(C-93) Simulation of nano-indentation on mineralized collagen fibril and extrafibrillar matrix of bone using a novel 2D cohesive finite element approach

Introduction:: Currently, bone mineral density (BMD) is commonly used to assess bone fracture risk and efficacy of therapeutical treatments. Previous studies indicated that BMD is not a reliable measure of bone fragility because other constituents in bone (i.e., Type I collagen fibrils, non-collagenous proteins, and water), may also play an important role in bone mechanical behavior. However, their contribution to bone fragility fractures is still poorly understood. In this study, we hypothesized that the energy dissipation during bone deformation and failure is mainly dependent on the behavior of organic interfaces residing in the mineralized collagen fibril (MCF) and extrafibrillar matrix (EFM). To test the hypothesis, a finite element model using a 2D cohesive finite element approach was performed to simulate the nano-indentation on MCF and EFM. The results were verified by comparing them with experimental results.


Materials and Methods:: A 2-D finite element model of sub-lamella structure of bone comprising both MCF and EFM was developed using ABAQUS 2021 (Fig. 1). The collagen molecules were not modeled explicitly, but modeled as a continuum collagen matrix in which mineral platelets are arranged in 40 nm gap regions. The intrafibrillar mineral (HA) platelets were assumed to be 40 nm long and 3 nm thick and deposited in the gap regions of the collagen fibrils. A layer of water molecules was modelled between the HA platelets and surrounding collagen matrix inside MCF. EFM was modelled as a random aggregate of HA polycrystals that were bounded via a thin layer of organic phase (e.g., non-collagenous proteins, NCPs). The average width of EFM was selected as 3-4 nm. The material property of the HA polycrystals was considered as isotropic linear elastic material with Young’s modulus Em=100 GPa, Poisson’s ratio vm=0.28. Collagen phase was considered as hyperelastic material using an exponential function in Abaqus. Then, a cohesive finite element model (Lin et al., 2017) was used to model three types of interfaces in the model: (1) the interfaces between HA platelets and collagen matrix inside MCF; (2) the interfaces between HA grains in EFM; and (3) the interface between EFM and MCF subunits. (2). Once unloading occurs, the unloading path follows the same slope as the initial slope of the traction-separation relationship. The indentation experiments were performed using AFM, and the experimental results were collected from our previous work (Han et al., 2021).

Results, Conclusions, and Discussions:: Results and Discussion: The results showed that the simulation of indentation matched well with the experimental results in terms of both energy dissipation and elastic modulus. Since the collagen molecules and the intrafibrillar mineral were modelled as elastic material, the results of this study implied that the energy dissipation was dependent on the organic interface, hence supporting the hypothesis of this study.

Conclusions: This preliminary study confirmed that the energy dissipation was dependent on the mechanical behavior of the organic interface, further proving that the organic interface is playing a significant role in bone mechanical behavior.


Acknowledgements (Optional): :

References (Optional): : [1] Liqiang, L., et.al JMBBM, 2017.

[2] Han,Y., et.al, JMBBM, 2021.