Inter-insertional distance is a poor correlate for ligament load: analysis from in vivo gait kinetics data

In many analytic models of the knee joint, inter-insertional distance is used as the measure to define the load in a ligament. In addition, the direction of the load is taken to be the direction between the two insertions. Our in vivo data on the ovine ligament loads during gait, however, indicate that a wide range of forces is possible in the ligament for any specified inter-insertional distance. To understand the complex relationship between the bone orientations and ligament load better, an artificial neural network (ANN) model was developed. The six degree-of-freedom (6-DOF) in vivo kinematics of femur relative to tibia (joint kinematics) was used as input, and the magnitude of the anterior cruciate ligament (ACL) load was used as output/target. While the trained network was able to predict peak ligament loads with remarkable accuracy (R-square=0.98), an explicit relationship between joint kinematics and ACL load could not be determined. To examine the experimental and ANN observations further, a finite element (FE) model of the ACL was created. The geometry of the FE model was reconstructed from magnetic resonance images (MRI) of an ACL, and an isotropic, hyperelastic, nearly incompressible constitutive model was implemented for the ACL. The FE simulation results also indicate that a range of loads is possible in the ACL for a given inter-insertional distance, in concordance with the experimental/ANN observations. This study provides new insights for models of the knee joint; a simple force-length relationship for the ligament is not exact, nor is a single point to single point direction. More detailed microstructure-function data is required.