On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon

An orthotropic continuum model with substructure evolution for describing bone remodeling: an interpretation of the primary mechanism behind Wolff's law

We propose a variational approach that employs a generalized principle of virtual work to estimate both the mechanical response and the changes in living bone tissue during the remodeling process. This approach provides an explanation for the adaptive regulation of the bone substructure in the context of orthotropic material symmetry. We specifically focus upon the crucial gradual adjustment of bone tissue as a structural material that adapts its mechanical features, such as materials stiffnesses and microstructure, in response to the evolving loading conditions. We postulate that the evolution process relies on a feedback mechanism involving multiple stimulus signals. The mechanical and remodeling behavior of bone tissue is clearly a complex process that is difficult to describe within the framework of classical continuum theories. For this reason, a generalized continuum elastic theory is employed as a proper mathematical context for an adequate description of the examined phenomenon. To simplify the investigation, we considered a two-dimensional problem. Numerical simulations have been performed to illustrate bone evolution in a few significant cases: the bending of a rectangular cantilever plate and a three-point flexure test. The results are encouraging because they can replicate the optimization process observed in bone remodeling. The proposed model provides a likely distribution of stiffnesses and accurately represents the arrangement of trabeculae macroscopically described by the orthotropic symmetry directions, as supported by experimental evidence from the trajectorial theory.

Gear-shaped carbonate apatite granules with a hexagonal macropore for rapid bone regeneration

Synthetic bone grafts are in high demand owing to increased age-related bone disorders in the global aging population. Here, we report fabrication of gear-shaped granules (G-GRNs) for rapid bone healing. G-GRNs possessed six protrusions and a hexagonal macropore in the granular center. These were composed of carbonate apatite, i.e., bone mineral, microspheres with ∼1-μm micropores in the spaces between the microspheres. G-GRNs formed new bone and blood vessels (both on the granular surface and within the macropores) 4 weeks after implantation in the rabbit femur defects. The formed bone structure was similar to that of cancellous bone. The bone percentage in the defect recovered to that in a normal rabbit femur at week-4 post-implantation, and the bone percentage remained constant for the following 8 weeks. Throughout the entire period, the bone percentage in the G-GRN-implanted group was ∼10% higher than that of the group implanted with conventional carbonate apatite granules. Furthermore, a portion of the G-GRNs resorbed at week-4, and resorption continued for the following 8 weeks. Thus, G-GRNs are involved in bone remodeling and are gradually replaced with new bone while maintaining a suitable bone level. These findings provide a basis for the design and fabrication of synthetic bone grafts for achieving rapid bone regeneration.

Prediction of osteoporotic degradation of tibia human bone at trabecular scale

A theoretical numerical model is proposed to predict patient dependent osteoporotic bone degradation. The model parameters are identified through a particle swarm optimization algorithm and based on individual patient high resolution peripherical quantitative computer tomography (HRpQCT) scan data. The degradation model is based on cellular activity initiated by the elastic strain energy developed in the bone microstructure through patient's body weight. The macro (organ scale) and meso (trabecular scale) scale analyses are carried out and predicted bone volume fraction and microstructure evolution are compared with in-vivo experimental bone degradation for four elderly women over a period of 10 years. A significant correlation (r > 0.9) is observed between the model predictions and in-vivo experiments in all cases with an average deviation error of 1.46%. The model can easily be extended to other patients and provide good predictions for different population categories such as ethnicity, gender, age, etc.

A lumped model for long bone behavior based on poroelastic deformation and Darcy flow

The present paper provides a simplified model for compact bone behavior by accounting for bone fluid flow coupled to the elasticity of the porous structure. The lumped model considers the bone material as a layered poroelastic structure and predicts normal pressure versus displacement, i.e, a stress-strain curve. There is a parametric dependency on porosity and permeability but, in addition, on pressure history. Specifically, the pressure impulse (the integral of pressure versus time) plays a key role. This factor is alluded to in several past studies, but not highlighted in a simplified fashion. Based on a global flow balance, bone displacement depends on the fluid flow in a channel according to the classical Darcy model of 1856, and on the rate of change of fluid within the porous solid according to the 1941 classical model of Biot. The present results agree with those of Perrin et al. which, in turn, agree with results of a detailed numerical simulation.

Patient-specific femoral implant design using metamaterials for improving load transfer at proximal-lateral region of the femur

Loading configuration of hip joint creates resultant bending effect on femoral implants. So, the lateral side of femoral implant which is under tension retracts from peri‑implant bone due to positive Poisson's ratio. This retraction of implant leads to load shielding and gap opening in proximal-lateral region, thereby allowing entry of wear particle to implant-bone interface. Retraction of femoral implant can be avoided by introducing auxetic metamaterial to the retracting side. This allows the implant to push peri‑implant bone under tensile condition by virtue of their auxetic (negative Poisson's ratio) nature. To develop such implants, a patient-specific conventional solid implant was first designed based on computed-tomography scan of a patient's femur. Two types of metamaterials (2D: type-1) and (3D: type-2) were employed to design femoral meta-implants. Type-1 and type-2 meta-implants were fabricated using metallic 3D printing method and mechanical compression testing was conducted. Three finite element (FE) models of the femur implanted with solid implant, type-1 meta-implant and type-2 meta-implant were developed and analysed under compression loading. Significant correlation (R² = 0.9821 and R² = 0.9977) was found between the experimental and FE predicted strains of the two meta-implants. In proximal-lateral region of the femur, an increase of 7.1% and 44.1% von-Mises strain was observed when implanted with type-1 and type-2 meta-implant over the solid implant. In this region, bone remodelling analysis revealed 2.5% bone resorption in case of solid implant. While bone apposition of 0.5% and 7.7% was observed in case of type-1 and type-2 meta-implants, respectively. The results of this study indicates that concept of introduction of metamaterial to the lateral side of femoral implant can prove to provide higher osseointegration-friendly environment in the proximal-lateral region of femur.

The sirtuin family in health and disease

Sirtuins (SIRTs) are nicotine adenine dinucleotide(+)-dependent histone deacetylases regulating critical signaling pathways in prokaryotes and eukaryotes, and are involved in numerous biological processes. Currently, seven mammalian homologs of yeast Sir2 named SIRT1 to SIRT7 have been identified. Increasing evidence has suggested the vital roles of seven members of the SIRT family in health and disease conditions. Notably, this protein family plays a variety of important roles in cellular biology such as inflammation, metabolism, oxidative stress, and apoptosis, etc., thus, it is considered a potential therapeutic target for different kinds of pathologies including cancer, cardiovascular disease, respiratory disease, and other conditions. Moreover, identification of SIRT modulators and exploring the functions of these different modulators have prompted increased efforts to discover new small molecules, which can modify SIRT activity. Furthermore, several randomized controlled trials have indicated that different interventions might affect the expression of SIRT protein in human samples, and supplementation of SIRT modulators might have diverse impact on physiological function in different participants. In this review, we introduce the history and structure of the SIRT protein family, discuss the molecular mechanisms and biological functions of seven members of the SIRT protein family, elaborate on the regulatory roles of SIRTs in human disease, summarize SIRT inhibitors and activators, and review related clinical studies.

A Proposal for a Novel Formulation Based on the Hyperbolic Cattaneo’s Equation to Describe the Mechano-Transduction Process Occurring in Bone Remodeling

In this paper, we propose a model for the mechanical stimulus involved in the process of bone remodeling together with its evolution over time. Accumulated evidence suggests that bone remodeling could be interpreted as a feedback control process in which the mechanical state of the bone tissue is monitored, then appropriate signals are derived from the daily mechanical usage of the bone, these signals are transmitted into the surrounding region, and then they are detected by other agents whose purpose is to adapt the bone mass to the mechanical requirements of the environment. Therefore, we employ the diffusion equation for mass transport which is improved with Cattaneo’s correction to model the stimulus. This last improvement considers the effects of relaxation and non-locality, which we believe play essential roles in signaling messengers transport phenomena and are essential to match the evidence that suggests time-dependent excitations provide a more significant response at specific frequencies. To illustrate this particular behavior, numerical simulations have been performed in a 2D framework. The results fit the central aspect addressed, related to the dependency of the time of the adaptive process of bone, suggesting that our model is promising and deserves further investigation, both theoretical and experimental.

An in silico model for woven bone adaptation to heavy loading conditions in murine tibia

Existing in silico models for lamellar bone adaptation to mechanical loading are unsuitable for predicting woven bone growth. This anomaly is due to the difference in mechanobiology of the woven bone with respect to that of the lamellar bone. The present study is aimed at developing an in silico bone-adaptation model for woven bone at cellular and tissue levels. The diffusion of Ca²⁺ ions reaching lining cells from the osteocytic network and the bone cortex in response to a mechanical loading on the cortical bone has been considered as a stimulus. The diffusion of ions within osteocytic network has been computed with a lacunar-canalicular network (LCN) in which bone cells are uniformly arranged. Strain energy density is assumed to regulate ion flow within the network when the induced normal strain is above a threshold level. If the induced strain exceeds another higher threshold level, then the strain with a power constant is additionally assumed to regulate the stimulus. The intracellular flow of Ca²⁺ ions within the LCN has been simulated using Fick's laws of diffusion, using a finite element method. The ion diffusion from bone cortex to vesicles has been formulated as a normal strain with a power constant. The stimuli reaching the surface cells are assumed to form the new bone. The mathematical model closely predicts woven bone growth in mouse and rat tibia for various in vivo loading conditions. This model is the first to predict woven bone growth at tissue and cellular levels in response to heavy mechanical loading.

Bone Remodeling Process Based on Hydrostatic and Deviatoric Strain Mechano-Sensing

A macroscopic continuum model intended to provide predictions for the remodeling process occurring in bone tissue is proposed. Specifically, we consider a formulation in which two characteristic stiffnesses, namely the bulk and shear moduli, evolve independently to adapt the hydrostatic and deviatoric response of the bone tissue to environmental changes. The formulation is deliberately simplified, aiming at constituting a preliminary step toward a more comprehensive modeling approach. The evolutive process for describing the functional adaptation of the two stiffnesses is proposed based on an energetic argument. Numerical experiments reveal that it is possible to model the bone remodeling process with a different evolution for more than one material parameter, as usually done. Moreover, the results motivate further investigations into the subject.

A peridynamic formulation for nonlocal bone remodelling

Bone remodelling is a complex biomechanical process, which has been studied widely based on the restrictions of local continuum theory. To provide a nonlocal bone remodelling framework, we propose, for the first time, a peridynamic formulation on the macroscale. We illustrate our implementation with a common benchmark test as well as two load cases of the proximal femur. On the one hand, results of our peridynamic model with diminishing nonlocality measure converge to the results of a local finite element model. On the other hand, increasing the neighbourhood size shows to what extent the additional degree of freedom, the nonlocality, can influence the density evolution.

Symmetry breaking and effects of nutrient walkway in time-dependent bone remodeling incorporating poroelasticity

Bone is an extraordinary biological material that continuously adapts its hierarchical microstructure to respond to static and dynamic loads for offering optimal mechanical features, in terms of stiffness and toughness, across different scales, from the sub-microscopic constituents within osteons—where the cyclic activity of osteoblasts, osteoclasts, and osteocytes redesigns shape and percentage of mineral crystals and collagen fibers—up to the macroscopic level, with growth and remodeling processes that modify the architecture of both compact and porous bone districts. Despite the intrinsic complexity of the bone mechanobiology, involving coupling phenomena of micro-damage, nutrients supply driven by fluid flowing throughout hierarchical networks, and cells turnover, successful models and numerical algorithms have been presented in the literature to predict, at the macroscale, how bone remodels under mechanical stimuli, a fundamental issue in many medical applications such as optimization of femur prostheses and diagnosis of the risk fracture. Within this framework, one of the most classical strategies employed in the studies is the so-called Stanford’s law, which allows uploading the effect of the time-dependent load-induced stress stimulus into a biomechanical model to guess the bone structure evolution. In the present work, we generalize this approach by introducing the bone poroelasticity, thus incorporating in the model the role of the fluid content that, by driving nutrients and contributing to the removal of wastes of bone tissue cells, synergistically interacts with the classical stress fields to change homeostasis states, local saturation conditions, and reorients the bone density rate, in this way affecting growth and remodeling. Through two paradigmatic example applications, i.e. a cylindrical slice with internal prescribed displacements idealizing a tract of femoral diaphysis pushed out by the pressure exerted by a femur prosthesis and a bone element in a form of a bent beam, it is highlighted that the present model is capable to catch more realistically both the transition between spongy and cortical regions and the expected non-symmetrical evolution of bone tissue density in the medium–long term, unpredictable with the standard approach. A real study case of a femur is also considered at the end in order to show the effectiveness of the proposed remodeling algorithm.

Identification osteogenic signaling pathways following mechanical stimulation: A systematic review

INTRODUCTION

It has been shown that mechanical forces can induce or promote osteogenic differentiation as well as remodeling of the new created bone tissues. To apply this characteristic in bone tissue engineering, it is important to know which mechanical stimuli through which signaling pathway has a more significant impact on osteogenesis.

METHODS

In this systematic study, an electronic search was conducted using PubMed and Google Scholar databases. This study has been prepared and organized according to the preferred reporting items for systematic reviews and meta-analyses (PRISMA) guidelines. Included studies were first categorized according to the in vivo and in vitro studies.

RESULTS

Six types of mechanical stresses were used in these articles and the most commonly used mechanical force and cell source were tension and bone marrow-derived mesenchymal stem cells (BMMSCs), respectively. These forces were able to trigger twelve signaling pathways in which Wnt pathway was so prominent.

CONCLUSION

1) Although specific signaling pathways are induced through specific mechanical forces, Wnt signaling pathways are predominantly activated by almost all types of force/stimulation, 2) All signaling pathways regulate expression of RUNX2, which is known as a master regulator of osteogenesis, 3) In Tension force, the mode of force administration, i.e, continuous or non-continuous tension is more important than the percentage of elongation.

Orthotropic bone remodelling around uncemented femoral implant: a comparison with isotropic formulation

Peri-prosthetic bone adaptation has usually been predicted using subject-specific finite element analysis in combination with remodelling algorithms and assuming isotropic bone material property. The objective of the study is to develop an orthotropic bone remodelling algorithm for evaluation of peri-prosthetic bone adaptation in the uncemented implanted femur. The simulations considered loading conditions from a variety of daily activities. The orthotropic algorithm was tested on 2D and 3D models of the intact femur for verification of predicted results. The predicted orthotropic directionality, based on principal stress directions, was in agreement with the trabecular orientation in a micro-CT data of proximal femur. The validity of the proposed strain-based algorithm was assessed by comparing the predicted results of the orthotropic model with those of the strain-energy-density-based isotropic formulation. Despite agreement in cortical densities [Formula: see text], the isotropic remodelling algorithm tends to predict relatively higher values around the distal tip of the implant as compared to the orthotropic model. Both formulations predicted 4-8% bone resorption in the proximal femur. A linear regression analysis revealed a significant correlation [Formula: see text] between the stresses and strains on the cortex of the proximal femur, predicted by the isotropic and orthotropic formulations. Despite reasonable agreement in peri-prosthetic bone density distributions, the quantitative differences with isotropic model predictions highlight the combined influences of bone orthotropy and mechanical stimulus in the adaptation process.

Modeling cortical bone adaptation using strain gradients

Cyclic and low-magnitude loading promotes osteogenesis (i.e. new bone formation). Normal strain, strain energy density and fatigue damage accumulation are typically considered as osteogenic stimuli in computer models to predict site-specific new bone formation. These models however had limited success in explaining osteogenesis near the sites of minimal normal strain, for example, neutral axis of bending. Other stimuli such as fluid motion or strain gradient also stimulate bone formation. In silico studies modeled the new bone formation as a function of fluid motion, however, computation of fluid motion involves complex mathematical calculations. Strain gradients drive fluid flow and thus can also be established as the stimulus. Osteogenic potential of strain gradients is however not well established. The present study establishes strain gradients as osteogenic stimuli. Bending-induced strain gradients are computed at cortical bone cross-sections reported in animal loading in vivo studies. Correlation analysis between strain gradients and site of osteogenesis is analyzed. In silico model is also developed to test the osteogenic potential of strain gradients. The model closely predicts in vivo new bone distribution as a function of strain gradients. The outcome establishes strain gradient as computationally easy and robust stimuli to predict site-specific osteogenesis. The present study may be useful in the development of biomechanical approaches to mitigate bone loss.

Bio-Inspired Design of a Porous Resorbable Scaffold for Bone Reconstruction: A Preliminary Study

The study and imitation of the biological and mechanical systems present in nature and living beings always have been sources of inspiration for improving existent technologies and establishing new ones. Pursuing this line of thought, we consider an artificial graft typical in the bone reconstruction surgery with the same microstructure of the bone living tissue and examine the interaction between these two phases, namely bone and the graft material. Specifically, a visco-poroelastic second gradient model is adopted for the bone-graft composite system to describe it at a macroscopic level of observation. The second gradient formulation is employed to consider possibly size effects and as a macroscopic source of interstitial fluid flow, which is usually regarded as a key factor in bone remodeling. With the help of the proposed formulation and via a simple example, we show that the model can be used as a graft design tool. As a matter of fact, an optimization of the characteristics of the implant can be carried out by numerical investigations. In this paper, we observe that the size of the graft considerably influences the interaction between bone tissue and artificial bio-resorbable material and the possibility that the bone tissue might substitute more or less partially the foreign graft for better bone healing.

SIRT1, a promising regulator of bone homeostasis

Sirtuin 1 (SIRT1), a nicotinamide adenine dinucleotide-dependent deacetylase, epigenetically regulates various cell metabolisms, including inflammation, tumorigenesis, and bone metabolism. Many clinical studies have found the potential of SIRT1 in predicting and treating bone-related disorders, such as osteoporosis and osteonecrosis, suggesting that SIRT1 might be a regulator of bone homeostasis. In order to identify the mechanisms that underlie the pivotal role of SIRT1 in bone homeostasis, many studies revealed that SIRT1 could maintain the balance between bone formation and absorption via regulating the ratio of osteoblasts to osteoclasts. SIRT1 controls the differentiation of mesenchymal stem cells (MSCs) and bone marrow-derived macrophages, increasing osteogenesis and reducing osteoclastogenesis. Besides, SIRT1 can enhance bone-forming cells' viability, including MSCs and osteoblasts under adverse conditions by resisting senescence, suppressing apoptosis, and promoting autophagy in favor of osteogenesis. Furthermore, the effect on bone vasculature homeostasis enables SIRT1 to become a valuable strategy for ischemic osteonecrosis and senile osteoporosis. The review systemically discusses SIRT1 pathways and the critical role in bone homeostasis and assesses whether SIRT1 is a potential target for manipulation and therapy, to lay a solid foundation for further researches in the future.

A mechano-chemo-biological model for bone remodeling with a new mechano-chemo-transduction approach

Bone remodeling is a fundamental biological process that develops in bone tissue along its whole lifetime. It refers to a continuous bone transformation with new bone formation and old bone resorption that changes the internal microstructure and composition of the tissue. The main objectives of bone remodeling are: repair of the internal microcracks; adaptation of the macroscopic stiffness and strength to the actual changing mechanical demands; and control of the calcium homeostasis. Understanding this process and predicting its evolution is critical to reduce the effects of long-term disuse as happens during periods of reduced mobility. It is also important in the design of bone implants to avoid long-term stress shielding. Many mathematical models have been proposed from the earliest purely phenomenological to the latest that include biological knowledge. However, there still exists a lack of connection between the mechanical driving force and the biochemical and cell processes it triggers. Here, and following previous works that model independently the mechanobiological and biochemical processes in bone remodeling, we present a more complete model, useful for both cortical and trabecular bone, that uses a new mechanotransduction approach based on the effect of strains onto the bonding-unbonding rate of RANK/RANKL/OPG receptor-ligand reactions. We compare the results of this model with previous ones, showing a good agreement in similar conditions. We also apply it to realistic situations such as a femoral bone after implantation of a hip prosthesis, getting similar results to the clinical ones in the final bone density distribution. Finally, we extend this approach to the anisotropic case, getting not only the mean density, but also the directional homogenization of the microstructure. This biochemical approach permits, not only to predict the bone evolution under changes in the mechanical loads, but also, to consider anabolic and catabolic drugs to control bone density, such as those used in osteoporosis.

Multiscale design of artificial bones with biomimetic elastic microstructures

Cancellous bone is a highly porous, heterogeneous, and anisotropic material which can be found at the epiphyses of long bones and in the vertebral bodies. The hierarchical architecture makes cancellous bone a prime example of a lightweight natural material that combines strength with toughness. Better understanding the mechanics of cancellous bone is of interest for the diagnosis of bone diseases, the evaluation of the risk of fracture, and for the design of artificial bones and bone scaffolds for tissue engineering. A multiscale optimization method to maximize the stiffness of artificial bones using biomimetic cellular microstructures described by a finite set of geometrical micro-parameters is presented here. The most outstanding characteristics of its implementation are the use of: an interior point optimization algorithm, a precalculated response surface methodology for the evaluation of the elastic tensor of the microstructure as an analytical function of the micro-parameters, and the adjoint method for the computation of the sensitivity of the macroscopic mechanical response to the variation of the micro-parameters. The performance and effectiveness of the tool are evaluated by solving a problem that consists in finding the optimal distribution of the microstructures for a proximal end of a femur subjected to physiological loads. Two strategies for the specification of the solid volume fraction constraints are assessed. The results are compared with data of a computed tomography study of an actual human bone. The model successfully predicts the main features of the spatial arrangement of the trabecular and cortical microstructures of the natural bone.