An analytical model of the knee for estimation of internal forces during exercise

J Biomech. 1998 Oct;31(10):963-7. doi: 10.1016/s0021-9290(98)00056-6.


An analytical model of the knee joint was developed to estimate the forces at the knee during exercise. Muscle forces were estimated based upon electromyographic activities during exercise and during maximum voluntary isometric contraction (MVIC), physiological cross-sectional area (PCSA), muscle fiber length at contraction and the maximum force produced by an unit PCSA under MVIC. Tibiofemoral compressive force and cruciate ligaments' tension were determined by using resultant force and torque at the knee, muscle forces, and orientations and moment arms of the muscles and ligaments. An optimization program was used to minimize the errors caused by the estimation of the muscle forces. The model was used in a ten-subject study of open kinetic chain exercise (seated knee extension) and closed kinetic chain exercises (leg press and squat). Results calculated with this model were compared to those from a previous study which did not consider muscle length and optimization. Peak tibiofemoral compressive forces were 3134 +/- 1040 N during squat, 3155 +/- 755 N during leg press and 3285 +/- 1927 N during knee extension. Peak posterior cruciate ligament tensions were 1868 +/- 878 N during squat, 1866 +/- 383 N during leg press and 959 +/- 300 N for seated knee extension. No significant anterior cruciate ligament (ACL) tension was found during leg press and squat. Peak ACL tension was 142 +/- 257 N during seated knee extension. It is demonstrated that the current model provided better estimation of knee forces during exercises, by preventing significant overestimates of tibiofemoral compressive forces and cruciate ligament tensions.

MeSH terms

  • Anterior Cruciate Ligament / physiology
  • Biomechanical Phenomena
  • Electromyography
  • Exercise*
  • Humans
  • Knee Joint / physiology*
  • Models, Biological*
  • Muscle Contraction / physiology
  • Muscle, Skeletal / physiology
  • Posterior Cruciate Ligament / physiology
  • Torque