Objectives

This study aimed to develop a simple and efficient numerical modeling approach for characterizing strain and total strain energy in bone scaffolds implanted in patient-specific anatomical sites.

Materials and methods

A simplified homogenization technique was developed to substitute a detailed scaffold model with the same size and equivalent orthotropic material properties. The effectiveness of the proposed modeling approach was compared with two other common homogenization methods based on periodic boundary conditions and the Hills-energy theorem. Moreover, experimental digital image correlation (DIC) measurements of full-field surface strain were conducted to validate the numerical results.

Results

The newly proposed simplified homogenization approach allowed for fairly accurate prediction of strain and total strain energy in tissue scaffolds implanted in a large femur mid-shaft bone defect subjected to a simulated in-vivo loading condition. The maximum discrepancy between the total strain energy obtained from the simplified homogenization approach and the one obtained from detailed porous scaffolds was 8.8%. Moreover, the proposed modeling technique could significantly reduce the computational cost (by about 300 times) required for simulating an in-vivo bone scaffolding scenario as the required degrees of freedom (DoF) was reduced from about 26 million for a detailed porous scaffold to only 90,000 for the homogenized solid counterpart in the analysis.

Conclusions

The simplified homogenization approach has been validated by correlation with the experimental DIC measurements. It is fairly efficient and comparable with some other common homogenization techniques in terms of accuracy. The proposed method is implicating to different clinical applications, such as the optimal selection of patient-specific fixation plates and screw system.

中文翻译：

---

用于临床方案的骨组织支架的非破坏性表征。

目标

这项研究旨在开发一种简单有效的数值建模方法，以表征植入患者特定解剖部位的骨支架中的应变和总应变能。

材料和方法

开发了一种简化的均质技术，以替代具有相同尺寸和等效正交各向异性材料特性的详细支架模型。将所提出的建模方法的有效性与基于周期边界条件和Hills-energy定理的其他两种常见的均化方法进行了比较。此外，进行了全场表面应变的实验数字图像相关性（DIC）测量，以验证数值结果。

结果

允许用于在经受模拟大股骨中间轴骨缺损植入组织支架的应变和总应变能的相当准确的预测新提出的简化均质化的方法 中的体内加载条件。从简化的均质化方法获得的总应变能与从详细的多孔支架获得的总应变能之间的最大差异为8.8％。此外，由于所需的自由度（DoF）从详细的多孔支架的约2600万减少到仅用于仿真的骨支架，因此拟议的建模技术可以显着降低模拟体内骨骼支架场景所需的计算成本（减少约300倍）。分析中均质固体对应物为90,000。

结论

简化的均质化方法已通过与实验DIC测量的相关性进行了验证。就准确性而言，它是相当有效的，并且可以与其他一些常见的均质化技术相媲美。所提出的方法涉及不同的临床应用，例如患者特定固定板和螺钉系统的最佳选择。