Moeinzadeh M H, Engin A E, Akkas N
J Biomech. 1983;16(4):253-64. doi: 10.1016/0021-9290(83)90133-1.
A mathematical dynamic model of the two-dimensional representation of the knee joint is presented. The profiles of the joint surfaces are determined from X-ray films and they are represented by polynomials. The joint ligaments are modelled as nonlinear elastic springs of realistic stiffness properties. Nonlinear equations of motion coupled with nonlinear constraint conditions are solved numerically. Time derivatives are approximated by Newmark difference formulae and the resulting nonlinear algebraic equations are solved employing the Newton-Raphson iteration scheme. Several dynamic loads are applied to the center of mass of the tibia and the ensuing motion is investigated. Numerical results on ligament forces, contact point locations between femur and tibia, and the orientation of tibia relative to femur are presented. The results are shown to be consistent with the anatomy of the knee joint.
提出了一种膝关节二维表示的数学动态模型。关节表面轮廓由X射线胶片确定，并用多项式表示。关节韧带被建模为具有实际刚度特性的非线性弹性弹簧。求解了与非线性约束条件耦合的非线性运动方程。时间导数用纽马克差分公式近似，所得非线性代数方程采用牛顿-拉夫逊迭代法求解。对胫骨质心施加几种动态载荷，并研究随之产生的运动。给出了韧带力、股骨与胫骨之间接触点位置以及胫骨相对于股骨的方位的数值结果。结果表明与膝关节的解剖结构一致。
