内、外侧半月板后根部完全撕裂对膝关节生物力学影响的有限元分析
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摘要
半月板根部是指半月板前、后角连接胫骨平台髁间区域的部分，并在该部位发生的撕脱伤或放射状撕裂定义为半月板后根部损伤。引起半月板根部损伤的原因有创伤或继发于关节退行性改变。急性损伤一般发生在年轻，活动能力强的病人，而退行性损伤则发生在老年患者。根据目前的文献，只有对半月板后根部损伤有报道，而且以内侧损伤为多见。内侧半月板后根部比外侧容易损伤的原因可能是由于内侧半月板活动度相对较小，而且在负重时所受的载荷比较大造成的。但对于前交叉韧带损伤的病人来说伴发外侧半月板后根部损伤要比内侧多见。随着核磁共振成像及关节镜在临床上的广泛应用以及对半月板生物力学的进一步研究，近年来，对半月板根部损伤诊断和治疗有了一定进展。然而，半月板根部损伤的发病机制以及对整个膝关节生物力学的影响并没有完整的认识。本研究基于高分辨率MRI图像建立膝关节三维有限元模型，然后对模型进行有效性验证；在此基础上建立内、外侧半月板后根部损伤及前交叉韧带和板股韧带缺损的模型，然后对各种损伤模型进行有限元仿真分析，探讨半月板后根部损伤对膝关节接触力学和运动学的影响，并对半月板后根部损伤的诊断和治疗提供理论依据。
第一部分：膝关节三维有限元模型的建立和验证。本研究的目的在于基于正常人膝关节核磁共振成像扫描数据，建立精确的膝关节三维有限元模型，并进行验证，为下一步实验做基础。利用志愿者左膝关节MRI数据，通过医学影像交互式Mimics软件来建立包括骨组织、关节软骨、半月板、前-后交叉韧带、内-外侧副韧带和后板股韧带的膝关节三维几何模型。利用Geomagic Studio软件对已建立的膝关节三维几何模型进行了优化、修饰。导入Abaqus软件后，参照文献给模型各个部件赋予材料属性。参照同类尸体实验，对膝关节有限元模型进行约束加载。在膝关节伸直位分别加载1000N轴向压缩载荷和134N前向推力，并将分析结果与其他学者体外实验和数字模拟分析结果进行比较，验证模型的有效性。结果表明我们建立了精确、比较完整的包括骨组织，软骨、半月板和主要韧带的膝关节三维有限元模型。验证实验结果与其他学者的体外实验和膝关节有限元数值计算结果相一致，从而验证了膝关节三维有限元模型的可靠性和有效性，为下一步生物力学模拟研究奠定了基础。
第二部分：内侧半月板后根部完全撕裂的有限元分析。本研究的目的是研究比较内侧半月板后根部完全撕裂对膝关节的生物力学影响。在前期建立的正常膝关节有限元模型基础上，建立内侧半月板后根部完全撕裂和内侧半月板全切除模型，并对各个模型分别施加1000N轴向压缩载荷和134N前向推力，对比研究各个模型的接触力学和运动学改变以及对膝关节前方稳定的影响。当内侧半月板后根部完全撕裂时，在1000N轴向压缩载荷下膝关节内侧间室关节软骨最大接触压力和压应力较正常膝关节明显增加，其大小接近内侧半月板全切除时的内侧间室最大接触压力和压应力值。膝关节外侧间室关节软骨最大接触压力和压应力也有所增加。同时较正常膝关节相比，内侧半月板后根部损伤膝关节股骨发生了明显的内旋和内侧和后方位移，而且受损的内侧半月板发生明显的径向位移。在134N前向推力作用下，较正常膝关节相比内侧半月板后根部损伤膝关节的胫骨有一定的前移，但前移程度小于内侧半月板全切除模型。分析结果表明，内侧半月板后根部完全撕裂导致膝关节接触力学、运动学和前方稳定等方面发生了明显改变，不利于膝关节发挥正常生理功能。
第三部分：外侧半月板后根部完全撕裂的有限元分析。本研究的目的是研究比较外侧半月板后根部完全撕裂对膝关节的生物力学影响。在前期建立的正常膝关节有限元模型基础上，建立外侧半月板后根部完全撕裂、前交叉韧带缺损合并外侧半月板后根部完全撕裂和外侧半月板全切除模型，并对各个模型分别施加1000N轴向压缩载荷和134N前向推力，对比研究各个模型的接触力学和运动学改变以及对膝关节前方稳定的影响。当外侧半月板后根部完全撕裂时，在1000N轴向压缩载荷下膝关节外侧间室关节软骨最大接触压力和压应力较正常膝关节显著增加。外侧半月板后根部完全撕裂还导致了受损膝关节股骨发生了外旋、外侧和后方位移。前交叉韧带完全缺损合并外侧半月板后根部完全撕裂时的外侧间室最大接触压力和压应力与单纯外侧半月板后根部完全撕裂相比，接触力学方面无明显差异，而在运动学改变方面较单纯外侧半月板后根部完全撕裂进一步恶化。在前向推力作用下，外侧半月板后根部完全撕裂对膝关节的前方稳定无明显影响外侧半月板后根部完全撕裂导致膝关节外侧间室接触压力和压应力明显增加，然而接触压力和压应力值明显小于外侧半月板全切除模型，由此可以看出，受损的外侧半月板还有这一定传导载荷的功能。第四部分：后板股韧带缺损对正常和外侧半月板后根部完全撕裂膝关节生物力学影
响的有限元分析。本研究通过有限元方法，在前期建立的正常膝关节有限元模型基础上通过人为地将板股韧带切除，比较分析轴向压缩载荷下各个模型在板股韧带切除前、后的应力分布情况，并初步探索后板股韧带的功能以及后板股韧带在外侧半月板后根部损伤膝关节中发挥的作用。结果发现在膝关节伸直位，后板股韧带协助外侧半月板传递一定的载荷，当外侧半月板后根部完全撕裂时，这种传递载荷的作用尤为明显，还能防止后根部撕裂的外侧半月板过度径向位移。
通过上述研究我们认为内、外侧半月板后根部完全撕裂导致受损膝关节发生了明显的接触力学和运动学改变，不利于膝关节发挥正常的生理功能。由于外侧半月板后角的双附着使外侧半月板后根部损伤的生物力学改变不等同于内侧半月板后根部损伤。该研究有助于认识内、外侧半月板后根部撕裂对膝关节生物力学的继发性改变，对研究半月板后根部损伤的诊疗有重要意义。后板股韧带在膝关节中协助外侧半月板发挥着一定的生理功能，因此我们建议在交叉韧带重建或半月板关节镜诊疗过程中尽量保留板股韧带。
The meniscus root is defined anatomically as the portion of the meniscus that attachesthe anterior and posterior horn of the meniscus to the central tibial plateau. The meniscus roottears caused by trauma or secondary to degenerative joint changes. Acute root tears generallyoccur in young, active individuals, and the elderly patients more likely suffer from attritionaldegenerative radial tearing. According to the available literature, only posterior meniscal roottear has been reported, and the most of the published literature regarding posterior root tearshas focused on medial meniscal root tears. The medial meniscus is less mobile than the lateralmeniscus and carries more force during weight bearing making it more prone to injury.However, posterior lateral meniscus root tears are injuries that are commonly associated withanterior cruciate ligament tears. In recent years, with technological advances in arthroscopyand magnetic resonance imaging and improved biomechanical studies of the meniscus, therehas been some progress in the diagnosis and treatment of injuries to the roots of the meniscus.However, the biomechanical effect of posterior meniscus root tears on the knee has not yetbecome clear. In this study, we developed a finite element model of the knee joint based onhigh resolution MRI images, and verified the validity of the model. The models of medial andlateral posterior meniscus root tear, anterior cruciate ligament and meniscofemoral ligamentdeficiencies, and total meniscectomy of the medial and lateral meniscus were generated on thebasis of the intact knee model. Finite element analysis (FEA) was performed to investigate thebiomechanical effects of the complete posterior root tears of medial and lateral meniscus onthe knee joint and to providing a theoretical basis for the diagnosis and treatment of meniscalroot tears.
Section one: Development and validation of3-D finite element model of knee joint. Theaim of this section is to develop and verify a three-dimensional (3D) computational model ofa knee joint that to be used to predict the biomechanical effect of posterior meniscus root tearson the knee. Numerical data of three-dimensional finite element models of the knee werebased on MRI images of an adult volunteer. The images were processed using MIMICS to construct the knee model consisted of the femur, the tibia and fibula, articular cartilage layers,the menisci and the main ligaments of the knee: anterior cruciate ligament (ACL), posteriorcruciate ligament (PCL), medial collateral ligament (MCL), lateral collateral ligament (LCL)and posterior meniscal femoral ligament(PMFL). The model was refined for finite elementanalysis using Geomagic Studio. Tetrahedral elements were used to mesh the entire model andit was then analyzed in ABAQUS. The material properties of the model were chosen fromvalues identified in the literature. In order to compare the obtained results with previousstudies, a compressive axial load of1000N and an anterior load of134Nwere applied to theFEA model. The results show that we have developed an accurate, relatively complete three-dimensional finite element model of knee joint, including bone tissue, cartilage, meniscus andmajor ligaments. This model was validated using experimental and numerical results obtainedby other authors. The results obtained from our study are in agreement with previouslypublished reports. This validated computational knee model can be used to predict kneebiomechanical mechanics and laid the foundation for further biomechanical study.
Section two: Finite element analysis of the complete posterior medial meniscus root tear.The purpose of this section was to determine the biomechanical effect of a complete posteriormedial meniscus root tear (PMMRT) on the knee joint. Based on the pre-established,validated finite element model of knee joint, we simulated different cases for intact knee, acomplete PMMRT, and total meniscectomy of the medial meniscus. Isolated axialcompressive load of1000N and anterior load of134N were applied in all cases to comparetheir contact mechanics, kinematics and knee stability. The results show that the completePMMRT increased the peak contact pressure and stress on the medial compartment undercompressive load and its values approximate to medial total meniscectomy. We also foundincreased contact pressure and stress in the lateral compartment, but it was not obviouscompared to the medial compartment. Significant increases in radial displacement of medialmeniscus, femoral internal rotation, posterior and medial translation, compared with the intactknee, were observed in association with the complete PMMRT. The anterior tibial translationunder the anterior tibial load in knee with tear in the posterior root of medial meniscus waslarger than in the intact knee, but it is smaller than values of total medial meniscectomy. Theresults show that the complete PMMRT leads to deleterious alteration of the loading profilesof the medial joint compartment and results in significant changes in knee joint kinematicsand stability. All these are not conducive to play a normal physiological function of the knee.
Section three: Finite element analysis of the complete posterior lateral meniscus root tear. The purpose of this section was to determine the biomechanical effect of a complete posteriorlateral meniscus root tear (PLMRT) on the knee joint. Based on the pre-established, validated,finite element model of knee joint, we simulate different cases for a complete PLMRT, acomplete PLMRT combined with ACL deficiency, and total meniscectomy of the lateralmeniscus. Isolated compressive load of1000N was applied in all cases to compare theircontact mechanics, kinematics and knee stability. The results show that the complete posteriorlateral meniscus root tear increased the peak contact pressure and stress on the lateralcompartment under compressive load, but it is smaller than values of total medialmeniscectomy. The complete PLMRT leads to significant increases in radial displacement oflateral meniscus, femoral external rotation, lateral and posterior translation, compared withthe intact knee. We also found that in the complete PLMRT combined with ACL deficientknee, there were no significant contact profiles alteration compared to the knee with tear inthe posterior root of lateral meniscus. However, there were deleterious alterations of kneekinematics. The complete PLMRT had no significant effect on the anterior tibial translationunder the anterior tibial load. The results show that the complete PLMRT is not functionallyequivalent to total meniscectomy. The posterior root torn lateral meniscus continues toprovide some load transmission and distribution functions across the joint.
Section four: Finite element analysis on the function of the posterior meniscofemoralligament on the knee with or without tear in the posterior root of lateral meniscus. Thepurpose of this section was to predict the function of the posterior meniscofemoral ligament(PMFL) on the knee with or without tear in the posterior root of lateral meniscus. In order todetermine the effects of PMFL deficiency on the knee with or without tear in posterior root oflateral meniscus, we used a computer-aided method to artificially remove the PMFL andcompared the contact variables of pre-and post-sectioning. After comparing the contactvariables of before and after removing the PMFL on the knee with or without a tear in theposterior root of the lateral meniscus, our results indicate that the PMFL assists the lateralmeniscus in transmitting a certain amount of stress and load in the lateral compartment of theknee and this effect more obvious in the knee with a torn lateral meniscus. Meanwhile, thePMFL prevents excessive radial displacement of the lateral meniscus with a torn posteriorroot under compressive load.
Posterior root tears of meniscus lead to deleterious alteration of the biomechanicalenvironment of knee joint. The presence of double attachment of lateral meniscus posteriorhorn makes the biomechanical consequences of PLMRT different from PMMRT. These findings improve our understanding of the effect of meniscal posterior root tear on thebiomechanics of the knee joint and could guide clinicians in making a diagnosis anddetermining the appropriate treatment plan in this type of injury. In addition, based on thebiomechanical contributions of the PMFL found in this study, we suggest PMFL retention inPCL and meniscal surgery.
第一部分：膝关节三维有限元模型的建立和验证。本研究的目的在于基于正常人膝关节核磁共振成像扫描数据，建立精确的膝关节三维有限元模型，并进行验证，为下一步实验做基础。利用志愿者左膝关节MRI数据，通过医学影像交互式Mimics软件来建立包括骨组织、关节软骨、半月板、前-后交叉韧带、内-外侧副韧带和后板股韧带的膝关节三维几何模型。利用Geomagic Studio软件对已建立的膝关节三维几何模型进行了优化、修饰。导入Abaqus软件后，参照文献给模型各个部件赋予材料属性。参照同类尸体实验，对膝关节有限元模型进行约束加载。在膝关节伸直位分别加载1000N轴向压缩载荷和134N前向推力，并将分析结果与其他学者体外实验和数字模拟分析结果进行比较，验证模型的有效性。结果表明我们建立了精确、比较完整的包括骨组织，软骨、半月板和主要韧带的膝关节三维有限元模型。验证实验结果与其他学者的体外实验和膝关节有限元数值计算结果相一致，从而验证了膝关节三维有限元模型的可靠性和有效性，为下一步生物力学模拟研究奠定了基础。
第二部分：内侧半月板后根部完全撕裂的有限元分析。本研究的目的是研究比较内侧半月板后根部完全撕裂对膝关节的生物力学影响。在前期建立的正常膝关节有限元模型基础上，建立内侧半月板后根部完全撕裂和内侧半月板全切除模型，并对各个模型分别施加1000N轴向压缩载荷和134N前向推力，对比研究各个模型的接触力学和运动学改变以及对膝关节前方稳定的影响。当内侧半月板后根部完全撕裂时，在1000N轴向压缩载荷下膝关节内侧间室关节软骨最大接触压力和压应力较正常膝关节明显增加，其大小接近内侧半月板全切除时的内侧间室最大接触压力和压应力值。膝关节外侧间室关节软骨最大接触压力和压应力也有所增加。同时较正常膝关节相比，内侧半月板后根部损伤膝关节股骨发生了明显的内旋和内侧和后方位移，而且受损的内侧半月板发生明显的径向位移。在134N前向推力作用下，较正常膝关节相比内侧半月板后根部损伤膝关节的胫骨有一定的前移，但前移程度小于内侧半月板全切除模型。分析结果表明，内侧半月板后根部完全撕裂导致膝关节接触力学、运动学和前方稳定等方面发生了明显改变，不利于膝关节发挥正常生理功能。
第三部分：外侧半月板后根部完全撕裂的有限元分析。本研究的目的是研究比较外侧半月板后根部完全撕裂对膝关节的生物力学影响。在前期建立的正常膝关节有限元模型基础上，建立外侧半月板后根部完全撕裂、前交叉韧带缺损合并外侧半月板后根部完全撕裂和外侧半月板全切除模型，并对各个模型分别施加1000N轴向压缩载荷和134N前向推力，对比研究各个模型的接触力学和运动学改变以及对膝关节前方稳定的影响。当外侧半月板后根部完全撕裂时，在1000N轴向压缩载荷下膝关节外侧间室关节软骨最大接触压力和压应力较正常膝关节显著增加。外侧半月板后根部完全撕裂还导致了受损膝关节股骨发生了外旋、外侧和后方位移。前交叉韧带完全缺损合并外侧半月板后根部完全撕裂时的外侧间室最大接触压力和压应力与单纯外侧半月板后根部完全撕裂相比，接触力学方面无明显差异，而在运动学改变方面较单纯外侧半月板后根部完全撕裂进一步恶化。在前向推力作用下，外侧半月板后根部完全撕裂对膝关节的前方稳定无明显影响外侧半月板后根部完全撕裂导致膝关节外侧间室接触压力和压应力明显增加，然而接触压力和压应力值明显小于外侧半月板全切除模型，由此可以看出，受损的外侧半月板还有这一定传导载荷的功能。第四部分：后板股韧带缺损对正常和外侧半月板后根部完全撕裂膝关节生物力学影
响的有限元分析。本研究通过有限元方法，在前期建立的正常膝关节有限元模型基础上通过人为地将板股韧带切除，比较分析轴向压缩载荷下各个模型在板股韧带切除前、后的应力分布情况，并初步探索后板股韧带的功能以及后板股韧带在外侧半月板后根部损伤膝关节中发挥的作用。结果发现在膝关节伸直位，后板股韧带协助外侧半月板传递一定的载荷，当外侧半月板后根部完全撕裂时，这种传递载荷的作用尤为明显，还能防止后根部撕裂的外侧半月板过度径向位移。
通过上述研究我们认为内、外侧半月板后根部完全撕裂导致受损膝关节发生了明显的接触力学和运动学改变，不利于膝关节发挥正常的生理功能。由于外侧半月板后角的双附着使外侧半月板后根部损伤的生物力学改变不等同于内侧半月板后根部损伤。该研究有助于认识内、外侧半月板后根部撕裂对膝关节生物力学的继发性改变，对研究半月板后根部损伤的诊疗有重要意义。后板股韧带在膝关节中协助外侧半月板发挥着一定的生理功能，因此我们建议在交叉韧带重建或半月板关节镜诊疗过程中尽量保留板股韧带。
The meniscus root is defined anatomically as the portion of the meniscus that attachesthe anterior and posterior horn of the meniscus to the central tibial plateau. The meniscus roottears caused by trauma or secondary to degenerative joint changes. Acute root tears generallyoccur in young, active individuals, and the elderly patients more likely suffer from attritionaldegenerative radial tearing. According to the available literature, only posterior meniscal roottear has been reported, and the most of the published literature regarding posterior root tearshas focused on medial meniscal root tears. The medial meniscus is less mobile than the lateralmeniscus and carries more force during weight bearing making it more prone to injury.However, posterior lateral meniscus root tears are injuries that are commonly associated withanterior cruciate ligament tears. In recent years, with technological advances in arthroscopyand magnetic resonance imaging and improved biomechanical studies of the meniscus, therehas been some progress in the diagnosis and treatment of injuries to the roots of the meniscus.However, the biomechanical effect of posterior meniscus root tears on the knee has not yetbecome clear. In this study, we developed a finite element model of the knee joint based onhigh resolution MRI images, and verified the validity of the model. The models of medial andlateral posterior meniscus root tear, anterior cruciate ligament and meniscofemoral ligamentdeficiencies, and total meniscectomy of the medial and lateral meniscus were generated on thebasis of the intact knee model. Finite element analysis (FEA) was performed to investigate thebiomechanical effects of the complete posterior root tears of medial and lateral meniscus onthe knee joint and to providing a theoretical basis for the diagnosis and treatment of meniscalroot tears.
Section one: Development and validation of3-D finite element model of knee joint. Theaim of this section is to develop and verify a three-dimensional (3D) computational model ofa knee joint that to be used to predict the biomechanical effect of posterior meniscus root tearson the knee. Numerical data of three-dimensional finite element models of the knee werebased on MRI images of an adult volunteer. The images were processed using MIMICS to construct the knee model consisted of the femur, the tibia and fibula, articular cartilage layers,the menisci and the main ligaments of the knee: anterior cruciate ligament (ACL), posteriorcruciate ligament (PCL), medial collateral ligament (MCL), lateral collateral ligament (LCL)and posterior meniscal femoral ligament(PMFL). The model was refined for finite elementanalysis using Geomagic Studio. Tetrahedral elements were used to mesh the entire model andit was then analyzed in ABAQUS. The material properties of the model were chosen fromvalues identified in the literature. In order to compare the obtained results with previousstudies, a compressive axial load of1000N and an anterior load of134Nwere applied to theFEA model. The results show that we have developed an accurate, relatively complete three-dimensional finite element model of knee joint, including bone tissue, cartilage, meniscus andmajor ligaments. This model was validated using experimental and numerical results obtainedby other authors. The results obtained from our study are in agreement with previouslypublished reports. This validated computational knee model can be used to predict kneebiomechanical mechanics and laid the foundation for further biomechanical study.
Section two: Finite element analysis of the complete posterior medial meniscus root tear.The purpose of this section was to determine the biomechanical effect of a complete posteriormedial meniscus root tear (PMMRT) on the knee joint. Based on the pre-established,validated finite element model of knee joint, we simulated different cases for intact knee, acomplete PMMRT, and total meniscectomy of the medial meniscus. Isolated axialcompressive load of1000N and anterior load of134N were applied in all cases to comparetheir contact mechanics, kinematics and knee stability. The results show that the completePMMRT increased the peak contact pressure and stress on the medial compartment undercompressive load and its values approximate to medial total meniscectomy. We also foundincreased contact pressure and stress in the lateral compartment, but it was not obviouscompared to the medial compartment. Significant increases in radial displacement of medialmeniscus, femoral internal rotation, posterior and medial translation, compared with the intactknee, were observed in association with the complete PMMRT. The anterior tibial translationunder the anterior tibial load in knee with tear in the posterior root of medial meniscus waslarger than in the intact knee, but it is smaller than values of total medial meniscectomy. Theresults show that the complete PMMRT leads to deleterious alteration of the loading profilesof the medial joint compartment and results in significant changes in knee joint kinematicsand stability. All these are not conducive to play a normal physiological function of the knee.
Section three: Finite element analysis of the complete posterior lateral meniscus root tear. The purpose of this section was to determine the biomechanical effect of a complete posteriorlateral meniscus root tear (PLMRT) on the knee joint. Based on the pre-established, validated,finite element model of knee joint, we simulate different cases for a complete PLMRT, acomplete PLMRT combined with ACL deficiency, and total meniscectomy of the lateralmeniscus. Isolated compressive load of1000N was applied in all cases to compare theircontact mechanics, kinematics and knee stability. The results show that the complete posteriorlateral meniscus root tear increased the peak contact pressure and stress on the lateralcompartment under compressive load, but it is smaller than values of total medialmeniscectomy. The complete PLMRT leads to significant increases in radial displacement oflateral meniscus, femoral external rotation, lateral and posterior translation, compared withthe intact knee. We also found that in the complete PLMRT combined with ACL deficientknee, there were no significant contact profiles alteration compared to the knee with tear inthe posterior root of lateral meniscus. However, there were deleterious alterations of kneekinematics. The complete PLMRT had no significant effect on the anterior tibial translationunder the anterior tibial load. The results show that the complete PLMRT is not functionallyequivalent to total meniscectomy. The posterior root torn lateral meniscus continues toprovide some load transmission and distribution functions across the joint.
Section four: Finite element analysis on the function of the posterior meniscofemoralligament on the knee with or without tear in the posterior root of lateral meniscus. Thepurpose of this section was to predict the function of the posterior meniscofemoral ligament(PMFL) on the knee with or without tear in the posterior root of lateral meniscus. In order todetermine the effects of PMFL deficiency on the knee with or without tear in posterior root oflateral meniscus, we used a computer-aided method to artificially remove the PMFL andcompared the contact variables of pre-and post-sectioning. After comparing the contactvariables of before and after removing the PMFL on the knee with or without a tear in theposterior root of the lateral meniscus, our results indicate that the PMFL assists the lateralmeniscus in transmitting a certain amount of stress and load in the lateral compartment of theknee and this effect more obvious in the knee with a torn lateral meniscus. Meanwhile, thePMFL prevents excessive radial displacement of the lateral meniscus with a torn posteriorroot under compressive load.
Posterior root tears of meniscus lead to deleterious alteration of the biomechanicalenvironment of knee joint. The presence of double attachment of lateral meniscus posteriorhorn makes the biomechanical consequences of PLMRT different from PMMRT. These findings improve our understanding of the effect of meniscal posterior root tear on thebiomechanics of the knee joint and could guide clinicians in making a diagnosis anddetermining the appropriate treatment plan in this type of injury. In addition, based on thebiomechanical contributions of the PMFL found in this study, we suggest PMFL retention inPCL and meniscal surgery.
引文
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