Papastavrou Areti, Pivonka Peter, Schmidt Ina, Steinmann Paul
Faculty of Mechanical Engineering, Technische Hochschule Nürnberg Georg Simon Ohm, Nuremberg, Germany.
School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, Australia.
Biomech Model Mechanobiol. 2025 Jun;24(3):975-998. doi: 10.1007/s10237-025-01948-5. Epub 2025 May 3.
Remodelling of cancellous bone due to the combined activity of osteoclasts and osteoblasts at the cellular scale has notable repercussions both at the meso (tissue) as well as the macro (organ) scale. At the meso scale, trabeculae adapt their geometry, typically in terms of their cross section, whereas the nominal bone density evolves at the macro scale, all in response to habitual mechanical loading and its perturbations. To capture this intricate scale coupling, we here propose a novel conceptual three-scale approach to the remodelling of cancellous bone. Therein, we combine a detailed bone cell population model at the cellular scale with an idealised trabecular truss network model with adaptive cross sections, that are driven by the cell population model, at the meso scale, which is eventually upscaled to a continuum bone density adaption model at the macro scale. Algorithmically, we solve the meso and macro problems concurrently within a finite element setting and update the cell activity in a staggered fashion. Our benchmark simulations demonstrate the applicability and effectivity of the three-scale approach to analyse bone remodelling in health and disease (here exemplified for the example of osteoporosis) with rich details, e.g. evolving anisotropy, resolved at each scale.
在细胞尺度上，破骨细胞和成骨细胞的联合活动导致的松质骨重塑，在中观（组织）和宏观（器官）尺度上都有显著影响。在中观尺度上，小梁会调整其几何形状，通常是在横截面方面，而名义骨密度则在宏观尺度上演变，所有这些都是对习惯性机械负荷及其扰动的响应。为了捕捉这种复杂的尺度耦合，我们在此提出一种新颖的概念性三尺度方法来研究松质骨重塑。其中，我们将细胞尺度上详细的骨细胞群体模型与具有自适应横截面的理想化小梁桁架网络模型相结合，该网络模型在中观尺度上由细胞群体模型驱动，最终在宏观尺度上向上扩展为连续的骨密度适应模型。在算法上，我们在有限元设置中同时求解中观和宏观问题，并以交错方式更新细胞活动。我们的基准模拟证明了这种三尺度方法在分析健康和疾病状态下（这里以骨质疏松症为例）骨重塑的适用性和有效性，能够在每个尺度上详细解析诸如不断变化的各向异性等丰富细节。
