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Article(id=1244321224424272120, tenantId=1146029695717560320, journalId=1244284848500682798, issueId=1244321215637209904, articleNumber=null, orderNo=null, doi=10.16156/j.1004-7220.2025.05.006, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1735574400000, receivedDateStr=2024-12-31, revisedDate=1738771200000, revisedDateStr=2025-02-06, acceptedDate=null, acceptedDateStr=null, onlineDate=1774598898273, onlineDateStr=2026-03-27, pubDate=1759248000000, pubDateStr=2025-10-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774598898273, onlineIssueDateStr=2026-03-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774598898273, creator=13701087609, updateTime=1774598898273, updator=13701087609, issue=Issue{id=1244321215637209904, tenantId=1146029695717560320, journalId=1244284848500682798, year='2025', volume='40', issue='5', pageStart='1079', pageEnd='1366', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1774598896178, creator=13701087609, updateTime=1774599509568, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1244323788452639476, tenantId=1146029695717560320, journalId=1244284848500682798, issueId=1244321215637209904, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1244323788452639477, tenantId=1146029695717560320, journalId=1244284848500682798, issueId=1244321215637209904, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1129, endPage=1135, ext={EN=ArticleExt(id=1244321226957631890, articleId=1244321224424272120, tenantId=1146029695717560320, journalId=1244284848500682798, language=EN, title=Effects of Early Postoperative Changes in Graft Viscoelasticity on Stress Distributions Within the Knee Joint Following Anterior Cruciate Ligament Reconstruction, columnId=1244321216404767539, journalTitle=Journal of Medical Biomechanics, columnName=Original Articles, runingTitle=null, highlight=null, articleAbstract=
Objective

To investigate stress distributions of the knee joint at 0 and 15th day after anterior cruciate ligament reconstruction (ACLR) under a compressive force through the axis of the femoral shaft onto the proximal femur.

Methods

A three-dimensional (3D) finite element model of the human knee joint incorporating viscoelastic material properties was developed. The one-dimensional (1D) Prony series viscoelastic constitutive model parameters for articular cartilage, menisci, ligaments, and anterior cruciate ligament (ACL) grafts were determined by fitting experimental creep curves. The viscoelastic parameters of ACL grafts at 15th day after ACLR surgery were extrapolated. Finite element simulations were then performed to analyze the von Mises stress distributions in knee ligaments, ACL grafts, articular cartilage, and menisci under 1.5 kN vertical downward compressive load applied to the femur, with loading durations of 1 second and 600 seconds.

Results

At 15th day after ACLR surgery, the initial relaxation modulus and equilibrium modulus of human ACL grafts remained elevated compared to native ACL tissues, resulting in a significantly higher stress concentration within the grafts relative to healthy ACL. Despite the compromised mechanical properties of the grafts after ACLR surgery, the vertical downward compressive force applied to the femur under both short-term (1 s) and prolonged (600 s) loading durations, exhibited a minimal biomechanical impact on articular cartilage and meniscal structures.

Conclusions

Following ACLR, vertical compressive loads during weight-bearing rehabilitation exercises such as standing demonstrate minimal impact on articular cartilage and meniscus, while promoting fibrous regeneration of the graft. This renders such exercises a prudent early-stage rehabilitation strategy. Graft preparation requires balanced consideration of elastic and viscous properties, with grafts exhibiting higher relaxation modulus and viscosity coefficient than healthy ACL proving more effective in maintaining early postoperative knee stability.

, correspAuthors=Bin YANG, Jie YAO, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Zizhan LIAN, Bin SUN, Shanjiang YU, Yichen YAN, Qinqin YANG, Bin YANG, Jie YAO), CN=ArticleExt(id=1244321231755916010, articleId=1244321224424272120, tenantId=1146029695717560320, journalId=1244284848500682798, language=CN, title=前交叉韧带重建术后短期内移植体黏弹性变化对膝关节应力分布的影响, columnId=1244321216576734006, journalTitle=医用生物力学, columnName=论著, runingTitle=null, highlight=null, articleAbstract=
目的

探究前交叉韧带重建（anterior cruciate ligament reconstruction，ACLR）术后0、15 d股骨受到垂直向下压力时膝关节内应力分布。

方法

建立添加黏弹性材料属性的人体膝关节三维有限元模型。采用拟合蠕变曲线的方法获取软骨、半月板、韧带和前交叉韧带（anterior cruciate ligament，ACL）移植体的一维Prony黏弹性本构模型参数。估计ACLR术后15 d移植体黏弹性材料属性参数，模拟分析股骨受到垂直向下1.5 kN压力时，持续1 s与600 s后膝关节韧带、ACL移植体、关节软骨与半月板von Mises应力分布。

结果

ACLR术后15 d移植体的初始松弛模量与平衡模量依旧高于人体ACL，ACL移植体所承受的应力相比健康ACL更高。尽管移植体的力学特性在ACLR术后降低，但股骨受到垂直向下施加压力1 s或600 s对软骨与半月板影响均较小。

结论

ACLR术后，站立等负重康复训练中膝关节所受垂直向下载荷对关节软骨及半月板影响较小，且对移植体纤维再生具有促进作用，故可作为术后早期较为稳妥的康复方案。移植体制备需综合考量其弹性与黏性特性；松弛模量与黏度系数高于健康ACL的移植体，可更有利于维持术后早期膝关节稳定性。

, correspAuthors=杨滨, 姚杰, authorNote=null, correspAuthorsNote=
姚杰，副教授，E-mail：；
杨滨，副主任医师，E-mail：

*

为共同通信作者
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作者贡献声明：

连子瞻负责研究实施、数据采集、论文撰写；孙彬、于善江负责研究实施；杨钦钦负责模型制作；严亦辰负责数据分析；杨滨负责研究指导及论文审阅；姚杰负责研究设计、论文修改。

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J Bone Joint Surg Am, 2020, 102(22): 1948-1955., articleTitle=Microstructural and mechanical properties of grafts commonly used for cruciate ligament reconstruction, refAbstract=null), Reference(id=1244321245068636647, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321224424272120, doi=null, pmid=null, pmcid=null, year=2018, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[21], rfOrder=21, authorNames=MARIESWARAN M, JAIN I, GARG B, journalName=Appl Bionics Biomech, refType=null, unstructuredReference=MARIESWARAN M, JAIN I, GARG B, et al. A review on biomechanics of anterior cruciate ligament and materials for reconstruction[J]. 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Material properties of cartilage, meniscus, ligaments, and grafts

, figureFileSmall=null, figureFileBig=null, tableContent=
参数软骨半月板ACL、韧带ACLR术后移植体
0 d15 d
g1/%0.8140.280.180.130.14
k1/%0.9820.280.180.130.14
τ/s24.111.126.370.660.54
E0/MPa4.380.7742.8192.2156.18
), ArticleFig(id=1244321239989334305, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321224424272120, language=CN, label=表1, caption=

软骨、半月板、膝关节内韧带及移植体材料属性

, figureFileSmall=null, figureFileBig=null, tableContent=
参数软骨半月板ACL、韧带ACLR术后移植体
0 d15 d
g1/%0.8140.280.180.130.14
k1/%0.9820.280.180.130.14
τ/s24.111.126.370.660.54
E0/MPa4.380.7742.8192.2156.18
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前交叉韧带重建术后短期内移植体黏弹性变化对膝关节应力分布的影响
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连子瞻 1 , 孙彬 2 , 于善江 2 , 严奕辰 1 , 杨钦钦 1 , 杨滨 2, * , 姚杰 1, *
医用生物力学 | 论著 2025,40(5): 1129-1135
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医用生物力学 | 论著 2025, 40(5): 1129-1135
前交叉韧带重建术后短期内移植体黏弹性变化对膝关节应力分布的影响
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连子瞻1, 孙彬2, 于善江2, 严奕辰1, 杨钦钦1, 杨滨2, * , 姚杰1, *
作者信息
  • 1.生物力学与力生物学教育部重点实验室；高端医疗装备与器械创新及转化工业和信息化部重点实验室；国家医学攻关（医工结合方向）高端医疗装备与器械产教融合创新平台；北京航空航天大学　生物与医学工程学院，北京　100191
  • 2.北京大学国际医院　骨科，北京　102206

通讯作者:

姚杰，副教授，E-mail：；
杨滨，副主任医师，E-mail：

*

为共同通信作者
Effects of Early Postoperative Changes in Graft Viscoelasticity on Stress Distributions Within the Knee Joint Following Anterior Cruciate Ligament Reconstruction
Zizhan LIAN1, Bin SUN2, Shanjiang YU2, Yichen YAN1, Qinqin YANG1, Bin YANG2 , Jie YAO1
Affiliations
  • 1.Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education; Key Laboratory of Innovation and Transformation of Advanced Medical Devices, Ministry of Industry and Information Technology; National Medical Innovation Platform for Industry-Education Integration in Advanced Medical Devices (Interdiscipline of Medicine and Engineering), School of Biological Science and Medical Engineering, Beihang University, Beijing 100191, China
  • 2.Department of Orthopedics, Peking University International Hospital, Beijing 102206, China
出版时间: 2025-10-01 doi: 10.16156/j.1004-7220.2025.05.006
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目的

探究前交叉韧带重建（anterior cruciate ligament reconstruction，ACLR）术后0、15 d股骨受到垂直向下压力时膝关节内应力分布。

方法

建立添加黏弹性材料属性的人体膝关节三维有限元模型。采用拟合蠕变曲线的方法获取软骨、半月板、韧带和前交叉韧带（anterior cruciate ligament，ACL）移植体的一维Prony黏弹性本构模型参数。估计ACLR术后15 d移植体黏弹性材料属性参数，模拟分析股骨受到垂直向下1.5 kN压力时，持续1 s与600 s后膝关节韧带、ACL移植体、关节软骨与半月板von Mises应力分布。

结果

ACLR术后15 d移植体的初始松弛模量与平衡模量依旧高于人体ACL，ACL移植体所承受的应力相比健康ACL更高。尽管移植体的力学特性在ACLR术后降低，但股骨受到垂直向下施加压力1 s或600 s对软骨与半月板影响均较小。

结论

ACLR术后，站立等负重康复训练中膝关节所受垂直向下载荷对关节软骨及半月板影响较小，且对移植体纤维再生具有促进作用，故可作为术后早期较为稳妥的康复方案。移植体制备需综合考量其弹性与黏性特性；松弛模量与黏度系数高于健康ACL的移植体，可更有利于维持术后早期膝关节稳定性。

前交叉韧带重建  /  移植体  /  黏弹性  /  有限元分析
Objective

To investigate stress distributions of the knee joint at 0 and 15th day after anterior cruciate ligament reconstruction (ACLR) under a compressive force through the axis of the femoral shaft onto the proximal femur.

Methods

A three-dimensional (3D) finite element model of the human knee joint incorporating viscoelastic material properties was developed. The one-dimensional (1D) Prony series viscoelastic constitutive model parameters for articular cartilage, menisci, ligaments, and anterior cruciate ligament (ACL) grafts were determined by fitting experimental creep curves. The viscoelastic parameters of ACL grafts at 15th day after ACLR surgery were extrapolated. Finite element simulations were then performed to analyze the von Mises stress distributions in knee ligaments, ACL grafts, articular cartilage, and menisci under 1.5 kN vertical downward compressive load applied to the femur, with loading durations of 1 second and 600 seconds.

Results

At 15th day after ACLR surgery, the initial relaxation modulus and equilibrium modulus of human ACL grafts remained elevated compared to native ACL tissues, resulting in a significantly higher stress concentration within the grafts relative to healthy ACL. Despite the compromised mechanical properties of the grafts after ACLR surgery, the vertical downward compressive force applied to the femur under both short-term (1 s) and prolonged (600 s) loading durations, exhibited a minimal biomechanical impact on articular cartilage and meniscal structures.

Conclusions

Following ACLR, vertical compressive loads during weight-bearing rehabilitation exercises such as standing demonstrate minimal impact on articular cartilage and meniscus, while promoting fibrous regeneration of the graft. This renders such exercises a prudent early-stage rehabilitation strategy. Graft preparation requires balanced consideration of elastic and viscous properties, with grafts exhibiting higher relaxation modulus and viscosity coefficient than healthy ACL proving more effective in maintaining early postoperative knee stability.

anterior cruciate ligament reconstruction  /  graft  /  viscoelasticity  /  finite element analysis
连子瞻, 孙彬, 于善江, 严奕辰, 杨钦钦, 杨滨, 姚杰. 前交叉韧带重建术后短期内移植体黏弹性变化对膝关节应力分布的影响. 医用生物力学, 2025 , 40 (5) : 1129 -1135 . DOI: 10.16156/j.1004-7220.2025.05.006
Zizhan LIAN, Bin SUN, Shanjiang YU, Yichen YAN, Qinqin YANG, Bin YANG, Jie YAO. Effects of Early Postoperative Changes in Graft Viscoelasticity on Stress Distributions Within the Knee Joint Following Anterior Cruciate Ligament Reconstruction[J]. Journal of Medical Biomechanics, 2025 , 40 (5) : 1129 -1135 . DOI: 10.16156/j.1004-7220.2025.05.006
正文
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前交叉韧带（anterior cruciate ligament，ACL）断裂是最常见的膝关节损伤[1]。ACL损伤后将导致膝关节前后向及旋转稳定性下降，这是诱发软骨发生退行性变，进而导致骨关节炎（osteoarthritis，OA）的因素之一[2]。前交叉韧带重建（anterior cruciate ligament reconstruction，ACLR）是ACL损伤的常规治疗手段，旨在恢复患者的运动功能和生活品质。研究表明，ACLR可以在一定程度上预防OA的发生[3]，但术后OA发生率仍显著高于健康膝关节，表明ACLR无法消除OA风险[4]。此外，在一项评估精英足球运动员在ACLR术后回归表现的研究中发现，与对照组相比，接受ACLR的运动员平均职业表现显著下降[5]。
在这一过程中，移植体的力学特性（尤其是黏性）对于手术成功率和术后康复具有关键影响[6]。理想的移植体需具备适宜的黏性，这有助于它在术后快速适应膝关节复杂的动态环境，提供即时约束，并促进新生组织的生长[7]。良好的黏性可在术后早期减小移植体的松弛程度，降低因移动造成的磨损和松脱风险，从而加速康复进程。本课题组研究发现，ACLR术后15 d内移植体黏性呈非规律性下降[8]，这可能是导致患者感到膝关节失稳、关节功能衰退的原因之一。然而移植体黏性的下降与膝关节内软骨、半月板以及移植体应力的联系，目前仍不明确。
有限元仿真虽广泛用于分析ACLR术后膝关节力学环境，但模型中各组织的黏性常被忽视。半月板、软骨和韧带等软组织表现出典型的黏弹性生物力学特性，即组织的应力与应变和持续时间均相关。但在以往进行的有限元分析研究中，软组织常被简化为只拥有线弹性或超弹性的弹性元件。这种简化表示应力只与应变相关，与时间迟滞无关，从而忽略了黏性的效果。此外，这种简化无法对载荷持续时间的长短进行区别和精确地计算。本文对关节软骨、半月板、韧带及ACL移植体赋予黏弹性材料属性；基于动物实验研究结果，采用等比例变化方法估算ACLR术后15 d移植体的材料参数；进一步分析ACLR术后15 d移植体黏弹性下降时，在股骨垂直载荷作用下，健康膝关节ACL、ACLR术后移植体及软骨、半月板的von Mises应力分布特征。
1　材料与方法
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1.1　有限元模型建立
本文有限元模型基于本课题组早期为研究ACLR术后隧道周围应力分布而建立并验证过的一个胫股关节有限元模型[9-10]。建模对象为1位经临床测试确认健康男性志愿者（年龄30岁，身高172 cm，体重65 kg）的右膝关节，沿矢状面做磁共振扫描。扫描层厚为2 mm，分辨率0.47 mm×0.47 mm。采用Mimics 21.0（Materialise公司，比利时）对膝关节中的股骨、胫骨、腓骨、关节软骨、半月板以及ACL、后交叉韧带（posterior cruciate ligament，PCL）、内侧副韧带（medial collateral ligament，MCL）和外侧副韧带（lateral collateral ligament，LCL）的三维几何模型进行重建。
将三维几何模型导入ABAQUS 2020（Simulia公司，美国）中进行网格划分、材料属性定义、接触面及边界条件定义。其中，股骨、胫骨、半月板和软骨被分割成四节点四面体单元。ACL及移植体、PCL、MCL、LCL和半月板前后角建模为一维非线性桁单元束。
由于软骨下骨可能对软骨应力产生影响[11-13]，但在磁共振图像中难以识别，因此，假设软骨下骨的厚度为1.5mm。设置股骨与胫骨的软骨下骨为线性各向同性弹性材料，弹性模量为1.15 GPa，泊松比0.25[14]；松质骨为线性各向同性弹性材料，弹性模量为0.4 GPa，泊松比为0.33；皮质骨为线性各向同性弹性材料，弹性模量为17 GPa，泊松比为0.33[15]。
由于本文重点分析移植体黏弹性属性变化对关节力学环境的影响，为了排除ACLR术中骨隧道建立对研究结果的干扰，采用更改ACL模型材料属性的方法，模拟ACLR术后0、15 d移植体。术后0 d的移植体黏弹性属性参考了腓骨长肌肌腱的数据[16]。假设软骨、半月板、韧带与移植体均为各向同性黏弹性材料，使用一维Prony模型进行定义：
式中：E为松弛模量；E0为初始松弛模量；E∞为平衡模量，τ为松弛时间，其定义公式为：
式中：σ0为平衡应力；ε∞为平衡应变；η为黏度系数。在各向同性黏弹性材料中：
式中：μ为泊松比。根据式（1），可计算得到Prony模型剪切模量归一化参数g1与体积模量归一化参数k1：
基于上述Prony参数计算方法，本文通过提取文献中半月板[17]、韧带[18]及移植体[16]的蠕变实验数据，计算得到其相应的一维Prony模型材料属性参数。而软骨材料参数直接采用文献[19]已发表的实验数据。上述各组织的完整Prony参数汇总如表1所示。
在本课题组前期的动物实验研究中，以雄性新西兰兔为实验对象，对侧跟腱为自体移植体，制作单侧膝关节ACLR兔模型。ACLR术后15 d，将实验兔安乐死并取出术后15 d的移植体，同时获取健康跟腱作为术后0 d移植体。测量两种移植体标本截面积与原始长度后，进行蠕变测试，并获得蠕变应变-时间曲线[8]。
为估计人体ACLR术后15 d移植体的材料属性，根据上述动物模型ACLR术后短期内移植体黏弹性变化规律，重新运用一维Prony本构模型对术后0、15 d兔移植体的蠕变曲线进行拟合。拟合后发现，ACLR术后15 d，移植体初始松弛模量E0下降为术前的60.93%，平衡模量E∞下降为术前的60.52%，η下降为术前的87.85%，可推算人体ACLR术后15 d移植体的Prony模型材料属性（见表1）。股骨和胫骨、股骨和半月板、胫骨和半月板之间的切向摩擦被定义为无摩擦行为。
1.2　载荷与边界条件
由于模型设计中考虑了软组织的黏弹性行为，故采用隐式动力学分析。为膝关节内韧带、移植体及半月板前后角设置3%预应变。采用1.5 kN压力的典型负荷，比较健康膝关节与ACLR术后不同时间膝关节的von Mises应力分布。载荷到达1.5 kN的持续时间分别为1 s与600 s。设定约束条件以固定胫骨，随后沿垂直向下方向向胫骨近端施加股骨载荷，并确保股骨仅保留相对胫骨的屈曲运动自由度，限制其余方向的相对运动（见图1）。
2　结果
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2.1　软骨应力分布
股骨受到垂直向下压力持续1 s后，健康和ACLR术后0、15 d膝关节的股骨软骨应力峰值分别为0.71、0.72、0.69 MPa。载荷施加600 s后，股骨软骨的应力集中位置发生转移，外侧髁应力集中点向后内侧偏移，内侧髁则向髁后方延伸。ACLR术后0、15 d膝关节应力峰值分别为0.91、0.90 MPa，与健康膝关节的0.90 MPa相差不大[见图2（a）]。
胫骨软骨的应力集中发生在内侧软骨前端与外侧软骨中部靠内侧。载荷施加1 s后，ACLR术后0、15 d胫骨软骨应力峰值分别为2.77、2.68 MPa，健康膝关节则为2.71 MPa。载荷施加600 s后，ACLR术后0、15 d胫骨软骨的应力峰值分别为1.45、1.69 MPa，健康膝关节则为1.46 MPa[见图2（b）]。
2.2　半月板应力分布
股骨受到垂直向下载荷持续1 s后，内侧半月板的应力较小，集中于其与胫骨前后连接角与中部白区（半月板靠近关节腔内部的1/3无血液供应区域）。健康和ACLR术后0、15 d膝关节内侧半月板的应力峰值均为0.01 MPa。载荷施加600 s后，内侧半月板的应力集中位置向后侧白区偏移，健康和ACLR术后0、15 d膝关节内侧半月板的应力峰值均为0.11 MPa[见图3（a）]。
无论载荷施加1 s或600 s，外侧半月板的应力集中位置均在中部白区。载荷施加1 s后，ACLR术后0、15 d外侧半月板的应力峰值分别为0.04、0.09 MPa，健康膝关节则为0.05 MPa。载荷施加600 s后，健康和ACLR术后0、15 d膝关节外侧半月板的应力峰值分别为0.14、0.13、0.16 MPa[见图3（b）]。
2.3　ACL与移植体应力
健康膝关节的ACL与ACLR术后移植体的应力存在较大差异。股骨受到垂直向下的压力持续1 s后，健康ACL和ACLR术后0、15 d移植体的应力分别为1.05、1.59、1.12 MPa；载荷施加600 s后，则分别为0.56、1.10、0.71 MPa（见图4）。
3　讨论
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ACLR术后，移植体的弹性与黏性均与健康ACL有所差异，且移植体力学特性也随时间推移发生改变。股骨受到垂直向下压力持续1 s后，ACLR术后膝关节软骨与内侧半月板上的应力分布与健康膝关节无明显差异，ACLR术后15 d关节外侧半月板的应力峰值略有提高。载荷持续600 s后，ACLR股骨软骨与半月板的应力峰值与健康膝关节相当，ACLR术后15 d胫骨软骨的应力峰值有所提高，但数值较小，说明膝关节在承受持续1 s或600 s的股骨垂直向下压力时，虽然ACL移植体的力学特性与健康ACL不同，但在垂直受压的载荷条件下对软骨和半月板的影响较小。
随着股骨受到垂直向下载荷的持续时间由1 s延长至600 s，健康ACL与ACL移植体的应力均有所下降，推测与其黏性行为相关。载荷持续1 s时，位移施加时间短，从而使ACL或移植体黏性提供的应力处于较高的水平。随着载荷持续时间延长，健康ACL与移植体发生松弛行为，应力呈下降趋势。值得注意的是，无论压力载荷持续时间1 s还是600 s，健康ACL所受应力都小于ACLR术后0、15 d的移植体。该结果表明，尽管移植体的力学特性有所下降，但在术后15 d时，其仍能够在膝关节承受股骨垂直向下的压力时，发挥维持膝关节稳定的作用。由于垂直向下载荷对ACLR术后膝关节软骨与半月板影响较小，且在移植体上提供一定的应力刺激，从而促进了愈合过程中移植体纤维的再生[20]。因此，站立或保持膝关节维持伸直状态的其他负重康复运动，是术后短期内较稳妥的康复运动之一。
随着载荷持续时间从1 s延长至600 s，无论是在健康还是ACLR术后膝关节内，关节软骨与半月板的应力峰值均发生改变。本文推测原因如下：①随着载荷持续时间延长，关节软骨与半月板因其黏弹性表现出蠕变行为，导致接触面积改变，进而引起应力峰值与分布特征的改变；②随着载荷持续时间的延长，关节内韧带发生了松弛行为，所承受应力逐渐降低，导致软骨与半月板的应力峰值与分布发生改变。
在以往的移植体选取与制备过程中，主要关注的是其弹性特性，而往往忽略了黏性特性；因此，在今后的制备过程中应当将二者综合加以考虑。本文发现，ACL移植体在ACLR术后15 d时，其初始松弛模量已出现较大幅度下降，表明移植体的弹性模量也发生了显著降低。从长远来看，这种变化很可能无法恢复至术前状态[21]。同时，移植体在术后15 d时的黏度系数也有所下降。因此，建议在移植体的选择与制备过程中，应尽可能使其松弛模量与黏度系数高于健康ACL的水平。
本研究的创新性在于建立了一种将蠕变实验结果转化为黏性材料参数的方法，从而为膝关节有限元模型中的软组织（包括关节软骨、韧带、半月板和ACL移植体）赋予了黏弹性属性。该模型能够模拟不同时间或加载速率下的关节活动，用于分析膝关节应力分布的变化规律，旨在为骨关节炎的临床预防与治疗提供理论支撑。
本研究的局限性如下：①利用动物模型中移植体在术后15 d时力学特性的变化比例估算人体ACLR术后的移植体黏弹性特性变化规律，与真实情况存在差异。ACLR术后移植体的力学特性变化规律还有待进一步探索。②为了比较移植体材料特定变化对膝关节力学环境的影响，未考虑骨隧道的影响。在真实情况下，骨隧道与移植体共同作用于ACLR术后膝关节力学环境的改变，且两者之间也存在着相互影响，这一复杂机制还需在后续研究中进一步探索和验证。③软骨、半月板、韧带与移植体均假设为各向同性材料，会对结果产生影响，但仍然能够看出变化趋势。真实人体膝关节组织各向异性的黏弹性本构关系还有待进一步研究确定。④没有考虑软骨液体随时间流逝的属性，关节软骨内的间隙液可保护基质免受机械应力，减少摩擦和磨损，负载与卸载下软骨内液体的渗出与恢复，对组织的生物力学和生物学功能至关重要，针对软骨内液体流失所导致的其生物力学特性变化，还需要后续设法进行实验研究。⑤只考虑股骨受到垂直向下的压力载荷，而未模拟其他复杂运动下的关节力学环境。由于ACLR术后患者下肢关节运动学通常发生改变，后续研究应结合在体运动学数据，为有限元模型提供载荷和边界条件，进而对其他复杂运动下的关节力学环境进行研究。
基金
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  • 国家重点研发计划项目(2023YFC3603901)
  • 北京大学国际医院院内科研基金(YN2023ZD03)
  • 中国科协青年人才托举工程(YESS 2015QNRC001)
  • 虚拟现实全国重点实验室资助项目
文献
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参考文献 引证文献
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2025年第40卷第5期
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doi: 10.16156/j.1004-7220.2025.05.006
  • 接收时间：2024-12-31
  • 首发时间：2026-03-27
  • 出版时间：2025-10-01
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  • 收稿日期：2024-12-31
  • 修回日期：2025-02-06
基金
国家重点研发计划项目(2023YFC3603901)
北京大学国际医院院内科研基金(YN2023ZD03)
中国科协青年人才托举工程(YESS 2015QNRC001)
虚拟现实全国重点实验室资助项目
作者信息
    1.生物力学与力生物学教育部重点实验室；高端医疗装备与器械创新及转化工业和信息化部重点实验室；国家医学攻关（医工结合方向）高端医疗装备与器械产教融合创新平台；北京航空航天大学　生物与医学工程学院，北京　100191
    2.北京大学国际医院　骨科，北京　102206

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姚杰，副教授，E-mail：；
杨滨，副主任医师，E-mail：

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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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