Zavatsky A B, O'Connor J J
Department of Engineering Science, University of Oxford.
Proc Inst Mech Eng H. 1993;207(1):7-18. doi: 10.1243/PIME_PROC_1993_207_263_02.
A mathematical model of the knee in the sagittal plane was used to investigate the ligament forces resulting when a posteriorly directed external force, applied to the tibia, resists extension of the knee under increasing isometric quadriceps contractions. The model is based on simple geometric representations of the bones, ligaments and muscles at the knee. An elementary mechanical analysis was used to predict which ligament, the anterior or posterior cruciate, was loaded at a given flexion angle and known line of action of the external force. Ligament force, as a proportion of the external force, was calculated first assuming the ligaments to be represented by single, inextensible lines. Modelling the ligaments as continuous arrays of extensible fibres then showed that tibio-femoral translations and ligament forces increased non-linearly with increasing muscle forces and approached asymptotic values which depended on flexion angle. In most positions of the joint, the calculated asymptotic ligament force values were less than the reported ultimate strength of human ligament, despite quadriceps forces of over three times body weight. The possibility of these asymptotic values of ligament force may explain why, at certain flexion angles, large forces can be developed by the muscles at the knee without ligament rupture.
利用膝关节矢状面的数学模型，研究当向后的外力作用于胫骨，在等长股四头肌收缩增强的情况下抵抗膝关节伸展时所产生的韧带力。该模型基于膝关节处骨骼、韧带和肌肉的简单几何表示。采用基本力学分析来预测在给定屈曲角度和已知外力作用线时，前交叉韧带或后交叉韧带哪条韧带会受力。首先假设韧带由单一不可伸长的线表示，计算韧带力占外力的比例。然后将韧带建模为可伸长纤维的连续阵列，结果表明胫股平移和韧带力随肌肉力增加而非线性增加，并接近取决于屈曲角度的渐近值。在关节的大多数位置，尽管股四头肌力超过体重的三倍，但计算出的韧带力渐近值仍小于报道的人类韧带极限强度。韧带力这些渐近值的可能性或许可以解释为什么在某些屈曲角度下，膝关节处的肌肉能够产生较大力量而不会导致韧带断裂。
