Model Of Bone Remodeling Research Articles

A frequency-dependent model for bone remodeling using a micromorphic porous medium subjected to harmonic mechanical loading

In this paper, the bone tissue was modeled as a linear viscoelastic material saturated with interstitial fluid. We considered a specific case of harmonic loading and related the mechanical stimuli to the loading frequency. In this way, we could include the inertial effect in the model while not having to deal with the perturbation during each loading period. Two types of mechanical signals were considered: strain energy and dissipation energy. A parametric study revealed the dependency of the two signals on loading frequency and material property. The evolution of the apparent mass density supported the parametric study’s findings. Under the three different frequency loadings, the strain energy-stimulated samples experienced identical remodeling scenarios. The samples stimulated with dissipation energy, on the other hand, exhibited a strong frequency dependence. An additional study was performed to investigate the effect of long-term variations in the loading frequency on the remodeling process. This demonstrated the model’s capabilities in designing and evaluating load regimes for rehabilitation following a bone injury or bone reconstruction.

Assessment of mechanical variables best describing bone remodelling responses based on their correlation with bone density

Density distribution in bones can be estimated using bone remodelling models (BRM) and applying daily normal loads to assess the stress/strain state to which the bone is subjected. These models locally relate a certain mechanical stimulus, derived from the stress/strain state, directly to bone density or to its variation over time. The background of this idea is Frost’s Mechanostat Theory, which states that overloading states tend to increase bone density and disuse states tend to decrease it. Different variables have been proposed in the literature to measure the mechanical stimulus. Strain energy density (SED) and stresses have been commonly used as mechanical stimuli, but to date their use has not been justified with convincing arguments. In this paper we have selected several variables derived from stress and strain tensors and correlated them with the distribution of bone density in the femur of 13 elderly women to conclude which would be most appropriate for use as a mechanical stimulus in a BRM. We have performed this correlation analysis for six different activities: walking normally, fast walking, stair ascent, stair descent, rising from and sitting on a chair, and jumping in place. Musculoskeletal models were used to estimate joint reaction and muscle forces of each individual for each activity. These were applied to the corresponding finite element model of the femur to obtain stress and strain tensors at each point. The variables proposed as mechanical stimulus and derived from these tensors were correlated to the actual density obtained for each individual from CT-scans. Our results show that stress variables are the best correlated with density. In contrast, the correlations of SED are very weak, so it is not a good candidate for mechanical stimulus. Strains are also weakly correlated to density, but in this case because their distribution across the femur is rather uniform. This is in agreement with the Mechanostat Theory which states that bone reacts to load changes by changing its stiffness so to keep strains in a certain interval. Consequently, a plausible choice for a remodelling criterion could be keeping that strain uniformity.

Part II: A new perspective for modeling the bone remodeling process: Biology, mechanics, and pathologies

In this paper, we explore the effects of biological (pathological) and mechanical damage on bone tissue within a benchmark model. Using the Finite Element Methodology, we analyze and numerically test the model’s components, capabilities, and performance under physiologically and pathologically relevant conditions. Our findings demonstrate the model’s effectiveness in simulating bone remodeling processes and self-repair mechanisms for micro-damage induced by biological internal conditions and mechanical external ones within bone tissue. This article is the second part of a series, where the first part presented the mathematical model and the biological and physical significance of the terms used in a simplified benchmark model. It explored the bone remodeling model’s application, implementation, and results under physiological conditions.

Osteostaticytes: A novel osteoclast subset couples bone resorption and bone formation

BackgroundOsteomyelitis (OM) is an inflammatory condition of bone characterized by cortical bone devascularization and necrosis. Dysregulation of bone remodelling is triggered by OM. Bone remodelling is precisely coordinated by bone resorption and formation via a reversal phase. However, the cellular and molecular mechanisms underlying bone remodelling failure after osteomyelitis remain elusive. MethodsTo elucidate the cellular and molecular mechanism underlying bone healing after osteomyelitis, we employed single-cell RNA sequencing (scRNA-seq) to depict the atlas of human cortical bone in normal, infected and reconstructed states. Dimensionality reduction by t-stochastic neighbourhood embedding (t-SNE) and graph-based clustering were applied to analyse the detailed clusters of osteoclast lineages. After trajectory analysis of osteoclast lineages over pseudotime, real-time PCR and immunofluorescence (IF) staining were applied to identify marker gene expression of various osteoclast lineages in the osteoclast induction model and human bone sections, respectively. The potential function and communication of osteoclasts were analysed via gene set enrichment analysis (GSEA) and CellChat. The chemotactic ability of mesenchymal stem cells (MSCs) and osteoclast lineage cells in various differentiation states was determined by transwell assays and coculture assays. The effects of various osteoclast lineages on the osteogenic differentiation potential of MSCs were also determined by using this coculture system. A normal mouse tibia fracture model and an osteomyelitis-related tibia fracture model were generated via injection of luciferase-labelled Staphylococcus aureus to verify the relationships between a novel osteoclast lineage and MSCs. Then, the infection was detected by a bioluminescence imaging system. Finally, immunofluorescence staining was used to detect the expression of markers of MSCs and novel osteoclast lineages in different remodelling phases in normal and infected bone remodelling models. ResultsIn this study, we constructed a cell atlas encompassing normal, infected, and reconstructed cortical bone. Then, we identified a novel subset at the earlier stage of the osteoclast lineage that exhibited increased expression of IDO1, CCL3, and CCL4. These IDO1highCCL3highCCL4high cells, termed osteostaticytes (OSCs), were further regarded as the reservoir of osteoclasts in the reversal phase. Notably, OSCs exhibited the highest chemotactic activity, surpassing other lineage subsets. We also discovered that cells at the earlier stage of the osteoclast lineage play a significant role in recruiting mesenchymal stem cells (MSCs). Finally, the data revealed that OSCs might be positively related to the occurrence of bone MSCs and the contribution of bone remodelling. ConclusionCollectively, our findings revealed a novel stage (OSC) within the osteoclast lineage, potentially representing elusive bone reversal cells due to its increased chemotactic ability towards MSCs and potential contribution to bone remodelling. This study provides valuable insights into the intricate mechanisms of the reversal phase during bone remodelling and unveils potential therapeutic strategies for diseases associated with bone uncoupling. Translational potential of this articleThis study identified a new subset, referred to as IDO1(plus symbol) CCL3(plus symbol) CCL4(plus symbol) osteostaticytes which displayed the highest chemotactic activity among all osteoclast lineages and may serve as reversal cells in bone remodelling. These findings offer new insights and insights for understanding bone reversal-related diseases and may serve as novel therapeutic targets for conditions such as osteomyelitis and delayed bone healing.

Preliminary study on AI-assisted diagnosis of bone remodeling in chronic maxillary sinusitis

ObjectiveTo construct the deep learning convolution neural network (CNN) model and machine learning support vector machine (SVM) model of bone remodeling of chronic maxillary sinusitis (CMS) based on CT image data to improve the accuracy of image diagnosis.MethodsMaxillary sinus CT data of 1000 samples in 500 patients from January 2018 to December 2021 in our hospital was collected. The first part is the establishment and testing of chronic maxillary sinusitis detection model by 461 images. The second part is the establishment and testing of the detection model of chronic maxillary sinusitis with bone remodeling by 802 images. The sensitivity, specificity and accuracy and area under the curve (AUC) value of the test set were recorded, respectively.ResultsPreliminary application results of CT based AI in the diagnosis of chronic maxillary sinusitis and bone remodeling. The sensitivity, specificity and accuracy of the test set of 93 samples of CMS, were 0.9796, 0.8636 and 0.9247, respectively. Simultaneously, the value of AUC was 0.94. And the sensitivity, specificity and accuracy of the test set of 161 samples of CMS with bone remodeling were 0.7353, 0.9685 and 0.9193, respectively. Simultaneously, the value of AUC was 0.89.ConclusionIt is feasible to use artificial intelligence research methods such as deep learning and machine learning to automatically identify CMS and bone remodeling in MSCT images of paranasal sinuses, which is helpful to standardize imaging diagnosis and meet the needs of clinical application.

An in silico approach to elucidate the pathways leading to primary osteoporosis: age-related vs. postmenopausal

Numerical models of bone remodelling have traditionally been used to perform in silico tests of bone loss in postmenopausal women and also to simulate the response to different drug treatments. These models simulate the menopausal oestrogen decline by altering certain signalling pathways. However, they do not consider the simultaneous effect that ageing can have on cell function and bone remodelling, and thus on bone loss. Considering ageing and oestrogen decline together is important for designing osteoporosis treatments that can selectively counteract one or the other disease mechanism. A previously developed bone cell population model was adapted to consider the effect of ageing through: (1) the decrease of TGF-β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} contained in the bone matrix and (2) an increased production of sclerostin by non-skeletal cells. Oestrogen deficiency is simulated in three different ways: (a) an increase in RANKL expression, (b) a decrease in OPG production, and (c) an increase in the responsiveness of osteoclasts to RANKL. The effect of ageing was validated using the cross-sectional study of (Riggs et al. in J Bone Miner Res 19: 1945-1954, 2004) on BMD of trabecular bone of the vertebral body of men. The joint effect of ageing and oestrogen deficiency was validated using these same clinical results but in women. In ageing, the effect of the increasing production of sclerostin is more important than the decrease of TGF-β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document}, while the three mechanisms used to simulate the effect of oestrogen deficiency produce almost identical responses. The results show that an early menopause leads to a lower average density in the fifth decade, but after the sixth decade the average density is independent of the age at menopause. Treatment of osteoporosis with denosumab was also simulated to conclude that the drug is not very effective if started before 10 years after menopause or before age 60.

A review of mathematical modeling of bone remodeling from a systems biology perspective

Bone remodeling is an essential, delicately balanced physiological process of coordinated activity of bone cells that remove and deposit new bone tissue in the adult skeleton. Due to the complex nature of this process, many mathematical models of bone remodeling have been developed. Each of these models has unique features, but they have underlying patterns. In this review, the authors highlight the important aspects frequently found in mathematical models for bone remodeling and discuss how and why these aspects are included when considering the physiology of the bone basic multicellular unit, which is the term used for the collection of cells responsible for bone remodeling. The review also emphasizes the view of bone remodeling from a systems biology perspective. Understanding the systemic mechanisms involved in remodeling will help provide information on bone pathology associated with aging, endocrine disorders, cancers, and inflammatory conditions and enhance systems pharmacology. Furthermore, some features of the bone remodeling cycle and interactions with other organ systems that have not yet been modeled mathematically are discussed as promising future directions in the field.

Topology optimization of embracing fixator considering bone remodeling to mitigate stress shielding effect

The embracing fixator is one of the widely used internal fixation implants for bone fracture treatment. However, the stress shielding effect, a stress imbalance between the implant and bone caused by the mismatch in mechanical properties between them, is a significant and critical issue that may lead to treatment failure. Thus, it is of great importance to design the implant with an appropriate stiffness which can mitigate the stress shielding effect and provide the most favorable mechanical environment for bone healing and remodeling. To this end, a time-dependent topology optimization algorithm considering bone remodeling is proposed to optimize an embracing fixator used in the tibia fracture treatment. The change of callus density over time is simulated based on a bone remodeling model, and the callus density after a period of bone remodeling is selected to be the design objective to maximize. The design constraints include volume and the compliance of the whole fixation system. Meanwhile, the influence of the constraints on the regularity of material distribution of the optimized result is also studied. Besides, to test the effectiveness of the consideration of the bone remodeling in the embracing fixator design, a topology optimization concerning the minimization of the compliance of the entire system is also performed to make a comparison. Finally, the safety performance of optimized results considering bone remodeling is also verified by static analysis.

IN VITRO MODELS MIMICKING THE BONE REMODELLING CYCLE

Metabolic bone diseases, such as osteoporosis and osteopetrosis, result from an imbalanced bone remodeling process. In vitro bone models are often used to investigate either bone formation or resorption independently, while in vivo, these processes are coupled. Combining these processes in a co-culture is challenging as it requires finding the right medium components to stimulate each cell type involved without interfering with the other cell type's differentiation. Furthermore, differentiation stimulating factors often comprise growth factors in supraphysiological concentrations, which can overshadow the cell-mediated crosstalk and coupling.To address these challenges, we aimed to recreate the physiological bone remodeling process, which follows a specific sequence of events starting with cell activation and bone resorption by osteoclasts, reversal, followed by bone formation by osteoblasts. We used a mineralized silk fibroin scaffold as a bone-mimetic template, inspired by bone's extracellular matrix composition and organization. Our model supported osteoclastic resorption and osteoblastic mineralization in the specific sequence that represents physiological bone remodeling.We also demonstrated how culture variables, such as different cell ratios, base media, and the use of osteogenic/osteoclast supplements, and the application of mechanical load, can be adjusted to represent either a high bone turnover system or a self-regulating system. The latter system did not require the addition of osteoclastic and osteogenic differentiation factors for remodeling, therefore avoiding growth factor use.Our in vitro model for bone remodeling has the potential to reduce animal experiments and advance in vitro drug development for bone remodeling pathologies like osteoporosis. By recreating the physiological bone remodeling cycle, we can investigate cell-cell and cell-matrix interactions, which are essential for understanding bone physiology and pathology. Furthermore, by tuning the culture variables, we can investigate bone remodeling under various conditions, potentially providing insights into the mechanisms underlying different bone disorders.

INTRAMEDULLARY NAIL OR LOCKING COMPRESSION PLATE FOR FIXING A FRACTURED DISTAL TIBIA: FINITE ELEMENT ANALYSIS ALONG WITH AN ADAPTATION MODEL

Intramedullary (IM) nailing and plating are two major options for the treatment of distal tibial fractures; each method has its own pros and cons. Bone loss due to IM nailing or plating can be a serious concern, which may lead to the premature failure of the implants. Thus, investigating bone remodeling in response to orthopedic implantation is of paramount importance for the purpose of designing more efficient prostheses. The main goal of this study was to predict the effects of nailing and plating on the bone apparent density distribution in tibia, through use of the finite element method (FEM) along with a bone remodeling model. To this end, three-dimensional geometry of tibia, with properties derived from computer tomography (CT) imaging data, IM nail and locking compression plate (LCP) were created. Then, a bone remodeling model and FEM, with physiological-like loading, were combined and implemented using Python programming language. The results showed that both nailing and plating methods cause a reduction in bone apparent density, but the plate affects just the distal part of the tibia, where the implant is present; whereas the IM nail affects almost the whole tibia. Moreover, in agreement with clinical observations, it was found here that the stress shielding effects of the LCP are less pronounced than that of IM nail, in the long term. Stress analysis revealed that the load, to most extent, transferred to IM nail; whereas it transferred to LCP just in the distal part of tibia. On the basis of the results of this work, it might be concluded that plating is a better choice than nailing for distal tibial fracture, from the bone remodeling point of view.

MULTISCALE MECHANOBIOLOGICAL MODELING OF THE CORTICAL/SPONGY INTERFACE USING FINITE ELEMENTS

In this paper, we describe a mathematical model of bone remodeling that integrates the activities of the bone cells and the mechanical behavior of the bone in an intermediate cortical/trabecular zone. This behavior decreases and increases as the bone moves from a dense cortical zone to a less dense porous trabecular zone. The bone remodeling is a combined process of resorption and formation driven primarily by osteoclasts and osteoblasts. The evolution of the bone cell population involves osteoblast-osteoclast signaling, which is mediated by the biological factors and receives a mechanical stimulus assessed at the microscopic scale. Excessive stress on the bone causes microdamage that induces changes in the structural integrity and microarchitecture. This phenomenon explains the attention paid to the mechanical properties of the bone. In this context, numerical simulations were performed in a mechanobiological model, in which different mechanical and biological parameters were considered. A three-dimensional finite-element model of a human proximal femur was generated, and the simulation of the bone remodeling algorithm was implemented. The current work is an exploratory numerical study, and the results obtained reveal the impact of the mechanical properties on the remodeling process of the intermediate bone subjected to cyclic loading, highlighting the effects of the selected parameters for the different remodeling periods.

Protective Effect of Bovine Milk Extracellular Vesicles on Alveolar Bone Loss.

Bovine milk extracellular vesicles (MEVs) have demonstrated therapeutic potential in regulating bone cell activity. However, the outcome of their use on alveolar bone loss has not yet been demonstrated. This study evaluates the effect of oral administration of MEVs on ovariectomized (OVX) mice. There is a reduced height of the alveolar bone crest in OVX mice by MEVs treatment, but the alveolar bone parameters are not altered. OVX mice are then submitted to a force-induced bone remodeling model by orthodontic tooth movement (OTM). MEVs-treated mice have markedly less bone remodeling movement, unlike the untreated OVX mice. Also, OVX mice treated with MEVs show an increased number of osteoblasts and osteocytes associated with higher sclerostin expression and reduce osteoclasts in the alveolar bone. Although the treatment with MEVs in OVX mice does not show differences in root structure in OTM, few odontoclasts are observed in the dental roots of OVX-treated mice. Compared to untreated mice, maxillary and systemic RANKL/OPG ratios are reduced in OVX mice treated with MEVs. Treatment with MEVs results in positive bone cell balance in the alveolar bone and dental roots, indicating its beneficial potential in treating alveolar bone loss in the nutritional context.

A gradient-enhanced bone remodelling approach to avoid the checkerboard phenomenon

Numerical simulation of bone remodelling enables the investigation of short- and long-term stability of bone implants and thus can be an essential tool for surgical planning. The first development of related mathematical models dates back to the early 90’s, and these models have been continuously refined since then. However, one issue which has been under discussion since those early days concerns a numerical instability known as checkerboarding. A literature review of recent approaches guided us to adopt a technique established in damage mechanics and topology optimisation, where similar mesh dependencies and instabilities occur. In our investigations, the so-called gradient enhancement is used to regularise the internal variable field, representing the evolution of the bone mass density. For this, a well-established mathematical model for load-adaptive bone remodelling is employed. A description of the constitutive model, the gradient enhancement extension and the implementation into an open-access Abaqus user element subroutine is provided. Parametric studies on the robustness of the approach are demonstrated using two benchmark examples. Finally, the presented approach is used to simulate a detailed femur model.

Computational Analysis of the Influence of Menopause and Ageing on Bone Mineral Density, Exploring the Impact of Bone Turnover and Focal Bone Balance-A Study on Overload and Underload Scenarios.

This study aims to investigate the impact of hormonal imbalances during menopause, compounded by the natural ageing process, on bone health. Specifically, it examines the effects of increased bone turnover and focal bone balance on bone mass. A three-dimensional computational bone remodeling model was employed to simulate the response of the femur to habitual loads over a 19-year period, spanning premenopause, menopause, and postmenopause. The model was calibrated using experimental bone mineral density data from the literature to ensure accurate simulations. The study reveals that individual alterations in bone turnover or focal bone balance do not fully account for the observed experimental outcomes. Instead, simultaneous changes in both factors provide a more comprehensive explanation, leading to increased porosity while maintaining the material-to-apparent density ratio. Additionally, different load scenarios were tested, demonstrating that reaching the clinical osteoporosis threshold is independent of the timing of load changes. However, underload scenarios resulted in the threshold being reached approximately 6 years earlier than overload scenarios. These findings hold significant implications for strategies aimed at delaying the onset of osteoporosis and minimizing fracture risks through targeted mechanical stimulation during the early stages of menopause.

The Impact of Culture Variables on a 3D Human In Vitro Bone Remodeling Model: A Design of Experiments Approach.

Human in vitro bone remodeling models, using osteoclast-osteoblast cocultures, can facilitate the investigation of human bone remodeling while reducing the need for animal experiments. Although current in vitro osteoclast-osteoblast cocultures have improved the understanding of bone remodeling, it is still unknown which culture conditions support both cell types. Therefore, in vitro bone remodeling models can benefit from a thorough evaluation of the impact of culture variables on bone turnover outcomes, with the aim to reach balanced osteoclast and osteoblast activity, mimicking healthy bone remodeling. Using a resolution III fractional factorial design, the main effects of commonly used culture variables on bone turnover markers in an in vitro human bone remodeling model are identified. This model is able to capture physiological quantitative resorption-formation coupling along all conditions. Culture conditions of two runs show promising results: conditions of one run can be used as a high bone turnover system and conditions of another run as a self-regulating system as the addition of osteoclastic and osteogenic differentiation factors is not required for remodeling. The results generated with this in vitro model allow for better translation between in vitro studies and in vivo studies, toward improved preclinical bone remodeling drug development.

Osteogenesis and osteoclastogenesis on a chip: Engineering a self-assembling 3D coculture

Healthy bone is maintained by the process of bone remodeling. An unbalance in this process can lead to pathologies such as osteoporosis which are often studied with animal models. However, data from animals have limited power in predicting the results that will be obtained in human clinical trials. In search for alternatives to animal models, human in vitro models are emerging as they address the principle of reduction, refinement, and replacement of animal experiments (3Rs). At the moment, no complete in vitro model for bone-remodeling exists. Microfluidic chips offer great possibilities, particularly because of the dynamic culture options, which are crucial for in vitro bone formation. In this study, a scaffold free, fully human, 3D microfluidic coculture model of bone remodeling is presented. A bone-on-a-chip coculture system was developed in which human mesenchymal stromal cells differentiated into the osteoblastic lineage and self-assembled into scaffold free bone-like tissues with the shape and dimensions of human trabeculae. Human monocytes were able to attach to these tissues and to fuse into multinucleated osteoclast-like cells, establishing the coculture. Computational modeling was used to determine the fluid flow induced shear stress and strain in the formed tissue. Furthermore, a set-up was developed allowing for long-term (35 days) on-chip cell culture with benefits including continuous fluid-flow, low bubble formation risk, easy culture medium exchange inside the incubator and live cell imaging options. This on-chip coculture is a crucial advance towards developing in vitro bone remodeling models to facilitate drug testing.

Piezoelectric effects on bone modeling for enhanced sustainability

Bone tissue possesses piezoelectric properties, allowing mechanical forces to be converted into electrical potentials. Piezoelectricity has been demonstrated to play a crucial role in bone remodelling and adaptability. Bone remodelling models that consider strain adaptation, both with and without piezoelectric effects, were simulated and validated in this study. This simulation help to better comprehend the interplay between mechanical and electrical stimulations during these processes. This study aimed to optimise the modelling of piezoelectric effects in bone modelling analysis. The connection between mechanical loads applied to bones and the resulting electrical charges generated by the piezoelectric effect was examined. Furthermore, mathematical modelling and simulation techniques were employed to enhance the piezoelectric effect and promote bone tissue growth and repair. The findings from this research have substantial implications for developing novel therapies for bone-related diseases and injuries. It was observed that electrically stimulated bone surfaces increased bone deposition. In some instances of physical disability or osteoporosis, therapeutic electrical stimulation can supplement the mechanical stresses of regular exercise to prevent bone loss. Consequently, the bone remodelling method on the software platform enables easy application and repetition of finite element analysis. This study significantly benefits bone tissue/biomedical engineering, particularly in bone remodelling, healing, and repair.

Modeling and simulation of bone cells dynamic behavior under the late effect of breast cancer treatments.

Breast Cancer (BC) treatments have been proven to interfere with the health of bones. Chemotherapy and endocrinal treatment regimens such as tamoxifen and aromatase inhibitors are frequently prescribed for women with BC. However, these drugs increase bone resorption and reduce the Bone Mineral Density (BMD), thus increasing the risk of bone fracture. In the current study, a mechanobiological bone remodeling model has been developed by coupling cellular activities, mechanical stimuli, and the effect of breast cancer treatments (chemotherapy, tamoxifen, and aromatase inhibitors). This model algorithm has been programmed and implemented on MATLAB software to simulate different treatment scenarios and their effects on bone remodeling and also predict the evolution of Bone Volume fraction (BV/TV) and the associated Bone Density Loss (BDL) over a period of time. The simulation results, achieved from different combinations of Breast Cancer treatments, allow the researchers to predict the intensity of each combination treatment on BV/TV and BMD. The combination of chemotherapy, tamoxifen, and aromatase inhibitors, followed by the combination of chemotherapy and tamoxifen remain the most harmful regimen. This is because they have a strong ability to induce the bone degradation which is represented by a decrease of 13.55% and 11.55% of the BV/TV value, respectively. These results were compared with the experimental studies and clinical observations which showed good agreement. The proposed model can be used by clinicians and physicians to choose the most appropriate combination of treatments, according to the patient's case.

Spatio-temporal simulations of bone remodelling using a bone cell population model based on cell availability.

Here we developed a spatio-temporal bone remodeling model to simulate the action of Basic Multicelluar Units (BMUs). This model is based on two major extensions of a temporal-only bone cell population model (BCPM). First, the differentiation into mature resorbing osteoclasts and mature forming osteoblasts from their respective precursor cells was modelled as an intermittent process based on precursor cells availability. Second, the interaction between neighbouring BMUs was considered based on a "metabolic cost" argument which warrants that no new BMU will be activated in the neighbourhood of an existing BMU. With the proposed model we have simulated the phases of the remodelling process obtaining average periods similar to those found in the literature: resorption ( days)-reversal (∼8days)-formation (∼65days)-quiescence (560-600days) and an average BMU activation frequency of ∼1.6BMUs/year/mm3. We further show here that the resorption and formation phases of the BMU become coordinated only by the presence of TGF-β (transforming growth factor β), i.e., a major coupling factor stored in the bone matrix. TGF-β is released through resorption so upregulating osteoclast apoptosis and accumulation of osteoblast precursors, i.e., facilitating the transition from the resorption to the formation phase at a given remodelling site. Finally, we demonstrate that this model can explain targeted bone remodelling as the BMUs are steered towards damaged bone areas in order to commence bone matrix repair.

Trabecular bone remodeling in the aging mouse: A micro-multiphysics agent-based in silico model using single-cell mechanomics.

Bone remodeling is regulated by the interaction between different cells and tissues across many spatial and temporal scales. Notably, in silico models are regarded as powerful tools to further understand the signaling pathways that regulate this intricate spatial cellular interplay. To this end, we have established a 3D multiscale micro-multiphysics agent-based (micro-MPA) in silico model of trabecular bone remodeling using longitudinal in vivo data from the sixth caudal vertebra (CV6) of PolgA(D257A/D257A) mice, a mouse model of premature aging. Our in silico model includes a variety of cells as single agents and receptor-ligand kinetics, mechanomics, diffusion and decay of cytokines which regulate the cells' behavior. We highlighted its capabilities by simulating trabecular bone remodeling in the CV6 of five mice over 4weeks and we evaluated the static and dynamic morphometry of the trabecular bone microarchitecture. Based on the progression of the average trabecular bone volume fraction (BV/TV), we identified a configuration of the model parameters to simulate homeostatic trabecular bone remodeling, here named basal. Crucially, we also produced anabolic, anti-anabolic, catabolic and anti-catabolic responses with an increase or decrease by one standard deviation in the levels of osteoprotegerin (OPG), receptor activator of nuclear factor kB ligand (RANKL), and sclerostin (Scl) produced by the osteocytes. Our results showed that changes in the levels of OPG and RANKL were positively and negatively correlated with the BV/TV values after 4weeks in comparison to basal levels, respectively. Conversely, changes in Scl levels produced small fluctuations in BV/TV in comparison to the basal state. From these results, Scl was deemed to be the main driver of equilibrium while RANKL and OPG were shown to be involved in changes in bone volume fraction with potential relevance for age-related bone features. Ultimately, this micro-MPA model provides valuable insights into how cells respond to their local mechanical environment and can help to identify critical pathways affected by degenerative conditions and ageing.