A semi-empirical cell dynamics model for bone turnover under external stimulus.

Bone remodeling is a biological process involving resorption and formation phases. It is regulated by external stimuli, bone cells, and ion levels. Prior research has shown that bone turnover is influenced by mechanical strain and calcium balance. However, the precise interaction between these factors remains unclear. This gap motivated the development of a model to simulate bone turnover under various strain conditions. Researchers have not yet resolved how different types of strain affect the timing of bone formation. The biological coupling between resorption and formation is complex and not fully understood. This study aims to address these uncertainties by using a semi-empirical approach. Understanding bone turnover is essential for clinical applications in bone health and disease.

This study aimed to develop a semi-empirical model of bone remodeling that accounts for external stimuli and biological interactions. The model focuses on the coupling between resorption and formation phases. It incorporates bone mass, bone fluid calcium, and three major bone cell types. The researchers wanted to investigate how different strain stimuli affect bone turnover. They also sought to determine the role of bone fluid calcium balance in the process. The model was designed to reflect known biological mechanisms and timeframes. The goal was to predict the formation time under various strain and calcium conditions. These predictions could help clarify the effects of mechanical loading on bone health.

The model uses a sequence of ordinary differential equations (ODEs) to represent the activation, resorption, and formation phases. Each phase is solved separately and sequentially to mimic biological coupling. The resorption phase is fixed at 20 days and 0.5% bone loss. Formation time is calculated as an output of the model. The model was tested under different strain stimuli and calcium balance conditions. Strain levels included constant 1000 and 2000 microstrain, strain-free, and monotonic increasing strain. Bone fluid calcium balance and imbalance were also simulated. The model outputs formation time for complete turnover under each condition.

Under bone fluid calcium balance, complete turnover occurred after 130 days of formation with constant 1000 microstrain. With 2000 microstrain, turnover occurred after 47 days of formation. Strain-free conditions required 173 days of formation for turnover. Monotonic increasing strain from 1000 to 2000 microstrain led to turnover after 80 days. Under calcium imbalance, turnover took 261 days with 1000 microstrain. Strain-free conditions under imbalance prevented turnover. Dynamic input strain at 1 Hz and 1000 microstrain amplitude did not affect these results. The model supports the idea that increased strain accelerates bone turnover.

The model predicts that bone turnover is influenced by strain levels and calcium balance. Increased strain shortens the formation phase, while strain absence delays or prevents turnover. Formation time under monotonic increasing strain is intermediate to constant strain levels. These findings align with Frost's mechanostat theory and known biology. The model does not claim to explain all aspects of bone remodeling. It focuses on the interaction between external stimuli and biological factors. The results suggest that mechanical loading plays a key role in bone health. The model provides a framework for further investigation into bone turnover mechanisms.