On the elastic properties of mineralized turkey leg tendon tissue: multiscale model and experiment

The elasto-plastic nano- and microscale compressive behaviour of rehydrated mineralised collagen fibres

The hierarchical design of bio-based nanostructured materials such as bone enables them to combine unique structure-mechanical properties. As one of its main components, water plays an important role in bone's material multiscale mechanical interplay. However, its influence has not been quantified at the length-scale of a mineralised collagen fibre. Here, we couple in situ micropillar compression, and simultaneous synchrotron small angle X-ray scattering (SAXS) and X-ray diffraction (XRD) with a statistical constitutive model. Since the synchrotron data contain statistical information on the nanostructure, we establish a direct connection between experiment and model to identify the rehydrated elasto-plastic micro- and nanomechanical fibre behaviour. Rehydration led to a decrease of 65%-75% in fibre yield stress and compressive strength, and 70% in stiffness with a 3x higher effect on stresses than strains. While in agreement with bone extracellular matrix, the decrease is 1.5-3x higher compared to micro-indentation and macro-compression. Hydration influences mineral more than fibril strain with the highest difference to the macroscale when comparing mineral and tissue levels. The effect of hydration seems to be strongly mediated by ultrastructural interfaces while results provide insights towards mechanical consequences of reported water-mediated structuring of bone apatite. The missing reinforcing capacity of surrounding tissue for an excised fibril array is more pronounced in wet than dry conditions, mainly related to fibril swelling. Differences leading to higher compressive strength between mineralised tissues seem not to depend on rehydration while the lack of kink bands supports the role of water as an elastic embedding influencing energy-absorption mechanisms. STATEMENT OF SIGNIFICANCE: Characterising structure-property-function relationships in hierarchical biological materials helps us to elucidate mechanisms that enable their unique properties. Experimental and computational methods can advance our understanding of their complex behaviour with the potential to inform bio-inspired material development. In this study, we close a gap for bone's fundamental mechanical building block at micro- and nanometre length scales. We establish a direct connection between experiments and simulations by coupling in situ synchrotron tests with a statistical model and quantify the behaviour of rehydrated single mineralised collagen fibres. Results suggest a high influence of hydration on structural interfaces, and the role of water as an elastic embedding by outlining important differences between wet and dry elasto-plastic properties of mineral nanocrystals, fibrils and fibres.

Establishment and Image based evaluation of a New Preclinical Rat Model of Osteoblastic Bone Metastases

Bone remodeling is disrupted in the presence of metastases and can present as osteolytic, osteoblastic or a mixture of the two. Established rat models of osteolytic and mixed metastases have been identified changes in structural and tissue-level properties of bone. The aim of this work was to establish a preclinical rat model of osteoblastic metastases and characterize bone quality changes through image-based evaluation. Female athymic rats (n = 22) were inoculated with human breast cancer cells ZR-75-1 and tumor development tracked over 3-4 months with bioluminescence and in-vivo µCT imaging. Bone tissue-level stereological features were quantified on ex-vivo µCT imaging. Histopathology verified the presence of osteoblastic bone. Bone mineral density distribution was assessed via backscattered electron microscopy. Newly formed osteoblastic bone was associated with reduced mineral content and increased heterogeneity leading to an overall degraded bone quality. Characterizing changes in osteoblastic bone properties is relevant to pre-clinical therapeutic testing and treatment planning.

An experimentally informed statistical elasto-plastic mineralised collagen fibre model at the micrometre and nanometre lengthscale

Bone is an intriguingly complex material. It combines high strength, toughness and lightweight via an elaborate hierarchical structure. This structure results from a biologically driven self-assembly and self-organisation, and leads to different deformation mechanisms along the length scales. Characterising multiscale bone mechanics is fundamental to better understand these mechanisms including changes due to bone-related diseases. It also guides us in the design of new bio-inspired materials. A key-gap in understanding bone's behaviour exists for its fundamental mechanical unit, the mineralised collagen fibre, a composite of organic collagen molecules and inorganic mineral nanocrystals. Here, we report an experimentally informed statistical elasto-plastic model to explain the fibre behaviour including the nanoscale interplay and load transfer with its main mechanical components. We utilise data from synchrotron nanoscale imaging, and combined micropillar compression and synchrotron X-ray scattering to develop the model. We see that a 10-15% micro- and nanomechanical heterogeneity in mechanical properties is essential to promote the ductile microscale behaviour preventing an abrupt overall failure even when individual fibrils have failed. We see that mineral particles take up 45% of strain compared to collagen molecules while interfibrillar shearing seems to enable the ductile post-yield behaviour. Our results suggest that a change in mineralisation and fibril-to-matrix interaction leads to different mechanical properties among mineralised tissues. Our model operates at crystalline-, molecular- and continuum-levels and sheds light on the micro- and nanoscale deformation of fibril-matrix reinforced composites.

Heat impact during laser ablation extraction of mineralised tissue micropillars

The underlying constraint of ultrashort pulsed laser ablation in both the clinical and micromachining setting is the uncertainty regarding the impact on the composition of material surrounding the ablated region. A heat model representing the laser-tissue interaction was implemented into a finite element suite to assess the cumulative temperature response of bone during ultrashort pulsed laser ablation. As an example, we focus on the extraction of mineralised collagen fibre micropillars. Laser induced heating can cause denaturation of the collagen, resulting in ultrastructural loss which could affect mechanical testing results. Laser parameters were taken from a used micropillar extraction protocol. The laser scanning pattern consisted of 4085 pulses, with a final radial pass being 22 [Formula: see text] away from the micropillar. The micropillar temperature was elevated to 70.58 [Formula: see text], remaining 79.42 [Formula: see text] lower than that of which we interpret as an onset for denaturation. We verified the results by means of Raman microscopy and Energy Dispersive X-ray Microanalysis and found the laser-material interaction had no effect on the collagen molecules or mineral nanocrystals that constitute the micropillars. We, thus, show that ultrashort pulsed laser ablation is a safe and viable tool to fabricate bone specimens for mechanical testing at the micro- and nanoscale and we provide a computational model to efficiently assess this.

Assessing the effective elastic properties of the tendon-to-bone insertion: a multiscale modeling approach

The interphase joining tendon to bone plays the crucial role of integrating soft to hard tissues, by effectively transferring stresses across two tissues displaying a mismatch in mechanical properties of nearly two orders of magnitude. The outstanding mechanical properties of this interphase are attributed to its complex hierarchical structure, especially by means of competing gradients in mineral content and collagen fibers organization at different length scales. The goal of this study is to develop a multiscale model to describe how the tendon-to-bone insertion derives its overall mechanical behavior. To this end, the effective anisotropic stiffness tensor of the interphase is predicted by modeling its elastic response at different scales, spanning from the nanostructural to the mesostructural levels, using continuum micromechanics methods. The results obtained at a lower scale serve as inputs for the modeling at a higher scale. The obtained predictions are in good agreement with stochastic finite element simulations and experimental trends reported in literature. Such model has implication for the design of bioinspired bi-materials that display the functionally graded properties of the tendon-to-bone insertion.

Extrafibrillar matrix yield stress and failure envelopes for mineralised collagen fibril arrays

Bone metabolic diseases such as osteoporosis constitute a major socio-economic challenge. A detailed understanding of the structure-property relationships of bone's underlying hierarchical levels has the potential to improve diagnosis and the ability to treat those diseases, especially with regards to the onset of failure. Therefore, elastic and yield properties of mineralised turkey leg tendon (MTLT), a mineralised tissue that is similar to bone but has a simpler multiscale structure, were investigated. Elastic properties were identified using a multiscale micromechanical model. The input parameters include constituent mechanical properties, volume fractions and inclusion aspect ratios and these were obtained from a wide variety of literature sources. The determined elastic properties were used to formulate micromechanically informed yield surfaces and to identify yield properties of MTLT at the nanometre length scale where failure is first reported to occur. This was done in conjunction with experimental results from the compression of micropillars extracted from individual mineralised collagen fibres. This data was then used to identify micromechanically informed failure envelopes. The shear yield stress of the extrafibrillar matrix, associated with interfibrillar sliding, was identified as 137.65 MPa. The ratio between tensile and compressive yield stress in the Drucker-Prager yield criterion was 0.65. For both criteria apparent yield stress of the mineralised collagen fibril decreased to 25.3-31.4% when varying fibril orientation from 0° to 90°. This study identified yield properties of extrafibrillar matrix using an aligned mineralised tissue. The ability to obtain yield stress data and unloading stiffness from micropillar compression tests of MTLT at the level of the mineralised collagen fibril array and downscaling these into the EM mitigates against possible errors associated with macroscopic stiffness predictions and proved to be an invaluable advantage compared to similar modelling approaches. Results may help to improve computational models that may then be used in pre-clinical testing or development of personalised treatment strategies.

Surface Motion Changes of Tympanic Membrane Damaged by Blast Waves

Eardrum or tympanic membrane (TM) is a multilayer soft tissue membrane located at the end of the ear canal to receive sound pressure and transport the sound into the middle ear and cochlea. Recent studies reported that the TM microstructure and mechanical properties varied after the ear was exposed to blast overpressure. However, the impact of such biomechanical changes of the TM on its movement for sound transmission has not been investigated. This paper reports the full-field surface motion of the human TM using the scanning laser Doppler vibrometry in human temporal bones under normal and postblast conditions. An increase of the TM displacement after blast exposure was observed in the posterior region of the TM in four temporal bone samples at the frequencies between 3 and 4 kHz. A finite element model of human TM with multilayer microstructure and orthogonal fiber network was created to simulate the TM damaged by blast waves. The consistency between the experimental data and the model-derived TM surface motion suggests that the tissue injuries were resulted from a combination of mechanical property change and regional discontinuity of collagen fibers. This study provides the evidences of surface motion changes of the TM damaged by blast waves and possible fiber damage locations.

Compressive behaviour of uniaxially aligned individual mineralised collagen fibres at the micro- and nanoscale

The increasing incidence of osteoporotic bone fractures makes fracture risk prediction an important clinical challenge. Computational models can be utilised to facilitate such analyses. However, they critically depend on bone's underlying hierarchical material description. To understand bone's irreversible behaviour at the micro- and nanoscale, we developed an in situ testing protocol that allows us to directly relate the experimental data to the mechanical behaviour of individual mineralised collagen fibres and its main constitutive phases, the mineralised collagen fibrils and the mineral nanocrystals, by combining micropillar compression of single fibres with small angle X-ray scattering (SAXS) and X-ray diffraction (XRD). Failure modes were assessed by SEM. Strain ratios in the elastic region at fibre, fibril and mineral levels were found to be approximately 22:5:2 with strain ratios at the point of compressive strength of 0.23 ± 0.11 for fibril-to-fibre and 0.07 ± 0.01 for mineral-to-fibre levels. Mineral-to-fibre levels showed highest strain ratios around the apparent yield point, fibril-to-fibre around apparent strength. The mineralised collagen fibrils showed a delayed mechanical response, contrary to the mineral phase, which points towards preceding deformations of mineral nanocrystals in the extrafibrillar matrix. No damage was measured at the level of the mineralised collagen fibre which indicates an incomplete separation of the mineral and collagen, and an extrafibrillar interface failure. The formation of kink bands and the gradual recruitment of fibrils upon compressive loading presumably led to localised strains. Our results from a well-controlled fibrillar architecture provide valuable input for micromechanical models and computational non-linear bone strength analyses that may provide further insights for personalised diagnosis and treatment as well as bio-inspired implants for patients with bone diseases. STATEMENT OF SIGNIFICANCE: Musculoskeletal diseases such as osteoporosis, osteoarthritis or bone cancer significantly challenge health care systems and make fracture risk prediction and treatment optimisation important clinical goals. Computational methods such as finite element models have the potential to optimise analyses but highly depend on underlying material descriptions. We developed an in situ testing set-up to directly relate experimental data to the mechanical behaviour of bone's fundamental building block, the individual mineralised collagen fibre and its main constituents. Low multilevel strain ratios suggest high deformations in the extrafibrillar matrix and energy dissipation at the interfaces, the absence of damage indicates both an incomplete separation between mineral and collagen and an extrafibrillar interface failure. The formation of kink bands in the fibril-reinforced composite presumably led to localised strains. The deformation behaviour of a well-controlled fibrillar architecture provides valuable input for non-linear bone strength analyses.

Multiscale modeling methods in biomechanics

More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space-time continuum. We are forced to consider multiple space-time continua, each representing the phenomenon of interest at a characteristic space-time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: 'causal confirmation,' where multiscale models are used as materializations of the causation theories; 'predictive accuracy,' where multiscale modeling is aimed to improve the predictive accuracy; and 'determination of effect,' where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space-time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375 For further resources related to this article, please visit the WIREs website.

Can a continuous mineral foam explain the stiffening of aged bone tissue? A micromechanical approach to mineral fusion in musculoskeletal tissues

Recent experimental data revealed a stiffening of aged cortical bone tissue, which could not be explained by common multiscale elastic material models. We explain this data by incorporating the role of mineral fusion via a new hierarchical modeling approach exploiting the asymptotic (periodic) homogenization (AH) technique for three-dimensional linear elastic composites. We quantify for the first time the stiffening that is obtained by considering a fused mineral structure in a softer matrix in comparison with a composite having non-fused cubic mineral inclusions. We integrate the AH approach in the Eshelby-based hierarchical mineralized turkey leg tendon model (Tiburtius et al 2014 Biomech.

MODEL

Mechanobiol. 13 1003-23), which can be considered as a base for musculoskeletal mineralized tissue modeling. We model the finest scale compartments, i.e. the extrafibrillar space and the mineralized collagen fibril, by replacing the self-consistent scheme with our AH approach. This way, we perform a parametric analysis at increasing mineral volume fraction, by varying the amount of mineral that is fusing in the axial and transverse tissue directions in both compartments. Our effective stiffness results are in good agreement with those reported for aged human radius and support the argument that the axial stiffening in aged bone tissue is caused by the formation of a continuous mineral foam. Moreover, the proposed theoretical and computational approach supports the design of biomimetic materials which require an overall composite stiffening without increasing the amount of the reinforcing material.

Skeletal maturation substantially affects elastic tissue properties in the endosteal and periosteal regions of loaded mice tibiae

Although it is well known that the bone adapts to changes in the mechanical environment by forming and resorbing the bone matrix, little is known about the influence of mechanical loading on tissue material properties of the pre-existing and newly formed bone. In this study, we analyzed the newly formed and pre-existing tissue after two weeks of controlled in vivo axial compressive loading in tibia of young (10 week-old) and adult (26 week-old) female mice and compared to the control contralateral limb, by means of scanning acoustic microscopy. Additionally, we used quantitative backscattered electron imaging to determine the bone mineral density distribution within the newly formed and pre-existing bone of young mice. No significant differences were found in tissue stiffness or mineral density in the pre-existing bone tissue as a result of external loading. In the endosteal region, 10 and 26 week loaded animals showed a 9% reduction in bone tissue stiffness compared to control animals. An increase of 200% in the mineral apposition rate in this region was observed in both age groups. In the periosteal region, the reduction in bone tissue stiffness and the increase in bone mineral apposition rate as a result of loading were two times higher in the 10 compared to the 26 week old animals. These data suggest that, during growth and skeletal maturation, the response of bone to mechanical loading is a deposition of new bone matrix, where the tissue amount but not its mineral or elastic properties are influenced by animal age.

Distribution of mesoscale elastic properties and mass density in the human femoral shaft

Cortical bone properties are determined by tissue composition and structure at several hierarchical length scales. In this study, the spatial distribution of micro- and mesoscale elastic properties within a human femoral shaft has been investigated. Microscale tissue degree of mineralization (DMB), cortical vascular porosity Ct.Po and the average transverse isotropic stiffness tensor C(Micro) of cylindrical-shaped samples (diameter: 4.4 mm, N = 56) were obtained from cortical regions between 20 and 85% of the total femur length and around the periphery (anterior, medial, posterior and lateral quadrants) by means of synchrotron radiation µCT (SRµCT) and 50-MHz scanning acoustic microscopy (SAM). Within each cylinder, the volumetric bone mineral density (vBMD) and the mesoscale stiffness tensor C(Meso) were derived using a numerical homogenization approach. Moreover, microelastic maps of the axial elastic coefficient c33 measured by SAM at distinct cross-sectional locations along the femur were used to construct a 3-D multiscale elastic model of the femoral shaft. Variations of vBMD (6.1%) were much lower than the variations of mesoscale elastic coefficients (11.1-21.3%). The variation of DMB was only a minor predictor for variations of the mesoscale elastic properties (0.05 ≤ R(2) ≤ 0.34). Instead, variations of the mesoscale elastic properties could be explained by variations of cortical porosity and microscale elastic properties. These data were suitable inputs for numerical evaluations and may help to unravel the relations between structure and composition on the elastic function in cortical bone.

To what extent can cortical bone millimeter-scale elasticity be predicted by a two-phase composite model with variable porosity?

An evidence gap exists in fully understanding and reliably modeling the variations in elastic anisotropy that are observed at the millimeter scale in human cortical bone. The porosity (pore volume fraction) is known to account for a large part, but not all, of the elasticity variations. This effect may be modeled by a two-phase micromechanical model consisting of a homogeneous matrix pervaded by cylindrical pores. Although this model has been widely used, it lacks experimental validation. The aim of the present work is to revisit experimental data (elastic coefficients, porosity) previously obtained from 21 cortical bone specimens from the femoral mid-diaphysis of 10 donors and test the validity of the model by proposing a detailed discussion of its hypotheses. This includes investigating to what extent the experimental uncertainties, pore network modeling, and matrix elastic properties influence the model's predictions. The results support the validity of the two-phase model of cortical bone which assumes that the essential source of variations of elastic properties at the millimeter-scale is the volume fraction of vascular porosity. We propose that the bulk of the remaining discrepancies between predicted stiffness coefficients and experimental data (RMSE between 6% and 9%) is in part due to experimental errors and part due to small variations of the extravascular matrix properties. More significantly, although most of the models that have been proposed for cortical bone were based on several homogenization steps and a large number of variable parameters, we show that a model with a single parameter, namely the volume fraction of vascular porosity, is a suitable representation for cortical bone. The results could provide a guide to build specimen-specific cortical bone models. This will be of interest to analyze the structure-function relationship in bone and to design bone-mimicking materials.