A unified framework of cell population dynamics and mechanical stimulus using a discrete approach in bone remodelling

Mechanobiological Model of Endochondral Ossification and Trabecular Bone Modeling

This work presents the integration of mechanobiological models to predict the natural evolution of bone modeling and remodeling processes to obtain the architecture of trabecular bone from the embryonic stage in mammalians. Bone modeling is simulated in two and three dimensions using a reaction-diffusion mechanism with parameters in Turing space. This approach involves the interaction of two molecular factors (VEGF and MMP13) released by hypertrophic chondrocytes that diffuse and interact within a hyaline cartilage matrix. The bone remodeling process follows the model proposed by Komarova et al. employing a set of differential equations to describe autocrine and paracrine interactions between osteoblastic and osteoclastic cells, determining cellular dynamics and changes in bone mass. Bidimensional and tridimensional results for a cartilage portion predict morphological self-organization parameters between VEGF and MMP13, similar to those present in the architecture of immature trabecular bone. These findings suggest that the dynamic properties of molecular factors play a crucial role in the temporal self-organization of bone mineralization metabolism, leading to a heterogeneous trabecular architecture characteristic of primary trabecular bone. Through the three-dimensional bone remodeling model performed on the surface of trabeculae, it is established that equilibrium in population dynamics leads to asynchronous homeostatic remodeling for bone renewal, culminating in the formation of secondary trabecular bone.

Modelling the Effects of Growth and Remodelling on the Density and Structure of Cancellous Bone

A two-stage model is proposed for investigating remodelling characteristics in bone over time and distance to the growth plate. The first stage comprises a partial differential equation (PDE) for bone density as a function of time and distance from the growth plate. This stage clarifies the contributions to changes in bone density due to remodelling and growth processes and tracks the rate at which new bone emanates from the growth plate. The second stage consists of simulating the remodelling process to determine remodelling characteristics. Implementing the second stage requires the rate at which bone moves away from the growth plate computed during the first stage. The second stage is also needed to confirm that remodelling characteristics predicted by the first stage may be explained by a realistic model for remodelling and to compute activation frequency. The model is demonstrated on microCT scans of tibia of juvenile female rats in three experimental groups: sham-operated control, oestrogen deprived, and oestrogen deprived followed by treatment. Model predictions for changes in bone density and remodelling characteristics agree with the literature. In addition, the model provides new insight into the role of treatment on the density of new bone emanating from the growth plate and provides quantitative descriptions of changes in remodelling characteristics beyond what has been possible to ascertain by experimentation alone.

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

Here we developed a spatio-temporal bone remodeling model to simulate the action of Basic Multicelluar Units (BMUs). This model is based on two major extensions of a temporal-only bone cell population model (BCPM). First, the differentiation into mature resorbing osteoclasts and mature forming osteoblasts from their respective precursor cells was modelled as an intermittent process based on precursor cells availability. Second, the interaction between neighbouring BMUs was considered based on a "metabolic cost" argument which warrants that no new BMU will be activated in the neighbourhood of an existing BMU. With the proposed model we have simulated the phases of the remodelling process obtaining average periods similar to those found in the literature: resorption ( ∼ 22 days)-reversal (∼8 days)-formation (∼65 days)-quiescence (560-600 days) and an average BMU activation frequency of ∼1.6 BMUs/year/mm³. We further show here that the resorption and formation phases of the BMU become coordinated only by the presence of TGF-β (transforming growth factor β), i.e., a major coupling factor stored in the bone matrix. TGF-β is released through resorption so upregulating osteoclast apoptosis and accumulation of osteoblast precursors, i.e., facilitating the transition from the resorption to the formation phase at a given remodelling site. Finally, we demonstrate that this model can explain targeted bone remodelling as the BMUs are steered towards damaged bone areas in order to commence bone matrix repair.