A Direct Comparison of Node and Element-Based Finite Element Modeling Approaches to Study Tissue Growth.
A Direct Comparison of Node and Element-Based Finite Element Modeling Approaches to Study Tissue Growth.
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研究组织生长的节点和基于单元的有限元建模方法的直接比较。
DOI：
10.1115/1.4051661
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Fisher,MatthewB
中科院分区：
文献类型：
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作者：
Howe,Danielle;Dixit,NikhilN;Saul,KatherineR;Fisher,MatthewB
有限元分析是模拟生物组织生长并预测刺激如何影响生长的有用工具。以前的工作使用基于节点或基于元素的方法来模拟增长，并且无论应用的增长模型如何，这种实现选择都可能影响预测的增长。本研究直接比较基于节点和基于元素的方法，通过模拟骨骼雏形几何形状的生长来了解实施方法对生长预测的孤立影响，并确定哪些条件在两种方法之间产生相似的结果。我们使用了之前报道的通过热膨胀实现的基于节点的方法和通过渗透膨胀实现的基于元素的方法，并且我们推导出了一个数学关系来关联这些方法产生的增长。我们发现材料属性（模量）影响基于单元的方法中的生长，相对于生长刺激，高模量值的生长完全受到限制，而低模量值则没有限制。基于节点的方法不受模数的影响。当基于初始模拟结果优化关联方法的转换系数时，基于节点和基于单元的方法的匹配程度稍好一些，而不是使用理论预测的转换系数（节点位置的中值差异分别为 0.042 cm 与 0.052 cm）。总之，我们在这里说明了选择生长建模实施方法的重要性，提供了在实施方法之间转换模型的框架，并强调了比较先前工作的结果和开发新的组织生长模型的重要考虑因素。
Finite element analysis is a useful tool to model growth of biological tissues and predict how growth can be impacted by stimuli. Previous work has simulated growth using node-based or element-based approaches, and this implementation choice may influence predicted growth, irrespective of the applied growth model. This study directly compared node-based and element-based approaches to understand the isolated impact of implementation method on growth predictions by simulating growth of a bone rudiment geometry, and determined what conditions produce similar results between the approaches. We used a previously reported node-based approach implemented via thermal expansion and an element-based approach implemented via osmotic swelling, and we derived a mathematical relationship to relate the growth resulting from these approaches. We found that material properties (modulus) affected growth in the element-based approach, with growth completely restricted for high modulus values relative to the growth stimulus, and no restriction for low modulus values. The node-based approach was unaffected by modulus. Node- and element-based approaches matched marginally better when the conversion coefficient to relate the approaches was optimized based on the results of initial simulations, rather than using the theoretically predicted conversion coefficient (median difference in node position 0.042 cm versus 0.052 cm, respectively). In summary, we illustrate here the importance of the choice of implementation approach for modeling growth, provide a framework for converting models between implementation approaches, and highlight important considerations for comparing results in prior work and developing new models of tissue growth.