The mechanical quality of trabecular bone is influenced by its mineral content and spatial distribution, which is controlled by bone remodelling and mineralisation. Mineralisation kinetics occur in two phases: a fast primary mineralisation and a secondary mineralisation that can last from several months to years. Variations in bone turnover and mineralisation kinetics can be observed in the bone mineral density distribution (BMDD). Here, we propose a statistical spatio-temporal bone remodelling model to study the effects of bone turnover (associated with the activation frequency \(\mathrm {Ac.f}\)) and mineralisation kinetics (associated with secondary mineralisation \(T_\textrm{sec}\)) on BMDD. In this model, individual basic multicellular units (BMUs) are activated discretely on trabecular surfaces that undergo typical bone remodelling periods. Our results highlight that trabecular BMDD is strongly regulated by \(\mathrm {Ac.f}\) and \(T_\textrm{sec}\) in a coupled way. Ca wt% increases with lower \(\mathrm {Ac.f}\) and short \(T_\textrm{sec}\). For example, a \(\mathrm {Ac.f}=\) 4 BMU/year/mm\(^3\) and \(T_\textrm{sec}\) = 8 years result in a mean Ca wt% of 25, which is in accordance with Ca wt% values reported in quantitative backscattered electron imaging (qBEI) experiments. However, for lower \(\mathrm {Ac.f}\) and shorter \(T_\textrm{sec}\) (from 0.5 to 4 years) one obtains a high Ca wt% and a very narrow skew BMDD to the right. This close link between \(\mathrm {Ac.f}\) and \(T_\textrm{sec}\) highlights the importance of considering both characteristics to draw meaningful conclusion about bone quality. Overall, this model represents a new approach to modelling healthy and diseased bone and can aid in developing deeper insights into disease states like osteoporosis.

小梁骨的机械质量受到其矿物质含量和空间分布的影响，而矿物质含量和空间分布受骨重塑和矿化控制。矿化动力学分为两个阶段：快速的初级矿化和可持续数月至数年的次级矿化。在骨矿物质密度分布 (BMDD) 中可以观察到骨转换和矿化动力学的变化。在这里，我们提出了一个统计时空骨重塑模型来研究骨转换（与激活频率\(\mathrm {Ac.f}\)相关）和矿化动力学（与二次矿化\(T_\textrm相关）的影响{sec}\) ) 在 BMDD 上。在此模型中，各个基本多细胞单位 (BMU) 在经历典型骨重塑期的小梁表面上被离散激活。我们的结果强调，小梁 BMDD 受到\(\mathrm {Ac.f}\)和\(T_\textrm{sec}\)以耦合方式强烈调节。Ca wt% 随着较低的\(\mathrm {Ac.f}\)和较短的\(T_\textrm{sec}\)增加。例如，\(\mathrm {Ac.f}=\) 4 BMU/year/mm \(^3\)和\(T_\textrm{sec}\) = 8 年导致平均 Ca wt% 25，这与定量背散射电子成像 (qBEI) 实验中报告的 Ca wt% 值一致。然而，对于较低的\(\mathrm {Ac.f}\)和较短的\(T_\textrm{sec}\)（从 0.5 到 4 年），可以获得较高的 Ca wt% 和向右倾斜的 BMDD 非常窄。\(\mathrm {Ac.f}\)和\(T_\textrm{sec}\)之间的密切联系凸显了考虑这两个特征以得出有关骨质量的有意义的结论的重要性。总体而言，该模型代表了一种对健康和患病骨骼进行建模的新方法，可以帮助深入了解骨质疏松症等疾病状态。