Modeling endochondral ossification: Effects of mechanical loading and bone shape

The influence of mechanical and biochemical factors has been extensively studied through the development of mathematical, computational and experimental research, offering insights into bone development and the complex interplay of contributing factors. This knowledge has potential applications in multiple areas of medical science. However, existing models lack flexibility in simulating diverse geometric and loading conditions. This study proposes the development of a model to address these limitations.

A computational approach employing parametric geometry and loading conditions was applied, accounting for the effects of stress on epiphyseal growth. Finite element analyses were conducted iteratively to predict potential sites of secondary ossification based on stress distribution. Three distinct scenarios with varying geometry and loading conditions were evaluated, revealing differences in the presence, number, and spatial distribution of secondary ossification centers (SOCs).

The variation in the onset of SOCs across different configurations and parameter adjustments was analyzed. The model predicts a shift in SOC location influenced by cartilage concavity and width; the formation of two ossification centers in concave heads subjected to dual loading; reduced surface ossification contributing to articular cartilage; and a decrease in the ossification index (OI) with increased volume.

The model emulates the formation of anatomically distinct human joints, though some certain outputs based on non-biological geometries were excluded. Moreover, the model focuses solely on mechanical and geometrical influences, while other aspects of mechanobiology should be incorporated in future work. Nevertheless, the model effectively captures the formation of various human joints and provides a foundation for future studies and diverse applications in medical research, particularly in bone growth disorders.