Institute of New Technologies and Applied Informatics, Faculty of Mechatronics, Informatics and Interdisciplinary Studies, Technical University of Liberec, Studentská 1402/2, 46117 Liberec, Czech Republic.
Institute of Structural Mechanics, Faculty of Civil Engineering, Brno University of Technology, Veveří 331/95, 60200 Brno, Czech Republic.
Clin Biomech (Bristol). 2022 Jul;97:105704. doi: 10.1016/j.clinbiomech.2022.105704. Epub 2022 Jun 15.
The spatially varying mechanical properties in finite element models of bone are most often derived from bone density data obtained via quantitative computed tomography. The key step is to accurately and efficiently map the density given in voxels to the finite element mesh.
The density projection is first formulated in least-squares terms and then discretized using a continuous and discontinuous variant of the finite element method. Both discretization variants are compared with the nodal and element approaches known from the literature.
In terms of accuracy in the L2 norm, energy distance and efficiency, the discontinuous zero-order variant appears to be the most advantageous. The proposed variant sufficiently preserves the spectrum of density at the edges, while keeping computational cost low.
The continuous finite element method is analogous to the nodal formulation in the literature, while the discontinuous finite element method is analogous to the element formulation. The two variants differ in terms of implementation, computational cost and ability to preserve the density spectrum. These differences cannot be described and measured by known indirect methods from the literature.
骨骼有限元模型中空间变化的力学性能通常源自通过定量计算机断层扫描获得的骨密度数据。关键步骤是准确、高效地将体素中的密度映射到有限元网格上。
首先以最小二乘法的形式对密度投影进行公式化，然后使用有限元法的连续和不连续变体进行离散化。将这两种离散变体与文献中已知的节点和单元方法进行比较。
就 L2 范数、能量距离和效率的准确性而言，不连续零阶变体似乎是最有利的。所提出的变体充分保留了密度在边缘的谱，同时保持低计算成本。
连续有限元法类似于文献中的节点公式化，而不连续有限元法则类似于单元公式化。这两种变体在实现、计算成本和保持密度谱的能力方面有所不同。这些差异无法通过文献中的已知间接方法来描述和测量。
