Pandy MARCUS G., Sasaki KOTARO, Kim SEONPIL
Department of Kinesiology and Department of Mechanical Engineering, University of Texas at Austin, Austin, Texas 78712, U.S.A.
Comput Methods Biomech Biomed Engin. 1998;1(2):87-108. doi: 10.1080/01495739708936697.
A three-dimensional model of the knee is developed to study the interactions between the muscles, ligaments, and bones during activity. The geometry of the distal femur, proximal tibia, and patella is based on cadaver data reported for an average-size knee. The shapes of the femoral condyles are represented by high-order polynomials; the tibial plateaux and patellar facets are approximated as flat surfaces. The contacting surfaces of the femur and tibia are modeled as deformable, while those of the femur and patella are assumed to be rigid. Interpenetration of the femur and tibia is taken into account by modeling cartilage as a thin, linear, elastic layer, mounted on rigid bone. Twelve elastic elements describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit modeled as a three-element muscle in series with tendon. The path of each muscle is approximated as a straight line, except where it contacts and wraps around bone and other muscles; changes in muscle paths are taken into account using data obtained from MRI. In the first part of this paper, the model is used to simulate passive knee flexion. Quantitative comparisons of the model results with experimental data reported in the literature indicate that the relative movements of the bones and the geometry of the ligaments and muscles in the model are similar to those evident in the real knee. In Part II, the model is used to describe knee-ligament function during anterior-posterior draw, axial rotation, and isometric knee-extension and knee-flexion exercises.
开发了一种膝关节三维模型，用于研究活动期间肌肉、韧带和骨骼之间的相互作用。股骨远端、胫骨近端和髌骨的几何形状基于报道的平均尺寸膝关节的尸体数据。股骨髁的形状由高阶多项式表示；胫骨平台和髌骨关节面近似为平面。股骨和胫骨的接触表面被建模为可变形的，而股骨和髌骨的接触表面被假定为刚性的。通过将软骨建模为安装在刚性骨上的薄的、线性的弹性层来考虑股骨和胫骨的相互穿透。十二个弹性元件描述了交叉韧带、侧副韧带和后关节囊的几何形状和力学性能。该模型由十三个肌肉肌腱单元驱动，每个单元被建模为与肌腱串联的三元件肌肉。每条肌肉的路径近似为一条直线，除非它与骨骼和其他肌肉接触并缠绕；使用从MRI获得的数据考虑肌肉路径的变化。在本文的第一部分，该模型用于模拟膝关节被动屈曲。将模型结果与文献中报道的实验数据进行定量比较表明，模型中骨骼的相对运动以及韧带和肌肉的几何形状与真实膝关节中明显的情况相似。在第二部分中，该模型用于描述前后拉伸、轴向旋转以及等长膝关节伸展和屈曲运动期间膝关节韧带的功能。
