Chinese Journal of Tissue Engineering Research ›› 2023, Vol. 27 ›› Issue (27): 4393-4400.doi: 10.12307/2023.388
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Peng Lu1, 2, Duan Zhili1, 2, Li Zhenyu3, 4, Li Junhui5, Li Yunhong4, Wang Song1, 6, Liu Weiqiang1, 2, 6
Received:
2022-05-27
Accepted:
2022-07-14
Online:
2023-09-28
Published:
2022-11-08
Contact:
Wang Song, PhD, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, Guangdong Province, China; Biomechanics and Biotechnology Lab, Research Institute of Tsinghua University in Shenzhen, Shenzhen 518057, Guangdong Province, China
About author:
Peng Lu, Master candidate, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, Guangdong Province, China; Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
Supported by:
CLC Number:
Peng Lu, Duan Zhili, Li Zhenyu, Li Junhui, Li Yunhong, Wang Song, Liu Weiqiang. Research status and progress of establishment and validation of finite element model of adolescent idiopathic scoliosis[J]. Chinese Journal of Tissue Engineering Research, 2023, 27(27): 4393-4400.
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常见的建模方法是通过人体影像学数据,利用三维重建软件重建脊柱三维模型。CT扫描图像是构建有限元三维模型的常用方法,能够将骨骼与软组织鲜明分离,但全脊柱CT扫描是在仰卧位或俯卧位下进行,因此建立的模型也应是卧位模型,同时辐射剂量较大,这些局限限制了CT图像扫描的应用。X射线作为诊断脊柱侧凸的常用手段,辐射剂量较小,但成像效果也相对较差,单视图X射线图像无法准确地反映脊柱的几何学形态,具有多平面自校准的X射线的EOS成像系统获取椎骨模型在降低对患者身体损害的同时能较好地兼顾图像清晰度,有着广泛的应用[46-50]。模型建立和分析过程主要包括医学影像处理、三维建模、模型修复、有限元前处理、有限元模型建立验证和仿真(材料赋值、网格划分及接触模式选择等)等几个步骤,根据开展有限元建模研究的流程顺序,该综述内容主要分为软件选择、椎骨建立、椎间盘建立、韧带建立和躯干建立几个部分,其中软件选择部分介绍了影像处理、三维建模、模型修复、有限元前处理及有限元模型建立的相关软件,椎骨建立、椎间盘建立、韧带建立和躯干建立几个部分按照解剖结构不同分别介绍相应子模型的材料赋值、网格划分及接触模式等建模细节[51-67]。 2.1.1 软件选择 常见期刊文献中缺少对建模过程的详细描述,文章参考了众多硕博论文,就如何建立青少年特发性脊柱侧凸有限元模型进行详细综述。文章总结了以往相关文献中涉及的软件[51-67],见表2。"
总之,学者们对皮质骨、松质骨的弹性模量、泊松比赋值较为统一,一般情况下认为皮质骨的弹性模量为12 000 MPa,泊松比为0.3,松质骨的弹性模量为100 MPa,泊松比为0.2。但是不同研究中皮质骨和松质骨的网格单元类型有所差异,四面体单元网格在体现模型几何形状和真实性的同时可以减少网格划分难度,但皮质骨采用壳单元、松质骨采用四面体单元可以更好地反映不同部位的形状特征及重要性。 有限元模型建立过程中材料赋值只能是均一的,但脊柱侧凸的出现说明身体两侧各个结构属性并不是完全对称的,且椎骨的不同节段之间也有所区别,这就决定了有限元模型与实体差异必然存在。为了减少其中误差,一些学者根据放射性影像中的灰度值判断对应区域的骨骼密度,通过骨密度和弹性模量之间的经验公式为材料赋值,但不同文献中使用的经验公式各不相同,目前还未形成统一标准。因此,常规椎骨的皮质骨和松质骨材料赋值已形成较为统一的认知,但针对青少年特发性脊柱侧凸模型的椎骨材料的差异性仍有待深入研究,尤其是不同节段和不对称结构材料的差异性。 2.1.3 椎间盘模型建立方法 根据脊柱解剖结构可知,椎骨之间是由椎间盘连接在一起,且由于椎间盘的灰度值与周围组织区分度并不明显,无法直接从CT图像中进行分离,需要通过椎骨模型对椎间盘进行模拟重建。不同文献中椎间盘建立方式大同小异,具体方法为提取椎体上、下表面,建立相应圆柱体;采用布尔运算,得到了椎间盘三维模型,这样生成的椎间盘和椎骨有较好贴合性,更符合人体椎间盘几何形状。一般认为髓核和纤维环的面积比例约为6∶4。弹性模量和泊松比赋值见表4。"
文章总结发现,不同文献中关于髓核和纤维环材料赋值数值相差不大。但在网格划分上有所区别,一些学者采用四面体网格划分纤维环和髓核,也有学者用六面体网格单元构建髓核和纤维环。例如,李劲松等[25]对比了四面体单元建立椎体,六面体单元建立椎间盘;六面体建立椎体和椎间盘;四面体单元建立椎体和椎间盘3种不同建模方式,认为采用四面体单元构建椎体和六面体单元构建椎间盘结构的有限元模型模拟人体脊柱运动单元生物力学特性效果较优。因此,目前椎间盘的模型建立主要通过布尔运算获得,且髓核和纤维环材料赋值数值相差不大,其主要区别在于不同的网格划分,网格结构不同也会导致其生物力学特征具有差异性。考虑到椎间盘的复杂解剖结构以及黏弹性材料属性,未来在椎间盘的建立方面应更多开展髓核纤维环精细结构建模,不同材料属性尤其是黏弹性材料特征的赋予等方面研究。 2.1.4 韧带模型构建方法 韧带的添加可以显著提升模型的精细化程度以及结果可信度。脊柱有限元模型中添加的韧带有6种,包括棘间韧带、棘上韧带、横突韧带、黄韧带、前纵韧带和后纵韧带,部分文献中也可见添加关节囊韧带。不同文献对韧带单元定义有所区别。由于定义方式不同,文献中对韧带材料特性选取也各不相同。一般将韧带定义为弹簧单元时会赋予刚度值,将韧带定义为杆、四面体单元和缆绳单元时一般赋予弹性模量、泊松比和横截面积。即使对韧带的单元定义相同,材料赋值也存在细微差别。文章汇总了不同文献的韧带单元类型以及各参数和数值情况[45,54,56,62-63,65-67,69],见表5。"
从表5中可知,盛文倩[63]利用solid四面体单元表示韧带,将在Mimics里面建好的模型导入3-matic软件,根据解剖学知识确定脊柱韧带附着点;在合适的区域划线模拟韧带的轮廓,然后将曲线闭合;生成一个表面,向内或向外平移表面1 mm 来模拟韧带的厚度;用Loft指令将2个面生成一个实体模型,生成的模型用布尔运算减去与椎体多余的重叠部分从而建立完整的韧带模型,通过材料赋值将韧带与椎骨等进行区分。而有研究认为韧带主要施加张力,支撑力可以忽略,采用缆绳单元定义韧带[67,73];黄盛佳等[54]认为韧带既会受压,也会受到拉力,采用杆单元定义韧带属性;HACHEM等[71]和吴晓薇等[66]用弹簧单元代替韧带,较好地模拟了脊柱变形时韧带的形变情况;也有研究提出用ANSYS中的Link10单元模拟韧带[38],进行生物力学分析。 因此,弹簧单元有自成体系的赋值方法,以刚度为参考标准,区别于其他材料以弹性模量和横截面积为标准。除此之外,杆单元的弹性模量赋值与四面体单元、缆绳单元和Link10单元有显著区别,这可能是为了杆单元模拟的韧带具有一定可压缩特性,所以其后纵韧带、棘间韧带、棘间韧带的弹性模量较大。对于四面体单元、缆绳单元和Link 10单元,它们的前纵韧带、后纵韧带、黄韧带、棘间韧带和棘上韧带的弹性模量数值较统一。因此,韧带单元类型和材料属性的选择会引起较大的结果差异,未来关于韧带建模的材料和网格划分属性仍有待系统深入对比。 2.1.5 躯干模型建立方法 躯干模型的建立可以提高有限元研究的精度。由于支具作用力直接施加在患者皮肤表面,进而传递到肋骨和椎骨,因此探究支具对躯干的作用区域和作用力分布对于支具设计、调整和治疗效果认定具有重要意义。20世纪90年代初,光学技术被应用于躯干模型建立中,研究人员利用可见光或紫外线对患者所处空间和患者自身进行扫描[74],通过集成了结构化投影仪和CCD相机的三维光学数字转化仪,获得躯干表面的几何形状。PAZOS等[75]用四台三维光学数字转化仪,对人体躯干连续投射黑白窄条纹图案,在4-6 s内就获得了躯干模型。有研究比较了手臂轻微外展于身体双侧和手掌贴于颈部双侧的不同姿势下躯干模型获取质量,发现前者的躯干图像无遮挡,质量更高[76]。也有学者提出根据椎体的位置逆向推断躯干模型[77],由于CT数据是在仰卧位获得的,而表面形貌扫描仪获得的躯干模型是站立位模型,这种方法从某种程度来具有更高精度。综上,采用扫描方式建立躯干模型是目前研究的主流,但其网格划分、材料赋值等内容较复杂,目前的研究仍较少涉及。 2.2 青少年特发性脊柱侧凸有限元模型验证方式 有限元模型的可靠性和真实性一直是值得商榷的问题,分析结果的正确与否取决于模型是否合理,能否反映青少年特发性脊柱侧凸的脊柱生物力学特性。常见的模型验证方法包括几何形态验证、与已有文献对比及实验验证等方法。模型验证的方法并不单一,多数文献都会采用多种方法从不同角度论证模型的有效性。 2.2.1 几何形态验证 几何验证是最常见的模型验证方法,其内容是将三维模型与患者原始CT图像作比较。该方法直观、方便,几乎所有文献在模型建立完成后均会采用该种方法判断模型是否合理。例如,盛文倩[63]将建立的有限元模型与原始仰卧位的X射线图像比较,发现有限元模型的几何形状与患者的医学图像基本相似,模型的Cobb角和影像学图像的Cobb角仅相差0.46°。邬超等[65]将优化后的模型与临床站立位的X射线图像对比,测量胸弯、腰弯Cobb角和各椎体到骶骨中线的距离,发现模型与X射线图像的误差在要求范围内。通过分析相关研究发现,Cobb角、腰椎前凸角、胸椎后凸角、各椎体质心相对骶骨中线的偏移距离是较为常见的几何验证中的比较参数。 2.2.2 文献结果验证 与已经发表的权威文献对比也是验证模型有效性的方式之一。由于青少年特发性脊柱侧凸建模涉及到T1-S的整段脊柱,目前关于整段脊柱的模型分析较少,且各模型病变位置不同,直接比较缺乏可行性。常用的验证模型方法是选择结构正常的节段,施加不同作用力,观察不同工况下脊柱活动度活动如与椎体位移是否与既有文献报道相仿[78-81],见表6。"
2.2.3 实验结果验证 实验验证有限元结果是最可靠的验证方式,一般是通过实际治疗效果与有限元分析结果对比来评估一致性。例如,VERGARI等[82]建立了42例青少年特发性脊柱侧凸患者的有限元模型,通过在胸腔上安放软圆柱形压力垫和在对关键椎施加位移的方法模拟支具的作用,与支具实际治疗效果对比,通过比较T1-T12后凸角、L1-L5前凸角、Cobb角、顶椎旋转角度及肋骨隆起6个参数在有限元模拟下和实际治疗时的均方根误差,发现模拟的均方根误差在容许范围内,进而验证了模型的有效性。 2.3 青少年特发性脊柱侧凸有限元模型的不足与发展方向 如今,青少年特发性脊柱侧凸有限元模型及其生物力学分析已被广泛地应用于青少年特发性脊柱侧凸的手术治疗、非手术治疗和病因研究3大方面[83],不仅可为治疗方案设计提供科学依据,也可对治疗结果进行科学预测。随着计算机性能的提升,有限元模型的精确程度也越来越高,模型可靠性也随之提升,模拟结果更加趋向于实际情况。但有限元模型本身就是对人体的一种以简化,和实际情况必然存在差异,当前有限元分析在材料赋值、结构设计及网格划分等方面还未形成统一标准,不同研究中采用不同的建模方式,相互之间并不互通,为形成可信结论埋下隐患。由于青少年特发性脊柱侧凸病情复杂,目前仍有多种疾病情况没有研究,未形成系统的模型库。针对患者的个性化建模费时费力,在临床治疗中难以普及,种种因素制约了有限元方法的发展。 因此,未来青少年特发性脊柱侧凸有限元模型的发展方向主要是:①有限元模型的精准化,既包括几何结构的精准也包括力学方案的精准,只有将有限元模型误差控制在一定范围内,其分析结果才具有可信度,才能有效为临床医生、支具设计师等相关人员提供治疗方案参考依据。根据前文建模文献分析可知,椎间盘、韧带和躯干等模型的结构、材料属性、网格划分等均有待深入对比分析。②有限元模型的标准化,包括不同软件之间对比依据、材料赋值、网格划分等方面,均需要建立相应的标准。③有限元模型的个性化,个性化既体现在个体差异性,也体现在要针对不同青少年特发性脊柱侧凸分型,建立相应的具有代表性的有限元模型数据库。"
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