The ability of bone to sense and react to its mechanical environment is well-known and undisputed. In qualitative terms, the prolonged exposure of bone tissue to increased mechanical loading (with respect to a "normal" physiological load level) leads to a corresponding increase in bone mass; usually associated with the filling of the bone tissue-surrounding pore spaces by additional bone tissue. A decreased mechanical loading, on the other hand, causes a corresponding depletion of bone tissue, leading to enlarged pore spaces and a decreased bone mass.

Several stimuli have been proposed as potentially relevant for the mechanobiological regulation of bone tissue, including direct cell stretching, hydrostatic pressure, and fluid flow-induced shear stresses. Furthermore, it is well known that bone tissue exhibits piezoelectric properties, and it has been suggested that piezoelectric excitation may be a contributing factor to the mechanobiological regulation of the activities of cells residing in the bone pore spaces as well. In this contribution, the focus is on the latter proposition. Due to the very small length scales at which the related processes occur, direct experimental validation or falsification of this hypothesis has turned out to be out of reach. Here, we investigate this potentially important mechanism by means of continuum micromechanics-inspired multiscale modeling.

In particular, the concept of continuum micromechanics, originally developed for elasticity upscaling (or, homogenization), was utilized for deriving and homogenizing a so-called electromechanical tensor, comprising stiffness as well as electrical quantities, and for up- and down-scaling mechanical and piezoelectric properties. This modeling concept was applied to bone tissue, spanning thereby the hierarchical organization from the molecular level of bone (where the so-called elementary constituents of bone can be identified) to macroscopic bone tissue. Applying this model to the multiscale micromechanical representation of bone tissue has revealed that the electrical stimuli arriving at the level of bone cells, in response to physiological macroscopic loading, is much too small for effectively stimulating bone cell activities. This result suggests that piezoelectric effects may be a contributing, but not a major factor for bone cell excitation. This contribution is concluded by an interpretation of the obtained results in the context of other mechanical stimuli - i.e., hydrostatic pressure and fluid flow-induced shear stresses - previously investigated also by means of continuum micromechanics-inspired multiscale methods, and by comparing their respective importance for the bone remodeling process (as suggested based on the computational results), revealing that the pressurization of bone pore spaces may be of bigger relevance than the other stimuli.

For accurate quantification of mineralised tissues using polychromatic lab x-ray sources, one needs to do two things: 1) to integrate for a very long time to get a good signal to noise ratio and 2) to calibrate the x-ray source and the detector response. At Queen Mary we build our own X-ray Micro-Tomography (XMT, synonym µCT) systems specifically designed for accurate quantification of mineral concentration. We build on the pioneering work of Professor James Elliott, the co-inventor of x-ray micro-tomography. We use CCD cameras and time delay integration to allow long integration times, and calibrate every scan with a multi-metal carousel, enabling us to correct beam hardening effects, model the x-ray emission spectrum and model our detector response which allow us to derive the sample Linear Attenuation Coefficient (LAC) and hence mineralisation.

Getting improved contrast [i.e., mineral concentration] resolution is crucial to all applications of XMT to studying skeletal tissues and especially where there are mixed tissue types with different degrees of mineralisation. The common clinically important fractures of the cortices of vertebral bodies and the femoral neck involve variable amounts of calcified ligament: this, and calcified cartilage in the end plates, reach higher levels of mineralisation than bone. They also have different histology, ‘grain’ and fracture properties. With our own systems, we can distinguish these tissue phases, but this is not possible in commercial systems. Mistakes will therefore be made is measuring cortical thickness – never mind that the tissue is not bone.

Context. Bone disorders like osteoporosis as well as active lifestyles increase the occurrence of bone fractures and joints damage. In orthopaedic and dental surgery, the implantation of biomaterials within bone tissue to restore the integrity of the treated organ has become a standard procedure. Their long-term stability relies on osseointegration phenomena, where bone grows onto and around metallic implants, creating a bone-implant interface. The bone tissue is a highly hierarchical material which evolves spatially and temporally during this healing phase. A deeper understanding of its biomechanical characteristics is needed, as they are determinant for the surgical success. In this context, we propose a multiscale homogenization model to compute the effective elastic properties of bone tissue (macroscale) as a function of the distance from the implant, based on the structure and composition at lower scales.

Methods. The model considers three scales: mineral foam, ultrastructure, and bone tissue. The elastic properties and the volume fraction of the elementary constituents of bone matrix (mineral, collagen and water), the orientation of the collagen fiber relatively to the implant surface and the mesoscale porosity constitute the input data of the model. At each scale, the continuum micromechanics theory based on the famous Eshelby’s representation of the uniform elastic field inside the ellipsoidal inclusion is applied. Experimental data were obtained from Ti6Al4V coin-shaped implants that were osseointegrated into cortical rabbit bones. The mineral platelet orientation -assumed to be parallel to the collagen fibers- and the mesoscale porosity were retrieved using small-angle X-ray scattering (SAXS) and using light microscopy, respectively (Le Cann et al., Acta Biomater, 116:391–399, 2020). The effect of their spatial variation on the bone anisotropic properties in the proximity of the implant were investigated.

Results and discussion. 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 is primarily sensitive to the porosity (mesoscale) rather than to the collagen fibers orientation (submicroscale). However, the orientation of the fibers has a significant influence on the isotropy of the bone tissue, leading to a high degree of anisotropy when the fibers are oriented with an angle close to 45° with respect to the implant surface. 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 fibers orientation. A decrease in the porosity leads to a decrease of the bone isotropy and to an increase of the impact of the fibers’ orientation.

Conclusions. These results demonstrate that the collagen fiber orientation affects the effective elastic properties of the bone throughout the remodeling process in the proximity of an implant. Collagen fiber orientation should be taken into account to properly describe the effective elastic anisotropy of bone at the organ scale.

Magnesium implants appear as promising technology for load-carrying, bioresorbable bone regeneration tools (Hofstetter 2014 [1], Kraus 2012 [2]). In this context, quantitative exploration of the biomechanics and mechano-biology of the bone-implant compound system is of great interest. As a corresponding contribution, we here present an analytical beam theory representation (Pircher 2021 [3]) of a cylindrical magnesium implant located roughly in the middle of a rat femur and approximately orthogonal to the axis of the femoral shaft, which we map onto CT and SAXS-tomographic images of the pre-clinical animal test setting (Liebi 2021 [4], Grünewald [5] ). This reveals the correspondence between mechanical stress state distributions and micro-texture (collagen fiber orientation) across the bony organ. In more detail, the femur is first represented as a polygon with two straight lines, one associated with the femoral neck, and the other one associated with the femoral shaft. This polygon is the basis of a beam representation, where the shaft line is fixed at the knee, and the femoral head (the end of the neck) is loaded by external forces arising from standing. For the stress analysis, the implant is represented by the geometrical object "solid circular cylinder“, such that the cylinder’s volume, its radial normal component of the inertia tensor, its center of gravity, and its principal axes are identical to the corresponding quantities describing all the voxels showing the implant in the CT image. In the same way, the shaft region in proximity of the implant is represented by (i) a full cylinder representing the entire shaft, and (ii) a hollow cylinder representing the cortical shaft compartment only. Then, classical Bernoulli-Euler beam theory is applied to the bony portions of the implant-bone compound structure, with the beam cross-sections being dictated by the interaction of the roughly orthogonally positioned geometrical objects. As a measure for correspondence between stress states and texture directions, we evaluated the dot products between principcal stress directions and directions of maximum shear stress. As a result, somewhat surprisingly, not the principal stress directions, but the loading directions associated with maximum shear stress appear as the key mechano-biological drivers. Accordingly, the shear tractions of largest magnitude act orthogonal as well as parallel to the main texture direction, i.e. the collagen fiber direction.

[1] Hofstetter et al. (2014) JOM 66.4, pp. 566–572, 10.1007/s11837-014-0875-5.

[2] Kraus et al. (2012) Acta Biomaterialia 8.3, pp. 1230–1238, 10.1016/j.actbio.2011.11.008

[3] Pircher (2021) Thesis Wien, 20.500.12708/79654

[4] Liebi et al (2021) Acta Biomaterialia, 134, 804-817, 10.1016/j.actbio.2021.07.060

[5] Grünewald et al (2016) Biomaterials 76, pp. 250–260, 10.1016/j.biomaterials.2015.10.054.

Bone remodeling is a very complex and fine-tuned process, which is necessary to ensure a healthy bone structure. If this process gets out of balance – e.g., because of hormonal disbalance or the impact of bone metastases – pathologies like osteoporosis can appear. In this contribution we introduce a novel computational approach to investigate this balance by connecting the bone remodeling process with its microenvironment. Our goal is to better understand the well-balanced and complex dynamic of the subprocesses involved in healthy bone remodeling.

We implement a 3D stochastic cellular automaton (SCA), where voxels interact only with their nearest neighbors in a scaffold representing bone tissue. At each time point, each voxel can take one of four different states that stand for the different phases of bone remodeling: formation, quiescent bone, resorption, and environment. To create a compact representation of the frequency-dependent interaction of those voxel states we make use of methods borrowed from evolutionary game theory for the update rule of the cellular automaton [1]. This representation encodes knowledge about the mutual impact the different actors of bone remodeling (osteocytes, osteoclasts and osteoblasts) have on each other. Each parameter in the model has therefore a direct connection to the biological processes.

First, we set up simulations of the model with either only resorption or only formation. This choice reduced the model complexity and allowed us to determine parameter spaces for a self-regulating behavior for each of them. The self-regulating behavior is defined by resorption or formation starting and ending without further parameter tuning. Parameters outside the range of self-regulation will lead to either osteolytic lesions (resorption) or heterotopic ossification (formation). Further analyses supported the approach of a spatial model with a small neighborhood to simulate the local phenomena observed in bone remodeling.

Next, we coupled the two processes of resorption and formation. In the limit of separation of time scales, our model showed that self-regulating resorption followed by self-regulating formation reproduces the physiological bone remodeling behavior. Further analysis will create a more fluid coupling of the two processes while involving more parameters.

The model has the potential to use the role of the microenvironment to evaluate the impact of additional factors, such as drugs or bone metastases. We are planning on using experimental in vivo data from a breast cancer bone metastasis mouse model [2], which includes spatial and temporal dynamic of early osteolytic lesions, to fit additional parameters. Hopefully, these findings will add to the discussion, how pathological behavior might be controlled, if not even reversed.

[1] M. D. Ryser and K.A. Murgas, Bone remodeling as a spatial evolutionary game, Journal of Theoretical Biology, 2017

[2] S. A. E. Young, A.-D. Heller et al., From breast cancer cell homing to the onset of early bone metastasis: dynamic bone (re)modeling as a driver of osteolytic disease, bioRxiv preprint

The mechanical quality of trabecular bone is influenced by its inhomogeneous mineral content and spatial distribution at a microscopic scale. The bone remodelling process, which is the concerted action of osteoclastic bone resorption followed by osteoblastic bone formation, controls bone turnover. During the bone formation process (FP) the deposited organic collagenous matrix (i.e., osteoid) becomes mineralised. The latter process is regulated by the mineralisation kinetics which exhibits two distinct phases: a fast primary mineralisation phase lasting for several days to a few weeks and a secondary mineralisation phase that can last from several months to years. Variations in bone turnover and mineralisation kinetics can be observed in the bone mineral density distribution (BMDD), which can be used to distinguish healthy from pathological bone tissue at the scale of the bone matrix. Here, we propose a discrete statistical spatio-temporal bone remodelling model to study the effects of activation frequency (Ac.f) and mineralisation kinematics on the BMD distribution. In this model individual basic multicellular units (BMUs) are activated discretely on trabecular surfaces which then undergo typical bone remodelling sequence, i.e., resorption, reversal, osteoid formation, and mineralisation, with the latter process following a double exponential law. Our simulation results highlight that trabecular BMDD is strongly regulated by Ac.f and kinetics of secondary mineralization (t₂) in a coupled way. Indeed, Ca wt% increases with lower Ac.f and fast secondary mineralisation, while lower Ca wt% values are obtained for higher Ac.f and slower secondary mineralisation. Accordingly, the dynamic equilibrium can be achieved for different combinations of Ac.f and t₂. For example, a mean Ca wt% of 25, which has been reported in the literature based on qBEI experiments, can be obtained with Ac.f = 4 BMU/year/mm³ and t₂ = 8 years or with Ac.f = 6 BMU/year/mm³ and t₂ = 6 years. This close link between Ac.f and t₂ on BMDD results shows the importance of taking both characteristics into account in order to draw meaningful conclusions about bone quality. Indeed, pathological conditions such as osteoporosis demonstrate a similar pattern. We investigated post-menopausal and senile osteoporosis (type I and type II, respectively) and hypothesised that high Ac.f or very long formation period (FP) would result in type I osteoporosis, whereas underfilling and no filling would result in type II osteoporosis. Our results show that the apparent density and bone mineral fraction were similar for all osteoporosis hypotheses except for the non-filling one. However, when examining BMDD, significant variations were observed, especially in type I simulations. High Ac.f resulted in low Ca wt%, consistent with post-menopausal osteoporosis, while large FP led to high Ca wt%, which is only seen in type II osteoporosis.

The unique and somewhat enigmatic properties of biological apatites have made them an attractive area of research for many decades, with studies aiming to provide a comprehensive understanding of apatite physiochemistry and biological properties. Our work, however, initially began unconventionally at the end of the story, through investigating how the unique properties of biological apatites could be applied to the fields of forensic science, medicine and archaeology and finally ending with understanding the fundamental features of these properties. Our work with Professor John Clement began in the late 1990’s, with a collaboration between Professor Keith Rogers and Dr Sophie Beckett, on species differentiation of heated bone. The results of the study clearly demonstrated that apatite characteristics of unheated and heated bone exhibit significant inter-species variation, quantifiable using X-ray diffraction analysis. The work also highlighted the potential capability of distinguishing human from non-human bone based on apatite physicochemistry. Discussions with John throughout this project centred around ‘apatites not being a fixed piece of chemistry’ and there being ‘a need to understand the fundamental features of apatites to truly appreciate the applications of the work’.

Dr Charlene Greenwood’s PhD project followed, which aimed to provide a new insight into the fundamental mechanisms and processes associated with physicochemical changes to bone during heat treatment. The work, which studied both unheated and heated bone mineral chemistry, considered a controversial in vivo crystallite size control mechanism for biological apatites and mathematically (through Arrenhius and Johnson-Mehl-Avrami equations) described crystallisation kinetics of apatite during heating. Of importance from this work, was the role of carbonate in biological apatite formation and crystal growth, with Dr Emily Arnold’s PhD furthering our understanding of carbonates within the apatite lattice through the application of X-ray pair distribution functions. The work allowed the carbonate within the apatite lattice to be examined on a local scale during heating, with the results suggesting that carbonate does affect intermediate (and therefore likely average) order, but not local order. This insight is significant when considering apatite physiochemistry and disease, and area of research our team is particularly focused on.

Our work in the field of apatites and disease focuses on understanding apatite physicochemisty and disease initiation and progression. Our work on osteoporosis, which was heavily supported by John and the Melbourne Femur Research Collection, identified new fracture risk biomarkers based on tissue features, with differences in apatite crystal chemistry, nanostructure and microstructure identified between fracture and non-fracture groups. John’s legacy has continued with our work on ectopic calcification chemistry and its association with cancer. The team are currently exploring the view that calcification physicochemical characteristics could contain additional or independent source of diagnostic information, and we are applying this hypothesis to both breast and prostate microcalcifications to identify new chemical biomarkers for early diagnostics and prognostics.

Our presentation aims to discuss our fascinating journey with apatites and John, from the applications to their fundamental properties, with the work and John’s legacy continuing, even if we did take ‘the long way round’.