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A musculoskeletal model of the knee for evaluating ligament forces during isometric contractions

Journal of Biomechanics
Publication Date
DOI: 10.1016/s0021-9290(96)00119-4
  • Knee Model
  • Muscle Contractions
  • Ligament Forces
  • Mathematics


Abstract A model of the knee in the sagittal plane was developed to study the forces in the ligaments induced by isometric contractions of the extensor and flexor muscles. The geometry of the distal femur was obtained from cadaver data. The tibial plateau and patellar facet were modeled as flat surfaces. Eleven elastic elements were used to describe the mechanical behavior of the anterior and posterior cruciate ligaments (ACL and PCL), the medial and lateral collateral ligaments (MCL and LCL), and the posterior capsule. The model knee was actuated by 11 musculotendinous units, each muscle represented by a Hill-type contractile element, a series-elastic element, and a parallel-elastic element. Tendon was assumed to be elastic. The response of the model to anterior-posterior drawer suggests that the geometrical and mechanical properties of the model ligaments approximate the behavior of real ligaments in the intact knee. Calculations for a simulated quadriceps leg raise indicate further that the two-dimensional model reproduces the response of the three-dimensional knee under similar conditions of loading and constraint. During maximum isometric contractions of the quadriceps, the model ACL is loaded from full extension to 80°C of flexion; the model PCL is loaded at 70° of flexion and greater. For maximum isometric extension, ACL forces in the range 0–20° of flexion depend most heavily upon the force-length properties of the quadriceps. At flexion angles greater than 20°, cruciate ligament forces are determined by the geometry of the articulating surfaces of the bones. During isolated contractions of the hamstrings and gastrocnemius muscles, the model ACL is loaded from full extension to 10° of flexion; the model PCL is loaded at all flexion angles greater than 10°. Isolated contractions of the flexor muscles cannot unload the ACL near full extension, as the behavior of the ACL in this region is governed by the shapes of the bones. At 10° of flexion or greater, the overall pattern of PCL force is explained by the force-length properties of the hamstrings and by the geometrical arrangement of the flexor muscles about the knee.

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