Chondrocyte hypertrophy in the growth plate promotes stress anisotropy affecting long bone development through chondrocyte column formation

The length of long bones is determined by column formation of proliferative chondrocytes and subsequent chondrocyte hypertrophy in the growth plate during bone development. Despite the importance of mechanical loading in long bone development, the mechanical conditions of the cells within the growth plate, such as the stress field, remain unclear owing to the difficulty in investigating spatiotemporal changes within dynamically growing tissues. In this study, the mechanisms of longitudinal bone growth were investigated from a mechanical perspective through column formation of proliferative chondrocytes within the growth plate before secondary ossification center formation using continuum-based particle models (CbPMs). A one-factor model, which simply describes essential aspects of a biological signaling cascade regulating cell activities within the growth plate, was developed and incorporated into CbPM. Subsequently, the developmental process and maintenance of the growth plate structure and resulting bone morphogenesis were simulated. Thus, stress anisotropy in the proliferative zone that affects bone elongation through chondrocyte column formation was identified and found to be promoted by chondrocyte hypertrophy. These results provide further insights into the mechanical regulation of multicellular dynamics during bone development.

Aging effects on osteoclast progenitor dynamics affect variability in bone turnover via feedback regulation

Bone turnover markers (BTMs) are commonly used in osteoporosis treatment as indicators of cell activities of bone-resorbing osteoclasts and bone-forming osteoblasts. The wide variability in their values due to multiple factors, such as aging and diseases, makes it difficult for physicians to utilize them for clinical decision-making. The progenitors of osteoclasts and osteoblasts are indispensable for a comprehensive interpretation of the variability in BTM values because these upstream progenitors strongly regulate the downstream cell activities of bone turnover. However, understanding the complex interactions among the multiple populations of bone cells is challenging. In this study, we aimed to gain a fundamental understanding of the mechanism by which the progenitor dynamics affect the variability in bone turnover through in silico experiments by exploring the cell dynamics with aging effects on osteoporosis. Negative feedback control driven by the consumptive loss of progenitors prevents rapid bone loss due to excessive bone turnover, and through feedback regulation, aging effects on osteoclast differentiation and osteoclast progenitor proliferation cause variability in the osteoclast and osteoblast activity balance and its temporal transition. By expressing the variability in the bone turnover status, our model describes the individualities of patients based on their clinical backgrounds. Therefore, our model could play a powerful role in assisting tailored treatment and has the potential to resolve the various health problems associated with osteoporosis worldwide.

Development of continuum-based particle models of cell growth and proliferation for simulating tissue morphogenesis

Biological tissues acquire various characteristic shapes through morphogenesis. Tissue shapes result from the spatiotemporally heterogeneous cellular activities influenced by mechanical and biochemical environments. To investigate multicellular tissue morphogenesis, this study aimed to develop a novel multiscale method that can connect each cellular activity to the mechanical behaviors of the whole tissue by constructing continuum-based particle models of cellular activities. This study proposed mechanical models of cell growth and proliferation that are expressed as volume expansion and cell division by extending the material point method. By simulating cell hypertrophy and proliferation under both free and constraint conditions, the proposed models demonstrated potential for evaluating the mechanical state and tracing cells throughout tissue morphogenesis. Moreover, the effect of a cell size checkpoint was incorporated into the cell proliferation model to investigate the mechanical behaviors of the whole tissue depending on the condition of cellular activities. Consequently, the accumulation of strain energy density was suppressed because of the influence of the checkpoint. In addition, the whole tissues acquired different shapes depending on the influence of the checkpoint. Thus, the models constructed herein enabled us to investigate the change in the mechanical behaviors of the whole tissue according to each cellular activity depending on the mechanical state of the cells during morphogenesis.

Computational framework for analyzing flow-induced strain on osteocyte as modulated by microenvironment

Osteocytes buried in bone matrix are major mechanosensory cells that regulate bone remodeling in response to interstitial fluid flow in a lacuno-canalicular porosity. To gain an understanding of the mechanism of osteocyte mechanosensing, it is important to be able to evaluate the local strain on the osteocyte process membrane induced by the interstitial fluid flow. The microenvironment of the osteocytes, including the pericellular matrix (PCM) and canalicular ultrastructure, is a key modulator of the flow-induced strain on the osteocyte process membrane because it produces heterogeneous flow patterns in the pericellular space. To investigate the effect of changes in the microenvironment of osteocytes on the flow-induced strain, we developed a novel computational framework for analyzing the fluid-structure interaction. Computer simulations based on the proposed framework enabled evaluation of the spatial distribution of flow-induced strain on the osteocyte process membrane according to changes in the PCM density and canalicular curvature. The simulation results reveal that a decrease in PCM density and an increase in canalicular curvature, each of which is associated with aging and bone disease, have the notable effect of enhancing local flow-induced strain on the osteocyte process membrane. We believe that the proposed computational framework is a promising framework for investigating cell-specific mechanical stimuli and that it has the potential to accelerate the mechanobiological study of osteocytes by providing a deeper understanding of their mechanical environment in living bone tissue.

High-resolution image-based simulation reveals membrane strain concentration on osteocyte processes caused by tethering elements

Osteocytes are vital for regulating bone remodeling by sensing the flow-induced mechanical stimuli applied to their cell processes. In this mechanosensing mechanism, tethering elements (TEs) connecting the osteocyte process with the canalicular wall potentially amplify the strain on the osteocyte processes. The ultrastructure of the osteocyte processes and canaliculi can be visualized at a nanometer scale using high-resolution imaging via ultra-high voltage electron microscopy (UHVEM). Moreover, the irregular shapes of the osteocyte processes and the canaliculi, including the TEs in the canalicular space, should considerably influence the mechanical stimuli applied to the osteocytes. This study aims to characterize the roles of the ultrastructure of osteocyte processes and canaliculi in the mechanism of osteocyte mechanosensing. Thus, we constructed a high-resolution image-based model of an osteocyte process and a canaliculus using UHVEM tomography and investigated the distribution and magnitude of flow-induced local strain on the osteocyte process by performing fluid–structure interaction simulation. The analysis results reveal that local strain concentration in the osteocyte process was induced by a small number of TEs with high tension, which were inclined depending on the irregular shapes of osteocyte processes and canaliculi. Therefore, this study could provide meaningful insights into the effect of ultrastructure of osteocyte processes and canaliculi on the osteocyte mechanosensing mechanism.

Intrauterine Pressures Adjusted by Reichert's Membrane Are Crucial for Early Mouse Morphogenesis

Mammalian embryogenesis proceeds in utero with the support of nutrients and gases from maternal tissues. However, the contribution of the mechanical environment provided by the uterus to embryogenesis remains unaddressed. Notably, how intrauterine pressures are produced, accurately adjusted, and exerted on embryos are completely unknown. Here, we find that Reichert's membrane, a specialized basement membrane that wraps around the implanted mouse embryo, plays a crucial role as a shock absorber to protect embryos from intrauterine pressures. Notably, intrauterine pressures are produced by uterine smooth muscle contractions, showing the highest and most frequent periodic peaks just after implantation. Mechanistically, such pressures are adjusted within the sealed space between the embryo and uterus created by Reichert's membrane and are involved in egg-cylinder morphogenesis as an important biomechanical environment in utero. Thus, we propose the buffer space sealed by Reichert's membrane cushions and disperses intrauterine pressures exerted on embryos for egg-cylinder morphogenesis.

Continuum modeling for neuronal lamination during cerebral morphogenesis considering cell migration and tissue growth

For neuronal lamination during cerebral morphogenesis, later-born neurons must migrate through already-accumulated neurons. This neuronal migration is biochemically regulated by signaling molecules and mechanically affected by tissue deformation. To understand the neuronal lamination mechanisms, we constructed a continuum model of neuronal migration in a growing deformable tissue. We performed numerical analyses considering the migration promoted by signaling molecules and the tissue growth induced by neuron accumulation. The results suggest that the promoted migration and the space ensured by tissue growth are essential for neuronal lamination. The proposed model can describe the coupling of mechanical and biochemical mechanisms for neuronal lamination.

Mechano-Regulation of Trabecular Bone Adaptation Is Controlled by the Local in vivo Environment and Logarithmically Dependent on Loading Frequency

It is well-established that cyclic, but not static, mechanical loading has anabolic effects on bone. However, the function describing the relationship between the loading frequency and the amount of bone adaptation remains unclear. Using a combined experimental and computational approach, this study aimed to investigate whether trabecular bone mechano-regulation is controlled by mechanical signals in the local in vivo environment and dependent on loading frequency. Specifically, by combining in vivo micro-computed tomography (micro-CT) imaging with micro-finite element (micro-FE) analysis, we monitored the changes in microstructural as well as the mechanical in vivo environment [strain energy density (SED) and SED gradient] of mouse caudal vertebrae over 4 weeks of either cyclic loading at varying frequencies of 2, 5, or 10 Hz, respectively, or static loading. Higher values of SED and SED gradient on the local tissue level led to an increased probability of trabecular bone formation and a decreased probability of trabecular bone resorption. In all loading groups, the SED gradient was superior in the determination of local bone formation and resorption events as compared to SED. Cyclic loading induced positive net (re)modeling rates when compared to sham and static loading, mainly due to an increase in mineralizing surface and a decrease in eroded surface. Consequently, bone volume fraction increased over time in 2, 5, and 10 Hz (+15%, +21% and +24%, p ≤ 0.0001), while static loading led to a decrease in bone volume fraction (-9%, p ≤ 0.001). Furthermore, regression analysis revealed a logarithmic relationship between loading frequency and the net change in bone volume fraction over the 4 week observation period (R 2 = 0.74). In conclusion, these results suggest that trabecular bone adaptation is regulated by mechanical signals in the local in vivo environment and furthermore, that mechano-regulation is logarithmically dependent on loading frequency with frequencies below a certain threshold having catabolic effects, and those above anabolic effects. This study thereby provides valuable insights toward a better understanding of the mechanical signals influencing trabecular bone formation and resorption in the local in vivo environment.

Theoretical concept of cortical to cancellous bone transformation

Microstructures of cortical and cancellous bones are altered continually by load-adaptive remodeling; in addition, their cellular mechanisms are similar despite the remarkably different porosities. The cortico-cancellous transitional zone is a site of vigorous remodeling, and intracortical remodeling cavitates the inner cortex to promote its trabecularization, which is considered the main cause of bone loss because of aging. Therefore, to prevent and treat age-related cortical bone loss effectively, it is indispensable to gain an integrated understanding of the cortical to the cancellous bone transformation via remodeling. We propose a novel theoretical concept to account for the transformation of dense cortical bone to porous cancellous bone. We develop a mathematical model of cortical and cancellous bone remodeling based on the concept that bone porosity is determined by the balance between the load-bearing function of mineralized bone and the material-transporting function of bone marrow. Remodeling simulations using this mathematical model enable the reproduction of the microstructures of cortical and cancellous bones simultaneously. Furthermore, current remodeling simulations have the potential to replicate cortical-to-cancellous bone transformation based on changes in the local balance between bone formation and resorption. We anticipate that the proposed mathematical model of cortical and cancellous bone remodeling will contribute to highlighting the essential features of cortical bone loss due to trabecularization of the cortex and help predict its spatial and temporal behavior during aging.

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A novel theoretical concept to account for cortical-to-cancellous bone transformation is proposed.

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A remodeling model to reproduce cortical and cancellous bone microstructures is developed.

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The remodeling simulation replicates cortical-to-cancellous bone transformation.

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The proposed method is valuable in clinical applications such as in predicting age-related cortical bone loss.

In silico experiments of bone remodeling explore metabolic diseases and their drug treatment

Bone structure and function are maintained by well-regulated bone metabolism and remodeling. Although the underlying molecular and cellular mechanisms are now being understood, physiological and pathological states of bone are still difficult to predict due to the complexity of intercellular signaling. We have now developed a novel in silico experimental platform, V-Bone, to integratively explore bone remodeling by linking complex microscopic molecular/cellular interactions to macroscopic tissue/organ adaptations. Mechano-biochemical couplings modeled in V-Bone relate bone adaptation to mechanical loading and reproduce metabolic bone diseases such as osteoporosis and osteopetrosis. V-Bone also enables in silico perturbation on a specific signaling molecule to observe bone metabolic dynamics over time. We also demonstrate that this platform provides a powerful way to predict in silico therapeutic effects of drugs against metabolic bone diseases. We anticipate that these in silico experiments will substantially accelerate research into bone metabolism and remodeling.

An energy landscape approach to understanding variety and robustness in tissue morphogenesis

During morphogenesis in development, multicellular tissues deform by mechanical forces induced by spatiotemporally regulated cellular activities, such as cell proliferation and constriction. Various morphologies are formed because of various spatiotemporal combinations and sequences of multicellular activities. Despite its potential to variations, morphogenesis is a surprisingly robust process, in which qualitatively similar morphologies are reproducibly formed even under spatiotemporal fluctuation of multicellular activities. To understand these essential characteristics of tissue morphogenesis, which involves the coexistence of various morphologies and robustness of the morphogenetic process, in this study, we propose a novel approach to capture the overall view of morphogenesis from mechanical viewpoints. This approach will enable visualization of the energy landscape, which includes morphogenetic processes induced by admissible histories of cellular activities. This approach was applied to investigate the morphogenesis of a sheet-like tissue with curvature, where it deformed to a concave or convex morphology depending on the history of growth and constriction. Qualitatively different morphologies were produced by bifurcation of the valley in the energy landscape. The depth and steepness of the valley near the stable states represented the degree of robustness to fluctuations of multicellular activities. Furthermore, as a realistic example, we showed an application of this approach to luminal folding observed in the initial stage of intestinal villus formation. This approach will be helpful to understand the mechanism of how various morphologies are formed and how tissues reproducibly achieve specific morphologies.

[Bone Cell Biology Assessed by Microscopic Approach. A mathematical approach to understand bone remodeling]

It is well known that bone tissue can change its outer shape and internal structure by remodeling according to a changing mechanical environment. However, the mechanism of bone functional adaptation induced by the collaborative metabolic activities of bone cells in response to mechanical stimuli remains elusive. In this article, we focus on the hierarchy of bone structure and function from the microscopic cellular level to the macroscopic tissue level. We provide an overview of a mathematical approach to understand the adaptive changes in trabecular morphology under the application of mechanical stress.

Interstitial fluid flow in canaliculi as a mechanical stimulus for cancellous bone remodeling: in silico validation

Cancellous bone has a dynamic 3-dimensional architecture of trabeculae, the arrangement of which is continually reorganized via bone remodeling to adapt to the mechanical environment. Osteocytes are currently believed to be the major mechanosensory cells and to regulate osteoclastic bone resorption and osteoblastic bone formation in response to mechanical stimuli. We previously developed a mathematical model of trabecular bone remodeling incorporating the possible mechanisms of cellular mechanosensing and intercellular communication in which we assumed that interstitial fluid flow activates the osteocytes to regulate bone remodeling. While the proposed model has been validated by the simulation of remodeling of a single trabecula, it remains unclear whether it can successfully represent in silico the functional adaptation of cancellous bone with its multiple trabeculae. In the present study, we demonstrated the response of cancellous bone morphology to uniaxial or bending loads using a combination of our remodeling model with the voxel finite element method. In this simulation, cancellous bone with randomly arranged trabeculae remodeled to form a well-organized architecture oriented parallel to the direction of loading, in agreement with the previous simulation results and experimental findings. These results suggested that our mathematical model for trabecular bone remodeling enables us to predict the reorganization of cancellous bone architecture from cellular activities. Furthermore, our remodeling model can represent the phenomenological law of bone transformation toward a locally uniform state of stress or strain at the trabecular level.

Microscale fluid flow analysis in a human osteocyte canaliculus using a realistic high-resolution image-based three-dimensional model

Osteocytes play a pivotal role in the regulation of skeletal mass. Osteocyte processes are thought to sense the flow of interstitial fluid that is driven through the osteocyte canaliculi by mechanical stimuli placed upon bone, but how this flow elicits a cellular response is virtually unknown. Modern theoretical models assume that osteocyte canaliculi contain ultrastructural features that amplify the fluid flow-derived mechanical signal. Unfortunately the calcified bone matrix has considerably hampered studies on the osteocyte process within its canaliculus. Using one of the few ultra high voltage electron microscopes (UHVEM) available worldwide, we applied UHVEM tomography at 2 MeV to reconstruct unique three-dimensional images of osteocyte canaliculi in 1 μm sections of human bone. A realistic three-dimensional image-based model of a single canaliculus was constructed, and the fluid dynamics of a Newtonian fluid flow within the canaliculus was analyzed. We created virtual 2.2 nm thick sections through a canaliculus and found that traditional TEM techniques create a false impression that osteocyte processes are directly attached to the canalicular wall. The canalicular wall had a highly irregular surface and contained protruding axisymmetric structures similar in size and shape to collagen fibrils. We also found that the microscopic surface roughness of the canalicular wall strongly influenced the fluid flow profiles, whereby highly inhomogeneous flow patterns emerged. These inhomogeneous flow patterns may induce deformation of cytoskeletal elements in the osteocyte process, thereby amplifying mechanical signals. Based on these observations, new and realistic models can be developed that will significantly enhance our understanding of the process of mechanotransduction in bone.

Effects of loading frequency on the functional adaptation of trabeculae predicted by bone remodeling simulation

The process of bone remodeling is regulated by metabolic activities of many bone cells. While osteoclasts and osteoblasts are responsible for bone resorption and formation, respectively, activities of these cells are believed to be controlled by a mechanosensory system of osteocytes embedded in the extracellular bone matrix. Several experimental and theoretical studies have suggested that the strain-derived interstitial fluid flow in lacuno-canalicular porosity serves as the prime mover for bone remodeling. Previously, we constructed a mathematical model for trabecular bone remodeling that interconnects the microscopic cellular activities with the macroscopic morphological changes in trabeculae through the mechanical hierarchy. This model assumes that fluid-induced shear stress acting on osteocyte processes is a driving force for bone remodeling. The validity of this model has been demonstrated with a remodeling simulation using a two-dimensional trabecular model. In this study, to investigate the effects of loading frequency, which is thought to be a significant mechanical factor in bone remodeling, we simulated morphological changes of a three-dimensional single trabecula under cyclic uniaxial loading with various frequencies. The results of the simulation show the trabecula reoriented to the loading direction with the progress of bone remodeling. Furthermore, as the imposed loading frequency increased, the diameter of the trabecula in the equilibrium state was enlarged by remodeling. These results indicate that our simulation model can successfully evaluate the relationship between loading frequency and trabecular bone remodeling.

Trabecular bone remodelling simulation considering osteocytic response to fluid-induced shear stress

In bone functional adaptation by remodelling, osteocytes in the lacuno-canalicular system are believed to play important roles in the mechanosensory system. Under dynamic loading, bone matrix deformation generates an interstitial fluid flow in the lacuno-canalicular system; this flow induces shear stress on the osteocytic process membrane that is known to stimulate the osteocytes. In this sense, the osteocytes behave as mechanosensors and deliver mechanical information to neighbouring cells through the intercellular communication network. In this study, bone remodelling is assumed to be regulated by the mechanical signals collected by the osteocytes. From the viewpoint of multi-scale biomechanics, we propose a mathematical model of trabecular bone remodelling that takes into account the osteocytic mechanosensory network system. Based on this model, a computational simulation of trabecular bone remodelling was conducted for a single trabecula under cyclic uniaxial loading, demonstrating functional adaptation to the applied mechanical loading as a load-bearing construct.

Effects of basicity and FeO concentration on the retention of 137Cs and 60Co in slag made from non-metallic radioactive wastes

Simulated non-metallic wastes containing 60Co, 137Cs and 152Eu were melted to examine the effects of basicity and FeO concentration on the retention of the radioactive nuclides in a resulting solidified product (Al2O3-CaO-FeO-SiO2 quaternary slag). The retention of 60Co was almost independent of chemical composition of slag. On the other hand, the retention of 137Cs decreased with an increase of the basicity of slag, defined as a ratio of CaO to SiO2 in wt. independent of FeO concentration. Energy dispersive X-ray fluorescence spectroscopic analysis and Mössbauer spectroscopic measurement were also conducted for the solidified product. Mössbauer spectra indicated that Fe2+ ions as well as Ca2+ ions existed as network modifying cations in a silicate network structure of slag. Referring to a structure model of silicate glasses, it is inferred that the retention of 137Cs reflects differences in chemical properties between Ca2+ and Fe2+ in the internetwork region formed by modifying cations and anionic non-bridging oxygen.

[Automated assay method for protein C anticoagulant activity]

We developed an automated assay method for protein C anticoagulant activity to prolong the APTT measured with automated coagulation apparatus. The automated assay method required following three reagents. One was 0.025 mol/l calcium chloride solution. The other two were a protein C deficient plasma and a phospholipid plus protein C activator both of which constituted a recomposed protein C assay kit (BMY). 0-50% activities of protein C and clotting times were regressed on normal linear curve, while 25-150% activities and clotting times were regressed on logarithmic curve. The coefficients of variation were 2.9-3.4% (intra-assay) and 3.6-3.9% (inter-assay). A correlation of protein C activities between measured by automated assay method and by ordinary manual method was good (r = 0.954). Our data suggest that this automated assay is a useful method for measuring the protein C anticoagulant activities utilizing a coagulation apparatus.