Strain amplification in bone mechanobiology: a computational investigation of the in vivo mechanics of osteocytes

The osteocyte is believed to act as the main sensor of mechanical stimulus in bone, controlling signalling for bone growth and resorption in response to changes in the mechanical demands placed on our bones throughout life. However, the precise mechanical stimuli that bone cells experience in vivo are not yet fully understood. The objective of this study is to use computational methods to predict the loading conditions experienced by osteocytes during normal physiological activities. Confocal imaging of the lacunar–canalicular network was used to develop three-dimensional finite element models of osteocytes, including their cell body, and the surrounding pericellular matrix (PCM) and extracellular matrix (ECM). We investigated the role of the PCM and ECM projections for amplifying mechanical stimulation to the cells. At loading levels, representing vigorous physiological activity (3000 µɛ), our results provide direct evidence that (i) confocal image-derived models predict 350–400% greater strain amplification experienced by osteocytes compared with an idealized cell, (ii) the PCM increases the cell volume stimulated more than 3500 µɛ by 4–10% and (iii) ECM projections amplify strain to the cell by approximately 50–420%. These are the first confocal image-derived computational models to predict osteocyte strain in vivo and provide an insight into the mechanobiology of the osteocyte.     

Effect of cryo-induced microcracks on microindentation of hydrated cortical bone tissue

Microcracks accumulate in cortical bone tissue as a consequence of everyday cyclic loading. However, it remains unclear to what extent microdamage accumulation contributes to an increase in fracture risk. A cryo-preparation technique was applied to induce microcracks in cortical bone tissue. Microcracks with lengths up to approximately 20 μm, which were initiated mainly on the boundaries of haversian canals, were observed with cryo-scanning electron microscopy. A microindentation technique was applied to study the mechanical loading effect on the microcracked hydrated bone tissue. The microindentation patterns were section-scanned using confocal laser scanning microscopy to understand the deformation and bone damage mechanisms made by mechanical loading. The results show that there was no significant difference with respect to microhardness between the original and microcracked hydrated cortical bone tissues (ANOVA, p > 0.05). The cryo-induced microcracks in the bone tissue were not propagated further under the mechanical loads applied. The deformation mechanism of the microcracked cortical bone tissue was plastic deformation, not brittle fracture.     

Tuning the phase of circadian entrainment

The circadian clock coordinates daily physiological, metabolic and behavioural rhythms. These endogenous oscillations are synchronized with external cues (‘zeitgebers’), such as daily light and temperature cycles. When the circadian clock is entrained by a zeitgeber, the phase difference ψ between the phase of a clock-controlled rhythm and the phase of the zeitgeber is of fundamental importance for the fitness of the organism. The phase of entrainment ψ depends on the mismatch between the intrinsic period τ and the zeitgeber period T and on the ratio of the zeitgeber strength to oscillator amplitude. Motivated by the intriguing complexity of empirical data and by our own experiments on temperature entrainment of mouse suprachiasmatic nucleus (SCN) slices, we present a theory on how clock and zeitgeber properties determine the phase of entrainment. The wide applicability of the theory is demonstrated using mathematical models of different complexity as well as by experimental data. Predictions of the theory are confirmed by published data on Neurospora crassa strains for different period mismatches τ − T and varying photoperiods. We apply a novel regression technique to analyse entrainment of SCN slices by temperature cycles. We find that mathematical models can explain not only the stable asymptotic phase of entrainment, but also transient phase dynamics. Our theory provides the potential to explore seasonal variations of circadian rhythms, jet lag and shift work in forthcoming studies.     

In vivo assessment of the effect of controlled high- and low-frequency mechanical loading on peri-implant bone healing

The aim of this study was to investigate the effect of controlled high- (HF) and low-frequency (LF) mechanical loading on peri-implant bone healing. Custom-made titanium implants were inserted in both tibiae of 69 adult Wistar rats. For every animal, one implant was loaded by compression through the axis of tibia (test), whereas the other one was unloaded (control). The test implants were randomly distributed among four groups receiving different loading regimes, which were determined by ex vivo calibration. Within the HF (40 Hz) or LF (2 Hz) loading category, the magnitudes were chosen as low- (LM) and high-magnitude (HM), respectively, leading to constant strain rate amplitudes for the two frequency groups. This resulted in the four loading regimes: (i) HF-LM (40 Hz–0.5 N); (ii) HF-HM (40 Hz–1 N); (iii) LF-LM (2 Hz–10 N); and (iv) LF-HM (2 Hz–20 N) loading. Loading was performed five times per week and lasted for one or four weeks. Tissue samples were processed for histology and histomorphometry (bone-to-implant contact, BIC; and peri-implant bone fraction, BF) at the cortical and medullar level. Data were analysed statistically with ANOVA and paired t-tests with the significance level set at 0.05. For the one-week experiments, an increased BF adjacent to the implant surface at the cortical level was exclusively induced by the LF-HM loading regime (2 Hz–20 N). Four weeks of loading resulted in a significant effect on BIC (and not on BF) in case of HF-LM loading (40 Hz–0.5 N) and LF-HM loading (2 Hz–20 N): BIC at the cortical level significantly increased under both loading regimes, whereas BIC at the medullar level was positively influenced only in case of HF-LM loading. Mechanical loading at both HF and LF affects osseointegration and peri-implant BF. Higher loading magnitudes (and accompanying elevated tissue strains) are required under LF loading to provoke a positive peri-implant bone response, compared with HF loading. A sustained period of loading at HF is needed to result in an overall enhanced osseointegration.     

Finite element modelling versus classic beam theory: comparing methods for stress estimation in a morphologically diverse sample of vertebrate long bones

Classic beam theory is frequently used in biomechanics to model the stress behaviour of vertebrate long bones, particularly when creating intraspecific scaling models. Although methodologically straightforward, classic beam theory requires complex irregular bones to be approximated as slender beams, and the errors associated with simplifying complex organic structures to such an extent are unknown. Alternative approaches, such as finite element analysis (FEA), while much more time-consuming to perform, require no such assumptions. This study compares the results obtained using classic beam theory with those from FEA to quantify the beam theory errors and to provide recommendations about when a full FEA is essential for reasonable biomechanical predictions. High-resolution computed tomographic scans of eight vertebrate long bones were used to calculate diaphyseal stress owing to various loading regimes. Under compression, FEA values of minimum principal stress (σ_min) were on average 142 per cent (±28% s.e.) larger than those predicted by beam theory, with deviation between the two models correlated to shaft curvature (two-tailed p = 0.03, r² = 0.56). Under bending, FEA values of maximum principal stress (σ_max) and beam theory values differed on average by 12 per cent (±4% s.e.), with deviation between the models significantly correlated to cross-sectional asymmetry at midshaft (two-tailed p = 0.02, r² = 0.62). In torsion, assuming maximum stress values occurred at the location of minimum cortical thickness brought beam theory and FEA values closest in line, and in this case FEA values of τ_torsion were on average 14 per cent (±5% s.e.) higher than beam theory. Therefore, FEA is the preferred modelling solution when estimates of absolute diaphyseal stress are required, although values calculated by beam theory for bending may be acceptable in some situations.     

Behaviour of stresses in circumferential butt welds of steel pipe under superimposed axial tension loading

A computational procedure is presented for analyzing behaviour of stresses in circumferential butt welds of carbon steel pipe subject to superimposed mechanical loading. Three-dimensional uncoupled thermo-mechanical finite element (FE) analysis method is developed in order to predict the weld residual stress states in circumferentially butt-welded steel pipe. The FE method is verified through the experimental work. Then, three-dimensional elastic–plastic FE analysis is carried out to investigate the behaviour of stresses in steel pipe circumferential welds undergoing superimposed axial tension loading using the weld residual stresses and plastic strains obtained from the thermo-mechanical FE method. The simulated results show that spatial variations of the weld residual stresses are present along the circumference and a rapid change of the residual stresses exists at the weld start/stop position, therefore three-dimensional FE analysis is essential to accurately simulate the circumferential welding of steel pipe. Moreover, when axial tension loading is applied to the circumferentially welded steel pipe, bending moment is generated at the weld area caused by the circumferential shrinkage of the weld during welding, thus affecting the axial and hoop stress evolutions in the course of mechanical loading.     

Shape optimization in exoskeletons and endoskeletons: a biomechanics analysis

This paper addresses the question of strength and mechanical failure in exoskeletons and endoskeletons. We developed a new, more sophisticated model to predict failure in bones and other limb segments, modelled as hollow tubes of radius r and thickness t. Five failure modes were considered: transverse fracture; buckling (of three different kinds) and longitudinal splitting. We also considered interactions between failure modes. We tested the hypothesis that evolutionary adaptation tends towards an optimum value of r/t, this being the value which gives the highest strength (i.e. load-carrying capacity) for a given weight. We analysed two examples of arthropod exoskeletons: the crab merus and the locust tibia, using data from the literature and estimating the stresses during typical activities. In both cases, the optimum r/t value for bending was found to be different from that for axial compression. We found that the crab merus experiences similar levels of bending and compression in vivo and that its r/t value represents an ideal compromise to resist these two types of loading. The locust tibia, however, is loaded almost exclusively in bending and was found to be optimized for this loading mode. Vertebrate long bones were found to be far from optimal, having much lower r/t values than predicted, and in this respect our conclusions differ from those of previous workers. We conclude that our theoretical model, though it has some limitations, is useful for investigating evolutionary development of skeletal form in exoskeletons and endoskeletons.     

Stress analysis in bone tissue around single implants with different diameters and veneering materials: A 3-D finite element study

The aim of this study was to evaluate the stress distribution on bone tissue with a single prosthesis supported by implants of large and conventional diameter and presenting different veneering materials using the 3-D finite element method. Sixteen models were fabricated to reproduce a bone block with implants, using two diameters (3.75 × 10 mm and 5.00 × 10 mm), four different veneering materials (composite resin, acrylic resin, porcelain, and NiCr crown), and two loads (axial (200 N) and oblique (100 N)). For data analysis, the maximum principal stress and von Mises criterion were used. For the axial load, the cortical bone in all models did not exhibit significant differences, and the trabecular bone presented higher tensile stress with reduced implant diameter. For the oblique load, the cortical bone presented a significant increase in tensile stress on the same side as the loading for smaller implant diameters. The trabecular bone showed a similar but more discreet trend. There was no difference in bone tissue with different veneering materials. The veneering material did not influence the stress distribution in the supporting tissues of single implant-supported prostheses. The large-diameter implants improved the transference of occlusal loads to bone tissue and decreased stress mainly under oblique loads. Oblique loading was more detrimental to distribution stresses than axial loading.     

Alkyl-π engineering in state control toward versatile optoelectronic soft materials

Organic π-conjugated molecules with extremely rich and tailorable electronic and optical properties are frequently utilized for the fabrication of optoelectronic devices. To achieve high solubility for facile solution processing and desirable softness for flexible device fabrication, the rigid π units were in most cases attached by alkyl chains through chemical modification. Considerable numbers of alkylated-π molecular systems with versatile applications have been reported. However, a profound understanding of the molecular state control through proper alkyl chain substitution is still highly demanded because effective applications of these molecules are closely related to their physical states. To explore the underlying rule, we review a large number of alkylated-π molecules with emphasis on the interplay of van der Waals interactions (vdW) of the alkyl chains and π–π interactions of the π moieties. Based on our comprehensive investigations of the two interactions’ impacts on the physical states of the molecules, a clear guidance for state control by alkyl-π engineering is proposed. Specifically, either with proper alkyl chain substitution or favorable additives, the vdW and π–π interactions can be adjusted, resulting in modulation of the physical states and optoelectronic properties of the molecules. We believe the strategy summarized here will significantly benefit the alkyl-π chemistry toward wide-spread applications in optoelectronic devices.     

Force transformation in spider strain sensors: white light interferometry

Scanning white light interferometry and micro-force measurements were applied to analyse stimulus transformation in strain sensors in the spider exoskeleton. Two compound or ‘lyriform’ organs consisting of arrays of closely neighbouring, roughly parallel sensory slits of different lengths were examined. Forces applied to the exoskeleton entail strains in the cuticle, which compress and thereby stimulate the individual slits of the lyriform organs. (i) For the proprioreceptive lyriform organ HS-8 close to the distal joint of the tibia, the compression of the slits at the sensory threshold was as small as 1.4 nm and hardly more than 30 nm, depending on the slit in the array. The corresponding stimulus forces were as small as 0.01 mN. The linearity of the loading curve seems reasonable considering the sensor''s relatively narrow biological intensity range of operation. The slits'' mechanical sensitivity (slit compression/force) ranged from 106 down to 13 nm mN⁻¹, and gradually decreased with decreasing slit length. (ii) Remarkably, in the vibration-sensitive lyriform organ HS-10 on the metatarsus, the loading curve was exponential. The organ is thus adapted to the detection of a wide range of vibration amplitudes, as they are found under natural conditions. The mechanical sensitivities of the two slits examined in this organ in detail differed roughly threefold (522 and 195 nm mN⁻¹) in the biologically most relevant range, again reflecting stimulus range fractionation among the slits composing the array.     

Solutions for a local equation of anisotropic plant cell growth: an analytical study of expansin activity

This paper presents a generalization of the Lockhart equation for plant cell/organ expansion in the anisotropic case. The intent is to take into account the temporal and spatial variation in the cell wall mechanical properties by considering the wall ‘extensibility’ (Φ), a time- and space-dependent parameter. A dynamic linear differential equation of a second-order tensor is introduced by describing the anisotropic growth process with some key biochemical aspects included. The distortion and expansion of plant cell walls initiated by expansins, a class of proteins known to enhance cell wall ‘extensibility’, is also described. In this approach, expansin proteins are treated as active agents participating in isotropic/anisotropic growth. Two-parameter models and an equation for describing α- and β-expansin proteins are proposed by delineating the extension of isolated wall samples, allowing turgor-driven polymer creep, where expansins weaken the non-covalent binding between wall polysaccharides. We observe that the calculated halftime (t_1/2 = εΦ₀ log 2) of stress relaxation due to expansin action can be described in mechanical terms.     

Two-time scale fatigue modelling: application to damage

A temporal multiscale modelling applied to fatigue damage evolution in cortical bone is presented. Microdamage accumulation in cortical bone, ensued from daily activities, leads to impaired mechanical properties, in particular by reducing the bone stiffness and inducing fatigue. However, bone damage is also known as a stimulus to bone remodelling, whose aim is to repair and generate new bone, adapted to its environment. This biological process by removing fatigue damage seems essential to the skeleton lifetime. As daily activities induce high frequency cycles (about 10,000 cycles a day), identifying two-time scale is very fruitful: a fast one connected with the high frequency cyclic loading and a slow one related to a quasi-static loading. A scaling parameter is defined between the intrinsic time (bone lifetime of several years) and the high frequency loading (few seconds). An asymptotic approach allows to decouple the two scales and to take into account history effects (Guennouni and Aubry in CR Acad Sci Paris Ser II 20:1765–1767, 1986). The method is here applied to a simple case of fatigue damage and a real cortical bone microstructure. A significant reduction in the amount of computation time in addition to a small computational error between time homogenized and non homogenized models are obtained. This method seems thus to give new perspectives to assess fatigue damage and, with regard to bone, to give a better understanding of bone remodelling.     

History effect in fatigue crack growth under mixed-mode loading conditions

Plastic deformation within the crack tip region introduces internal stresses that modify subsequent behaviour of the crack and are at the origin of history effects in fatigue crack growth. Consequently, fatigue crack growth models should include plasticity-induced history effects. A model was developed and validated for mode I fatigue crack growth under variable amplitude loading conditions. The purpose of this study was to extend this model to mixed-mode loading conditions. Finite element analyses are commonly employed to model crack tip plasticity and were shown to give very satisfactory results. However, if millions of cycles need to be modelled to predict the fatigue behaviour of an industrial component, the finite element method becomes computationally too expensive. By employing a multiscale approach, the local results of FE computations can be brought to the global scale. This approach consists of partitioning the velocity field at the crack tip into plastic and elastic parts. Each part is partitioned into mode I and mode II components, and finally each component is the product of a reference spatial field and an intensity factor. The intensity factor of the mode I and mode II plastic parts of the velocity fields, denoted by dρ_I/dt and dρ_II/dt, allow measuring mixed-mode plasticity in the crack tip region at the global scale. Evolutions of dρ_I/dt and dρ_II/dt, generated using the FE method for various loading histories, enable the identification of an empirical cyclic elastic–plastic constitutive model for the crack tip region at the global scale. Once identified, this empirical model can be employed, with no need of additional FE computations, resulting in faster computations. With the additional hypothesis that the fatigue crack growth rate and direction can be determined from mixed-mode crack tip plasticity (dρ_I/dt and dρ_II/dt), it becomes possible to predict fatigue crack growth under I/II mixed-mode and variable amplitude loading conditions. To compare the predictions of this model with experiments, an asymmetric four point bend test system was setup. It allows applying any mixed-mode loading case from a pure mode I condition to a pure mode II. Initial experimental results showed an increase of the mode I fatigue crack growth rate after the application of a set of mode II overload cycles.     

The influence of gait stance on pedestrian lower limb injury risk

The effect of pedestrian gait on lower limb kinematics and injuries has not been analyzed. The purpose of this paper was therefore to investigate the effect of pedestrian gait on kinematics and injury risk to the lower limbs using the Total Human Model for Safety adult male pedestrian model together with FE models of vehicle front structures. The modeling results indicate that the tibia and femur cortical bone von-Mises stress and the lateral knee bending angle of an adult pedestrian are strongly dependent on the gait stance when struck by both a sedan car and an SUV at 40 km/h. The gait analysis shows that generally the leg of an adult pedestrian has lower injury risk when the knee is flexed and linear regressions show high negative correlation between knee flexion angle during impact and knee lateral bending angle and also high negative correlation between lower leg axial rotation during impact and knee lateral bending angle. Furthermore, in some gait stances a self-contact between the legs occurs, and the peak bones stresses and knee shearing displacement in the leg are then increased. Assessment of pedestrian lower limb injury should take account of these gait stance effects.     

Graphene oxide‐ellagic acid nanocomposite as effective anticancer and antimicrobial agent

In this study, ellagic acid (ELA), a skin anticancer drug, is capped on the surface(s) of functionalised graphene oxide (GO) nano‐sheets through electrostatic and π–π staking interactions. The prepared ELA‐GO nanocomposite have been thoroughly characterised by using eight techniques: Fourier‐transform infrared spectroscopy (FTIR), zeta potential, X‐ray diffraction (XRD), thermogravimetric analysis (TGA), Raman spectroscopy, atomic force microscopy (AFM) topographic imaging, transmission electron microscopy (TEM), and surface morphology via scanning electron microscopy (SEM). Furthermore, ELA drug loading and release behaviours from ELA‐GO nanocomposite were studied. The ELA‐GO nanocomposite has a uniform size distribution averaging 88 nm and high drug loading capacity of 30 wt.%. The in vitro drug release behaviour of ELA from the nanocomposite was investigated by UV–Vis spectrometry at a wavelength of λ _max 257 nm. The data confirmed prolonged ELA release over 5000 min at physiological pH (7.4). Finally, the IC ₅₀ of this ELA‐GO nanocomposite was found to be 6.16 µg/ml against B16 cell line; ELA and GO did not show any cytotoxic effects up to 50 µg/ml on the same cell lines.     

A novel in vivo method for quantifying the interfacial biochemical bond strength of bone implants

Quantifying the in vivo interfacial biochemical bond strength of bone implants is a biological challenge. We have developed a new and novel in vivo method to identify an interfacial biochemical bond in bone implants and to measure its bonding strength. This method, named biochemical bond measurement (BBM), involves a combination of the implant devices to measure true interfacial bond strength and surface property controls, and thus enables the contributions of mechanical interlocking and biochemical bonding to be distinguished from the measured strength values. We applied the BBM method to a rabbit model, and observed great differences in bone integration between the oxygen (control group) and magnesium (test group) plasma immersion ion-implanted titanium implants (0.046 versus 0.086 MPa, n=10, p=0.005). The biochemical bond in the test implants resulted in superior interfacial behaviour of the implants to bone: (i) close contact to approximately 2 μm thin amorphous interfacial tissue, (ii) pronounced mineralization of the interfacial tissue, (iii) rapid bone healing in contact, and (iv) strong integration to bone. The BBM method can be applied to in vivo experimental models not only to validate the presence of a biochemical bond at the bone–implant interface but also to measure the relative quantity of biochemical bond strength. The present study may provide new avenues for better understanding the role of a biochemical bond involved in the integration of bone implants.     

Intrinsic frequency for a systems approach to haemodynamic waveform analysis with clinical applications

The reductionist approach has dominated the fields of biology and medicine for nearly a century. Here, we present a systems science approach to the analysis of physiological waveforms in the context of a specific case, cardiovascular physiology. Our goal in this study is to introduce a methodology that allows for novel insight into cardiovascular physiology and to show proof of concept for a new index for the evaluation of the cardiovascular system through pressure wave analysis. This methodology uses a modified version of sparse time–frequency representation (STFR) to extract two dominant frequencies we refer to as intrinsic frequencies (IFs; ω₁ and ω₂). The IFs are the dominant frequencies of the instantaneous frequency of the coupled heart + aorta system before the closure of the aortic valve and the decoupled aorta after valve closure. In this study, we extract the IFs from a series of aortic pressure waves obtained from both clinical data and a computational model. Our results demonstrate that at the heart rate at which the left ventricular pulsatile workload is minimized the two IFs are equal (ω₁ = ω₂). Extracted IFs from clinical data indicate that at young ages the total frequency variation (Δω = ω₁ − ω₂) is close to zero and that Δω increases with age or disease (e.g. heart failure and hypertension). While the focus of this paper is the cardiovascular system, this approach can easily be extended to other physiological systems or any biological signal.     

Thermal Behavior of Muscovite Sheet Mica

The three spectral types of muscovite sheet mica, i.e., very pink ruby, light green, and dark green, were subjected to heat treatments at temperatures up to 600 °C. The changes in the apparent optic axial angle and in the absorption spectra (0.3 to 15 μ) were studied along with color.The differentiation of muscovite sheet according to these spectral types extends to the behavior of apparent optic axial angle and to certain regions of the spectrum under heat treatment. The pink associated absorption region (0.47 to 0.6 μ) can be enhanced or bleached away by appropriate thermal treatment, although the associated infrared multiplet at 3 to 3.5 μ is little affected. The absorption band at 12 μ increases in intensity with temperature of treatment. It is suspected that the 0.47 to 0.6 μ absorption is the result of color centers.It has been shown that measurable differences exist in apparent optic axial angle and absorption spectrum, as well as in color, for muscovite sheet micas. These differences indicate that there must be basic chemical and structural variations. They further provide a quantitative, though complex, categorization of the material [1].¹The present paper reports the effect of heat treatment on color, apparent optic axial angle, and absorption spectrum for several of the representative categories of the material so established. The treatments were at temperatures of 600 °C and less, usually considered to be below the decomposition point.