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摘要: 为了模拟和预测肌体组织复杂的再生修复过程，提出基于力学环境和血液供给条件建立骨折愈合仿真模型.针对骨折固定的力学条件和生物学因素，用一种时间动态模型模拟二期骨折愈合阶段的机械稳定性、血管再生和组织分化之间复杂的作用关系.与以往模型不同，本研究建立骨折的三维几何模型，通过有限元法计算骨痂局部力刺激，并与模糊逻辑相结合，将血液浓度作为时-空状态变量引入到模型中，描述骨痂力学及组织分化过程.通过前进欧拉法进行组织浓度等时间步长的迭代更新，在Visual Studio 2012环境下实现愈合进程模拟.最后，利用仿真模型预测稳定与不稳定环境下骨间动度随骨折愈合时间的变化情况，并将仿真结果数据与实验数据进行对比，结果表明，仿真结果与实验数据在趋势和数值上都有较好的吻合，仿真结果数据全部分布在实验数据平均偏差范围内.该结果验证了骨折愈合模型的精确性以及在模拟骨折愈合过程方面的优势.Abstract: A fracture healing model considering mechanical environment and blood supply conditions is proposed to simulate and predict the complex regenerative repair process for tissue. For mechanics condition of fracture fixation and biological factors, a dynamic spatio-temporal model is developed to simulate the complex interactions of mechanical stability, revascularization and tissue differentiation in secondary fracture healing. Unlike previous study, a three-dimensional finite element model is established. The blood perfusion regarded as a spatio-temporal state variable is included into the model to simulate the revascularization process. With finite element method and fuzzy logic, the dynamic model can describe the callus mechanics and biological processes of tissue differentiation. The callus healing process is simulated in Visual Studio 2012 by forward Euler integration method over equidistant time steps iterative loop. Finally, the model predicates the course of interfragmentary movement of two groups with a different axial stability. Through the comparison with the experiment data, it turned out that the simulation result distributed within the scope of the average deviation of the experimental data, which corresponds well to the experiment curve trend and value. The agreement of simulation results with experiment results verifies the accuracy of the fracture healing model and the advantage of the simulating healing process.
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Key words:
- Fracture healing /
- three-dimensional model /
- fuzzy rules /
- tissue differentiation /
- finite element
1) 本文责任编委 田捷 -
图 8 骨间动度仿真与实验数据的对比
Fig. 8 Comparison between interfragmentary movement over time and test results
图 9 骨间动度仿真与Simon仿真结果的对比
Fig. 9 Comparison between simulated interfragmentary movement and Simon results
表 1 组织成分的力学特性
Table 1 Material properties of tissue types
组织成分 弹性模量(MPa) 泊松比 皮质骨 10 000 0.36 编织骨 4 000 0.36 纤维软骨 200 0.45 结缔组织 3 0.30 
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表 2 二期骨折愈合的模糊规则
Table 2 The fuzzy rules of the fracture healing
分化过程 血供 相邻血供 骨密度 邻骨密度 软骨密度 膨胀应变 畸变应变 $\Delta$血供 $\Delta$骨密度 $\Delta$软骨密度 1 低 中或高 $- $ $- $ $- $ 非负中 非中 增高 $- $ $- $ 2 中 高 $- $ $- $ $- $ 非负中 非中 增高 $- $ $- $ 3 高 $- $ $- $ $- $ $- $ 非负中 非中 增高 $- $ $- $ 4 $- $ $- $ $- $ $- $ $- $ 负中 $- $ 降低 $- $ $- $ 5 高 $- $ $- $ 中或高 低 负低 低 $- $ 增高 $- $ 6 高 $- $ $- $ 中或高 低 正低 低 $- $ 增高 $- $ 7 $- $ $- $ 低或中 $- $ 低 负中 非过载 $- $ $- $ 增高 8 $- $ $- $ $- $ $- $ 中或高 负中 非过载 $- $ $- $ 增高 9 $- $ $- $ $- $ $- $ 高 负低 非过载 $- $ $- $ 增高 10 不低 $- $ $- $ 中或高 中或高 正低 零 $- $ 增高 降低 11 不低 $- $ $- $ 中或高 中或高 负中 零 $- $ 增高 降低 12 不低 $- $ $- $ 中或高 中或高 负中 低 $- $ 增高 降低 13 不低 $- $ $- $ 中或高 中或高 负低 低 $- $ 增高 降低 14 不低 高 高 $- $ 低 负低 低 $- $ 增高 降低 15 不低 高 高 $- $ 低 负低 零 $- $ 增高 降低 16 高 $- $ $- $ $- $ $- $ 零 零 $- $ 降低 $- $ 17 $- $ $- $ $- $ $- $ $- $ 负过载 $- $ 降低 降低 降低 18 $- $ $- $ $- $ $- $ $- $ 正过载 $- $ 降低 降低 降低 19 $- $ $- $ $- $ $- $ $- $ $- $ 过载 降低 降低 降低 20 $- $ $- $ $- $ $- $ $- $ 非负过载 $- $ 不变 不变 不变 21 $- $ $- $ $- $ $- $ $- $ 非正过载 $- $ 不变 不变 不变
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表 3 初始条件和边界条件(%)
Table 3 Initial condition and boundary condition (%)
血液浓度 骨密度 软骨密度 结缔组织 骨皮质 100 100 0 0 断端间骨痂 0 0 0 100 骨痂外边缘 30 0 0 100
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