摘要
第一部分腰椎运动节段精确三维非线性有限元模型的建立与验证
研究设计：
腰椎运动节段有限元建模研究。
目的：
采用一种新型计算机辅助设计方法精确建立腰椎L4-L5节段三维非线性有限元模型，并进行充分验证。
背景知识：
脊柱有限元模型建模方法有基于医学图像建模方法、使用数字化仪建模方法和采用解剖学数据建模方法。使用数字化仪建模方法，手工操作过程繁琐，误差较大，且只能在裸露的尸体腰椎上测量，不能完整体现脊柱生理弯曲等解剖结构，也无法实现脊柱有限元建模的个体化。采用解剖学数据建模方法(如基于3D-MAX软件的腰椎几何模型建模法)属手工建模法；无法实现有限元建模的数字化，且不包含任何先进的算法，建模技术粗糙，国外有限元研究多不采用。基于CT图像的建模方法具有自动、标准、快速建模等优点，是腰椎运动节段几何模型建模的主要研究方法。
目前基于CT图像的腰椎有限元建模方法多为首先在其他CAD软件中创建几何模型，然后通过数据接口导入有限元软件进行网格划分的间接建模法。这种间接建模法虽然建模效率、网格划分质量较Goel(1988)的直接建模法有所提高，但在从CT扫描图像获取建模数据时，多数间接建模法仍局限于将每个单层图像的轮廓形状信息叠加在一起获取椎体的原始几何信息；同时，生成有限元模型中的体元是以平齐于CT扫描平面的方式排列，未能正确反映脊柱的复杂解剖结构特征(如生理前凸等)。此外，腰椎有限元模型不同部位单元的大小疏密要求也不相同，以往的建模方法缺少相应的控制机制。
方法：
采用改良的“非种子区域分割方法”提取腰椎CT图像数据中目标区域得到二值图像，用Marching Cubes方法由二值数据生成初始表面模型。采用反应腰椎生理弯曲的“最佳切割平面”从初始表面模型获得非平行的切割轮廓线并建立“分段线性子空间”，后者经仿射变换到“规则子空间”快速重构腰椎曲面，最后逆变换恢复腰椎原三维空间形状特征。将表面模型所有结点的坐标数据和三角面片信息导入ANSYS有限元软件进行网格划分精确建立L4-L5节段三维非线性有限元模型。约束L5椎体和棘突底面上所有结点平移和转动共6个自由度，有限元模型分别在垂直压缩载荷3000N，屈曲、后伸、侧屈、扭转力矩载荷15Nm条件下分步加载。有限元模型预测结果与相同边界条件体外实验生物力学研究结果进行比较验证。
结果：
所构建IA-L5运动节段有限元模型包括94794个Solid单元，1196个Link单元，1170个Shell单元，768个Target单元，464个Contact单元；包含终板、关节突关节面等所有重要解剖结构，同时包含了几何非线性、材料非线性与接触非线性三种非线性类型。不同载荷条件下L4-L5节段有限元模型的预测结果与相同边界条件下体外实验生物力学研究结果近似。
结论：
基于先进算法精确建立的腰椎L4-L5节段表面模型实现了二值图像提取、腰椎曲面重构的全数字化过程，具有极佳的仿真效果：不同载荷条件下，L4-L5节段非线形有限元模型获得充分验证。
第二部分个性化退变腰椎有限元模型库的建立与验证
目的：根据退变腰椎的形态特征，采用CAD方法精确建立不同形态改变的退变腰椎L4-L5运动节段三维有限元模型。
方法：
采用一系列新型CAD方法精确建立L4-L5运动节段有限元模型。利用人性化交互修改工具，通过“界面”划分，将L4-L5节段表面模型分解为前部椎体和后部结构2个基本“结构模块”。分别改变正常腰椎基本“结构模块”的椎间盘高度、上下终板凹陷角角度、椎间盘前凸角度、小关节矢状面角度等几何参数，建立包括椎间盘高度降低、终板凹陷角改变、椎间盘前凸角改变以及小关节角改变在内的9种退变腰椎基本“结构模块”表面模型，表面模型数据导入ANSYS获得各“结构模块”有限元模型后，通过界面间的拼接粘贴构建退变腰椎有限元模型，通过纤维环纤维及各组韧带结点的固定编码确定纤维环纤维及韧带Link单元起止点位置，最终得到包含18种不同形态改变的退变腰椎有限元模型。退变腰椎有限元模型分别在垂直压缩载荷150N，屈曲、后伸力矩载荷7.5Nm，前剪、后剪载荷150N条件下加载，不同载荷条件下退变有限元模型预测结果与相同边界条件体外实验生物力学研究结果进行比较。
结果：
所构建的单参数变化的退变腰椎有限元模型包含L4-L5节段所有重要解剖结构，不同载荷条件下退变腰椎有限元模型预测结果与体外实验生物力学研究结果相符合。
结论：
基于CT数据的CAD方法实现了个性化退变腰椎有限元模型库的建立。
第三部分小关节角矢状化、椎间盘退变对退变性腰椎滑移作用的有限元研究
目的：
探讨小关节矢状化与椎间盘退变间的关系及其对退变性腰椎滑移的作用和意义。
方法：
采用一系列新型CAD方法精确构建65°小关节角、45°小关节角、25°小关节角与正常椎间盘、轻度退变椎间盘、重度退变椎间盘相组配的9种腰椎L4-L5运动节段有限元模型。生理压缩载荷下，分别对9种有限元模型的生物力学参数进行测试。
结果：
与小关节角45°、25°有限元模型相比，小关节角65°有限元模型的矢状方向椎体前移位增加，关节突、峡部等效应力，关节突水平方向接触力明显增加：同时，小关节角65°有限元模型的终板膨出减小，纤维环基质应力增加。与正常有限元模型相比，椎间盘轻度退变有限元模型刚度下降，小关节突及峡部应力轻度增加。9种有限元模型中，轻度退变椎间盘结合小关节角65°有限元模型的抗前剪力能力最差。
结论：
小关节角矢状化既是退变性腰椎滑移的原发诱因，又是局部应力变化导致关节突再塑形的继发病理改变，矢状型小关节腰椎运动节段矢状方向内在不稳定性受椎间盘退变程度的影响，椎间盘退变对小关节角矢状化无明显促进作用。
第四部分终板凹陷角变化对腰椎运动节段生物力学影响的有限元分析
目的：
探讨终板凹陷程度变化对腰椎运动节段生物力学影响。
方法：
在以往建立的腰椎L4-L5运动节段三维非线性有限元模型基础上，采用CAD方法精确构建三种不同终板凹陷角改变的有限元模型，有限元模型的椎间盘前凸角、小关节间隙等其余形态学参数及网格划分均保持一致。垂直压缩、屈曲、伸直、前后剪力5种载荷条件下，分别对三种有限元模型生物力学参数进行测试。
结果：
加载条件下，终板凹陷角增加、终板凹陷程度减小可导致终板-椎间盘界面应变减小，椎间盘刚度及髓核内压增加，椎间盘膨出、纤维环纤维张应力、纤维环基质应力、腰椎后部结构应力以及关节突接触力减小。
结论：
终板凹陷程度的减小增强了椎间盘对椎体的保护作用，同时可通过影响终板的形变减小对椎间盘的营养传递。
Study Design:
Foundation and validation of FE model of lumbar motion segment. Objective:
To present a new kind of CAD method for constructing a detailed, 3-D, anatomically accurate FE model of lumbar L4-L5 segment from CT data and to thoroughly validate it.
Summary and Background Data:
Currently there are many spinal FE modeling approaches proposed in the literature, which can be roughly ranged into three major groups based on the source data used. One group extracts geometric information from medical image, one group is based on direct measurement on embalmed vertebra using a digitiser, the third group uses anatomy data from literature. With the manual operation process being tedious and the error bigger, the modelling method basing on digitiser only can survey on the embalmed vertebra of the corpse, cannot completely embody complex anatomical structure such as the physical curve of the spine and is unable to realize the spinal FE modelling individuation. With the modelling technology being rough, the modelling method using anatomy data (for example geometrial model modelling of lumbar spine basing on 3D-MAX software) belongs to the manual modelling method, which is unable to realize the FE modelling digitization and does not contain any advanced algorithm, so the overseas FE studies commonly does not adopt it. Respecting its advantage of automation, standard and prompt modelling, the spinal FE
modeling approach basing CT scans is the predominant research method of reconstruction of lumbar geometry model.
At present the lumbar FE modelling methods basing on CT mostly belong to indirect modelling approaches. These kind of indirect modelling approaches first set up the geometry model in other CAD software, which was then imported into FE software through the data connection to carry on the grid division. However, though the modelling efficiency and the quality of the mesh partition of the spinal FE modelling approach basing CT scans have upgraded than that of Goel(1988). When acquiring CT scans data, most methods still took the primitive geometrial data from superposition of monolayer profile information. Meanwhile, the base geometry information was extracted on cross-section planes parallel to orthogonal plane of the CT images, which does not properly account for the preferential orientation feature (e.g. lordosis) of the lumbar spine . Besides, the request of the size and density of FE elements in the different regions of lumbar spine is not uniform, and the foregoing modelling approaches lack the corresponding control mechanism.
Methods:
A modified "no-seed region segmentation" was done to extract the interest region in the CT scan images and produce a binary image. "Best cross-section planes" accounting for the preferential direction dictated by lumbar spine were placed on the initial iso-surface model, forming a "non-regular piecewise subspace". This subspace and the embedded iso-surface mode were transformed by local affine transforms to a "regular subspace", in which a surface mesh of high quality was generated quickly. Finally a reverse transform procedure was employed to recover the shape feature of the lumbar surface mesh of lumbar L4-L5 in the original 3-D space, which was then importing into ANSYS for the 3-D FE mesh construction. All nodes of the inferior surface of L5 vertebral body and its spinous process were fixed in 6 freedom degree of translation and rotation. Axial compressive force of 3000N and flexion、
extension、 lateral bending and axial torsion moment of 15Nm were applied in given increments. Under the same boundary conditions, the predicted results of the current FE model are compared with the results from experimental studies in vitro.
Results:
The developed FE model consisted of 94794 solid elements, 1196 link elements, 1170 shell elements, 768 target elements and 464 contact elements. The model well replicated the actual geometry of all complicated anatomical features of the spine. Three types of non-linearities (i.e. geometrical, material and contact non-linearity) exhibited by the lumbar motion segment were incorporated into the model. The predicted results of FE model correlated well with experimental data under similar loading configurations.
Conclusion:
Accurately represented surface model of L4-L5 segment implements the total digitization of extraction of binary imaging and reconstruction of lumbar lordosis, taking on the best simulation. The current non-linear FE model of L4-L5 segment acquires adequate validation under different loading condition.
Objective:
To develop and validate 3-D FE models of the degenerative lumbar L4-L5 segment with different morphological characteristics using CAD technique.
Methods:
A series of new CAD methods were used to accurately establish FE model of lumbar L4-L5 motion segment. Humane interactive modification means is employed to construct the "interface" which divided the surface model of L4-L5 segment into two basic "structure module" of anterior vertebral body and posterior structure. 9 surface models of the degenerative lumbar spine were constituted by the basic "structure modules" by altering the parameter of disc height, endplate concave angle, sagittal angle of facet joint and lordosis angle of the intervertebral disc. The data of surface model were respectively input into ANSYS to form FE models of "structure module", which then constituted FE models of degenerative lumbar spine with different morphous through gluing and splicing of the interfaces. 18 FE models of degenerative lumbar spine were obtained at last by determining the location of enthesis of anulus fibrosus and lumbar ligaments from their fixed coding. FE models of degenerative lumbar spine were loaded respectively under the axial compression loading of 150N, moment loading of flexion and extension of 7.5Nm and anterior and posterior shear forces of 150N. Under the different loading, the predicted results of FE models of degenerative lumbar spine are compared with the previous findings of experimental biomechanics in the
identical boundary condition. Results:
The FE models of lumbar L4-L5 segment represented all complex spinal components. The predicted results of intact and degenerative L4-L5 segment FE models were closely correlated with published experimental data.
Conclusions:
The individually FE models libraries of degenerative lumbar spine were established basing CT data and CAD method.
Objective:
To research the association between the sagittal orientation of facet joints and disc degeneration in lumbar spine and to investigate the contribution and significance of which to development of the degenerative spondylolisthesis.
Methods:
A new effective CAD method was used to accurately establish 9 FE models which were assembled respectively by facet-joint angle 65° 、facet-joint angle 45° 、 facet-joint angle 25 ° and normal disc 、 light degenerative disc 、 severe degenerative disc. The biomechanical parameters of 9 FE models were measured under axial compressive load within physiological range.
Results:
Compared with FE models with facet-joint angle 45° and 25°, anterior displacement of L4 vertebra in FE models with facet-joint angle 65° was increased, where the maximum von Mises stresses on facet surface and isthmus and the contact force on facet surface in horizontal orientation were obviously increased. Meanwhile, FE models with facet-joint angle 65° showed a decrease in end-plate bulge and an increase in stress of annular matrix. The stiffness in light degenerative disc FE models was reduced and the von Mises stresses on facet surface and isthmus was slightly increased compared with the normal disc FE models. In all FE models, the FE models with facet-joint angle 65° and light degenerative disc displayed a poorest appearance in resisting anterior shear force.
Conclusions:
Sagittal orientation of facet joints is not only the primary motivation of the degenerative spondylolisthesis, but the secondary pathological change of remodelling of the facet-joints induced by the regional stress change. The inherent instability of lumbar motion segment of sagittal orientation of facet joints is influenced by the lumbar disc degeneration. The lumbar disc degeneration has no manifested contribution to the aggravation of the sagittal orientation of facet joints.
Objective:
To investigate the effect of variations in vertebral endplate concavity on the mechanical behavior of the lumbar motion segment.
Methods:
A 3-D nonlinear geometrical and mechanical accurate FE model of lumbar L4-L5 segment was developed. CAD methods were used to establish three FE models with different endplate concave angle, where disc lordosis angle, the gap of facet joint and all other geometrical parameters and FE mesh partition were kept constant. The effect of endplate concavity on the mechanical properties of the lumbar segment was studied for two moment loads (flexion and extension) and for three different direct forces (compression, anterior and posterior shear forces).
Results:
The decrease in the endplate concavity, simulated by an increasing endplate concave angle would result in decreased strains of the endplate and vertebral body, increased disc stiffness and nucleus pressure, decreased annular fiber stress, radial disc bulge and stress in the annulus ground substance, and simultaneously produce decreased facet contact force and stresses in posterior structure.
Conclusions:
The decrease of endplate concavity enhances the protective effect of the
disc on the breakage of the vertebral body. Smaller endplate deformations resulted from the decreasing endplate concavity would contribute to reduction of the nutritional diffusion to the disc.
引文
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