Modeling of bone formation and resorption mediated by parathyroid hormone: response to estrogen/PTH therapy

Mechanobiochemical bone remodelling around an uncemented acetabular component: influence of bone orthotropy

Mechanical loosening of an implant is often caused by bone resorption, owing to stress/strain shielding. Adaptive bone remodelling elucidates the response of bone tissue to alterations in mechanical and biochemical environments. This study aims to propose a novel framework of bone remodelling based on the combined effects of bone orthotropy and mechanobiochemical stimulus. The proposed remodelling framework was employed in the finite element model of an implanted hemipelvis to predict evolutionary changes in bone density and associated orthotropic bone material properties. In order to account for variations in load transfer during common daily activities, several musculoskeletal loading conditions of hip joint corresponding to sitting down/up, stairs ascend/descend and normal walking were considered. The bone remodelling predictions were compared with those of isotropic strain energy density (SED)-based, isotropic mechanobiochemical and orthotropic strain-based bone remodelling formulations. Although similar trends of bone resorption were predicted by orthotropic mechanobiochemical (MBC) and orthotropic strain-based models across implanted acetabulum, more volume (10-20%) of bone elements was subjected to bone resorption for the orthotropic MBC model. Higher bone resorption (75-85%) was predicted by the orthotropic strain-based and orthotropic MBC models compared to the isotropic MBC and SED-based models. Higher bone apposition (35-160%) across the implanted acetabulum was predicted by the isotropic MBC model, compared to the SED-based model. The remodelling predictions indicated that a reduction in estrogen level might lead to an increase in bone resorption. The study highlighted the importance of including mechanobiochemical stimulus and bone anisotropy to predict bone remodelling adequately.

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.

The Role of Irisin in Exercise-Mediated Bone Health

Exercise training promotes physical and bone health, and is the first choice of non-drug strategies that help to improve the prognosis and complications of many chronic diseases. Irisin is a newly discovered peptide hormone that modulates energy metabolism and skeletal muscle mass. Here, we discuss the role of irisin in bone metabolism via exercise-induced mechanical forces regulation. In addition, the role of irisin in pathological bone loss and other chronic diseases is also reviewed. Notably, irisin appears to be a key determinant of bone mineral status and thus may serve as a novel biomarker for bone metabolism. Interestingly, the secretion of irisin appears to be mediated by different forms of exercise and pathological conditions such as diabetes, obesity, and inflammation. Understanding the mechanism by which irisin is regulated and how it regulates skeletal metabolism via osteoclast and osteoblast activities will be an important step toward applying new knowledge of irisin to the treatment and prevention of bone diseases such as osteolysis and other chronic disorders.

[Prolonged continuous infusion of teriparatide promotes bone metabolism in normal but not in castrated mice]

OBJECTIVE

To investigate the effects of continuous pumping of teriparatide (TPTD) on bone metabolism in ovariectomized and normal mice and provide experimental evidence for the selection of animal models for studying the effects of TPTD and its related peptides on osteoclasts.

METHODS

Twenty-four female C57BL mice (6-weeks old) were subjected to ovariectomy (OVX) or sham operation followed 7 days later by continuous pumping of TPTD or the solvent vehicle (VEH) via a micropump (SHAM-VEH, SHAM-TPTD, OVX-VEH, and OVX-TPTD groups; n=6). Two weeks later, the tibial and femoral bones were harvested for micro-CT scanning to measure the parameters of the tibia and the femoral cortical bone. Histopathological examinations of the tibial tissue were conducted using HE staining and TRAP staining and the number of osteoclasts and the growth plate thickness were determined. The serum Ca2 + levels of the mice were measured. The primary osteoblasts from the cranial bone were treated with estradiol (E2) and TPTD for 48 h, and the expressions of β-catenin and RANKL protein in the cells were analyzed.

RESULTS

The trabecular bone mass of OVX mice was significantly lower than that of sham-operated mice (P < 0.05). Continuous TPTD pumping significantly reduced tibial cancellous bone mass and femoral cortical bone area in the sham-operated mice, while in the castrated mice, TPTD pumping increased the cancellous bone mass without changing the cortical bone area. TRAP staining showed that cancellous osteoblasts in the tibia increased significantly in the castrated mice as compared with the sham-operated mice, and TPTD pumping significantly increased the number of cancellous osteoblasts in the sham-operated mice (P < 0.05). In the primary cultured osteoblasts, treatment with both E2 and TPTD obviously lowered the expression of β-catenin and increased the expression of RANKL as compared with TPTD treatment alone.

CONCLUSIONS

Continuous pumping of TPTD promotes bone resorption in normal mice but does not produce obvious bone resorption effect in the ovariectomized mice, suggesting that castrated mice are not suitable models for studying the effect of TPTD and the related peptides on the osteoclasts.

Computational model of the dual action of PTH - Application to a rat model of osteoporosis

This paper presents a pharmacokinetic/pharmacodynamic (PK/PD) model of the action of PTH(1-34) on bone modelling and remodelling, developed for quantitatively investigating the dose- and administration pattern-dependency of the bone tissue response to this drug. Firstly, a PK model of PTH(1-34) was developed, accounting for administration via subcutaneous injections. Subsequently, the PK model was coupled to a (mechanistic) bone cell population model of bone modelling and remodelling, taking into account the effects of PTH(1-34) on the differentiation of lining cells into active osteoblasts, on the apoptosis of active osteoblasts, and on proliferation of osteoblast precursors, as well as on the key regulatory pathways of bone cell activities. Numerical simulations show that the coupled PK/PD model is able to distinguish between continuous and intermittent administration patterns of PTH(1-34), in terms of yielding both catabolic bone responses (if drug administration is carried out continuously) and anabolic bone responses (if drug administration is carried out intermittently). The model also features a non-linear relation between bone gain and drug dose (as known from experiments); doubling the dose from 80 μg/kg/day to 160 μg/kg/day induced a 1.3-fold increase of the bone volume-to-total volume ratio. Furthermore, the model presented in this paper confirmed that bone modelling represents an essential mechanism of the anabolic response of bone to PTH(1-34) administration in rat models, and that the large amount of bone formation observed in such models cannot be explained via remodelling alone.

A computational study of the dual effect of intermittent and continuous administration of parathyroid hormone on bone remodeling

Bone remodeling is a process known to be governed by constant interactions between osteoblast and osteoclast through complex pathway networks mediated by signaling factors. Experimental studies show that intermittent and continuous administration of PTH/PTHrP led to opposite outcomes in terms of bone mass. To investigate this dual effect of PTH/PTHrP, we develop a computational model based on a simplified signaling pathway network which includes relevant molecular effectors and cells. Multiple ordinary differential equations linking all considered components in the signaling pathway network through reaction kinetics are solved with dose values and patterns of injection from experiments as input. Modeling results show good agreement with experimental observations in that continuous injection of PTH/PTHrP generates catabolic effect on bone mass while intermittent injection yields anabolic effect. The signaling factors governing the interaction between osteoblast and osteoclast indeed play a key role in the dual effect of PTH/PTHrP. Furthermore, there appears to be an optimal interval for intermittent injection of PTH/PTHrP for yielding the most bone regeneration, and a synergistic outcome could be achieved by combining intermittent injection of PTH/PTHrP with application of a treatment (to mimic the filling of bone defects with polymeric scaffolds). This modeling work sheds valuable insights into the influence of temporal control of PTH/PTHrP on bone mass and presents a possible path toward bridging bioengineering approaches with clinical treatment strategies. STATEMENT OF SIGNIFICANCE: A computational model considering simplified signaling pathways containing crucial components of PTH, PTHrP, osteoblast precursor, osteoblast, osteoclast precursor, osteoclast, RANKL and IL-6 family cytokoines has been developed to study the dual effect of PTH/PTHrP on bone metabolism. The model takes the dose values and patterns of injection from experiments as input and yields predictions that convincingly match experimental measurements. This work highlights the importance of providing an optimal hormone treatment strategy for maintaining healthy bone metabolism. Moreover, the integrative approach of relying on experimental observations to find reasonable values for relevant modeling parameters has been proven to be powerful in advancing our understanding of biological interactions among cells and signaling factors.

A new biological bone remodeling in silico model combined with advanced discretization methods

Bone remodeling remains a highly researched topic investigated by many strands of science. The main purpose of this work is formulating a new computational framework for biological simulation, extending the version of the bone remodeling model previously proposed by Komarova. Thus, considering only the biological aspect of the remodeling process, the action of osteoclasts and osteoblasts is taken into account as well as its impact on bone mass. It is conducted a spatiotemporal analysis of a remodeling cycle obtaining a dynamic behavior of bone cells very similar to the biological process already described in the literature. The numerical example used is based on bone images obtained with scanning electron microscopy. During simulation, it is possible to observe the variation of bone's architecture through isomaps. These maps are obtained through the combination of biological bone remodeling models with three distinct numerical techniques-finite element method (FEM), radial point interpolation method (RPIM), and natural neighbor radial point interpolation method (NNRPIM). A study combining these numerical techniques allows to compare their performance. Ultimately, this work supports the inclusion of meshless methods due to their smoother results and its easiness to be combined with medical images from CT scans and MRI.

Osteoblasts Are the Centerpiece of the Metastatic Bone Microenvironment

The tumor microenvironment is comprised of diverse stromal cell populations in addition to tumor cells. Increasing evidence now clearly supports the role of microenvironment stromal cells in tumor progression and metastasis, yet the regulatory mechanisms and interactions among tumor and stromal cells remain to be elucidated. Bone metastasis is the major problem in many types of human malignancies including prostate, breast and lung cancers, and the biological basis of bone metastasis let alone curative approaches are largely undetermined. Among the many types of stromal cells in bone, osteoblasts are shown to be an important player. In this regard, osteoblasts are a key target cell type in the development of bone metastasis, but there are currently no drugs or therapeutic approaches are available that specifically target osteoblasts. This review paper summarizes the current knowledge on osteoblasts in the metastatic tumor microenvironment, aiming to provide clues and directions for future research endeavor.

MODEL-BASED ANALYSIS OF IGF-1 EFFECT ON OSTEOBLAST AND OSTEOCLAST REGULATION IN BONE TURNOVER

The main determinant of bone Ca accretion is a bimolecular regulatory network on osteoblast (OB) and osteoclast (OC). Even though IGF-1 is known as an important regulator in bone cell cycle, little has been done to model IGF-1 action in bone cell regulation. Thus, the objective is to develop a mathematical model that depicts the regulatory action of IGF-1 onto the OB and OC interaction, and to evaluate adolescent and adult bone Ca accretion in response to differences in IGF-1 levels. As a result, a dynamic model of OB and OC with two main regulatory systems, i.e., Receptor Activator for Nuclear Factor [Formula: see text]B (RANK)-RANK Ligand (RANKL)-osteoprogerin (OPG) system, and TGF-[Formula: see text], was augmented with the IGF-1, and incorporated into Ca kinetic data to predict exchangeable bone Ca. The developed model could predict a change in OB and OC levels in response to perturbations in regulators, producing results consistent with bone physiology and published experimental data. The model also estimated parametric difference in regulators between adults and adolescents, suggesting that RANKL/OPG in adolescents was about 4 times higher than in adults, while adolescent serum PTH and IGF-1 concentrations were 60% and 220% of those of adults, respectively. This study highlighted the influence of IGF-1 on the regulation of bone cells in positively modulating bone Ca, suggesting that IGF-1 may be an effective target for reducing bone loss by promoting mature OB.

Mathematical modelling of the pathogenesis of multiple myeloma-induced bone disease

Multiple myeloma (MM) is the second most common haematological malignancy and results in destructive bone lesions. The interaction between MM cells and the bone microenvironment plays an important role in the development of the tumour cells and MM-induced bone disease and forms a 'vicious cycle' of tumour development and bone destruction, intensified by suppression of osteoblast activity and promotion of osteoclast activity. In this paper, a mathematical model is proposed to simulate how the interaction between MM cells and the bone microenvironment facilitates the development of the tumour cells and the resultant bone destruction. It includes both the roles of inhibited osteoblast activity and stimulated osteoclast activity. The model is able to mimic the temporal variation of bone cell concentrations and resultant bone volume after the invasion and then removal of the tumour cells and explains why MM-induced bone lesions rarely heal even after the complete removal of MM cells. The behaviour of the model compares well with published experimental data. The model serves as a first step to understand the development of MM-induced bone disease and could be applied further to evaluate the current therapies against MM-induced bone disease and even suggests new potential therapeutic targets.

Predicting Bone Remodeling in Response to Total Hip Arthroplasty: Computational Study Using Mechanobiochemical Model

Periprosthetic bone loss following total hip arthroplasty (THA) is a serious concern leading to the premature failure of prosthetic implant. Therefore, investigating bone remodeling in response to hip arthroplasty is of paramount for the purpose of designing long lasting prostheses. In this study, a thermodynamic-based theory, which considers the coupling between the mechanical loading and biochemical affinity as stimulus for bone formation and resorption, was used to simulate the femoral density change in response to THA. The results of the numerical simulations using 3D finite element analysis revealed that in Gruen zone 7, after remarkable postoperative bone loss, the bone density started recovering and got stabilized after 9% increase. The most significant periprosthetic bone loss was found in Gruen zone 7 (−17.93%) followed by zone 1 (−13.77%). Conversely, in zone 4, bone densification was observed (+4.63%). The results have also shown that the bone density loss in the posterior region of the proximal metaphysis was greater than that in the anterior side. This study provided a quantitative figure for monitoring the distribution variation of density throughout the femoral bone. The predicted bone density distribution before and after THA agree well with the bone morphology and previous results from the literature.

Connecting mechanics and bone cell activities in the bone remodeling process: an integrated finite element modeling

Bone adaptation occurs as a response to external loadings and involves bone resorption by osteoclasts followed by the formation of new bone by osteoblasts. It is directly triggered by the transduction phase by osteocytes embedded within the bone matrix. The bone remodeling process is governed by the interactions between osteoblasts and osteoclasts through the expression of several autocrine and paracrine factors that control bone cell populations and their relative rate of differentiation and proliferation. A review of the literature shows that despite the progress in bone remodeling simulation using the finite element (FE) method, there is still a lack of predictive models that explicitly consider the interaction between osteoblasts and osteoclasts combined with the mechanical response of bone. The current study attempts to develop an FE model to describe the bone remodeling process, taking into consideration the activities of osteoclasts and osteoblasts. The mechanical behavior of bone is described by taking into account the bone material fatigue damage accumulation and mineralization. A coupled strain-damage stimulus function is proposed, which controls the level of autocrine and paracrine factors. The cellular behavior is based on Komarova et al.'s (2003) dynamic law, which describes the autocrine and paracrine interactions between osteoblasts and osteoclasts and computes cell population dynamics and changes in bone mass at a discrete site of bone remodeling. Therefore, when an external mechanical stress is applied, bone formation and resorption is governed by cells dynamic rather than adaptive elasticity approaches. The proposed FE model has been implemented in the FE code Abaqus (UMAT routine). An example of human proximal femur is investigated using the model developed. The model was able to predict final human proximal femur adaptation similar to the patterns observed in a human proximal femur. The results obtained reveal complex spatio-temporal bone adaptation. The proposed FEM model gives insight into how bone cells adapt their architecture to the mechanical and biological environment.

The kinetics of vitamin D₃ in the osteoblastic cell

Experimental evidence is presented on the translocation of vitamin D metabolite, 1,25-(OH)₂D₃, from the membrane to the nucleus in osteoblast progenitor cells. A mathematical model permitting traversal of the cytoplasm at either a fixed velocity or by diffusion is formulated in order to determine whether transport along the cytoskeletal tracks is more consistent with the observed spatial-temporal distribution than diffusion, and it is so found. The model includes reactions in the nucleus involving D₃ to form other compounds, such as protegerin, and thus also makes predictions of the concentrations of these compounds in various regions of the cell.

Serum receptor activator of nuclear factor-κ B ligand, osteoprotegrin, and intact parathyroid hormone in hemodialysis and renal transplant patients

Serum receptor activator of nuclear factor-κ B ligand and osteoprotegrin are mediated to vascular calcification in the general population. Our knowledge is very sparse in hemodialysis and renal transplant patients. Receptor activator of nuclear factor-κ B ligand, osteoprotegrin, intact parathyroid hormone, calcium, and phosphorus were measured in blood samples of 45 hemodialysis and 45 age-matched renal transplant patients. Osteoprotegrin (P = 0.001) and intact parathyroid hormone (P = 0.001) levels in the hemodialysis patients were higher than the renal transplant recipients. Osteoprotegrin had positive correlation with duration of dialysis and age in the hemodialysis (r = 0.88, P = 0.001 and r = 0.34, P = 0.02, respectively) and renal transplant patients (r = 0.92, P = 0.001 and r = 0.46, P = 0.001, respectively). Hemodialysis patients have higher osteoprotegrin levels than the renal transplant recipients. It may act as a protective factor for renal osteodystrophy or only as a secondary phenomenon of advanced renal failure.

A semi-empirical cell dynamics model for bone turnover under external stimulus

The normal periodic turnover of bone is referred to as remodeling. In remodeling, old or damaged bone is removed during a 'resorption' phase and new bone is formed in its place during a 'formation' phase in a sequence of events known as coupling. Resorption is preceded by an 'activation' phase in which the signal to remodel is initiated and transmitted. Remodeling is known to involve the interaction of external stimuli, bone cells, calcium and phosphate ions, and several proteins, hormones, molecules, and factors. In this study, a semi-empirical cell dynamics model for bone remodeling under external stimulus that accounts for the interaction between bone mass, bone fluid calcium, bone calcium, and all three major bone cell types, is presented. The model is formulated to mimic biological coupling by solving separately and sequentially systems of ODEs for the activation, resorption, and formation phases of bone remodeling. The charateristic time for resorption (20 days) and the amount of resorption (~0.5%) are fixed for all simulations, but the formation time at turnover is an output of the model. The model was used to investigate the effects of different types of strain stimuli on bone turnover under bone fluid calcium balance and imbalance conditions. For bone fluid calcium balance, the model predicts complete turnover after 130 days of formation under constant 1000 microstrain stimulus; after 47 days of formation under constant 2000 microstrain stimulus; after 173 days of formation under strain-free conditions, and after 80 days of formation under monotonic increasing strain stimulus from 1000 to 2000 microstrain. For bone fluid calcium imbalance, the model predicts that complete turnover occurs after 261 days of formation under constant 1000 microstrain stimulus and that turnover never occurs under strain-free conditions. These predictions were not impacted by mean dynamic input strain stimuli of 1000 and 2000 microstrain at 1 Hz and 1000 microstrain amplitude. The formation phase of remodeling lasts longer than the resorption phase, increased strain stimulus accelerates bone turnover, while absence of strain significantly delays or prevents it, and formation time for turnover under monotonic increasing strain conditions is intermediate to those for constant strain stimuli at the minimum and maximum monotonic strain levels. These results are consistent with the biology, and with Frost's mechanostat theory.

Coping with time scales in disease systems analysis: application to bone remodeling

In this study we demonstrate the added value of mathematical model reduction for characterizing complex dynamic systems using bone remodeling as an example. We show that for the given parameter values, the mechanistic RANK-RANKL-OPG pathway model proposed by Lemaire et al. (J Theor Biol 229:293-309, 2004) can be reduced to a simpler model, which can describe the dynamics of the full Lemaire model to very good approximation. The response of both models to changes in the underlying physiology and therapeutic interventions was evaluated in four physiologically meaningful scenarios: (i) estrogen deficiency/estrogen replacement therapy, (ii) Vitamin D deficiency, (iii) ageing, and (iv) chronic glucocorticoid treatment and its cessation. It was found that on the time scale of disease progression and therapeutic intervention, the models showed negligible differences in their dynamic properties and were both suitable for characterizing the impact of estrogen deficiency and estrogen replacement therapy, Vitamin D deficiency, ageing, and chronic glucocorticoid treatment and its cessation on bone forming (osteoblasts) and bone resorbing (osteoclasts) cells. It was also demonstrated how the simpler model could help in elucidating qualitative properties of the observed dynamics, such as the absence of overshoot and rebound, and the different dynamics of onset and washout.

A theoretical study of bone remodelling under PEMF at cellular level

Pulsed electromagnetic field (PEMF) devices have been used clinically to slow down osteoporosis and accelerate the healing of bone fractures for many years. However, the underlying mechanism by which bone remodelling under PEMF is regulated remains poorly understood. In this paper, a mathematical model of bone cell population of bone remodelling under PEMF at cellular level is developed to address this issue for the first time. On the basis of this model and control theory, parametric study of control mechanisms is carried out and a number of possible control mechanisms are identified. These findings will help further the understanding of bone remodelling under PEMF and advance therapies and pharmacological developments in clinical trials.

Mathematical modeling in bone biology: from intracellular signaling to tissue mechanics

Although conceptual and experimental models are historically well incorporated in bone biology studies, mathematical modeling has been much less-frequently utilized. This review aims to introduce mathematical modeling to readers who are not familiar with the concept underlying this methodology, to outline how mathematical models can help to improve current understanding of bone biology and to discuss examples where mathematical modeling was used to provide new insights into important questions of bone biology.

Bone remodeling in a new biomimetic polymer-composite hip stem

Adaptive bone remodeling is an important factor that leads to bone resorption in the surrounding femoral bone and implant loosening. Taking into account this factor in the design of hip implants is of clinical importance, because it allows the prediction of the bone-density redistribution and enables the monitoring of bone adaptation after prosthetic implantation. In this article, adaptive bone remodeling around a new biomimetic polymer-composite-based (CF/PA12) hip prosthesis is investigated to evaluate the amount of stress shielding and bone resorption. The design concept of this new prosthesis is based on a hollow substructure made of hydroxyapatite-coated, continuous carbon fiber (CF)-reinforced polyamide 12 (PA12) composite with an internal soft polymer-based core. Strain energy density theory coupled with 3D Finite Element models is used to predict bone density redistributions in the femoral bone before and after total hip replacement (THR) using both polymer-composite and titanium (Ti) stems. The result of numerical simulations of bone remodeling revealed that the CF/PA12 composite stem generates a better bone density pattern compared with the Ti-based stem, indicating the effectiveness of the composite stem to reduce bone resorption caused by stress-shielding phenomenon. This may result in an extended lifetime of THR.

A physiologically based mathematical model of integrated calcium homeostasis and bone remodeling

Bone biology is physiologically complex and intimately linked to calcium homeostasis. The literature provides a wealth of qualitative and/or quantitative descriptions of cellular mechanisms, bone dynamics, associated organ dynamics, related disease sequela, and results of therapeutic interventions. We present a physiologically based mathematical model of integrated calcium homeostasis and bone biology constructed from literature data. The model includes relevant cellular aspects with major controlling mechanisms for bone remodeling and calcium homeostasis and appropriately describes a broad range of clinical and therapeutic conditions. These include changes in plasma parathyroid hormone (PTH), calcitriol, calcium and phosphate (PO4), and bone-remodeling markers as manifested by hypoparathyroidism and hyperparathyroidism, renal insufficiency, daily PTH 1-34 administration, and receptor activator of NF-kappaB ligand (RANKL) inhibition. This model highlights the utility of systems approaches to physiologic modeling in the bone field. The presented bone and calcium homeostasis model provides an integrated mathematical construct to conduct hypothesis testing of influential system aspects, to visualize elements of this complex endocrine system, and to continue to build upon iteratively with the results of ongoing scientific research.

Model structure and control of bone remodeling: a theoretical study

It is generally accepted that RANKL is highly expressed in osteoblast precursor cells while OPG is highly expressed in mature osteoblasts, but to date no functional utility to the BMU has been proposed for this particular ligand-decoy-receptor expression profile. As discovered in the mid 90s, the RANK-RANKL-OPG signaling cascade is a major signaling pathway regulating bone remodeling. In this paper we study theoretically the functional implications of particular RANKL/OPG expression profiles on bone volume. For this purpose we formulate an extended bone-cell dynamics model describing functional behaviour of basic multicellular units (BMUs) responsible for bone resorption and formation. This model incorporates the RANK-RANKL-OPG signaling together with the regulating action of TGF-beta on bone cells. The bone-cell population model employed here builds on the work of Lemaire et al. (2004) [1], but incorporates the following significant modifications: (i) addition of a rate equation describing changes in bone volume with time as the key 'output function' tracking functional behaviour of BMUs, (ii) a rate equation describing release of TGF-beta from the bone matrix, (iii) expression of OPG and RANKL on both osteoblastic cell lines, and (iv) modified activator/repressor functions. Using bone volume as a functional selection criterion, we find that there is a preferred arrangement for ligand expression on particular cell types, and further, that this arrangement coincides with biological observations. We then investigate the model parameter space combinatorially, searching for preferred 'groupings' of changes in differentiation rates of various cell types. Again, a criterion of bone volume change is employed to identify possible ways of optimally controlling BMU responses. While some combinations of changes in differentiation rates are clearly unrealistic, other combinations of changes in differentiation rates are potentially functionally significant. Most importantly, the combination of parameter changes representing the signaling pathway for TGF-beta gives a unique result that appears to have a clear biological rationale. The methodological approach for the investigation of model structure described here offers a theoretical explanation as to why TGF-beta has its particular suite of biological effects on bone-cell differentiation rates.

Materials in particulate form for tissue engineering. 2. Applications in bone

Materials in particulate form have been the subjects of intensive research in view of their use as drug delivery systems. While within this application there are still issues to be addressed, these systems are now being regarded as having a great potential for tissue engineering applications. Bone repair is a very demanding task, due to the specific characteristics of skeletal tissues, and the design of scaffolds for bone tissue engineering presents several difficulties. Materials in particulate form are now seen as a means of achieving higher control over parameters such as porosity, pore size, surface area and the mechanical properties of the scaffold. These materials also have the potential to incorporate biologically active molecules for release and to serve as carriers for cells. It is believed that the combination of these features would create a more efficient approach towards regeneration. This review focuses on the application of materials in particulate form for bone tissue engineering. A brief overview of bone biology and the healing process is also provided in order to place the application in its broader context. An original compilation of molecules with a documented role in bone tissue biology is listed, as they have the potential to be used in bone tissue engineering strategies. To sum up this review, examples of works addressing the above aspects are presented.

Allosteric control model of bone remodelling containing periodical modes

To help to understand the modelling process that occurs when a scaffold is implanted it is vital to understand the rather complex bone remodelling process prevalent in native bone. We have formulated a mathematical model that predicts osteoactivity both in scaffolds, as well as in bone in vivo and could set a basis for the more detailed allosteric models. The model is extended towards a bio-cybernetic vision of basic multicellular unit (BMU) action, when some of the regulation loops have been modified to reflect the allosteric control mechanisms, developed by Michaels-Menten, Hill, Koshland-Nemethy-Filmer, Monod-Wyman-Changeux. By implementation of this approach a four-dimensional system was obtained that shows steady cyclic behaviour using a wide range of constants with clear biological meaning. We have observed that a local steady state appears as a limiting cycle in multi-dimensional phase space and this is discussed in this paper. Physiological interpretation of this limiting four-dimension cycle possibly related to a conservative-like value has been proposed. Analysis and simulation of the model has shown an analogy between this conservative value, as a kind of substrate-energy regenerative potential of the bone remodelling system with a molecular nature, and to the classical physical value--energy. This dynamic recovery potential is directed against both mechanical and biomechanical damage to the bone. Furthermore, the current model has credibility when compared to the normal bone remodelling process. In the framework of widely recognised Hill mechanisms of allosteric regulation the cyclic attractor, described formerly for a pure cellular model, prevails for different forms of feedback control. This result indicates the viability of the proposed existence of a conservative value (analogous to energy) that characterises the recovery potential of the bone remodelling cycle. Linear stability analysis has been performed in order to determine the robustness of the basic state, however, additional work is required to study a wider range of constants.

Influence of hormones on osteogenic differentiation processes of mesenchymal stem cells

Bone development, regeneration and maintenance are governed by osteogenic differentiation processes from mesenchymal stem cells through to mature bone cells, which are directed by local growth and differentiation factors and modulated strongly by hormones. Mesenchymal stem cells develop from both mesoderm and neural crest and can give rise to development, regeneration and maintenance of mesenchymal tissues, such as bone, cartilage, muscle, tendons and discs. There are only limited data regarding the effects of hormones on early events, such as regulation of stemness and maintenance of the mesenchymal stem cell pool. Hormones, such as estrogens, vitamin D-hormone and parathyroid hormone, besides others, are important modulators of osteogenic differentiation processes and bone formation, starting off with fate decision and the development of osteogenic offspring from mesenchymal stem cells, which end up in osteoblasts and osteocytes. Hormones are involved in fetal bone development and regeneration and, in childhood, adolescence and adulthood, they control adaptive needs for growth and reproduction, nutrition, physical power and crisis adaptation. As in other tissues, aging in mesenchymal stem cells and their osteogenic offspring is accompanied by the accumulation of genomic and proteomic damage caused by oxidative burden and insufficient repair. Failsafe programs, such as apoptosis and cellular senescence avoid tumorigenesis. Hormones can influence the pace of such events, thus supporting the quality of tissue regeneration in aging organisms in vivo; for example, by delaying osteoporosis development. The potential for hormones in systemic therapeutic strategies is well appreciated and some concepts are approved for clinical use already. Their potential for cell-based therapeutic strategies for tissue regeneration is probably underestimated and could enhance the quality of tissue-engineering constructs for transplantation and the concept of in situ-guided tissue regeneration.

On allosteric control model of bone turnover cycle containing osteocyte regulation loop

One approach to developing a mathematical model that predicts osteoactivity both in bio-scaffolds, as well as the in bone tissue in vivo, is based on a bio-cybernetic vision of basic multicellular unit (BMU) action. In the case of the model presented in this paper, some of the loops of regulation have been modified to reflect the range of allosteric control mechanisms: Michaelis-Menten, Hill, Adair, Koshland-Nemethy-Filmer (KNF), Monod-Wyman-Changeux (MWC). This approach has resulted in a four-dimensional system that shows steady cyclic behaviour using a range of constants with clear biological meaning. The initial findings suggesting that a steady state appears as a cycle in multidimensional phase space and this is discussed in this paper. The existence of this cycle in the osteoclasts-osteoblasts-osteocytes-bone subspace indicates that there is a conservative value along steady trajectories for this dynamic system. Biophysical interpretation of this conservative value has been proposed as a kind of substrate-energy regenerative potential of the bone remodelling system with a similarity to the classical physical value-energy. Such a recovery "potential" is directed against both mechanical and biomechanical damage to the bone. The current model has credibility when compared to the normal bone remodelling process. In the framework of widely recognised Michaelis-Menten mechanisms of allosteric regulation the cyclic attractor, described formerly for a pure cellular model, prevails for different forms of feedback control. This finding demonstrates the viability of the suggestion of the subsistence of conservative value (analogous to energy) that characterises the recovery potential of the bone remodelling cycle. The results indicate that the robust behaviour of the model is maintained from the simple cellular level to the molecular biochemical level of regulation.

Bone Remodeling in Health and Disease: Lessons From Mathematical Modeling

Parathyroid hormone is the single anabolic treatment for osteoporosis currently approved by U.S. Food and Drug Administration. The physiology underlying anabolic actions of parathyroid hormone remains mysterious, since only when applied intermittently, does it increase bone mass. This study employs mathematical modeling to consider multiple concomitant effects of parathyroid hormone and local regulators on bone turnover. Remarkably, due to coupling between osteoclasts and osteoblasts, anabolic effects of parathyroid hormone emerged from a single action-stimulation of osteoclastic bone resorption. This study provides a novel conceptual framework for the development of highly desirable anabolic treatments for bone diseases.

Mathematical modeling and analysis of force induced bone growth

Bone is a dynamic living tissue that undergoes continuous adaptation of its mass and structure in response to mechanical and biological environment demands. Studies of bone adaptation have focused on metabolic or mechanical stimulus, but mathematical models of bone adaptation considering both, are not available by now. In this paper, we propose a mathematical model of bone adaptation during a remodeling cycle due to mechanical stimulus with the introduction of osteocytes as mechanotransducers. The model captures qualitatively very well the bone adaptation and cell interactions during the bone remodeling.

Response to continuous and pulsatile PTH dosing: a mathematical model for parathyroid hormone receptor kinetics

In this paper, we propose a mathematical model for parathyroid hormone receptor (PTH1R) kinetics, focusing on the receptor's response to PTH dosing to discern bone formation responses from bone resorption. The PTH1R is a major target for new osteoporosis treatments, as pulsatile PTH dosing has been shown to induce net bone formation in both animals and humans, and PTH(1-34) was recently FDA approved for the treatment of post-menopausal osteoporosis. PTH has also been shown to cause net bone loss when given continuously, so that the net action of PTH on bone is dependent on the dosing pattern. We have developed a simplified two-state receptor kinetics model for the PTH1R, based on the concepts of Segel et al., to distinguish the activity of active and inactive receptor and receptor-ligand complexes. The goal is to develop a plausible model of the minimal essential biological relationships necessary for understanding the responses to PTH dosing. A two-state model is able to effectively discriminate between continuous and pulsatile PTH dosing using the active species as surrogates for the downstream anabolic response. For continuous PTH dosing, the model predicts a desensitized system dominated by the inactive receptor and complex, consistent with downstream net bone loss that has been demonstrated experimentally. Using pulsatile PTH dosing, the model system predicts a highly sensitized state dominated by the active receptor and complex, corresponding to net bone formation. These results are consistent with the hypothesis that the kinetics of the receptor plays a critical role in the downstream effects of PTH dosing. Moreover, these results indicate that within a range of biologically relevant PTH doses, the two-state model is able to capture the differential behavior of the system for both continuous and pulsatile PTH dosing. The development of such a model provides a rational basis for developing more biologically extensive models that may support the design of optimal dosing strategies for PTH-based anti-osteoporosis treatments. Moreover, this model provides a unique starting point from which to design experiments investigating PTH receptor biology.

Modeling the interactions between osteoblast and osteoclast activities in bone remodeling

We propose a mathematical model explaining the interactions between osteoblasts and osteoclasts, two cell types specialized in the maintenance of the bone integrity. Bone is a dynamic, living tissue whose structure and shape continuously evolves during life. It has the ability to change architecture by removal of old bone and replacement with newly formed bone in a localized process called remodeling. The model described here is based on the idea that the relative proportions of immature and mature osteoblasts control the degree of osteoclastic activity. In addition, osteoclasts control osteoblasts differentially depending on their stage of differentiation. Despite the tremendous complexity of the bone regulatory system and its fragmentary understanding, we obtain surprisingly good correlations between the model simulations and the experimental observations extracted from the literature. The model results corroborate all behaviors of the bone remodeling system that we have simulated, including the tight coupling between osteoblasts and osteoclasts, the catabolic effect induced by continuous administration of PTH, the catabolic action of RANKL, as well as its reversal by soluble antagonist OPG. The model is also able to simulate metabolic bone diseases such as estrogen deficiency, vitamin D deficiency, senescence and glucocorticoid excess. Conversely, possible routes for therapeutic interventions are tested and evaluated. Our model confirms that anti-resorptive therapies are unable to partially restore bone loss, whereas bone formation therapies yield better results. The model enables us to determine and evaluate potential therapies based on their efficacy. In particular, the model predicts that combinations of anti-resorptive and anabolic therapies provide significant benefits compared with monotherapy, especially for certain type of skeletal disease. Finally, the model clearly indicates that increasing the size of the pool of preosteoblasts is an essential ingredient for the therapeutic manipulation of bone formation. This model was conceived as the first step in a bone turnover modeling platform. These initial modeling results are extremely encouraging and lead us to proceed with additional explorations into bone turnover and skeletal remodeling.