Investigating the Stress and Strain fields in Porous Synthetic Bone Graft Substitute Materials with Varied Porosity Levels

Abstract

Porous hydroxyapatite (PHA) ceramic granules have been found to be highly successful synthetic bone graft substitute (BGS) materials, encouraging rapid, good quality bone healing. Key to the success of these materials is a hierarchical multi-scale pore structure, consisting of both macro pores (Larger than 50 𝜇m in diameter) giving the granules their characteristic foam-like pore structure, and smaller micro pores (less than 20 𝜇m in diameter) which are found within the ‘struts’ or ‘body’ of the foam structure. It has been widely reported that control of the level of total porosity (dominated by the macro pores) has an impact on bone healing in BGS, the rate of remodelling and the nature of bone growth. However, within porous hydroxyapatite (PHA) granules the level of strut porosity and micro porosity have also been found to be key to the rate and pattern of bone growth. This has been hypothesised to be due to the variation in the macro-structure and micro-architecture of the BGS resulting in different level of strains experienced within the niche environments of the implanted granule masses, which in turn stimulates or supresses bone growth through mechano-transduction pathways. The aim of this study was to develop, simulate and analyse finite element models of PHA granule masses. This is to identify whether changes in the level of strut and total porosities, could alter the patterns of stresses and strains exhibited within granule masses to effect local bone formation. Models for finite element analysis (FEA) were generated from micro-CT scans of cylinders packed with granule masses of different combinations of total and strut porosities. The procedure captured the natural porous architecture in a novel approach to the analysis of PHA. The study demonstrated that PHA granules as a material maintain their heterogeneity and density at different scales and thus lend themselves to homogenisation techniques to create representative volume entities (RVEs). The analysis incorporated RVEs of different sizes to investigate the continuity of the material behaviour. All the models were energetically validated. They were modelled using a linear elastic model as well as a plastic non-linear one typically used in soil and powder modelling applications. The non-linear Drucker-Prager cap model, was utilised combining a mathematical approach and mechanical testing techniques, to obtain the model’s parameters, in an attempt to eliminate the need for extensive mechanical tests. FEA on the representative volumes demonstrated a wholesale change in strain levels and distribution associated with the level of porosity. Changes in strut porosities showed a direct effect on the peak strain levels within the porous structures. Where the location of both stress and strain peaks as well as fields favoured the pore waists throughout all simulations with slight variation in the precision of concentration in response to changes in strut porosity. These observations could explain the differences observed in the structure of bone growth within BGS materials with matched total porosities but varied levels of strut porosities. Moreover, they may also explain the phenomena where by bone formation within PHA has been observed to occur simultaneously within a single pore via both endochondral and mesenchymal pathways. These results suggest that the models generated in this PhD could be used to further investigate the effect of structure and strain manipulation to control the rate and quality of bone regeneration within bone graft substitutes