Modelo in silico de consolidação de fratura óssea no contexto da osteoporose durante a menopausa

Abstract

Bone remodeling is a complex process regulated by the immune system, involving multiple cellular and molecular events across different temporal and spatial scales. The balance between bone formation and resorption is essential for skeletal stability and may be disrupted, leading to increased resorption due to exacerbated osteoclast activity or reduced osteoblast function. Estrogen plays a protective role in bone resorption; however, its decline during postmenopause promotes this imbalance. Mathematical modeling provides an alternative means of understanding complex processes such as bone remodeling, allowing exploration of the immune system’s influence on bone healing and elucidation of underlying molecular mechanisms. In this work, we build upon a model from the literature, based on coupled nonlinear differential equations, which incorporates complex interactions between immune and bone cells at the fracture site. We propose an updated version of this model to include the effect of estrogen depletion, thereby providing a more accurate representation of bone healing during the pre- and postmenopausal periods. The resulting systems of equations are studied both analytically and numerically. Numerical analysis demonstrated that estradiol reduction compromises bone formation capacity, delays consolidation, and prolongs the persistence of bone debris. These findings corroborate experimental evidence that hormonal decline is strongly associated with increased bone fragility. It is concluded that the updated model provides a quantitative and qualitative framework for investigating the relationship between immunological and hormonal alterations and bone healing, thereby contributing to the understanding of the mechanisms that render postmenopausal women more susceptible to fractures. Moreover, the results highlight the potential of computational modeling to support the development of new therapeutic strategies and pharmacological interventions targeting osteoporosis, ultimately contributing to advances in fracture treatment and drug development.