literature. The framework uses mathematical expressions to represent the interwoven phenomena present during degradation. Three ceramic-specific models were then created by particularising the framework for three common calcium-based fillers, namely tricalcium phosphate (TCP), hydroxyapatite (HA) and calcium carbonate (CC). In these models, the degradation of a bioresorbable composite is described with four parameters: the non-catalytic and auto-catalytic polymer degradation rates, $k_1$ and $k_2'$ respectively and the ceramic dissolution rate and exponent, $A_\text{d}$ and $\theta$ respectively. A comprehensive data mining exercise was carried out by surveying the existing literature in order to obtain quantitative degradation data for bioresorbable composites containing TCP, HA and CC. This resulted in a database with a variety of case studies. Subsequently, each case study was analysed using the corresponding ceramic-specific model returning a set of values for the four degradation constants. Both cases with agreement and disagreement between model prediction and experimental data were studied. 76% of the 107 analysed case studies displayed the expected behaviour. In general terms, the analysis of the harvested data with the models showed that a wide range of degradation behaviours can be attained using different polymeric matrix - ceramic filler combinations. Furthermore, the existence of discrepancies in degradation behaviour between a priori similar bioresorbable composites became apparent, highlighting the high number of hidden factors affecting composite degradation such as polymer tacticity or ceramic impurities. The analysis of the case studies also highlighted that the ceramic dissolution rate needed to depict the portrayed degradation behaviours is significantly higher than that reported for ceramics alone in dissolution studies under physiological conditions, indicating that studies of the filler elements alone do not provide a complete picture. Lastly, the computational analysis provided insight into the complex influence of factors such as sample porosity and degradation protocol in the degradation behaviour. In addition to the computational analysis of literature data, an experimental degradation study was carried out with nanocomposites made of calcium carbonate and poly(D,L-lactide-co-glycolide). This study showed the existence of a clear buering effect with the addition of the ceramic filler and confirmed the assumptions employed in the modelling framework in this particular bioresorbable composite. The detailed nature and modest size of these data enabled a more precise and thorough analysis using the CC composites degradation model. In summary, the modelling framework is able to capture the main degradation behaviour of bioresorbable composites and also point to factors responsible for dissimilar behaviours. The degradation maps generated with the values of $k_1$, $k_2'$, $A_\text{d}$ and $\theta$ output by the models appear to be a good tool to summarise, classify and facilitate the analysis and search of specific bioresorbable composites.
description: This author acknowledges the financial support from Lucideon and "La Caixa Europe Programme".