Phenomenological model of bone remodeling cycle containing osteocyte regulation loop

Biological parameters, such as bone resorption and formation constants, are important variables to achieve optimised hard tissue scaffolds design. To help to understand the modelling process that occurs when a scaffold is implanted it is vital to understand the rather complex bone remodeling process prevalent in native bone. One approach to developing a mathematical model that predicts osteoactivity both in scaffolds, as well as in bone in vivo, is based on a bio-cybernetic vision of basic multicellular unit (BMU) action -. In the case of the model presented in this paper, an additional loop of regulation based on osteocyte activity has been added. This approach has resulted in a four-dimensional system, which shows steady-quasi-cyclic behaviour using a particular range of constants with real biological meaning. The initial findings suggesting that the basic steady-state appears as a torus in multidimensional phase space have been discussed. The existence of this surface in the osteoclasts-osteoblasts-osteocytes-bone subspace indicates that there is a first integral for this dynamic system. Biological and physical interpretation of this integral as a conservative value has been proposed. It is possible to draw an analogy between this conservative value, as a kind of substrate-energy regenerative potential of the bone remodeling system with a molecular nature, to the classical physical value (energy). There are clear indications that there is recovering potential within the BMU that results in a steady operating genetically predominated bone remodeling process. This recovering potential is directed against both mechanical and biomechanical damage to the bone. The current model has credibility when compared to the normal bone remodeling process. However, additional work is required to study a wider range of constants.     

Continuum remodeling revisited

Recent research effort in bone remodeling has been directed toward describing interstitial fluid flow in the lacuno-canalicular system and its potential as a cellular stimulus. Regardless of the precise contents of the mechanotransduction “black box”, it seems clear that the fluid flow on which the remodeling is predicated cannot occur under static loading conditions. In an attempt to help continuum remodeling simulations catch up with cellular and subcellular research, this paper presents a simple, strain rate driven remodeling algorithm for density allocation and principal material direction rotations. An explicit finite element code was written and deployed on a supercomputer which discretizes the remodeling process and uses an objective hypoelastic constitutive law to simulate trabecular realignment. Results indicate that a target strain rate for this dynamic approach is |D _I ^*| = 1.7% per second which seems reasonable when compared to observed strain rates. Simulations indicate that a morpho-mechanically realistic three-dimensional bone can be synthesized by applying a few dynamic loads at the envelope of common daily physiological rates, even with no static loading component.     

A histological and biomechanical study of bone stress and bone remodeling around immediately loaded implants

Immediate loading(IL)increases the risk of marginal bone loss.The present study investigated the biomechanical response of peri-implant bone in rabbits after IL,aiming at optimizing load management.Ninety-six implants were installed bilaterally into femurs of 48 rabbits.Test implants on the left side created the maximal initial stress of 6.9 and 13.4 MPa in peri-implant bone and unloaded implants on the contralateral side were controls.Bone morphology and bone-implant interface strength were measured with histological examination and push-out testing during a 12-week observation period.Additionally,the animal data were incorporated into finite element(FE)models to calculate the bone stress distribution at different levels of osseointegration.Results showed that the stress was concentrated in the bone margin and the bone stress gradually decreased as osseointegration proceeded.A stress of about 2.0 MPa in peri-implant bone had a positive effect on new bone formation,osseointegration and bone-implant interface strength.Bone loss was observed in some specimens with stress exceeding 4.0 MPa.Data indicate that IL significantly increases bone stress during the early postoperative period,but the load-bearing capacity of peri-implant bone increases rapidly with an increase of bone-implant contact.Favorable bone responses may be continually promoted when the stress in peri-implant bone is maintained at a definite level.Accordingly,the progressive loading mode is recommended for IL implants.     

A supra-cellular model for coupling of bone resorption to formation during remodeling: lessons from two bone resorption inhibitors affecting bone formation differently

The bone matrix is maintained functional through the combined action of bone resorbing osteoclasts and bone forming osteoblasts, in so-called bone remodeling units. The coupling of these two activities is critical for securing bone replenishment and involves osteogenic factors released by the osteoclasts. However, the osteoclasts are separated from the mature bone forming osteoblasts in time and space. Therefore the target cell of these osteoclastic factors has remained unknown. Recent explorations of the physical microenvironment of osteoclasts revealed a cell layer lining the bone marrow and forming a canopy over the whole remodeling surface, spanning from the osteoclasts to the bone forming osteoblasts. Several observations show that these canopy cells are a source of osteoblast progenitors, and we hypothesized therefore that they are the likely cells targeted by the osteogenic factors of the osteoclasts. Here we provide evidence supporting this hypothesis, by comparing the osteoclast-canopy interface in response to two types of bone resorption inhibitors in rabbit lumbar vertebrae. The bisphosphonate alendronate, an inhibitor leading to low bone formation levels, reduces the extent of canopy coverage above osteoclasts. This effect is in accordance with its toxic action on periosteoclastic cells. In contrast, odanacatib, an inhibitor preserving bone formation, increases the extent of the osteoclast-canopy interface. Interestingly, these distinct effects correlate with how fast bone formation follows resorption during these respective treatments. Furthermore, canopy cells exhibit uPARAP/Endo180, a receptor able to bind the collagen made available by osteoclasts, and reported to mediate osteoblast recruitment. Overall these observations support a mechanism where the recruitment of bone forming osteoblasts from the canopy is induced by osteoclastic factors, thereby favoring initiation of bone formation. They lead to a model where the osteoclast-canopy interface is the physical site where coupling of bone resorption to bone formation occurs.     

Development of the lateral line canal system through a bone remodeling process in zebrafish

The lateral line system of teleost fish is composed of mechanosensory receptors (neuromasts), comprising superficial receptors and others embedded in canals running under the skin. Canal diameter and size of the canal neuromasts are correlated with increasing body size, thus providing a very simple system to investigate mechanisms underlying the coordination between organ growth and body size. Here, we examine the development of the trunk lateral line canal system in zebrafish. We demonstrated that trunk canals originate from scales through a bone remodeling process, which we suggest is essential for the normal growth of canals and canal neuromasts. Moreover, we found that lateral line cells are required for the formation of canals, suggesting the existence of mutual interactions between the sensory system and surrounding connective tissues.     

Density-based load estimation using two-dimensional finite element models: a parametric study

A parametric investigation was conducted to determine the effects on the load estimation method of varying: (1) the thickness of back-plates used in the two-dimensional finite element models of long bones, (2) the number of columns of nodes in the outer medial and lateral sections of the diaphysis to which the back-plate multipoint constraints are applied and (3) the region of bone used in the optimization procedure of the density-based load estimation technique. The study is performed using two-dimensional finite element models of the proximal femora of a chimpanzee, gorilla, lion and grizzly bear. It is shown that the density-based load estimation can be made more efficient and accurate by restricting the stimulus optimization region to the metaphysis/epiphysis. In addition, a simple method, based on the variation of diaphyseal cortical thickness, is developed for assigning the thickness to the back-plate. It is also shown that the number of columns of nodes used as multipoint constraints does not have a significant effect on the method.     

Osteoclast and its roles in calcium metabolism and bone development and remodeling

Osteoclasts are multinucleated cells responsible for bone resorption and play important roles in normal skeletal development, in the maintenance of its integrity throughout life, and in calcium metabolism. During bone resorption, the cytoskeleton of osteoclasts undergoes extensive reorganization, with polarization and formation of ruffled borders to secrete acid and formation of sealing zone to prevent leakage. The differentiation and function of osteoclasts are in turn regulated by osteoblasts, stromal cells, and bone. They are also subjected to negative feedback regulation by extracellular and intracellular calcium concentrations.     

Theoretical investigation of the role of the RANK-RANKL-OPG system in bone remodeling

The RANK-RANKL-OPG system is an essential signaling pathway involved in bone cell-cell communication, with ample evidence that modification of the RANK-RANKL-OPG signaling pathway has major effects on bone remodeling. The first focus of this paper is to demonstrate that a theoretical model of bone cell-cell interactions is capable of qualitatively reproducing changes in bone associated with RANK-RANKL-OPG signaling. To do this we consider either biological experiments or bone diseases related to receptor and/or ligand deficiencies, including RANKL over-expression, ablation of OPG production and/or RANK receptor modifications. The second focus is to investigate a wide range of possible therapeutic strategies for re-establishing bone homeostasis for various pathologies of the RANK-RANKL-OPG pathway. These simulations indicate that bone diseases associated with the RANK-RANKL-OPG pathway are very effective in triggering bone resorption compared to bone formation. These results align with Hofbauer's “convergence hypothesis”, which states that catabolic bone diseases most effectively act through the RANK-RANKL-OPG system. Additionally, we demonstrate that severity of catabolic bone diseases strongly depends on how many components of this pathway are affected. Using optimization algorithms and the theoretical model, we identify a variety of successful “virtual therapies” for different disease states using both single and dual therapies.     

A novel approach to estimate trabecular bone anisotropy using a database approach

Continuum finite element (FE) models of bones have become a standard pre-clinical tool to estimate bone strength. These models are usually based on clinical CT scans and material properties assigned are chosen as isotropic based only on the density distribution. It has been shown, however, that trabecular bone elastic behavior is best described as orthotropic. Unfortunately, the use of orthotropic models in FE analysis derived from CT scans is hampered by the fact that the measurement of a trabecular orientation (fabric) is not possible from clinical CT images due to the low resolution of such images. In this study, we explore the concept of using a database (DB) of high-resolution bone models to derive the fabric information that is missing in clinical images. The goal of this study was to investigate if models with fabric derived from a relatively small database can already produce more accurate results than isotropic models.     

Long-term study of bone remodelling after femoral stem: a comparison between dexa and finite element simulation

A hip replacement with a cemented or cementless femoral stem produces an effect on the bone called adaptive remodelling, attributable to mechanical and biological factors. The objective of all of cementless prostheses designs has been to achieve a perfect transfer of loads in order to avoid stress-shielding, which produces an osteopenia. In order to quantify this, the long term and mass-produced study with dual energy X-ray absorptiometry (DEXA) is necessary. Finite element (FE) simulation makes possible the explanation of the biomechanical changes which are produced in the femur after stem implantation. The good correlation obtained between the results of the FE simulation and the densitometric study allow, on one hand, to explain from the point of view of biomechanical performance the changes observed in bone density in the long-term, where it is clear that these are due to a different transfer of load in the implanted model compared to the healthy femur; on the other hand, it validates the simulation model, in a way that it can be used in different conditions and at different time periods, to carry out a sufficiently precise prediction of the evolution of the bone density from the biomechanical behaviour in the interaction between the prosthesis and femur.     

A theoretical model to predict distribution of the fabric tensor and apparent density in cancellous bone

 The adaptation of cancellous bone to mechanical forces is well recognized. Theoretical models for predicting cancellous bone architecture have been developed and have mainly focused on the distribution of trabecular mass or the apparent density. The purpose of this study was to develop a theoretical model which can simultaneously predict the distribution of trabecular orthotropy/orientation, as represented by the fabric tensor, along with apparent density. Two sets of equations were derived under the assumption that cancellous bone is a biological self-optimizing material which tends to minimize strain energy. The first set of equations provide the relationship between the fabric tensor and stress tensor, and have been verified to be consistent with Wolff’s law of trabecular architecture, that is, the principal directions of the fabric tensor coincide with the principal stress trajectories. The second set of equations yield the apparent density from the stress tensor, which was shown to be identical to those obtained based on local optimization with strain energy density of true bone tissue as the objective function. These two sets of equations, together with elasticity field equations, provide a complete mathematical formulation for the adaptation of cancellous bone. Received: 25 February 1997/Revised version: 23 September 1997     

Expression of RANKL/OPG during bone remodeling in vivo

The interaction between receptor activator of nuclear factor κB ligand (RANKL) and osteoprotegerin (OPG) plays a dominant role in osteoclastogenesis. As both proteins are produced by osteoblast lineage cells, they are considered to represent a key link between bone formation and resorption. In this study, we investigated the expression of RANKL and OPG during bone remodeling in vivo to determine the relationship between osteoclastogenic stimulation and osteoblastic differentiation.Total RNA was prepared from rat femurs after marrow ablation on days 0, 3, 6, and 9. The temporal activation patterns of osteoblast-related genes (procollagen α1 (I), alkaline phosphatase, osteopontin, and osteocalcin) were examined by Northern blot analysis. An appreciable increase in the expression of these osteoblast markers was observed on day 3. The peak increase in gene expression was observed on day 6 followed by a slight reduction by day 9. Real-time PCR analysis showed that the OPG mRNA expression was markedly upregulated on day 6 and slightly decreased on day 9. In contrast, RANKL mRNA expression was increased by more than 20-fold on day 9. The RANKL/OPG ratio, an index of osteoclastogenic stimulation, peaked on day 9. Histological analysis showed that RANKL and OPG immunoreactivity were predominantly associated with bone marrow cells. The expression of bone formation markers was activated in the bone formation phase, followed by the stimulation of RANKL/OPG expression in the bone resorption phase, which confirmed that these molecules are key factors linking bone formation to resorption during bone remodeling.     

Engineered bone culture in a perfusion bioreactor: a 2D computational study of stationary mass and momentum transport

Successful bone cell culture in large implants still is a challenge to biologists and requires a strict control of the physicochemical and mechanical environments. This study analyses from the transport phenomena viewpoint the limiting factors of a perfusion bioreactor for bone cell culture within fibrous and porous large implants (2.5 cm in length, a few cubic centimetres in volume, 250 μm in fibre diameter with approximately 60% porosity).

A two-dimensional mathematical model, based upon stationary mass and momentum transport in these implants is proposed and numerically solved. Cell oxygen consumption, in accordance theoretically with the Michaelis–Menten law, generates non linearity in the boundary conditions of the convection diffusion equation. Numerical solutions are obtained with a commercial code (Femlab® 3.1; Comsol AB, Stockholm, Sweden). Moreover, based on the simplification of transport equations, a simple formula is given for estimating the length of the oxygen penetration within the implant.

Results show that within a few hours of culture process and for a perfusion velocity of the order of 10^? 4 m s^? 1, the local oxygen concentration is everywhere sufficiently high to ensure a suitable cell metabolism. But shear stresses induced by the fluid flow with such a perfusion velocity are found to be locally too large (higher than 10^? 3 Pa). Suitable shear stresses are obtained by decreasing the velocity at the inlet to around 2 × 10^? 5 m s^? 1. But consequently hypoxic regions (low oxygen concentrations) appear at the downstream part of the implant.

Thus, it is suggested here that in the determination of the perfusion flow rate within a large implant, a compromise between oxygen supply and shear stress effects must be found in order to obtain a successful cell culture.     

Stress to endoplasmic reticulum of mouse osteoblasts induces apoptosis and transcriptional activation for bone remodeling

ATF4 is an essential regulator in osteogenesis as well as in stress responses to the endoplasmic reticulum (ER). We addressed a question: Does ER stress to osteoblasts upregulate ATF4 expression? If so, do they exhibit ATF4-mediated bone remodeling or apoptosis? ER stress, induced by Thapsigargin and tunicamycin, elevated a phosphorylated form of eIF2alpha and ATF4, but the cellular fate depended on treatment duration. The treatment for 1h, for instance, activated Runx2, and type I collagen, while the treatment for 24h induced apoptosis. Our observations suggest that there is a threshold for ER stress and osteoblasts present a bi-phasic pattern of their fate.     

卵蛋白反复吸入哮喘小鼠气道重构模型的建立与评价

目的：探讨哮喘小鼠气道重构模型的建立的方法。方法：SPF级BALB／C6-8周龄雌性小鼠40只随机分成正常对照组、哮喘模型组,每组20只。哮喘组经卵蛋白（OVA）混悬液0．2ml致敏并反复雾化吸入2周、4周,正常对照组由生理盐水代替。各组分别于末次雾化激发后进行取材,收集肺组织,制作石蜡切片,HE染色观察气道中嗜酸性粒细胞;Masson三色染色法观察气道周围胶原沉积情况;PAS染色法观察气道黏液分泌情况;测定单位气道面积基底膜周径（Pbm）、管壁总面积（WAt）、内壁面积（wAi）、平滑肌面积（WAm）、胶原面积（Wcol）、粘液面积。结果：哮喘模型组WAt／Pbm、WAi／Pbm、WAm/Pbm、Wcol／Pbm、粘液分泌面积较正常对照组明显增加。哮喘4周组上述指标均高于其对应2周组（P〈0．05）。结论：反复的过敏原（OVA）吸入可导致哮喘气道重构的发生,是一种较好的建立哮喘小鼠气道重构模型的的方法。     

Semaphorin 3A: A new player in bone remodeling

Semaphorin 3A (Sema3A) is a protein identified originally as a diffusible axonal chemorepellent. Sema3A has multifunctional roles in embryonic development, immune regulation, vascularization, and oncogenesis. Bone remodeling consists of two phases: the removal of mineralized bone by osteoclasts and the formation of new bone by osteoblasts, and plays an essential role in skeletal diseases such as osteoporosis. Recent studies have shown that Sema3A is implicated in the regulation of osteoblastgenesis and osteoclastgenesis. Moreover, low bone mass in mice with specific knockout of Sema3A in the neurons indicates that Sema3A regulates bone remodeling indirectly. This review highlights recent advances on our understanding of the role of sema3A as a new player in the regulation of bone remodeling and proposes the potential of sema3A in the diagnosis and therapy of bone diseases.     

Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture

A method is presented to find orthotropic elastic symmetries and constants directly from the elastic coefficients in the overall stiffness matrix of trabecular bone test specimens. Contrary to earlier developed techniques, this method does not require pure orthotropic behavior or additional fabric measurements. The method uses high-resolution computer reconstructions of trabecular bone specimens as input for large-scale FE-analyses to determine all the 21 elastic coefficients in the overall stiffness matrix of the specimen, using a direct mechanics approach. An optimization procedure is then used to find the coordinate transformation that yields the best orthotropic representation of this matrix. The method is illustrated here relative to two trabecular bone specimens. The techniques developed here can be used to obtain a complete characterization of the mechanical properties of trabecular architecture. With the development of in vivo reconstruction techniques, even in vivo measurements will be possible.     

Patterns of femoral bone remodeling dynamics in a medieval Nubian population

The relationship between age, sex and histomorphometry in femoral cortical bone was examined in a skeletal population of late Medieval antiquity (AD 1250–1450) from Kulubnarti, in Sudanese Nubia. These skeletal remains are naturally mummified and in an excellent state of preservation. The study sample consisted of femoral cross sections from 24 females and 19 males ranging in age from 20 to 50+ years. Femoral cross sections were examined using an image analysis system. Numbers of secondary osteons and osteon fragments were counted, osteon area and Haversian canal area were measured, and several variables were calculated to assess differences between sexes and among age groups in bone remodeling variables. The results indicate significant differences between the sexes in osteon number and size. Males had significantly more intact osteons than females, whereas females had significantly larger osteons than males. Haversian canal dimensions were not statistically significant between the sexes. Sex differences in activity patterns in which males were involved in more physically strenuous tasks may have contributed to differences in remodeling variables. Interpopulational comparisons suggest that mechanical strain affects the microstructural features examined in this study. In particular, small Haversian canals in some archaeological skeletal populations are associated with higher bone volume, which may result from high levels of mechanical strain. Am J Phys Anthropol 104:133–146, 1997. © 1997 Wiley-Liss, Inc.