Physiologically based mathematical model of transduction of mechanobiological signals by osteocytes

Advances in computational modeling of cytokine and growth factor dynamics in bone healing: a scoping review

Bone healing is a complex process regulated by intricate biological and mechanical factors and spatially varied regions over time. This scoping review synthesizes current computational models that incorporate cytokines and growth factors, examining their role in bone healing. Through a systematic analysis of 71 studies, this review identifies and categorizes the modeling methodologies used, including mathematical, finite element, agent-based, mechanobiological, pharmacobiological, and hybrid approaches. The findings highlight the predominant use of mathematical models while noting a recent shift toward more sophisticated techniques like finite element and agent-based models. Key cytokines and growth factors, such as TGF-β, RANK-RANKL-OPG, and PTH, are repeatedly used, underscoring their essential roles in regulating cellular processes. This review also analyzes parameter selection and validation strategies, identifying gaps in current practices and emphasizing the need for high-quality experimental validation to improve model reliability. Some bibliometric analyses provide insights into citation networks and keyword co-occurrence, illustrating influential studies in the field and central themes. The findings offer a foundation for future research to enhance model accuracy, aiming toward more predictive and clinically relevant models accounting for biology and mechanics in bone healing.

Prediction of cortical bone mineral apposition rate in response to loading using an adaptive neuro-fuzzy inference system

Daily activities such as aerobic movements and athletic events found effective in mitigating bone loss as it promotes osteogenesis. Computational model considered normal strain, or strain energy density as a stimulus to predict site specific osteogenesis. This model, however, fails to predict site specific osteogenesis as cortical bone surfaces exhibit different remodelling rate to mechanical loading. Remodelling rate or mineral apposition rate depends upon the loading parameters such as loading cycle, frequency, and magnitude of strain. Therefore, the present study aims to develop an adaptive neuro-fuzzy inference system (ANFIS) model for finding a robust relationship between loading parameters like strain magnitude, frequency, and cycle, and a bone remodelling parameter i.e. mineral apposition rate (MAR). The model is trained, tested, and checked with the experimental data. The results indicate that ANFIS model outperformed state of the art Artificial Neural Network (ANN) models during the prediction of MAR at periosteal and endosteal surface. A strong corelation R² = 0.92 and R² = 0.97 was observed at 70% of the input data at periosteal and endosteal surface respectively. Result concludes that endosteal surface was more promisable as compared to periosteal surface in predicting accurate MAR. The outcomes of present study may be used to precisely predict site-specific osteogenesis in cortical bone as function of loading parameters.

Local stimulation of osteocytes using a magnetically actuated oscillating beam

Mechanical loading on bone tissue is an important physiological stimulus that plays a key role in bone growth, fracture repair, and treatment of bone diseases. Osteocytes (bone cells embedded in bone matrix) are well accepted as the sensor cells to mechanical loading and play a critical role in regulating the bone structure in response to mechanical loading. To understand the response of osteocytes to differential mechanical stimulation in physiologically relevant arrangements, there is a need for a platform which can locally stimulate bone cells with different levels of fluid shear stress. In this study, we developed a device aiming to achieve non-contact local mechanical stimulation of osteocytes with a magnetically actuated beam that generates the fluid shear stresses encountered in vivo. The stimulating beam was made from a composite of magnetic powder and polymer, where a magnetic field was used to precisely oscillate the beam in the horizontal plane. The beam is placed above a cell-seeded surface with an estimated gap height of 5 μm. Finite element simulations were performed to quantify the shear stress values and to generate a shear stress map in the region of interest. Osteocytes were seeded on the device and were stimulated while their intracellular calcium responses were quantified and correlated with their position and local shear stress value. We observed that cells closer to the oscillating beam respond earlier compared to cells further away from the local shear stress gradient generated by the oscillating beam. We have demonstrated the capability of our device to mimic the propagation of calcium signalling to osteocytes outside of the stimulatory region. This device will allow for future studies of osteocyte network signalling with a physiologically accurate localized shear stress gradient.

Micro-finite-element method to assess elastic properties of trabecular bone at micro- and macroscopic level

OBJECTIVE OF THE STUDY

The objective of the present study is to assess the mechanical behavior of trabecular bone based on microCT imaging and micro-finite-element analysis. In this way two methods are detailed: (i) direct determination of macroscopic elastic property of trabecular bone; (ii) inverse approach to assess mechanical properties of trabecular bone tissue.

PATIENTS

Thirty-five females and seven males (forty-two subjects) mean aged (±SD) 80±11.7 years from hospitals of Assistance publique-Hôpitaux de Paris (AP-HP) diagnosed with osteoporosis following a femoral neck fracture due to a fall from standing were included in this study.

MATERIALS AND METHODS

Fractured heads were collected during hip replacement surgery. Standardized bone cores were removed from the femoral head's equator by a trephine in a water bath. MicroCT images acquisition and analysis were performed with CTan^® software and bone volume fraction was then determined. Micro-finite-element simulations were per-formed using Abaqus 6.9-2^® software in order to determine the macroscopic mechanical behaviour of the trabecular bone. After microCT acquisition, a longitudinal compression test was performed and the experimental macroscopic Young's Modulus was extracted. An inverse approach based on the whole trabecular bone's mechanical response and micro-finite-element analysis was performed to determine microscopic mechanical properties of trabecular bone.

RESULTS

In the present study, elasticity of the tissue was shown to be similar to that of healthy tissue but with a lower yield stress.

CONCLUSION

Classical histomorphometric analysis form microCT imaging associated with an inverse micro-finite-element method allowed to assess microscopic mechanical trabecular bone parameters.

From mechanical stimulus to bone formation: A review

Bone is a remarkable tissue that can respond to external stimuli. The importance of mechanical forces on the mass and structural development of bone has long been accepted. This adaptation behaviour is very complex and involves multidisciplinary concepts, and significant progress has recently been made in understanding this process. In this review, we describe the state of the art studies in this area and highlight current insights while simultaneously clarifying some basic yet essential topics related to the origin of mechanical stimulus in bone, the biomechanisms associated with mechanotransduction, the nature of physiological bone stimuli and the test systems most commonly used to study the mechanical stimulation of bone.

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.

Mathematical modeling of postmenopausal osteoporosis and its treatment by the anti-catabolic drug denosumab

Denosumab, a fully human monoclonal antibody, has been approved for the treatment of postmenopausal osteoporosis. The therapeutic effect of denosumab rests on its ability to inhibit osteoclast differentiation. Here, we present a computational approach on the basis of coupling a pharmacokinetics model of denosumab with a pharmacodynamics model for quantifying the effect of denosumab on bone remodeling. The pharmacodynamics model comprises an integrated systems biology-continuum micromechanics approach, including a bone cell population model, considering the governing biochemical factors of bone remodeling (including the action of denosumab), and a multiscale micromechanics-based bone mechanics model, for implementing the mechanobiology of bone remodeling in our model. Numerical studies of postmenopausal osteoporosis show that denosumab suppresses osteoclast differentiation, thus strongly curtailing bone resorption. Simulation results also suggest that denosumab may trigger a short-term bone volume gain, which is, however, followed by constant or decreasing bone volume. This evolution is accompanied by a dramatic decrease of the bone turnover rate by more than one order of magnitude. The latter proposes dominant occurrence of secondary mineralization (which is not anymore impeded through cellular activity), leading to higher mineral concentration per bone volume. This explains the overall higher bone mineral density observed in denosumab-related clinical studies.

Endocortical bone loss in osteoporosis: the role of bone surface availability

Age-related bone loss and postmenopausal osteoporosis are due to a dysregulation of bone remodelling in which less bone is reformed than resorbed. This dysregulation of bone remodelling does not occur with equal strength in all bone regions. Loss of bone is more pronounced near the endocortical surface. This leads to thinning of the cortical wall proceeding from the endosteum, a process sometimes called 'trabecularisation'. In this paper, we investigate the influence of the nonuniform distribution of bone surface within bone tissue for osteoporotic bone losses. We use a spatio-temporal computational model of bone remodelling in which microstructural changes of bone tissue are represented by a phenomenological relationship between bone specific surface and bone porosity. The simulation of an osteoporotic condition by our model shows that the evolution of bone porosity within a bone cross section is significantly influenced by the nonuniform availability of bone surface. Greater bone loss occurs near the endocortical wall, leading to cortical wall thinning and to an expansion of the medullary cavity similar to cross-sectional observations from human femur midshafts. Our model suggests that the rate of cortical wall thinning is fast/slow in the presence/absence of an adjacent trabecular or trabecularised bone compartment.

Textural versus electrostatic exclusion-enrichment effects in the effective chemical transport within the cortical bone: a numerical investigation

Interstitial fluid within bone tissue is known to govern the remodelling signals' expression. Bone fluid flow is generated by skeleton deformation during the daily activities. Due to the presence of charged surfaces in the bone porous matrix, the electrochemical phenomena occurring in the vicinity of mechanosensitive bone cells, the osteocytes, are key elements in the cellular communication. In this study, a multiscale model of interstitial fluid transport within bone tissues is proposed. Based on an asymptotic homogenization method, our modelling takes into account the physicochemical properties of bone tissue. Thanks to this multiphysical approach, the transport of nutrients and waste between the blood vessels and the bone cells can be quantified to better understand the mechanotransduction of bone remodelling. In particular, it is shown that the electrochemical tortuosity may have stronger implications in the mass transport within the bone than the purely morphological one.

The effect of rotative stress on CAII, FAS, FASL, OSCAR, and TRAP gene expression in osteoclasts

This study was designed to explore the effects of rotative stress on carbonic anhydrase II (CAII), TNF receptor superfamily member 6 (FAS), FAS ligand (FASL), osteoclast-associated receptor (OSCAR), and tartrate-resistant acid phosphatase (TRAP) gene expression in osteoclasts. Osteoclasts were induced from RAW264.7 cells cultured in medium containing recombinant murine soluble receptor activator of NF-Kβ ligand (sRANKL). The mRNA and protein expression of CAII, FAS, FASL, OSCAR, and TRAP genes in osteoclasts was detected by RT-PCR and Western blot, respectively, after osteoclasts were loaded at various rotative stress strengths and times. No significant differences in mRNA and protein expression were observed between any of the control groups (P > 0.05). Importantly, rotative stress had a significant effect on the mRNA and protein expression of these genes (P < 0.05). We found a negative relationship between rotative stress strength and prolonged loading time and the expression of FAS/FASL genes in osteoclasts. In addition, there was a positive relationship between rotative stress strength and prolonged loading time and the expression of CAII, OSCAR, or TRAP genes in osteoclasts. Based on these results, rotative stress has a significant effect on CAII, FAS, FASL, OSCAR, and TRAP gene expression in osteoclasts.

Mechanical stress induces bone formation in the maxillary sinus in a short-term mouse model

OBJECTIVES

Clinicians occasionally face the challenge of moving a tooth through the maxillary sinus. The objective of this study was to evaluate tissue remodeling during tooth movement into the maxillary sinus, more specifically as regards to bone formation.

MATERIALS AND METHODS

The maxillary first molar of 20 male mice was moved toward the palatal side by a nickel-titanium super elastic wire for 1 to 14 days, and the bone remodeling around the root was evaluated using histomorphometry and immunodetection of bone-restricted Ifitm-like (Bril) protein, a novel marker of active bone formation.

RESULTS

When mechanical stress was applied to the tooth, the periodontal ligament on the palatal side was immediately compressed to approximately half of its original width by the tipping movement of the tooth. At the same time, osteoblasts deposited new bone on the wall of the maxillary sinus prior to bone resorption by osteoclasts on the periodontal side, as evidenced by the high level of expression of Bril at this site. As a result of these sequential processes, bone on the sinus side maintained a consistent thickness during the entire observation period. No root resorption was observed.

CONCLUSIONS

Bone formation on the surface of the maxillary sinus was evoked by mechanotransduction of mechanical stress applied to a tooth over a 2-week period, and was induced ahead of bone resorption on the periodontal ligament side.

CLINICAL RELEVANCE

Mechanical stress can be exploited to induce bone formation in the maxillary sinus so that teeth can be moved into the sinus without losing bone or causing root damage.