Institute for Surgical Technology and Biomechanics, University of Bern, Switzerland.
Institute for Surgical Technology and Biomechanics, University of Bern, Switzerland.
J Mech Behav Biomed Mater. 2014 Feb;30:279-89. doi: 10.1016/j.jmbbm.2013.11.019. Epub 2013 Dec 3.
Numerical models of the intervertebral disc, which address mechanical questions commonly make use of the difference in water content between annulus and nucleus, and thus fluid and solid parts are separated. Despite this simplification, models remain complex due to the anisotropy and nonlinearity of the annulus and regional variations of the collagen fibre density. Additionally, it has been shown that cross-links make a large contribution to the stiffness of the annulus. Because of this complex composite structure, it is difficult to reproduce several sets of experimental data with one single set of material parameters. This study addresses the question to which extent the ultrastructure of the intervertebral disc should be modelled so that its moment-angle behaviour can be adequately described. Therefore, a hyperelastic constitutive law, based on continuum mechanical principles was derived, which does not only consider the anisotropy from the collagen fibres, but also interactions among the fibres and between the fibres and the ground substance. Eight ovine lumbar intervertebral discs were tested on a custom made spinal loading simulator in flexion/extension, lateral bending and axial rotation. Specimen-specific geometrical models were generated using CT images and T2 maps to distinguish between annulus fibrosus and nucleus pulposus. For the identification of the material parameters the annulus fibrosus was described with two scenarios: with and without fibre-matrix and fibre-fibre interactions. Both scenarios showed a similar behaviour on a load displacement level. Comparing model predictions to the experimental data, the mean RMS of all specimens and all load cases was 0.54±0.15° without the interaction and 0.54±0.19° when the fibre-matrix and fibre-fibre interactions were included. However, due to the increased stiffness when cross-links effects were included, this scenario showed more physiological stress-strain relations in uniaxial and biaxial stress states. Thus, the present study suggests that fibre-matrix and fibre-fibre interactions should be considered in the constitutive law when the model addresses questions concerning the stress field of the annulus fibrosus.
椎间盘的数值模型,常用于解决力学问题,通常利用纤维环和核之间的水分含量差异,从而将其分为流体部分和固体部分。尽管这种简化方式,模型仍然很复杂,因为纤维环的各向异性和非线性以及胶原纤维密度的区域变化。此外,已经表明交联对纤维环的刚度有很大贡献。由于这种复杂的复合材料结构,很难用一组材料参数来再现多组实验数据。本研究旨在探讨椎间盘的超微结构应如何建模,才能充分描述其力矩-角度行为。因此,基于连续介质力学原理,推导了一种超弹性本构定律,该定律不仅考虑了胶原纤维的各向异性,还考虑了纤维之间以及纤维与基质之间的相互作用。在定制的脊柱加载模拟器上,对 8 个绵羊腰椎间盘进行了屈伸、侧屈和轴向旋转测试。使用 CT 图像和 T2 图谱生成了具有特定于样本的几何模型,以区分纤维环和核髓。为了识别材料参数,纤维环采用了两种情况进行描述:有纤维-基质和纤维-纤维相互作用,以及无纤维-基质和纤维-纤维相互作用。两种情况在负载位移水平上表现出相似的行为。将模型预测与实验数据进行比较,在没有相互作用的情况下,所有样本和所有负载情况的平均均方根误差(RMS)为 0.54±0.15°,当包含纤维-基质和纤维-纤维相互作用时,平均 RMS 为 0.54±0.19°。然而,由于交联效应增加了刚度,这种情况下在单轴和双轴应力状态下显示出更符合生理的应力-应变关系。因此,本研究表明,当模型涉及纤维环的应力场问题时,在本构定律中应考虑纤维-基质和纤维-纤维相互作用。