Mechanobiological Model Research Articles

Impact of hypertension and arterial wall expansion on transport properties and atherosclerosis progression

This study explored the impact of hypertension on atheroma plaque formation through a mechanobiological model. The model incorporates blood flow via the Navier–Stokes equation. Plasma flow through the endothelium is determined by Darcy’s law and the Kedem–Katchalsky equations, which consider the three-pore model utilized for substance flow across the endothelium. The behaviour of these substances within the arterial wall is described by convection–diffusion–reaction equations, while the arterial wall itself is modelled as a hyperelastic material using Yeoh’s model. To accurately evaluate hypertension’s influence, adjustments were made to incorporate wall compression-induced wall compaction by radial compression. This compaction impacts three key variables of the transport phenomena: diffusion, porosity, and permeability. Based on the obtained findings, we can conclude that hypertension significantly augments plaque growth, leading to an over 400% increase in plaque thickness. This effect persists regardless of whether wall mechanics are considered. Tortuosity, arterial wall permeability, and porosity have minimal impact on atheroma plaque growth under normal arterial pressure. However, the atheroma plaque growth changes dramatically in hypertensive cases. In such scenarios, the collective influence of all factors—tortuosity, permeability, and porosity—results in nearly a 20% increase in plaque growth. This emphasizes the importance of considering wall compression due to hypertension in patient studies, where elevated blood pressure and high cholesterol levels commonly coexist.

Exploring vertebral bone density changes in a trunk with adolescent idiopathic scoliosis: a mechanobiological modeling investigation of intact and unilaterally paralyzed muscles

This study aimed to elucidate the vertebral bone density variations associated with adolescent idiopathic scoliosis (AIS), specifically examining the impact of unilateral muscle paralysis using an integrated approach combining Frost’s Mechanostat theory, a three-dimensional subject-specific finite element model and a musculoskeletal model of the L2 vertebra. The findings revealed a spectrum of bone density values ranging from 0.29 to 0.31 g/cm3, along with vertebral micro-strain levels spanning from 300 to 2200, consistent with existing literature. Furthermore, the ratio of maximum von Mises stress between the concave and convex side in the AIS model with intact muscles was approximately 1.08, which decreased by 4% due following unilateral paralysis of longissimus thoracis pars thoracic muscle. Overall, this investigation contributes to a deeper understanding of AIS biomechanics and lays the groundwork for future research endeavors aimed at optimizing clinical management approaches for individuals with this condition.

Impact of geometric and hemodynamic changes on a mechanobiological model of atherosclerosis

Background and Objective:In this work, the analysis of the importance of hemodynamic updates on a mechanobiological model of atheroma plaque formation is proposed. Methods:For that, we use an idealized and axisymmetric model of carotid artery. In addition, the behavior of endothelial cells depending on hemodynamical changes is analyzed too. A total of three computational simulations are carried out and their results are compared: an uncoupled model and two models that consider the opposite behavior of endothelial cells caused by hemodynamic changes. The model considers transient blood flow using the Navier–Stokes equation. Plasma flow across the endothelium is determined with Darcy’s law and the Kedem–Katchalsky equations, considering the three-pore model, which is also employed for the flow of substances across the endothelium. The behavior of the considered substances in the arterial wall is modeled with convection–diffusion–reaction equations, and the arterial wall is modeled as a hyperelastic Yeoh’s material. Results:Significant variations are noted in both the morphology and stenosis ratio of the plaques when comparing the uncoupled model to the two models incorporating updates for geometry and hemodynamic stimuli. Besides, the phenomenon of double-stenosis is naturally reproduced in the models that consider both geometric and hemodynamical changes due to plaque growth, whereas it cannot be predicted in the uncoupled model. Conclusions:The findings indicate that integrating the plaque growth model with geometric and hemodynamic settings is essential in determining the ultimate shape and dimensions of the carotid plaque.

Impact of Tissue Damage and Hemodynamics on Restenosis Following Percutaneous Transluminal Angioplasty: A Patient-Specific Multiscale Model.

Multiscale agent-based modeling frameworks have recently emerged as promising mechanobiological models to capture the interplay between biomechanical forces, cellular behavior, and molecular pathways underlying restenosis following percutaneous transluminal angioplasty (PTA). However, their applications are mainly limited to idealized scenarios. Herein, a multiscale agent-based modeling framework for investigating restenosis following PTA in a patient-specific superficial femoral artery (SFA) is proposed. The framework replicates the 2-month arterial wall remodeling in response to the PTA-induced injury and altered hemodynamics, by combining three modules: (i) the PTA module, consisting in a finite element structural mechanics simulation of PTA, featuring anisotropic hyperelastic material models coupled with a damage formulation for fibrous soft tissue and the element deletion strategy, providing the arterial wall damage and post-intervention configuration, (ii) the hemodynamics module, quantifying the post-intervention hemodynamics through computational fluid dynamics simulations, and (iii) the tissue remodeling module, based on an agent-based model of cellular dynamics. Two scenarios were explored, considering balloon expansion diameters of 5.2 and 6.2mm. The framework captured PTA-induced arterial tissue lacerations and the post-PTA arterial wall remodeling. This remodeling process involved rapid cellular migration to the PTA-damaged regions, exacerbated cell proliferation and extracellular matrix production, resulting in lumen area reduction up to 1-month follow-up. After this initial reduction, the growth stabilized, due to the resolution of the inflammatory state and changes in hemodynamics. The similarity of the obtained results to clinical observations in treated SFAs suggests the potential of the framework for capturing patient-specific mechanobiological events occurring after PTA intervention.

A Graphical Approach to Visualize and Interpret Biochemically Coupled Biomechanical Models.

The last decade has seen the emergence of progressively more complex mechanobiological models, often coupling biochemical and biomechanical components. The complexity of these models makes interpretation difficult, and although computational tools can solve model equations, there is considerable potential value in a simple method to explore the interplay between different model components. Pump and system performance curves, long utilized in centrifugal pump selection and design, inspire the development of a graphical technique to depict visually the performance of biochemically-coupled mechanical models. Our approach is based on a biochemical performance curve (analogous to the classical pump curve) and a biomechanical performance curve (analogous to the system curve). Upon construction of the two curves, their intersection, or lack thereof, describes the coupled model's equilibrium state(s). One can also observe graphically how an applied perturbation shifts one or both curves, and thus how the other component will respond, without rerunning the full model. While the upfront cost of generating the performance curve graphic varies with the efficiency of the model components, the easily interpretable visual depiction of what would otherwise be nonintuitive model behavior is valuable. Herein, we outline how performance curves can be constructed and interpreted for biochemically-coupled biomechanical models and apply the technique to two independent models in the cardiovascular space. The performance curve approach can illustrate and help identify weaknesses in model construction, inform user-applied perturbations and fitting procedures to generate intended behaviors, and improve the efficiency of the model generation and application process.

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.

Virtual Design of 3D-Printed Bone Tissue Engineered Scaffold Shape Using Mechanobiological Modeling: Relationship of Scaffold Pore Architecture to Bone Tissue Formation.

Large bone defects are clinically challenging, with up to 15% of these requiring surgical intervention due to non-union. Bone grafts (autographs or allografts) can be used but they have many limitations, meaning that polymer-based bone tissue engineered scaffolds (tissue engineering) are a more promising solution. Clinical translation of scaffolds is still limited but this could be improved by exploring the whole design space using virtual tools such as mechanobiological modeling. In tissue engineering, a significant research effort has been expended on materials and manufacturing but relatively little has been focused on shape. Most scaffolds use regular pore architecture throughout, leaving custom or irregular pore architecture designs unexplored. The aim of this paper is to introduce a virtual design environment for scaffold development and to illustrate its potential by exploring the relationship of pore architecture to bone tissue formation. A virtual design framework has been created utilizing a mechanical stress finite element (FE) model coupled with a cell behavior agent-based model to investigate the mechanobiological relationships of scaffold shape and bone tissue formation. A case study showed that modifying pore architecture from regular to irregular enabled between 17 and 33% more bone formation within the 4-16-week time periods analyzed. This work shows that shape, specifically pore architecture, is as important as other design parameters such as material and manufacturing for improving the function of bone tissue scaffold implants. It is recommended that future research be conducted to both optimize irregular pore architectures and to explore the potential extension of the concept of shape modification beyond mechanical stress to look at other factors present in the body.

Foreword to the special issue entitled "Progress and future directions in soft tissue mechanics" in the Journal Biomechanics and Modeling in Mechanobiology.

Foreword to the special issue entitled "Progress and future directions in soft tissue mechanics" in the Journal Biomechanics and Modeling in Mechanobiology.

Neonatal Hip Loading in Developmental Dysplasia: Finite Element Simulation of Proximal Femur Growth and Treatment.

Abnormal prenatal hip joint loading can lead to compromised hip joint function. Early intervention is crucial for favorable outcomes. This study investigates the impact of treatment timing (initiation and duration) on cartilage growth and ossification in the proximal femur of infants with developmental dysplasia of the hip, a condition affecting newborns. We used a mechanobiological model to simulate proximal femur growth during treatment durations of 3 months, 6 months, and a late-start treatment. The findings indicate that the timing of treatment initiation is crucial, while a longer treatment duration does not contribute to improved morphological development of the hip joint. Mechanobiological models of growth can be used to develop treatments and therapies that correct loading conditions. Growing bone is particularly sensitive to loading conditions, and altered loading during growth can affect bone shape and functionality.

Computational mechanobiology model evaluating healing of postoperative cavities following breast-conserving surgery

Breast cancer is the most commonly diagnosed cancer type worldwide. Given high survivorship, increased focus has been placed on long-term treatment outcomes and patient quality of life. While breast-conserving surgery (BCS) is the preferred treatment strategy for early-stage breast cancer, anticipated healing and breast deformation (cosmetic) outcomes weigh heavily on surgeon and patient selection between BCS and more aggressive mastectomy procedures. Unfortunately, surgical outcomes following BCS are difficult to predict, owing to the complexity of the tissue repair process and significant patient-to-patient variability. To overcome this challenge, we developed a predictive computational mechanobiological model that simulates breast healing and deformation following BCS. The coupled biochemical-biomechanical model incorporates multi-scale cell and tissue mechanics, including collagen deposition and remodeling, collagen-dependent cell migration and contractility, and tissue plastic deformation. Available human clinical data evaluating cavity contraction and histopathological data from an experimental porcine lumpectomy study were used for model calibration. The computational model was successfully fit to data by optimizing biochemical and mechanobiological parameters through Gaussian process surrogates. The calibrated model was then applied to define key mechanobiological parameters and relationships influencing healing and breast deformation outcomes. Variability in patient characteristics including cavity-to-breast volume percentage and breast composition were further evaluated to determine effects on cavity contraction and breast cosmetic outcomes, with simulation outcomes aligning well with previously reported human studies. The proposed model has the potential to assist surgeons and their patients in developing and discussing individualized treatment plans that lead to more satisfying post-surgical outcomes and improved quality of life.

Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta

Thoracic aortic aneurysms are characterized by a progressive loss of biomechanical functionality resulting from degenerative changes in wall composition, microstructure, and mechanical properties. Among the many causes of these lesions, Marfan syndrome is the most common heritable condition, resulting from mutations to the gene that codes the elastin-associated glycoprotein fibrillin-1. Key histopathological features of the aneurysmal Marfan aorta include extensive degradation of elastic fibres, significant remodelling of fibrillar collagens and compromised smooth muscle cell function. Computational growth and remodelling models have confirmed the importance of compromised elastic fibre integrity in aneurysmal dilatation, but we show here that this contributor alone is not sufficient to describe biomechanical data collected from the two most common mouse models of Marfan syndrome. Rather, our simulations suggest that compromised mechanosensing and mechanoregulation of extracellular matrix by mural cells also play central roles in the natural history. Determination of optimal disease-contributing parameters further suggests a rapid reduction in cellular mechanosensing and mechanoregulation relative to diminished elastic fibre integrity, highlighting the importance of inter- and intra-lamellar elastin in the Marfan aorta. Aneurysmal dilatation in Marfan syndrome thus results from multiple contributors to progressive degeneration of the aortic wall, and computational mechanobiological models can help disentangle these contributions.

A mechanobiological model for tumor spheroid evolution with application to glioblastoma: A continuum multiphysics approach

Background:Spheroids are in vitro quasi-spherical structures of cell aggregates, eventually cultured within a hydrogel matrix, that are used, among other applications, as a technological platform to investigate tumor formation and evolution. Several interesting features can be replicated using this methodology, such as cell communication mechanisms, the effect of gradients of nutrients, or the creation of realistic 3D biological structures. The main objective of this work is to link the spheroid evolution with the mechanical activity of cells, coupled with nutrient consumption and the subsequent cell dynamics. Method:We propose a continuum mechanobiological model which accounts for the most relevant phenomena that take place in tumor spheroid evolution under in vitro suspension, namely, nutrient diffusion in the spheroid, kinetics of cellular growth and death, and mechanical interactions among the cells. The model is qualitatively validated, after calibration of the model parameters, versus in vitro experiments of spheroids of different glioblastoma cell lines. Results:Our model is able to explain in a novel way quite different setups, such as spheroid growth (up to six times the initial configuration for U-87 MG cell line) or shrinking (almost half of the initial configuration for U-251 MG cell line); as the result of the mechanical interplay of cells driven by cellular evolution. Conclusions:Glioblastoma tumor spheroid evolution is driven by mechanical interactions of the cell aggregate and the dynamical evolution of the cell population. All this information can be used to further investigate mechanistic effects in the evolution of tumors and their role in cancer disease.

Peri-implant cell differentiation in delayed and immediately-loaded dental implant: A mechanobiological simulation

ObjectiveThis study aimed to investigate the effect of immediate versus delayed dental implant placement strategies on cell differentiation in a dental callus. DesignThe implant was placed in the mandible with two nearby teeth using an idealized two-dimensional finite element model. Eight weeks after surgery, the mechanobiological modeling of healing was used to estimate cell differentiation. It was assumed that the callus was initially filled by mesenchymal cells. The model then transformed mechanical stimuli received by the callus from loadings in terms of distortional and dilatational strains into predictions of the cellular phenotypes, including fibroblasts, chondrocytes, and osteoblasts, or whether they would remain unchanged or die. ResultsThe results demonstrated that delayed loading led to greater bone formation than immediate loading. Osteoblast colonies were observed in the base of threads in the immediately-loaded implant, whereas the delayed loading caused distant bone formation from the surrounding bone side towards the implant. The osteoblasts were differentiated from both intramembranous and endochondral mechanisms of ossification. After eight weeks, approximately 61 % of the callus was ossified in the delayed placement model compared to 35 % in the immediate placement model, resulting in a greater amount of fibrocartilaginous tissue on the bone side of the callus. ConclusionsImmediate and delayed loading models generated different results. In the delayed strategy, bone cells were supplied appropriately during the first few weeks following surgery, whereas the immediate loading caused fibrocartilaginous tissue differentiation. In the form of distant osseointegration, the secondary stability of the dental implant was higher and faster due to the delayed placement.

An in silico study on the influence of extracellular matrix mechanics on vasculogenesis

Background and objectives: Blood vessels form a network of capillaries throughout the body that perform essential functions for life. Vasculogenesis, i.e. the formation of new blood vessels, is regulated by many factors, biochemical ones being among the most important. However, others such as the biomechanical influence on shape, organization and structure of vessel networks require further investigation. In this paper, we develop a 3D agent-based mechanobiological model of vasculogenesis with the aim of analyzing how the mechanics of the extracellular matrix (ECM) affects vasculogenesis. Methods: For this purpose, we consider a growing domain composed of different cells: tip cells, which are the driving cells located at the end of the vessels and stalk cells, which are found in the interior of the vascular network. ECM is considered as particles (agents) that surround the growth of the vascular network. Depending on the cell type, different sets of forces are considered, such as chemotactic, mechanical, random and viscoelastic forces among others. Results: The growth of the network is iteratively analyzed and updated at each time step based on a mechanically-driven proliferation rule. The influence of different biomechanical factors, such as ECM stiffness or viscoelasticity are explored through in silico simulations. A number of indicators are defined along the algorithm, like number of cells, branches, tortuosity and anisotropy, in order to compare topological differences of the vascular network during vasculogenesis under different ECM conditions. The obtained results are qualitatively compared with other related works in the literature. Conclusions: The present study sheds some light and partially explain, from an in silico perspective, the role of ECM mechanics on vasculogenesis. The main conclusions of this work are: (i) increased stiffness increases proliferation, (ii) the network tends to migrate towards stiffer areas, and (iii) increased viscoelasticity decreases proliferation.

Injury-related cell death and proteoglycan loss in articular cartilage: Numerical model combining necrosis, reactive oxygen species, and inflammatory cytokines.

Osteoarthritis (OA) is a common musculoskeletal disease that leads to deterioration of articular cartilage, joint pain, and decreased quality of life. When OA develops after a joint injury, it is designated as post-traumatic OA (PTOA). The etiology of PTOA remains poorly understood, but it is known that proteoglycan (PG) loss, cell dysfunction, and cell death in cartilage are among the first signs of the disease. These processes, influenced by biomechanical and inflammatory stimuli, disturb the normal cell-regulated balance between tissue synthesis and degeneration. Previous computational mechanobiological models have not explicitly incorporated the cell-mediated degradation mechanisms triggered by an injury that eventually can lead to tissue-level compositional changes. Here, we developed a 2-D mechanobiological finite element model to predict necrosis, apoptosis following excessive production of reactive oxygen species (ROS), and inflammatory cytokine (interleukin-1)-driven apoptosis in cartilage explant. The resulting PG loss over 30 days was simulated. Biomechanically triggered PG degeneration, associated with cell necrosis, excessive ROS production, and cell apoptosis, was predicted to be localized near a lesion, while interleukin-1 diffusion-driven PG degeneration was manifested more globally. Interestingly, the model also showed proteolytic activity and PG biosynthesis closer to the levels of healthy tissue when pro-inflammatory cytokines were rapidly inhibited or cleared from the culture medium, leading to partial recovery of PG content. The numerical predictions of cell death and PG loss were supported by previous experimental findings. Furthermore, the simulated ROS and inflammation mechanisms had longer-lasting effects (over 3 days) on the PG content than localized necrosis. The mechanobiological model presented here may serve as a numerical tool for assessing early cartilage degeneration mechanisms and the efficacy of interventions to mitigate PTOA progression.

Predicting the formation of different tissue types during Achilles tendon healing using mechanoregulated and oxygen-regulated frameworks

During Achilles tendon healing in rodents, besides the expected tendon tissue, also cartilage-, bone- and fat-like tissue features have been observed during the first twenty weeks of healing. Several studies have hypothesized that mechanical loading may play a key role in the formation of different tissue types during healing. We recently developed a computational mechanobiological framework to predict tendon tissue production, organization and mechanical properties during tendon healing. In the current study, we aimed to explore possible mechanobiological related mechanisms underlying formation of other tissue types than tendon tissue during tendon healing. To achieve this, we further developed our recent framework to predict formation of different tissue types, based on mechanobiological models established in other fields, which have earlier not been applied to study tendon healing. We explored a wide range of biophysical stimuli, i.e., principal strain, hydrostatic stress, pore pressure, octahedral shear strain, fluid flow, angiogenesis and oxygen concentration, that may promote the formation of different tissue types. The numerical framework predicted spatiotemporal formation of tendon-, cartilage-, bone- and to a lesser degree fat-like tissue throughout the first twenty weeks of healing, similar to recent experimental reports. Specific features of experimental data were captured by different biophysical stimuli. Our modeling approach showed that mechanobiology may play a role in governing the formation of different tissue types that have been experimentally observed during tendon healing. This study provides a numerical tool that can contribute to a better understanding of tendon mechanobiology during healing. Developing these tools can ultimately lead to development of better rehabilitation regimens that stimulate tendon healing and prevent unwanted formation of cartilage-, fat- and bone-like tissues.

Effect of the accordion technique on bone regeneration during distraction osteogenesis: A computational study

Background and objectiveDistraction osteogenesis (DO), a bone lengthening technique, is widely employed to treat congenital and acquired limb length discrepancies and large segmental bone defects. However, a major issue of DO is the prolonged consolidation phase (10–36 months) during which patients must wear a cumbersome external fixator. Attempts have been made to accelerate the healing process of DO by an alternating distraction and compression mode (so-called “accordion” technique or AT). However, it remains unclear how varied AT parameters affect DO outcomes and what the most effective AT mode is. MethodsBased on an experimentally-verified mechanobiological model, we performed a parametric analysis via in silico simulation of the bone regeneration process of DO under different AT modes, including combinations of varied application times (AT began at week 1–8 of the consolidation phase), durations (AT was used continuously for 1 week, 2 weeks or 4 weeks) and rates (distraction or compression at 0.25, 0.5, 0.75, and 1 mm/12 h). The control group had no AT applied during the consolidation phase. ResultsCompared with the control group (no AT), AT applied at an early consolidation stage (e.g. week 1 of the consolidation phase) significantly enhanced bone formation and reduced the overall healing time. However, the effect of AT on bone healing was dependent on its duration and rate. Specifically, a moderate rate of AT (e.g. 0.5 mm/12 h) lasting for two weeks promoted blood perfusion recovery and bone regeneration, ultimately shortening the healing time. Conversely, over-high rates (e.g. 1 mm/12 h) and longer durations (e.g. 4 weeks) of AT adversely affected bone regeneration and blood perfusion recovery, thereby delaying bone bridging. ConclusionsThese results suggest that the therapeutic effects of AT on DO are highly dependent of the AT parameters of choice. Under appropriate durations and rates, the AT applied at an early consolidation phase is beneficial for blood recovery and bone regeneration. These results may provide a basis for selecting effective AT modes to accelerate consolidation and reduce the overall treatment period of DO.

Multi-scale mechanobiological model for skeletal muscle hypertrophy.

Skeletal muscle adaptation is correlated to training exercise by triggering different signaling pathways that target many functions; in particular, the IGF1-AKT pathway controls protein synthesis and degradation. These two functions regulate the adaptation in size and strength of muscles. Computational models for muscle adaptation have focused on: the biochemical description of signaling pathways or the mechanical description of muscle function at organ scale; however, an interrelation between these two models should be considered to understand how an adaptation in muscle size affects the protein synthesis rate. In this research, a dynamical model for the IGF1-AKT signaling pathway is linked to a continuum-mechanical model describing the active and passive mechanical response of a muscle; this model is used to study the impact of the adaptive muscle geometry on the protein synthesis at the fiber scale. This new computational model links the signaling pathway to the mechanical response by introducing a growth tensor, and links the mechanical response to the signaling pathway through the evolution of the protein synthesis rate. The predicted increase in cross sectional area (CSA) due to an 8 weeks training protocol excellently agreed with experimental data. Further, our results show that muscle growth rate decreases, if the correlation between protein synthesis and CSA is negative. The outcome of this study suggests that multi-scale models coupling continuum mechanical properties and molecular functions may improve muscular therapies and training protocols.

Experimental-based mechanobiological modeling of the anabolic and catabolic effects of breast cancer on bone remodeling.

Bone is a biological tissue characterized by its hierarchical organization. This material has the ability to be continually renewed, which makes it highly adaptative to external loadings. Bone renewing is managed by a dynamic biological process called bone remodeling (BR), where continuous resorption of old bone and formation of new bone permits to change the bone composition and microstructure. Unfortunately, because of several factors, such as age, hormonal imbalance, and a variety of pathologies including cancer metastases, this process can be disturbed leading to various bone diseases. In this study, we have investigated the effect of breast cancer (BC) metastases causing osteolytic bone loss. BC has the ability to affect bone quantity in different ways in each of its primary and secondary stages. Based on a BR mathematical model, we modeled the BC cells' interaction with bone cells to assess their effect on bone volume fraction (BV/TV) evolution during the remodeling process. Some of the parameters used in our model have been determined experimentally using the enzyme-linked immune-sorbent assay (ELISA) and the MTT assay. Our numerical simulations show that primary BC plays a significant role in enhancing bone-forming cells' activity leading to a 6.22% increase in BV/TV over 1 year. On the other hand, secondary BC causes a noticeable decrease in BV/TV reaching 15.74% over 2years.

The interplay between BMU activity linked to mechanical stress, specific surface and inhibitory theory dictate bone mass distribution: Predictions from a 3D computational model

Bone mechanical and biological properties are closely linked to its internal tissue composition and mass distribution, which are in turn governed by the purposeful action of the basic multicellular units (BMUs). The orchestrated action of osteoclasts and osteoblasts, the resorbing and forming tissue cells respectively, in BMUs is responsible for tissue maintenance, repair and adaptation to changing load demands through the phenomenon known as remodelling. In this work, a computational mechano-biological model of bone remodelling based on the inhibitory theory and a new scheme of bone resorption introduced previously in a 2D model, is extended to a 3D model of the real external geometry of a femur under normal walking loads. Starting from a uniform apparent density (ratio of tissue local mass to total local volume) distribution, the BMU action can be shown to lead naturally to an internal density distribution similar to that of a real bone, provided that the initial density value is high enough to avoid unrealistic final mass deposition in zones of high energy density and excessive damage. Physiological internal density values are reached throughout the whole 3D geometry, and at the same time a ‘boomerang’-like relationship between apparent and material density (ratio of tissue mass to tissue volume) emerges naturally under the proposed remodelling scheme. It is also shown here that bone-specific surface is a key parameter that determines the intensity of BMU action linked to the mechanical and biological requirements. Finally, by engaging in simulations of bone in disuse, we were able to confirm the appropriate selection of the model parameters. As an example, our results show good agreement with experimental measurements of bone mass on astronauts a fact that strengthens our belief in the insightful nature of our novel 3D computational model.