Fasser Marie-Rosa, Kuravi Ramachandra, Bulla Marian, Snedeker Jess G, Farshad Mazda, Widmer Jonas
Spine Biomechanics, Department of Orthopedic Surgery, Balgrist University Hospital, Zurich, Switzerland.
Institute for Biomechanics, ETH Zurich, Zurich, Switzerland.
Front Bioeng Biotechnol. 2022 Dec 13;10:1034441. doi: 10.3389/fbioe.2022.1034441. eCollection 2022.
Intervertebral discs are microstructurally complex spinal tissues that add greatly to the flexibility and mechanical strength of the human spine. Attempting to provide an adjustable basis for capturing a wide range of mechanical characteristics and to better address known challenges of numerical modeling of the disc, we present a robust finite-element-based model formulation for spinal segments in a hyperelastic framework using tetrahedral elements. We evaluate the model stability and accuracy using numerical simulations, with particular attention to the degenerated intervertebral discs and their likely skewed and narrowed geometry. To this end, 1) annulus fibrosus is modeled as a fiber-reinforced Mooney-Rivlin type solid for numerical analysis. 2) An adaptive state-variable dependent explicit time step is proposed and utilized here as a computationally efficient alternative to theoretical estimates. 3) Tetrahedral-element-based FE models for spinal segments under various loading conditions are evaluated for their use in robust numerical simulations. For flexion, extension, lateral bending, and axial rotation load cases, numerical simulations reveal that a suitable framework based on tetrahedral elements can provide greater stability and flexibility concerning geometrical meshing over commonly employed hexahedral-element-based ones for representation and study of spinal segments in various stages of degeneration.
椎间盘是微观结构复杂的脊柱组织，极大地增强了人类脊柱的灵活性和机械强度。为了提供一个可调整的基础来捕捉广泛的机械特性，并更好地应对椎间盘数值建模中已知的挑战，我们提出了一种基于有限元的稳健模型公式，用于在超弹性框架下使用四面体单元对脊柱节段进行建模。我们通过数值模拟评估模型的稳定性和准确性，特别关注退变的椎间盘及其可能出现的几何形状偏斜和变窄。为此，1）将纤维环建模为纤维增强的穆尼 - 里夫林型固体用于数值分析。2）提出并在此使用一种自适应的依赖状态变量的显式时间步长，作为理论估计的一种计算高效的替代方法。3）评估基于四面体单元的脊柱节段有限元模型在各种加载条件下用于稳健数值模拟的情况。对于屈曲、伸展、侧弯和轴向旋转载荷情况，数值模拟表明，基于四面体单元的合适框架在几何网格划分方面比常用的基于六面体单元的框架具有更大的稳定性和灵活性，可用于表示和研究退变各个阶段的脊柱节段。
