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软骨终板退化对颈椎椎间盘物质运输和力学响应的影响

刘景龙 徐鹏 李侨 王丽珍 樊瑜波

刘景龙, 徐鹏, 李侨, 王丽珍, 樊瑜波. 软骨终板退化对颈椎椎间盘物质运输和力学响应的影响[J]. 应用数学和力学, 2024, 45(6): 763-774. doi: 10.21656/1000-0887.450017
引用本文: 刘景龙, 徐鹏, 李侨, 王丽珍, 樊瑜波. 软骨终板退化对颈椎椎间盘物质运输和力学响应的影响[J]. 应用数学和力学, 2024, 45(6): 763-774. doi: 10.21656/1000-0887.450017
LIU Jinglong, XU Peng, LI Qiao, WANG Lizhen, FAN Yubo. Effects of Cartilage Endplate Degeneration on Metabolic Transport and Biomechanical Responses of Cervical Intervertebral Discs[J]. Applied Mathematics and Mechanics, 2024, 45(6): 763-774. doi: 10.21656/1000-0887.450017
Citation: LIU Jinglong, XU Peng, LI Qiao, WANG Lizhen, FAN Yubo. Effects of Cartilage Endplate Degeneration on Metabolic Transport and Biomechanical Responses of Cervical Intervertebral Discs[J]. Applied Mathematics and Mechanics, 2024, 45(6): 763-774. doi: 10.21656/1000-0887.450017

软骨终板退化对颈椎椎间盘物质运输和力学响应的影响

doi: 10.21656/1000-0887.450017
基金项目: 

国家自然科学基金(“叶企孙”科学基金项目) U2241273

详细信息
    作者简介:

    刘景龙(1996—),男,博士生(E-mail: jinglongliu@buaa.edu.cn)

    通讯作者:

    李侨(1993—),女,博士(通讯作者. E-mail: qiaoli@buaa.edu.cn)

  • 中图分类号: O39;R318.01

Effects of Cartilage Endplate Degeneration on Metabolic Transport and Biomechanical Responses of Cervical Intervertebral Discs

  • 摘要:

    软骨终板内的液体流动是椎间盘营养供给和代谢废物运输的主要途径. 退化的终板刚度增加、渗透性和含水量下降,会影响椎间盘内物质运输和力学响应. 基于人体颈椎计算机断层扫描数据建立了C5-C6节段的多孔介质有限元模型. 对验证后的模型施加压缩、前屈、后伸、轴向旋转和侧弯五种载荷,通过改变终板渗透性、孔隙比和模量,分析了正常、钙化和硬化三种状态下椎间盘的响应. 结果表明:软骨终板退化增加了软骨终板和髓核的多孔压力,降低了软骨终板的流体速度. 前屈载荷下,与正常终板对比,钙化和硬化终板导致髓核内流体的多孔压力分别增加了50.8%和88.9%. 退化终板渗透率和含水量的降低导致髓核内液体不易流动,增加了髓核基体的应力,在压缩和轴向旋转载荷下,硬化终板导致髓核基体的最大主应力分别增加了122.2%和100.0%.

  • 图  1  C5-C6节段有限元模型的建立过程及各部分示意图

      为了解释图中的颜色,读者可以参考本文的电子网页版本,后同.

    Figure  1.  The construction process and components of the C5-C6 finite element model

    图  2  轴向压缩500 N时椎间盘高度丢失百分比验证[30-31]

    Figure  2.  Validation of percentages of height losses of the FE model under a 500 N compression[30-31]

    图  3  髓核及软骨终板在压缩、前屈、后伸、轴向旋转及侧弯载荷下的最大多孔压力

    Figure  3.  Maximum pore pressures in the nucleus pulposus and the cartilage endplate under compression(comp), flexion (flex), extension (ext), axial rotation (AR) and lateral bending (LB)

    图  4  髓核及软骨终板在压缩、前屈、后伸、轴向旋转及侧弯载荷下的最大流体速度

    Figure  4.  Maximum fluid velocities in the nucleus pulposus and the cartilage endplate under compression (comp), flexion (flex), extension (ext), axial rotation (AR) and lateral bending (LB)

    图  5  髓核在压缩、前屈、后伸、轴向旋转及侧弯载荷下的流体速度云图

    Figure  5.  Contours of fluid velocities in the nucleus pulposus under compression (comp), flexion (flex), extension (ext), axial rotation (AR) and lateral bending (LB)

    图  6  髓核及软骨终板在压缩、前屈、后伸、轴向旋转及侧弯载荷下的最大主应力

    Figure  6.  Maximum principal stresses in the nucleus pulposus and the cartilage endplate under compression (comp), flexion (flex), extension (ext), axial rotation (AR) and lateral bending (LB)

    图  7  髓核在压缩、前屈、后伸、轴向旋转及侧弯载荷下的最大主应力云图

    Figure  7.  Contours of maximum principal stresses in the nucleus pulposus under compression (comp), flexion (flex), extension (ext), axial rotation (AR) and lateral bending (LB)

    表  1  多孔介质有限元模型材料参数

    Table  1.   Material parameters of the porous finite element model

    component Young’s modulus E/MPa Poisson’s ratio ν void ratio e0 permeability k0/(mm4/(N·s)) reference
    cortical bone 16 800 0.3 - - [23]
    cancellous bone 450 0.3 0.41 5.773 5E-2 [16, 24]
    posterior bone 3 500 0.3 - - [24]
    articular cartilage 10 0.4 - - [19]
    nucleus pulposus 1 0.49 5.67 1.56E-4 [16, 24]
    annulus substance Mooney-Rivlin
    C10=0.133,
    C01=0.033 3, D1=0.6
    2.45 1.56E-4 [16, 25]
    annulus fibrosus 110 0.3 - - [25]
    boney endplate 5 600 0.3 0.8 7.500E-2 [13, 19]
    cartilage endplate healthy calcified sclerotic 5
    3 500
    0.4 4
    0.11
    4.041E-3
    4.041E-4
    4.041E-5
    [16, 24]
    [13, 26]
    ligament ALL 28.2 0.4 - - [27-28]
    PLL 23 0.4
    LF 3.5 0.4
    CL 4.8 0.4
    ISL 5 0.4
    下载: 导出CSV

    表  2  髓核及软骨终板在压缩、前屈、后伸、轴向旋转及侧弯载荷下的最大多孔压力比较

    Table  2.   Comparison of maximum pore pressures in the nucleus pulposus and the cartilage endplate under compression (comp), flexion (flex), extension (ext), axial rotation (AR) and lateral bending (LB)

    component degree of cartilage endplate degeneration loading condition
    comp flex ext AR LB
    nucleus pulposus calcified 12.5% 50.8% 1.4% 14.3% 1.5%
    sclerotic 55.0% 88.9% 1.4% 48.2% 19.7%
    cartilage endplate calcified 95.7% 97.9% 60.0% 42.2% 38.6%
    sclerotic 169.6% 147.9% 80.0% 84.4% 56.1%
    下载: 导出CSV

    表  3  髓核及软骨终板在压缩、前屈、后伸、轴向旋转及侧弯载荷下的最大流体速度比较

    Table  3.   Comparison of maximum fluid velocities in the nucleus pulposus and the cartilage endplate under compression (comp), flexion (flex), extension (ext), axial rotation (AR) and lateral bending (LB)

    component degree of cartilage endplate degeneration loading condition
    comp flex ext AR LB
    nucleus pulposus calcified -29.1% 9.5% -8.6% 0.7% -1.3%
    sclerotic -19.4% 46.7% 2.6% 15.0% 14.6%
    cartilage endplate calcified -32.3% -19.5% -70.0% -60.9% -67.8%
    sclerotic -89.3% -89.5% -96.4% -94.5% -95.4%
    下载: 导出CSV

    表  4  髓核及软骨终板在压缩、前屈、后伸、轴向旋转及侧弯载荷下的最大主应力比较

    Table  4.   Comparison of maximum principal stresses in the nucleus pulposus and the cartilage endplate under compression (comp), flexion (flex), extension (ext), axial rotation (AR) and lateral bending (LB)

    component degree of cartilage endplate degeneration loading condition
    comp flex ext AR LB
    nucleus pulposus calcified 77.8% 70.6% 12.5% 69.2% 31.3%
    sclerotic 122.2% 94.1% 43.8% 100.0% 56.3%
    cartilage endplate calcified 330.0% 390.6% 571.4% 325.0% 492.3%
    sclerotic 335.0% 384.4% 595.4% 320.8% 480.8%
    下载: 导出CSV
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  • 收稿日期:  2024-01-25
  • 修回日期:  2024-05-09
  • 刊出日期:  2024-06-01

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