Bone tissue exhibits piezoelectric properties and thus is capable of transforming mechanical stress into electrical potential. Piezoelectricity has been shown to play a vital role in bone adaptation and remodelling processes. Therefore, to better understand the interplay between mechanical and electrical stimulation during these processes, strain-adaptive bone remodelling models without and with considering the piezoelectric effect were simulated using the Python-based open-source software framework. To discretise numerical attributes, the finite element method (FEM) was used for the spatial variables and an explicit Euler scheme for the temporal derivatives. The predicted bone apparent density distributions were qualitatively and quantitatively evaluated against the radiographic scan of a human proximal femur and the bone apparent density calculated using a bone mineral density (BMD) calibration phantom, respectively. Additionally, the effect of the initial bone density on the resulting predicted density distribution was investigated globally and locally. The simulation results showed that the electrically stimulated bone surface enhanced bone deposition and these are in good agreement with previous findings from the literature. Moreover, mechanical stimuli due to daily physical activities could be supported by therapeutic electrical stimulation to reduce bone loss in case of physical impairment or osteoporosis. The bone remodelling algorithm implemented using an open-source software framework facilitates easy accessibility and reproducibility of finite element analysis made.

中文翻译：

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使用开源框架对具有压电效应的骨骼重塑进行有限元分析。

骨组织表现出压电特性，因此能够将机械应力转化为电势。压电已显示在骨骼适应和重塑过程中起着至关重要的作用。因此，为了更好地理解这些过程中机械和电刺激之间的相互作用，使用基于Python的开源软件框架模拟了不考虑压电效应且不考虑压电效应的应变自适应骨骼重塑模型。为了离散化数值属性，对空间变量使用了有限元方法（FEM），对时间导数使用了明确的Euler方案。预测的骨表观密度分布相对于人类近端股骨的放射线照相进行了定性和定量评估，并分别使用骨矿物质密度（BMD）校准体模计算了骨表观密度。另外，整体和局部研究了初始骨密度对所得预测密度分布的影响。仿真结果表明，电刺激的骨表面增强了骨沉积，并且与文献中的先前发现非常吻合。此外，可以通过治疗性电刺激来支持由于日常身体活动而引起的机械刺激，以减少身体受损或骨质疏松情况下的骨质流失。