Theoretical estimates of cruciate ligament forces: effects of tibial surface geometry and ligament orientations

Proc Inst Mech Eng H. 1997;211(6):425-39. doi: 10.1243/0954411981534556.


A mathematical model of the knee in the sagittal plane was used to analyse the effect of tibial surface geometry and ligament orientations on the estimates of cruciate ligament forces. An elementary mechanical analysis was used to calculate the ligament forces L during a simulated antero-posterior (A-P) laxity test (passive test), and during isometric quadriceps contraction (IQE). Three sets of anatomical parameters (sites of bony attachments and lengths of the ligaments) were used from the literature. Flat, concave and convex shapes were considered for the tibial plateau articulating with a compatible convex femoral condyle. Also, the effects of position and posterior tilt of the tibial plateau were analysed for the concave and flat surfaces. The analysis showed that the ligament forces rose steeply as they approached collinearity with the contact force, C. For a flat tibia, the direction of C remained independent of flexion angle or position of the tibial plateau. For the concave tibia, the direction of C varied with flexion as well as with position of the centre of curvature, O, of the tibial plateau. C had an anterior component synergistic with the posterior cruciate ligament (PCL) when the point of contact, F, was anterior to O. On the other hand, C had a posterior component synergistic with the anterior cruciate ligament (ACL) when F was posterior to O. Also, posterior tilt of the flat or concave surfaces resulted in an increase in the anterior component of C. The effects of the convex tibial surface were opposite to those of the concave surface. During the A-P laxity test, the ligament forces arising from the concave tibia were very sensitive to the A-P position of O and to the posterior tilt of the plateau which allowed C and L to approach collinearity. Proximo-distal movement of O had a relatively insignificant effect on the ligament force. Similarly, compared to the concave surface, the posterior tilt of the flat tibia had a lesser effect on the ligament forces. Compared to the passive test, use of the muscle forces during IQE resulted in larger ligament forces, though the trends in force behaviour over the flexion range remained the same. The analysis emphasizes the importance of correct graft placement during ligament reconstruction, and the need to avoid steep inclination (more than 70 degrees to tibial plateau). Increasing the inclination from 70 to 80 degrees doubles the ligament force. Further, the analysis suggests that, in bicompartmental knee replacement, the efficacy of concave surfaces in replacing cruciate ligament function depends critically on the horizontal placement of the tibial component and its orientation about the mediolateral axis.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Anterior Cruciate Ligament / physiology*
  • Humans
  • Isometric Contraction / physiology
  • Knee Joint / anatomy & histology
  • Knee Joint / physiology
  • Models, Biological*
  • Movement / physiology
  • Reference Values
  • Stress, Mechanical
  • Surface Properties
  • Tibia / anatomy & histology*
  • Tibia / physiology