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首页> 外文期刊>Computer Methods and Programs in Biomedicine: An International Journal Devoted to the Development, Implementation and Exchange of Computing Methodology and Software Systems in Biomedical Research and Medical Practice >Optimal bone density distributions: Numerical analysis of the osteocyte spatial influence in bone remodeling
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Optimal bone density distributions: Numerical analysis of the osteocyte spatial influence in bone remodeling

机译：最佳骨密度分布：骨重建中骨细胞空间影响的数值分析

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摘要

In this paper a control and optimization procedure for bone remodeling simulations was adopted to study the effect of the osteocyte influence range on the predicted density distribution. In order to reach this goal, the osteocyte network regulating bone remodeling process in a 2-D bone sample was numerically simulated. The assumed proportional-integral-derivative (PID) bone remodeling rule was related to the error signal between the strain energy density and a selected target. Furthermore the control parameters and the target were optimally determined minimizing a suitable cost index: the goal was to minimize the final mass and the energy thus maximizing the stiffness. The continuum model results show that the developed and adapted trabecular structure was consistent with the applied loads and only depended on the external forces, the value of the cost index, the maximum attainable elastic modulus value (hence, the maximum density value) and the value of the energy target. The remodeling phenomenon determined the number and thickness of the trabeculae which are formed from a uniform distribution of mass density in the considered domain; this number and these thicknesses are controlled by the values assigned to the parameters of the model. In particular, the osteocyte decay distance (D) of the influence range affected the trabecular patterns formation, showing an important effect in the adaptive capacity of the optimization numerical model.
机译：本文采用控制和优化程序进行骨重塑仿真，以研究骨细胞影响范围对预测密度分布的影响。为了达到这个目的，对二维骨样品中调节骨重塑过程的骨细胞网络进行了数值模拟。假定的比例积分微分（PID）骨骼重塑规则与应变能密度和选定目标之间的误差信号有关。此外，最优地确定了控制参数和目标，以最小化合适的成本指数：目标是最小化最终质量和能量，从而最大化刚度。连续模型的结果表明，开发并适应的小梁结构与所施加的载荷一致，并且仅取决于外力，成本指标的值，最大可达到的弹性模量值（因此，最大密度值）和能源目标。重塑现象决定了小梁的数量和厚度，这些小梁是由所考虑区域中质量密度的均匀分布形成的;此数字和这些厚度由分配给模型参数的值控制。特别是，影响范围的骨细胞衰变距离（D）影响了小梁样式的形成，在优化数值模型的自适应能力中显示了重要的作用。

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