臼杯假体高度对臼杯-骨界面应力应变影响的有限元分析

doi:10.3877/cma.j.issn.1674-134X.2020.05.010

目的

探究臼杯假体模拟植入Crowe Ⅱ/Ⅲ型DDH髋臼的不同高度时臼杯-骨界面间应力和应变分布特征。

方法

基于3位Crowe Ⅱ/Ⅲ型DDH患者髋关节的CT扫描数据，利用计算机软件作髋臼三维建模，在距髋臼下缘连线垂直高度为15、21、30 mm处分别模拟植入臼杯模型，并转化为三维有限元网格模型，施加静力载荷，记录臼杯-骨界面的应力和应变数据，行配对t检验或Wilcoxon符号秩检验分析各组最大应力及应变的差异。

结果

3组臼杯模型在距髋臼下缘连线垂直高度为21 mm处的最大应力值最小，分别为患者A 10.03 Mpa、患者B 17.67 Mpa和患者C 14.99 Mpa。在安装高度为15 mm和30 mm处，臼杯的最大应力值分别为患者A 20.64、12.03 Mpa，患者B 22.06、23.02 Mpa和患者C 34.72、17.88 Mpa。对15、21、30 mm处骨质、臼杯的最大应力及应变行两两配对检验显示各组差异无统计学意义(校正后P>0.0167)。不同安装高度下臼杯假体及假体周围骨组织应变量没有明显分布规律。

结论

对于Crowe Ⅱ/Ⅲ型DDH患者行全髋关节置换术，适当上移臼杯旋转中心能减少臼杯假体最大应力。

关键词: 髋关节, 人工关节, 生物力学, 有限元分析

Objective

To investigate the stress and strain feature at the acetabular cup-bone interface at different heights of the Crowes Ⅱ/Ⅲ DDH acetabular implant.

Methods

The hip CT scan data of three Crowe Ⅱ/Ⅲ DDH patients were used for acetabular three-dimensional model reconstruction, then the cup models were implanted at vertical distance of 15, 21, 30mm respectively from the inferior edge of the acetabulum. The model was transformed into a three-dimensional finite element mesh model, and applied a static load to record the stress and strain at the cup-bone interface. The differences of the stress and strain at the cup-bone interface were analyzed by paired-sample t test or Wilcoxon rank test.

Results

The minimal value of maximal stress was appeared at the vertical height of 21 mm, patient A 10.03 Mpa, patient B 17.67 Mpa and patient C 14.99 Mpa. At the height of 15mm and 30mm, the maximal values of maximal stress of the cup were as follows: patient A 20.64 and 12.03 Mpa, patient B 22.06 and 23.02 Mpa, patient C 34.72 and 17.88 Mpa. Paired-samples t test revealed no significant difference in the stress and strain at the cup-bone interface(P>0.0167, P value was corrected). There was no specific pattern on the strain of the acetabulum and the bone tissue at different heights.

Conclusion

For total hip arthroplasty in the patients with Crowe Ⅱ/Ⅲ DDH, the cup model implanted upward appropriately can decrease the maximal stress of the cup model.

Key words: Hip, Joint prosthesis, Biomechanical phenomena, Finite element analysis

图1 半骨盆三维实体模型及其与不同高度臼杯安放位置的三维实体模型。图A皮质骨三维模型；图B松质骨三维模型；图C距髋臼下缘连线垂直高度15 mm；图D距髋臼下缘连线垂直高度21 mm；图E距髋臼下缘连线垂直高度30 mm

图2 三维半骨盆和臼杯有限元网格模型(蓝色：外侧皮质骨；绿色：内侧松质骨；黄色：臼杯模型)

表1 各组有限元网格参数

	患者A			患者B			患者C
	15 mm	21 mm	30 mm	15 mm	21 mm	30 mm	15 mm	21 mm	30 mm
节点	397997	395617	393292	431488	430731	431488	443636	442981	442991
单元	241502	239956	238199	264864	264268	264864	269289	268584	270368

表1 各组有限元网格参数

	患者A			患者B			患者C
	15 mm	21 mm	30 mm	15 mm	21 mm	30 mm	15 mm	21 mm	30 mm
节点	397997	395617	393292	431488	430731	431488	443636	442981	442991
单元	241502	239956	238199	264864	264268	264864	269289	268584	270368

表2 各部分材料属性参数

材料	弹性模量(MPa)	泊松比
皮质骨	17000.0	0.3
松质骨	4300.0	0.3
钛合金	110000.0	0.3

表2 各部分材料属性参数

材料	弹性模量(MPa)	泊松比
皮质骨	17000.0	0.3
松质骨	4300.0	0.3
钛合金	110000.0	0.3

图3 三维模型边界条件和载荷(红色箭头表示施加应力方向)

图4 髋关节臼杯假体以及周围骨质部分的应力与应变分布云图。图A～C为髋关节臼杯假体以及周围骨质部分的应力分布云图：臼杯假体外上部区域可测得应力最大值，为应力集中区域(红色区域)；图D～F为臼杯假体以及周围骨质部分的应变云图：臼杯假体外上部及骨质髋臼外上侧应变较其他部分稍大，但整体差异不大

表3 假体周围不同部位骨质部分最大应力与应变结果

	例数	最大应力[Mpa，M(P₂₅，P₇₅)]	最大应变[mm，(±s)]
15 mm	3	24.29(23.39，29.50)	0.08±0.05
21 mm	3	17.95(17.83，20.15)	0.08±0.05
30 mm	3	22.44(20.16，26.10)	0.08±0.04
统计值		Z＝-1.604^a，-1.604^b，-0.535^c	t＝0.061^a，0.854^b 0.378^c
P值^*		>0.0167^abc	>0.0167^abc

表3 假体周围不同部位骨质部分最大应力与应变结果

	例数	最大应力[Mpa，M(P₂₅，P₇₅)]	最大应变[mm，(±s)]
15 mm	3	24.29(23.39，29.50)	0.08±0.05
21 mm	3	17.95(17.83，20.15)	0.08±0.05
30 mm	3	22.44(20.16，26.10)	0.08±0.04
统计值		Z＝-1.604^a，-1.604^b，-0.535^c	t＝0.061^a，0.854^b 0.378^c
P值^*		>0.0167^abc	>0.0167^abc

表4 臼杯模型最大应力与应变结果

	例数	最大应力()[Mpa，(±s)]	最大应变[mm，M(P₂₅，P₇₅)]
15mm	3	25.81±7.75	0.07(0.05，0.08)
21mm	3	14.23±3.88	0.07(0.05，0.07)
30mm	3	17.74±5.50	0.07(0.05，0.07)
统计值		t＝2.599^a，-3.407^b，1.587^c	Z＝-1.342^a，-1.000^b 1.342^c
P值		>0.0167^abc	>0.0167^abc

表4 臼杯模型最大应力与应变结果

	例数	最大应力()[Mpa，(±s)]	最大应变[mm，M(P₂₅，P₇₅)]
15mm	3	25.81±7.75	0.07(0.05，0.08)
21mm	3	14.23±3.88	0.07(0.05，0.07)
30mm	3	17.74±5.50	0.07(0.05，0.07)
统计值		t＝2.599^a，-3.407^b，1.587^c	Z＝-1.342^a，-1.000^b 1.342^c
P值		>0.0167^abc	>0.0167^abc

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Finite element analysis of effects of stress and strain on acetabular cup-bone interface at different heights

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Finite element analysis of effects of stress and strain on acetabular cup-bone interface at different heights