Abstract
The process of bone remodeling requires a strict coordination of bone resorption and formation in time and space in order to maintain consistent bone quality and quantity. Bone-resorbing osteoclasts and bone-forming osteoblasts are the two major players in the remodeling process. Their coordination is achieved by generating the appropriate number of osteoblasts since osteoblastic-lineage cells govern the bone mass variation and regulate a corresponding number of osteoclasts. Furthermore, diverse hormones, cytokines and growth factors that strongly link osteoblasts to osteoclasts coordinated these two cell populations. The understanding of this complex remodeling process and predicting its evolution is crucial to manage bone strength under physiologic and pathologic conditions. Several mathematical models have been suggested to clarify this remodeling process, from the earliest purely phenomenological to the latest biomechanical and mechanobiological models. In this current article, a general mathematical model is proposed to fill the gaps identified in former bone remodeling models. The proposed model is the result of combining existing bone remodeling models to present an updated model, which also incorporates several important parameters affecting bone remodeling under various physiologic and pathologic conditions. Furthermore, the proposed model can be extended to include additional parameters in the future. These parameters are divided into four groups according to their origin, whether endogenous or exogenous, and the cell population they affect, whether osteoclasts or osteoblasts. The model also enables easy coupling of biological models to pharmacological and/or mechanical models in the future.
Highlights
Fragility fracture rates are growing exponentially, mainly due to population aging
Since osteoblastic-lineage cells have been found to govern the bone mass variation, the mechanical stimulus was included in the proposed model as an exogenous paracrine model acting on osteoblast concentrations, which, in turn, act on the osteoclast concentrations
The focus of this article was to provide a pharmaco-biological bone remodeling model that could be coupled with mechanical models and was extendable to be able to include various parameters, and allowing the simulation of bone physiologic metabolism for pathologic disorders
Summary
Fragility fracture rates are growing exponentially, mainly due to population aging. The World Health Organization has recorded a substantial increase in population growth and aging, with a life expectancy rising from about 65 years old in 2005 up to 73 years old in 2019; while in Africa this latter age is around 64 years old, and it is around 78 years old in Europe and the Western Pacific. The second research group was Lemaire et al [17], who developed a model including the RANK-RANKL-OPG signaling pathway, combined with the influence of the transforming growth factor-β (TGFβ) and the parathyroid hormone (PTH) on bone cell activities, while taking into account the differentiation stages of the osteoblasts and osteoclasts. Coupling mechanical and chemical phenomenon together with mechanosensing [34], which is a lesser-known component of the remodeling process [35,36,37], requires various simplified assumptions Following these steps, with the aim to create a novel mechano-pharmaco-biological model, the current article provides a first step towards this goal. Since osteoblastic-lineage cells have been found to govern the bone mass variation, the mechanical stimulus was included in the proposed model as an exogenous paracrine model acting on osteoblast concentrations, which, in turn, act on the osteoclast concentrations
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