Search

Bone remodeling is regulated by the interaction between different cells and tissues across many spatial and temporal scales. Notably, in silico models are regarded as powerful tools to further understand the signaling pathways that regulate this intricate spatial cellular interplay. To this end, we have established a 3D multiscale micro-multiphysics agent-based (micro-MPA) in silico model of trabecular bone remodeling using longitudinal in vivo data from the sixth caudal vertebra (CV6) of PolgA (D257A/D257A) mice, a mouse model of premature aging. Our in silico model includes a variety of cells as single agents and receptor-ligand kinetics, mechanomics, diffusion and decay of cytokines which regulate the cells' behavior. We highlighted its capabilities by simulating trabecular bone remodeling in the CV6 of five mice over 4 weeks and we evaluated the static and dynamic morphometry of the trabecular bone microarchitecture. Based on the progression of the average trabecular bone volume fraction (BV/TV), we identified a configuration of the model parameters to simulate homeostatic trabecular bone remodeling, here named basal. Crucially, we also produced anabolic, anti-anabolic, catabolic and anti-catabolic responses with an increase or decrease by one standard deviation in the levels of osteoprotegerin (OPG), receptor activator of nuclear factor kB ligand (RANKL), and sclerostin (Scl) produced by the osteocytes. Our results showed that changes in the levels of OPG and RANKL were positively and negatively correlated with the BV/TV values after 4 weeks in comparison to basal levels, respectively. Conversely, changes in Scl levels produced small fluctuations in BV/TV in comparison to the basal state. From these results, Scl was deemed to be the main driver of equilibrium while RANKL and OPG were shown to be involved in changes in bone volume fraction with potential relevance for age-related bone features. Ultimately, this micro-MPA model provides valuable insights into how cells respond to their local mechanical environment and can help to identify critical pathways affected by degenerative conditions and ageing., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Boaretti, Marques, Ledoux, Singh, Kendall, Wehrle, Kuhn, Bansod, Schulte and Müller.)

Bone mechanobiology is the study of the physical, biological and mechanical processes that continuously affect the multiscale multicellular system of the bone from the organ to the molecular scale. Current knowledge derives from experimental studies, which are often limited to gathering qualitative data in a cross-sectional manner, up to a restricted number of time points. Moreover, the simultaneous collection of information about 3D bone microarchitecture, cell activity as well as protein distribution and level is still a challenge. In silico models can expand qualitative information with hypothetical quantitative systems, which allow quantification, testing and comparison to existing quantifiable experimental data. An overview of multiscale, multiphysics, agent-based and hybrid techniques and their applications to bone mechanobiology is provided in the present review. The study analysed how mechanical signals, cells and proteins can be modelled in silico to represent bone remodelling and adaptation. Hybrid modelling of bone mechanobiology could combine the methods used in multiscale, multiphysics and agent-based models into a single model, leading to a unified and comprehensive understanding of bone mechanobiology. Numerical simulations of in vivo multicellular systems aided in hypothesis testing of such in silico models. Recently, in silico trials have been used to illustrate the mechanobiology of cells and signalling pathways in clinical biopsies and animal bones, including the effects of drugs on single cells and signalling pathways up to the organ level. This improved understanding may lead to the identification of novel therapies for degenerative diseases such as osteoporosis.

The piezoelectricity of bone is known to play a crucial role in bone adaptation and remodeling. The application of an external stimulus such as mechanical strain or electric field has the potential to enhance bone formation and implant osseointegration. Therefore, in the present study, the objective is to investigate bone remodeling under electromechanical stimulation as a step towards establishing therapeutic strategies. For the first time, piezoelectric bone remodeling in the human proximal tibia under electro-mechanical loads was analyzed using the finite element method in an open-source framework. The predicted bone density distributions were qualitatively and quantitatively assessed by comparing with the computed tomography (CT) scan and the bone mineral density (BMD) calculated from the CT, respectively. The effect of model parameters such as uniform initial bone density and reference stimulus on the final density distribution was investigated. Results of the parametric study showed that for different values of initial bone density the model predicted similar but not identical final density distribution. It was also shown that higher reference stimulus value yielded lower average bone density at the final time. The present study demonstrates an increase in bone density as a result of electrical stimulation. Thus, to minimize bone loss, for example, due to physical impairment or osteoporosis, mechanical loads during daily physical activities could be partially replaced by therapeutic electrical stimulation., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Bansod, Kebbach, Kluess, Bader and van Rienen.)

Bone tissue exhibits piezoelectric properties and thus is capable of transforming mechanical stress into electrical potential. Piezoelectricity has been shown to play a vital role in bone adaptation and remodelling processes. Therefore, to better understand the interplay between mechanical and electrical stimulation during these processes, strain-adaptive bone remodelling models without and with considering the piezoelectric effect were simulated using the Python-based open-source software framework. To discretise numerical attributes, the finite element method (FEM) was used for the spatial variables and an explicit Euler scheme for the temporal derivatives. The predicted bone apparent density distributions were qualitatively and quantitatively evaluated against the radiographic scan of a human proximal femur and the bone apparent density calculated using a bone mineral density (BMD) calibration phantom, respectively. Additionally, the effect of the initial bone density on the resulting predicted density distribution was investigated globally and locally. The simulation results showed that the electrically stimulated bone surface enhanced bone deposition and these are in good agreement with previous findings from the literature. Moreover, mechanical stimuli due to daily physical activities could be supported by therapeutic electrical stimulation to reduce bone loss in case of physical impairment or osteoporosis. The bone remodelling algorithm implemented using an open-source software framework facilitates easy accessibility and reproducibility of finite element analysis made.

Natural bone remodeling is the mechanism that regulates the relationship between bone morphology and external mechanical loads applied to it. This phenomenon has been studied extensively, including multiple numerical models that have been formulated to predict the density distribution and its evolution in several bone types. However, despite these models, bone remodeling mechanism under different stimuli is still not well understood. We implemented a recently proposed electromechanically driven bone remodeling model that encompasses both mechanical and therapeutic electrical stimuli using an open-source software framework, and studied a two-dimensional (2D) plate model and a femur bone model, respectively. For discretization, we employed the finite element method (FEM) for the spatial quantities and Euler scheme for the time derivatives. The simulation results demonstrate that the density distribution is changed under electrical stimulation, generally resulting in a greater mass deposition. This study supports the possibility of enhancing and accelerating the bone remodeling process via simultaneous application of electrical and mechanical stimulus.

Mechanical interaction of cell with extracellular environment affects its function. The mechanisms by which mechanical stimuli are sensed and transduced into biochemical responses are still not well understood. Considering this, two finite element (FE) bendo-tensegrity models of a cell in different states are proposed with the aim to characterize cell deformation under different mechanical loading conditions: a suspended cell model elucidating the global response of cell in tensile test simulation and an adherent cell model explicating its local response in atomic force microscopy (AFM) indentation simulation. The force-elongation curve obtained from tensile test simulation lies within the range of experimentally obtained characteristics of smooth muscle cells (SMCs) and illustrates a nonlinear increase in reaction force with cell stretching. The force-indentation curves obtained from indentation simulations lie within the range of experimentally obtained curves of embryonic stem cells (ESCs) and exhibit the influence of indentation site on the overall reaction force of cell. Simulation results have demonstrated that actin filaments (AFs) and microtubules (MTs) play a crucial role in the cell stiffness during stretching, whereas actin cortex (AC) along with actin bundles (ABs) and MTs are essential for the cell rigidity during indentation. The proposed models quantify the mechanical contribution of individual cytoskeletal components to cell mechanics and the deformation of nucleus under different mechanical loading conditions. These results can aid in better understanding of structure-function relationships in living cells.