Equivalent geometry’ of the knee and the prediction of tensions along the cruciates: an experimental study

In this paper we introduce the concept of the functional (or equivalent) geometry of the knee, which is an attempt to reduce the natural knee with its complex geometry, frictional resistance and deformable cartilage into a two-dimensional joint comprising rigid femur and tibia in frictionless contact. An apparatus and method are described to measure the slope of the tangent to the surfaces of the ‘equivalent’ bones at their ‘point’ of contact. An antero–posterior force of ±300–500 N and axial compressive load of twice body weight were applied on cadaveric knee joints. The corresponding displacement of the tibia in the saggital plane was measured firstly with both cruciates intact and then when each was severed in turn. From the data obtained both the slope of the tangent mentioned above and the tensions developed along the cruciates under the influence of the forces applied were calculated. The results showed that the functional geometry of the knee in the saggital plane can be represented by a convex femur and a concave tibia. The tensions along the cruciates calculated on the basis of the experimental measurements were nearly always lower than the antero–posterior force applied, and although this corroborated the trend demonstrated in a previous theoretical analysis, they were lower still. The reason for this may be the deformation of the cartilage under load, thus modifying the geometry of contact resulting in a more concave tibia of the ‘equivalent’ knee joint, than that of the rigid model used in the theoretical analysis.