Factors of mineralization dynamics — A mathematical model for microstructural bone remodeling

Abstract

Bone mineralization critically influences bone strength and fracture risk, yet the dependency on bone porosity across the range from cortical to trabecular bone remains incompletely understood. We present a novel mathematical framework that explicitly models bone mineralization dynamics as a function of bone turnover, which can be linked to porosity. Unlike existing fixed-porosity models, our approach incorporates porosity-dependent cellular activity based on remodeling surface availability, enabling analysis across the entire porosity range. We tested three biologically motivated hypotheses to explain mineral content variations with porosity, involving variations in turnover rate, targeted resorption and mineral apposition rate. Through systematic hypothesis testing validated against experimental data, we successfully reproduced the characteristic relationship between material and apparent density observed across varying bone porosities. Results indicate that porosity-dependent turnover and mineral apposition rate primarily drive mineralization. Global sensitivity analysis confirmed the mineral apposition rate as the most influential parameter. Additionally, our analysis supports that dispersion in mid-porosity experimental data can be explained by trabecular microarchitectural variations, specifically the proportion of rod-like versus plate-like structures affecting specific surface area. This framework provides a mechanistic explanation for bone mineralization variations across the porosity range.