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In orthopedic and dental surgery, the implantation of biomaterials within the bone to restore the integrity of the treated organ has become a standard procedure. Their long-term stability relies on the osseointegration phenomena, where bone grows onto and around metallic implants, creating a bone-implant interface. Bone is a highly hierarchical material that evolves spatially and temporally during this healing phase. A deeper understanding of its biomechanical characteristics is needed, as they are determinants for surgical success. In this context, we propose a multiscale homogenization model to evaluate the effective elastic properties of bone as a function of the distance from the implant, based on the tissue's structure and composition at lower scales. The model considers three scales: hydroxyapatite foam (nanoscale), ultrastructure (microscale), and tissue (mesoscale). The elastic properties and the volume fraction of the elementary constituents of bone matrix (mineral, collagen, and water), the orientation of the collagen fibril relative to the implant surface, and the mesoscale porosity constitute the input data of the model. The effect of a spatiotemporal variation in the collagen fibrils' orientation on the bone anisotropic properties in the proximity of the implant was investigated. The findings revealed a strong variation of the components of the effective elasticity tensor of the bone as a function of the distance from the implant. The effective elasticity appears to be primarily sensitive to the porosity (mesoscale) rather than to the collagen fibrils' orientation (sub-micro scale). However, the orientation of the fibrils has a significant influence on the isotropy of the bone. When analyzing the symmetry properties of the effective elasticity tensor, the ratio between the isotropic and hexagonal components is determined by a combination of the porosity and the fibrils' orientation. A decrease in porosity leads to a decrease in bone isotropy and, in turn, an increase in the impact of the fibrils' orientation. These results demonstrate that the collagen fibril orientation should be taken into account to properly describe the effective elastic anisotropy of bone at the organ scale., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Ultrasound stimulation is thought to influence bone remodelling process. But recently, the efficiency of ultrasound therapy for bone healing has been questioned. Despite an extensive literature describing the positive effect of ultrasound on bone regeneration-cell cultures, animal models, clinical studies-there are more and more reviews denouncing the inefficiency of clinical devices based on low-intensity pulsed ultrasound stimulation (LIPUS) of the bone healing. One of the reasons to cause controversy comes from the persistent misunderstanding of the underlying physical and biological mechanisms of ultrasound stimulation of bone repair. As ultrasonic waves are mechanical waves, the process to be studied is the one of the mechanotransduction. Previous studies on the bone mechanotransduction have demonstrated the key role of the osteocytes in bone mechano-sensing. Osteocytes are bone cells ubiquitous inside the bone matrix; they are immersed in the interstitial fluid (IF) inside the lacuno-canalicular network (LCN). They are considered as particularly sensitive to a particular type of mechanical stress: wall shear stress on osteocytes due to the IF flow in the LCN. Inspired from these findings and observations, the present work investigates the effect of LIPUS on the cortical bone from the tissue to the osteocytes, considering that the impact of the ultrasound stimulation applied at the tissue scale is related to the mechanical stress experimented by the bone cells. To do that simulations based on the finite element method are carried out in the commercial software Comsol Multiphysics to assess the wall shear stress levels induced by the LIPUS on the osteocytes. Two formulations of the wall shear stress were investigated based on two IF flow models inside the LCN and associated with two different values of the LCN permeability. The wall shear stress estimate is very different depending on the assumption considered. One of these two models provides wall shear stress values in accordance with previous works published on bone mechanotransduction. This study presents the preliminary results of a computational model that could provide keys to understanding the underlying mechanisms of the LIPUS.

Reliability of multiscale models of bone is related to the accuracy of the experimental information available on bone microstructure. X-ray-based imaging techniques allow to inspect bone structure and mineralization in vitro at the micrometre scale. However, spatial resolution achievable in vivo is much coarser and can produce blurry, uncertain information on bone microstructure. Working with uncertain data calls for new modelling paradigms able to propagate uncertainty through the scales. In this paper we investigate the effects of uncertain bone mineralization on the elastic coefficients of the bone matrix. To this aim, some stochastic concepts were developed and compared with one another in order to identify the best way to account for uncertain input data. These concepts step from a deterministic micromechanical model of bone matrix which was extended in order to account for uncertain bone composition. Uncertainty was introduced by assuming to know only mean value and dispersion of the parameters describing bone composition. Thus, these parameters were modelled as random variables and their distribution functions were obtained using the maximum entropy principle. Either the tissue mineral density (TMD) or the ensuing volume fractions of collagen and mineral were used to describe uncertain bone composition. Moreover, mean value and dispersion were estimated at the scales of either 10 or a few 100 [Formula: see text]m, representative of standard in vitro and in vivo spatial resolutions, respectively. Analysis of these modelling concepts suggests that TMD measured at the sub-millimetre scale can be used to obtain reliable statistical information about the elastic coefficients of bone matrix.

Accurate and reliable assessment of bone quality requires predictive methods which could probe bone microstructure and provide information on bone mechanical properties. Multiscale modelling and simulation represent a fast and powerful way to predict bone mechanical properties based on experimental information on bone microstructure as obtained through X-ray-based methods. However, technical limitations of experimental devices used to inspect bone microstructure may produce blurry data, especially in in vivo conditions. Uncertainties affecting the experimental data (input) may question the reliability of the results predicted by the model (output). Since input data are uncertain, deterministic approaches are limited and new modelling paradigms are required. In this paper, a novel stochastic multiscale model is developed to estimate the elastic properties of bone while taking into account uncertainties on bone composition. Effective elastic properties of cortical bone tissue were computed using a multiscale model based on continuum micromechanics. Volume fractions of bone components (collagen, mineral, and water) were considered as random variables whose probabilistic description was built using the maximum entropy principle. The relevance of this approach was proved by analysing a human bone sample taken from the inferior femoral neck. The sample was imaged using synchrotron radiation micro-computed tomography. 3-D distributions of Haversian porosity and tissue mineral density extracted from these images supplied the experimental information needed to build the stochastic models of the volume fractions. Thus, the stochastic multiscale model provided reliable statistical information (such as mean values and confidence intervals) on bone elastic properties at the tissue scale. Moreover, the existence of a simpler "nominal model", accounting for the main features of the stochastic model, was investigated. It was shown that such a model does exist, and its relevance was discussed.

Dental implant stability, which is an important parameter for the surgical outcome, can now be assessed using quantitative ultrasound. However, the acoustical propagation in dental implants remains poorly understood. The objective of this numerical study was to understand the propagation phenomena of ultrasonic waves in cylindrically shaped prototype dental implants and to investigate the sensitivity of the ultrasonic response to the surrounding bone quantity and quality. The 10-MHz ultrasonic response of the implant was calculated using an axisymetric 3D finite element model, which was validated by comparison with results obtained experimentally and using a 2D finite difference numerical model. The results show that the implant ultrasonic response changes significantly when a liquid layer is located at the implant interface compared to the case of an interface fully bounded with bone tissue. A dedicated model based on experimental measurements was developed in order to account for the evolution of the bone biomechanical properties at the implant interface. The effect of a gradient of material properties on the implant ultrasonic response is determined. Based on the reproducibility of the measurement, the results indicate that the device should be sensitive to the effects of a healing duration of less than one week. In all cases, the amplitude of the implant response is shown to decrease when the dental implant primary and secondary stability increase, which is consistent with the experimental results. This study paves the way for the development of a quantitative ultrasound method to evaluate dental implant stability.

Canalicular fluid flow is acknowledged to play a major role in bone functioning, allowing bone cells' metabolism and activity and providing an efficient way for cell-to-cell communication. Bone canaliculi are small canals running through the bone solid matrix, hosting osteocyte's dendrites, and saturated by an interstitial fluid rich in ions. Because of the small size of these canals (few hundred nanometers in diameter), fluid flow is coupled with electrochemical phenomena. In our previous works, we developed a multi-scale model accounting for coupled hydraulic and chemical transport in the canalicular network. Unfortunately, most of the physical and geometrical information required by the model is hardly accessible by nowadays experimental techniques. The goal of this study was to numerically assess the influence of the physical and material parameters involved in the canalicular fluid flow. The focus was set on the electro-chemo-mechanical features of the canalicular milieu, hopefully covering any in vivo scenario. Two main results were obtained. First, the most relevant parameters affecting the canalicular fluid flow were identified and their effects quantified. Second, these findings were given a larger scope to cover also scenarios not considered in this study. Therefore, this study gives insight into the potential interactions between electrochemistry and mechanics in bone and provides the rational for further theoretical and experimental investigations.

It is well known that microcracks act as a stimulus for bone remodelling, initiating resorption by osteoclasts and new bone formation by osteoblasts. Moreover, microcracks are likely to alter the fluid flow and convective transport through the bone tissue. This paper proposes a quantitative evaluation of the strain-induced interstitial fluid velocities developing in osteons in presence of a microcrack in the interstitial bone tissue. Based on Biot theory in the low-frequency range, a poroelastic model is carried out to study the hydro-mechanical behaviour of cracked osteonal tissue. The finite element results show that the presence of a microcrack in the interstitial osteonal tissue may drastically reduce the fluid velocity inside the neighbouring osteons. This fluid inactive zone inside osteons can cover up to 10% of their surface. Consequently, the fluid environment of bone mechano-sensitive cells is locally modified.