School of Information Science and Engineering, Central South University, Changsha 410083, China.
Comput Methods Programs Biomed. 2012 Nov;108(2):536-47. doi: 10.1016/j.cmpb.2011.04.005. Epub 2011 May 13.
Although it is well known that human bone tissues have obvious orthotropic material properties, most works in the physical modeling field adopted oversimplified isotropic or approximated transversely isotropic elasticity due to the simplicity. This paper presents a convenient methodology based on harmonic fields, to construct volumetric finite element mesh integrated with complete orthotropic material. The basic idea is taking advantage of the fact that the longitudinal axis direction indicated by the shape configuration of most bone tissues is compatible with the trajectory of the maximum material stiffness. First, surface harmonic fields of the longitudinal axis direction for individual bone models were generated, whose scalar distribution pattern tends to conform very well to the object shape. The scalar iso-contours were extracted and sampled adaptively to construct volumetric meshes of high quality. Following, the surface harmonic fields were expanded over the whole volumetric domain to create longitudinal and radial volumetric harmonic fields, from which the gradient vector fields were calculated and employed as the orthotropic principal axes vector fields. Contrastive finite element analyses demonstrated that elastic orthotropy has significant effect on simulating stresses and strains, including the value as well as distribution pattern, which underlines the relevance of our orthotropic modeling scheme.
尽管众所周知，人体骨骼组织具有明显的各向异性材料特性，但由于其简单性，物理建模领域的大多数工作采用了过于简化的各向同性或近似横观各向同性弹性。本文提出了一种基于调和场的便捷方法，用于构建具有完整各向异性材料的体积有限元网格。基本思想是利用大多数骨骼组织的形状配置所指示的纵轴方向与最大材料刚度轨迹相吻合的事实。首先，针对单个骨骼模型生成了纵轴方向的面调和场，其标量分布模式非常符合物体形状。提取标量等距线并自适应采样以构建高质量的体积网格。然后，将面调和场扩展到整个体积域，创建纵向和径向体积调和场，从中计算梯度向量场，并将其用作各向异性主轴向量场。对比有限元分析表明，弹性各向异性对模拟应力和应变具有显著影响，包括值和分布模式，这强调了我们的各向异性建模方案的相关性。
