Effect of cyclic loading on the nanoscale deformation of hydroxyapatite and collagen fibrils in bovine bone

Cyclic compressive loading tests were carried out on bovine femoral bones at body temperature $(37\,^{\circ }\hbox {C})$ , with varying mean stresses ( $-55$ to $-80$  MPa) and loading frequencies (0.5–5 Hz). At various times, the cyclic loading was interrupted to carry out high-energy X-ray scattering measurements of the internal strains developing in the hydroxyapatite (HAP) platelets and the collagen fibrils. The residual strains upon unloading were always tensile in the HAP and compressive in the fibrils, and each increases in magnitude with loading cycles, which can be explained from damage at the HAP–collagen interface and accumulation of plastic deformation within the collagen phase. The samples tested at a higher mean stress and stress amplitude, and at lower loading frequencies exhibit greater plastic deformation and damage accumulation, which is attributed to greater contribution of creep. Synchrotron microcomputed tomography of some of the specimens showed that cracks are produced during cyclic loading and that they mostly occur concentric with Haversian canals.     

Dynamic permeability of the lacunar–canalicular system in human cortical bone

A new method for the experimental determination of the permeability of a small sample of a fluid-saturated hierarchically structured porous material is described and applied to the determination of the lacunar–canalicular permeability \((K_\mathrm{LC})\) in bone. The interest in the permeability of the lacunar–canalicular pore system (LCS) is due to the fact that the LCS is considered to be the site of bone mechanotransduction due to the loading-driven fluid flow over cellular structures. The permeability of this space has been estimated to be anywhere from \(10^{-17}\;\) to \(10^{-25}\; \hbox {m}^{2}\) . However, the vascular pore system and LCS are intertwined, rendering the permeability of the much smaller-dimensioned LCS challenging to measure. In this study, we report a combined experimental and analytical approach that allowed the accurate determination of the \(K_\mathrm{LC}\) to be on the order of \(10^{-22}\; \hbox {m}^{2}\) for human osteonal bone. It was found that the \(K_\mathrm{LC}\) has a linear dependence on loading frequency, decreasing at a rate of \(2 \times 10^{-24}\; \hbox {m}^{2}\) /Hz from 1 to 100 Hz, and using the proposed model, the porosity alone was able to explain 86 % of the \(K_\mathrm{LC}\) variability.     

Bone refilling in cortical basic multicellular units: insights into tetracycline double labelling from a computational model

Bone remodelling is carried out by ‘bone multicellular units’ ( $\text{ BMU }$ s) in which active osteoclasts and active osteoblasts are spatially and temporally coupled. The refilling of new bone by osteoblasts towards the back of the $\text{ BMU }$ occurs at a rate that depends both on the number of osteoblasts and on their secretory activity. In cortical bone, a linear phenomenological relationship between matrix apposition rate and $\text{ BMU }$ cavity radius is found experimentally. How this relationship emerges from the combination of complex, nonlinear regulations of osteoblast number and secretory activity is unknown. Here, we extend our previous mathematical model of cell development within a single cortical $\text{ BMU }$ to investigate how osteoblast number and osteoblast secretory activity vary along the $\text{ BMU }$ ’s closing cone. The mathematical model is based on biochemical coupling between osteoclasts and osteoblasts of various maturity and includes the differentiation of osteoblasts into osteocytes and bone lining cells, as well as the influence of $\text{ BMU }$ cavity shrinkage on osteoblast development and activity. Matrix apposition rates predicted by the model are compared with data from tetracycline double labelling experiments. We find that the linear phenomenological relationship observed in these experiments between matrix apposition rate and $\text{ BMU }$ cavity radius holds for most of the refilling phase simulated by our model, but not near the start and end of refilling. This suggests that at a particular bone site undergoing remodelling, bone formation starts and ends rapidly, supporting the hypothesis that osteoblasts behave synchronously. Our model also suggests that part of the observed cross-sectional variability in tetracycline data may be due to different bone sites being refilled by $\text{ BMU }$ s at different stages of their lifetime. The different stages of a $\text{ BMU }$ ’s lifetime (such as initiation stage, progression stage, and termination stage) depend on whether the cell populations within the $\text{ BMU }$ are still developing or have reached a quasi-steady state whilst travelling through bone. We find that due to their longer lifespan, active osteoblasts reach a quasi-steady distribution more slowly than active osteoclasts. We suggest that this fact may locally enlarge the Haversian canal diameter (due to a local lack of osteoblasts compared to osteoclasts) near the $\text{ BMU }$ ’s point of origin.     

Preparation of allogeneic bone for alveolar ridge augmentation

Implant treatment is safe and predictable with sufficient amount and quality of bone tissue. In case of severely reduced bone tissue after a tooth was lost, augmentation of such tissue is necessary before implant embedment. Retrospective evaluation covered 380 alveolar ridge reconstructions. The study material consisted of human grafts prepared by the Department of Transplantology and Central Tissue Bank, Medical University of Warsaw. Presentation of laboratory procedures in the context of physical parameters of frozen, radiation sterilised, allogeneic corticocancellous material was presented. The preparation process makes it possible to obtain two types of bone material: granules and blocks. Women underwent 164 procedures with the use of bone granules and 61 augmentations with bone blocks. In case of men 122 packages of granules were used as well as 33 bone blocks. Based on the results an evaluation of usability of available allogeneic grafts was performed with reference to planned alveolar ridge augmentation procedures, which they were used for.

1. 1.
   The opportunity to prepare allogeneic material of different textures allowed selection to meet augmentation requirements while providing biological safety.
    
2. 2.
   Allogeneic granules should be used in multi-wall defects, such as a double, closed sinus lift and post-extraction socket augmentation.
    
3. 3.
   Owing to their superior mechanical parameters, bone blocks were successfully used in extending the width and height of the alveolar ridge and in open sinus lifts with one-wall or two-wall defects and adequate location of the lamellar bone in a graft prevented substantial graft resorption.
    

     

Linear viscoelasticity - bone volume fraction relationships of bovine trabecular bone

Trabecular bone has been previously recognized as time-dependent (viscoelastic) material, but the relationships of its viscoelastic behaviour with bone volume fraction (BV/TV) have not been investigated so far. Therefore, the aim of the present study was to quantify the time-dependent viscoelastic behaviour of trabecular bone and relate it to BV/TV. Uniaxial compressive creep experiments were performed on cylindrical bovine trabecular bone samples (\(\textit{n}\,{=}\,13\)) at loads corresponding to physiological strain level of 2000 \({\upmu }{\upvarepsilon }\). We assumed that the bone behaves in a linear viscoelastic manner at this low strain level and the corresponding linear viscoelastic parameters were estimated by fitting a generalized Kelvin–Voigt rheological model to the experimental creep strain response. Strong and significant power law relationships (\(r^2\,{=}\,0.73,\ p\,{<}\,0.001\)) were found between time-dependent creep compliance function and BV/TV of the bone. These BV/TV-based material properties can be used in finite element models involving trabecular bone to predict time-dependent response. For users’ convenience, the creep compliance functions were also converted to relaxation functions by using numerical interconversion methods and similar power law relationships were reported between time-dependent relaxation modulus function and BV/TV.     

Magnetic resonance elastography in nonlinear viscoelastic materials under load

Characterisation of soft tissue mechanical properties is a topic of increasing interest in translational and clinical research. Magnetic resonance elastography (MRE) has been used in this context to assess the mechanical properties of tissues in vivo noninvasively. Typically, these analyses rely on linear viscoelastic wave equations to assess material properties from measured wave dynamics. However, deformations that occur in some tissues (e.g. liver during respiration, heart during the cardiac cycle, or external compression during a breast exam) can yield loading bias, complicating the interpretation of tissue stiffness from MRE measurements. In this paper, it is shown how combined knowledge of a material’s rheology and loading state can be used to eliminate loading bias and enable interpretation of intrinsic (unloaded) stiffness properties. Equations are derived utilising perturbation theory and Cauchy’s equations of motion to demonstrate the impact of loading state on periodic steady-state wave behaviour in nonlinear viscoelastic materials. These equations demonstrate how loading bias yields apparent material stiffening, softening and anisotropy. MRE sensitivity to deformation is demonstrated in an experimental phantom, showing a loading bias of up to twofold. From an unbiased stiffness of \(4910.4 \pm 635.8\) Pa in unloaded state, the biased stiffness increases to 9767.5 \(\pm \,\)1949.9 Pa under a load of \(\approx \) 34% uniaxial compression. Integrating knowledge of phantom loading and rheology into a novel MRE reconstruction, it is shown that it is possible to characterise intrinsic material characteristics, eliminating the loading bias from MRE data. The framework introduced and demonstrated in phantoms illustrates a pathway that can be translated and applied to MRE in complex deforming tissues. This would contribute to a better assessment of material properties in soft tissues employing elastography.

     

Plausibility and parameter sensitivity of micro-finite element-based joint load prediction at the proximal femur

A micro-finite element-based method to estimate the bone loading history based on bone architecture was recently presented in the literature. However, a thorough investigation of the parameter sensitivity and plausibility of this method to predict joint loads is still missing. The goals of this study were (1) to analyse the parameter sensitivity of the joint load predictions at one proximal femur and (2) to assess the plausibility of the results by comparing load predictions of ten proximal femora to in vivo hip joint forces measured with instrumented prostheses (available from www.orthoload.com). Joint loads were predicted by optimally scaling the magnitude of four unit loads (inclined \(-20^{\circ }\) to \(100^{\circ }\) with respect to the vertical axis) applied to micro-finite element models created from high-resolution computed tomography scans (\(30.3~\upmu \)m voxel size). Parameter sensitivity analysis was performed by varying a total of nine parameters and showed that predictions of the peak load directions (range 10\(^{\circ }\)–\(30^{\circ }\)) are more robust than the predicted peak load magnitudes (range 2344.8–4689.5 N). Comparing the results of all ten femora with the in vivo loading data of ten subjects showed that peak loads are plausible both in terms of the load direction (in vivo: \(18.2\pm 2.0^{\circ }\), predicted: \(20.0^{\circ }\)) and magnitude (in vivo: \(2707.6\pm 443.3~\hbox {N}\), predicted: \(3372.2\pm 597.9~\hbox {N}\)). Overall, this study suggests that micro-finite element-based joint load predictions are both plausible and robust in terms of the predicted peak load direction, but predicted load magnitudes should be interpreted with caution.     

Estimation of the effective yield properties of human trabecular bone using nonlinear micro-finite element analyses

Micro-finite element (\(\upmu \)FE) analyses are often used to determine the apparent mechanical properties of trabecular bone volumes. Yet, these apparent properties depend strongly on the applied boundary conditions (BCs) for the limited size of volumes that can be obtained from human bones. To attenuate the influence of the BCs, we computed the yield properties of samples loaded via a surrounding layer of trabecular bone (“embedded configuration”). Thirteen cubic volumes (10.6 mm side length) were collected from \(\upmu \)CT reconstructions of human vertebrae and femora and converted into \(\upmu \)FE models. An isotropic elasto-plastic material model was chosen for bone tissue, and nonlinear \(\upmu \)FE analyses of six uniaxial, shear, and multi-axial load cases were simulated to determine the yield properties of a subregion (5.3 mm side length) of each volume. Three BCs were tested. Kinematic uniform BCs (KUBCs: each boundary node is constrained with uniform displacements) and periodicity-compatible mixed uniform BCs (PMUBCs: each boundary node is constrained with a uniform combination of displacements and tractions mimicking the periodic BCs for an orthotropic material) were directly applied to the subregions, while the embedded configuration was achieved by applying PMUBCs on the larger volumes instead. Yield stresses and strains, and element damage at yield were finally compared across BCs. Our findings indicate that yield strains do not depend on the BCs. However, KUBCs significantly overestimate yield stresses obtained in the embedded configuration (+43.1 ± 27.9%). PMUBCs underestimate (?10.0 ± 11.2%), but not significantly, yield stresses in the embedded situation. Similarly, KUBCs lead to higher damage levels than PMUBCs (+51.0 ± 16.9%) and embedded configurations (+48.4 ± 15.0%). PMUBCs are better suited for reproducing the loading conditions in subregions of the trabecular bone and deliver a fair estimation of their effective (asymptotic) yield properties.     

A simple method to estimate the exponential material parameters of heart valve tissue based on analogy between uniaxial tension and micropipette aspiration

Micropipette aspiration (MA) has been widely used to measure the biomechanical properties of cells and biomaterials. To estimate material parameters from MA experimental data, analytical half-space models and inverse finite element (FE) analyses are typically used. The half-space model is easy to implement but cannot account for nonlinear material properties and complex geometrical boundary conditions that are inherent to MA. Inverse FE approaches can account for geometrical and material nonlinearities, but their implementation is resource-intensive and not widely available. Here, by making analogy between an analytical uniaxial tension model and a FE model of MA, we proposed an easily implementable and accurate method to estimate the material parameters of tissues tested by MA. We first adopted a strain invariant-based isotropic exponential constitutive model and implemented it in both the analytical uniaxial tension model and the FE model. The two models were fit to experimental data generated by MA of porcine aortic valve tissue (45 spots on four leaflets) to estimate material parameters. We found no significant differences between the effective moduli estimated by the two models ( $p > 0.39$ ), with the effective moduli estimated by the uniaxial tension model correlating significantly with those estimated by the FE model ( $p < 0.001; R^{2}= 0.96$ ) with a linear regression slope that was not different than unity ( $p = 0.38$ ). Thus, the analytical uniaxial tension model, which avoids solving resource-intensive numerical problems, is as accurate as the FE model in estimating the effective modulus of valve tissue tested by MA.     

Simulated bone remodeling around tilted dental implants in the anterior maxilla

Dental implants have to be placed with the long axis in different angulations due to the change in bone morphology. The objective of this study was to investigate the different bone remodeling response induced by the tilted dental implants and to assess whether it could lead to bone loss and implant failure. In this study, bone remodeling due to palato-labially inclined dental implants placed in the anterior maxillary incisor region was simulated. CT-based finite element models of a maxillary bone with dental implants were created herein. Five dental implants were placed at \(+10^{\circ }\), \(+5^{\circ }\), \(0^{\circ }\), \(-5^{\circ }\) and \(-10^{\circ }\), respectively. The remodeling progression was recorded and compared. Model \(-10^{\circ }\) (palatal side) shows the highest bone density values, but the inclined implant at \(+10^{\circ }\) (labial side) leads to significant bone loss. From a biomechanical perspective, it is speculated that a palatally inclined implant is more likely to enhance the bone density in the maxillary anterior region, but labial inclination of implant could jeopardize its stability.     

Approximating the dynamics of communicating cells in a diffusive medium by ODEs—homogenization with localization

Bacteria may change their behavior depending on the population density. Here we study a dynamical model in which cells of radius $R$ within a diffusive medium communicate with each other via diffusion of a signalling substance produced by the cells. The model consists of an initial boundary value problem for a parabolic PDE describing the exterior concentration $u$ of the signalling substance, coupled with $N$ ODEs for the masses $a_i$ of the substance within each cell. We show that for small $R$ the model can be approximated by a hierarchy of models, namely first a system of $N$ coupled delay ODEs, and in a second step by $N$ coupled ODEs. We give some illustrations of the dynamics of the approximate model.     

Mimetization of the elastic properties of cancellous bone via a parameterized cellular material

Bone tissue mechanical properties and trabecular microarchitecture are the main factors that determine the biomechanical properties of cancellous bone. Artificial cancellous microstructures, typically described by a reduced number of geometrical parameters, can be designed to obtain a mechanical behavior mimicking that of natural bone. In this work, we assess the ability of the parameterized microstructure introduced by Kowalczyk (Comput Methods Biomech Biomed Eng 9:135–147, 2006. doi: 10.1080/10255840600751473) to mimic the elastic response of cancellous bone. Artificial microstructures are compared with actual bone samples in terms of elasticity matrices and their symmetry classes. The capability of the parameterized microstructure to combine the dominant isotropic, hexagonal, tetragonal and orthorhombic symmetry classes in the proportions present in the cancellous bone is shown. Based on this finding, two optimization approaches are devised to find the geometrical parameters of the artificial microstructure that better mimics the elastic response of a target natural bone specimen: a Sequential Quadratic Programming algorithm that minimizes the norm of the difference between the elasticity matrices, and a Pattern Search algorithm that minimizes the difference between the symmetry class decompositions. The pattern search approach is found to produce the best results. The performance of the method is demonstrated via analyses for 146 bone samples.     

d-Aspartate acts as a signaling molecule in nervous and neuroendocrine systems

d-Aspartate (d-Asp) is an endogenous amino acid in the central nervous and reproductive systems of vertebrates and invertebrates. High concentrations of d-Asp are found in distinct anatomical locations, suggesting that it has specific physiological roles in animals. Many of the characteristics of d-Asp have been documented, including its tissue and cellular distribution, formation and degradation, as well as the responses elicited by d-Asp application. d-Asp performs important roles related to nervous system development and hormone regulation; in addition, it appears to act as a cell-to-cell signaling molecule. Recent studies have shown that d-Asp fulfills many, if not all, of the definitions of a classical neurotransmitter—that the molecule’s biosynthesis, degradation, uptake, and release take place within the presynaptic neuron, and that it triggers a response in the postsynaptic neuron after its release. Accumulating evidence suggests that these criteria are met by a heterogeneous distribution of enzymes for d-Asp’s biosynthesis and degradation, an appropriate uptake mechanism, localization within synaptic vesicles, and a postsynaptic response via an ionotropic receptor. Although d-Asp receptors remain to be characterized, the postsynaptic response of d-Asp has been studied and several l-glutamate receptors are known to respond to d-Asp. In this review, we discuss the current status of research on d-Asp in neuronal and neuroendocrine systems, and highlight results that support d-Asp’s role as a signaling molecule.     

A hyperelastic fibre-reinforced continuum model of healing tendons with distributed collagen fibre orientations

The healing process of ruptured tendons is problematic due to scar tissue formation and deteriorated material properties, and in some cases, it may take nearly a year to complete. Mechanical loading has been shown to positively influence tendon healing; however, the mechanisms remain unclear. Computational mechanobiology methods employed extensively to model bone healing have achieved high fidelity. This study aimed to investigate whether an established hyperelastic fibre-reinforced continuum model introduced by Gasser, Ogden and Holzapfel (GOH) can be used to capture the mechanical behaviour of the Achilles tendon under loading during discrete timepoints of the healing process and to assess the model’s sensitivity to its microstructural parameters. Curve fitting of the GOH model against experimental tensile testing data of rat Achilles tendons at four timepoints during the tendon repair was used and achieved excellent fits (\(0.9903 < R^{2 }<0.9986\)). A parametric sensitivity study using a three-level central composite design, which is a fractional factorial design method, showed that the collagen-fibre-related parameters in the GOH model—\(\kappa , {k_{{1}}}^{{\prime }}\) and \({k_{{2}}}^{{\prime }}\)—had almost equal influence on the fitting. This study demonstrates that the GOH hyperelastic fibre-reinforced model is capable of describing the mechanical behaviour of healing tendons and that further experiments should focus on establishing the structural and material parameters of collagen fibres in the healing tissue.     

Simulation of cell-substrate traction force dynamics in response to soluble factors

Finite element (FE) simulations of contractile responses of vascular muscular thin films (vMTFs) and endothelial cells resting on an array of microposts under stimulation of soluble factors were conducted in comparison with experimental measurements reported in the literature. Two types of constitutive models were employed in the simulations, i.e. smooth muscle cell type and non-smooth muscle cell type. The time histories of the effects of soluble factors were obtained via calibration against experimental measurements of contractile responses of tissues or cells. The numerical results for vMTFs with micropatterned tissues suggest that the radius of curvature of vMTFs under stimulation of soluble factors is sensitive to width of the micropatterned tissue, i.e. the radius of curvature increases as the tissue width decreases. However, as the tissue response is essentially isometric, the time history of the maximum principal stress of the micropatterned tissues is not sensitive to tissue width. Good agreement has been achieved for predictions of the vasoconstrictor endothelin-1-induced contraction stress between the FE numerical simulation and the experiment-based approach of Alford (Integr Biol 3:1063–1070, 2011) for the vMTFs with 40, 60, 80 and 100 \(\upmu \hbox {m}\) width patterns. This may suggest the contraction stress is weakly sensitive to the tissue width for these patterns. However, for 20 \(\upmu \hbox {m}\) width tissue patterning, the numerical simulation result for contraction stress is less than the average value of experimental measurements, which may suggest the thinner and more elongated spindle-like cells within the 20 \(\upmu \hbox {m}\) width tissue patterning have higher contractile output. The constitutive model for non-smooth muscle cells was used to simulate the contractile response of the endothelial cells. The substrate was treated as an effective continuum. For agonists such as lysophosphatidic acid and vascular endothelial growth factor, the deformation of the cell diminishes from edge to centre and the central part of the cell is essentially under isometric state. Numerical studies demonstrated the scenarios that cell polarity can be triggered via manipulation of the effective stiffness and Possion’s ratio of the substrate.     

Source Mechanisms for Unit Activity in Isolated Crayfish Central Nervous System

As a tool for the identification of source mechanisms underlying the activity of single interneurons in the isolated crayfish abdominal cord, pulse trains from a sample of such neurons are statistically described (shape, mean, standard deviation, and serial correlation coefficient of interval distributions). These statistics were measured under four independent means of obtaining different average frequencies: (a) naturally occurring frequencies under standard conditions, (b) temperature control, (c) dc polarization, and (d) electrical stimulation of presynaptic fibers. 40 of 44 units studied had unimodal histograms, symmetrical when the mean interval was small and positively skewed with large means. Under standard conditions these units had SD = k (mean)ⁿ, with n approximately 2. Fifteen single units were caused to fire at varied frequencies by cooling or dc stimulation. The resulting SD-vs.-mean plots for single units showed: (a)all points for a given unit fell approximately on a single line, regardless of whether temperature, dc, or neither was used to vary frequency, and (b) the average value of n (slope of log SD vs. log mean) for the fifteen units was 1.9 ± 0.2. A paradox arises from interpretation of these data via gamma distributions. It is concluded that most of the spontaneous activity in the isolated abdominal cord may result from pacemaker activity within each cell and does not require a network of active units. Finally, the fact that the SD-mean relation was found not to depend measurably on temperature is interpreted as a useful restriction on models for neuronal noise processes.     

Regulation of hepatic l-serine dehydratase and l-serine-pyruvate aminotransferase in the developing neonatal rat

1. The activities of l-serine dehydratase and l-serine–pyruvate aminotransferase were determined in rat liver during foetal and neonatal development. 2. l-Serine–pyruvate aminotransferase activity begins to develop in late-foetal liver, increases rapidly at birth to a peak during suckling and then decreases at weaning to the adult value. 3. l-Serine dehydratase activity is very low prenatally, but increases rapidly after birth to a transient peak. After a second transient peak around the time weaning begins, activity gradually rises to the adult value. Both of these peaks have similar isoenzyme compositions. 4. In foetal liver both l-serine dehydratase and l-serine–pyruvate aminotransferase activities are increased after injection in utero of glucagon or dibutyryl cyclic AMP. Cycloheximide or actinomycin D inhibited the prenatal induction of both enzymes and actinomycin D blocked the natural increase of l-serine dehydratase immediately after birth. Glucose or insulin administration also blocked the perinatal increase of l-serine dehydratase. 5. After the first perinatal peak of l-serine dehydratase, activity is increased by cortisol and this is inhibited by actinomycin D. After the second postnatal peak, activity is increased by amino acids or cortisol and this is insensitive to actinomycin D inhibition. Glucose administration blocks the cortisol-stimulated increase in l-serine dehydratase and also partially lowers the second postnatal peak of activity. 6. The developmental patterns of the enzymes are discussed in relation to the pathways of gluconeogenesis from l-serine. The regulation of enzyme activity by hormonal and dietary factors is discussed with reference to the changes in stimuli that occur during neonatal development and to their possible mechanisms of action.