Bone biomechanics at the ultrastructural level: A finite element study using phase-field fracture modelling

Lamellar bone is a critical structural unit in cortical and trabecular bone at the sub-microscale, and consists of mineralised collagen fibrils (MCFs) made of hydroxyapatite (HA) minerals within staggered collagen molecules. These MCFs are surrounded by an extra-fibrillar matrix, containing HA minerals covered with non-collagenous proteins (NCPs). Traditionally, it was believed that most minerals resided within the MCFs, primarily in the gaps between collagen molecules. However, recent studies suggest that MCFs cannot accommodate the majority of minerals, with a significant portion existing outside the MCFs, reported as platelets or grains, wrapped around each fibril. Understanding bone mechanics at the sub-microscale and nanoscale—critical due to their influence on bone fragility—and requires thorough examinations of different parameters such as the content and distribution of minerals and their interaction with the organic matrix. This thesis investigates these aspects using finite element models and a multiscale homogenisation approach. At the nanoscale, detailed representative volume elements (RVEs) for MCFs and the extra-fibrillar matrix were developed. At the sub-microscale, several RVEs for lamellar bone were created to analyse each component's contribution to the bone's mechanical properties. This framework employs a homogenisation strategy to calculate effective elastic properties, meanwhile to study fracture properties, a phase field fracture model was developed and implemented. The analysis incorporates recent findings on the distribution of mineral platelets around collagen fibrils, enhancing the model's accuracy in predicting lamellar bone's mechanical response. In the elastic regime, the results of showed that the extra-fibrillar matrix, rich in HA minerals and characterized by a highly ordered arrangement of mineral platelets along the MCFs, predominantly influences the tissue's elastic properties. This suggests that the extra-fibrillar matrix plays a more significant role in bone stiffness than previously assumed intra-fibrillar mineralisation. Beyond the elastic properties, the second study introduces a two-dimensional micromechanics damage-based RVE with a phase-field damage model to simulate fracture behaviour in lamellar bone, particularly under transverse loads. This advanced model emphasises the importance of mineral-mineral and mineral-fibril interactions, mediated by NCPs, in determining bone strength and toughness. It reveals that fractures often initiate in the mineral-rich extra-fibrillar matrix but are influenced by the presence and distribution of MCFs. MCFs do not affect crack path at low volume content. However, at high volume fraction depending on the interphase strength, MCFs can either facilitate or hinder crack propagation, affecting the tissue's fracture resistance and energy dissipation. Finally, the role of mineral morphology on mechanical performance was investigated, with the results showed that platelet-shaped minerals offer superior load-bearing capacity compared to granular forms. Both MCFs and extra-fibrillar platelet minerals act as barriers to crack propagation, significantly enhancing the tissue's toughness. These findings advance our understanding of bone mechanics across structural levels and underscore the complex interplay of mineral and organic components that contribute to lamellar bone's unique mechanical properties.

Funder

European Research Council (ERC)

Publisher

University of Galway

Rights

CC BY-NC-ND

cbn

Collections

University of Galway Theses (PhD Theses)