The derivation of knee joint types from the geometry of the cruciate ligament four-bar system.

The system of the anterior (a) and posterior (p) cruciate ligaments and their distances between attachments to femur (f) and tibia (t) as found in the knee joint of tetrapods is considered as a planar crossed four-bar linkage. The shape of the femoral articulating surfaces (condyles) can be calculated starting from a flat or curved tibial articulating surface and known bar-lengths (Menschik, 1974 Z. Orthop. 112, 481-495; Huson 1974 Orthopäde 3, 119-126). Regression analysis of the dimensions of the cruciate ligament four-bar system of 11 species of mammal and one species of bird revealed a general ratio of (a): (t): (p): (f) = (7.1): (7.9): (10.0): (6.1). These data differ from the results obtained by Badoux (1984 Acta Anat. 119, 60-64) who examined only dog and horse. Our data of the dog agree with those of Badoux, i.e. (a): (t): (p): (f) approximately equal to (10): (8): (10): (4). Based on these ratios between bar-lengths, two types of knee joint shapes were distinguished. The shape of the dog's joint ("type A") has a very large femoral condyle compared with the tibial articulating surface. Maximum knee angulation is 170-180 degrees. Sliding between the articulating surfaces of this joint is distributed approximately uniformly over the whole angulation range. The general shape obtained from the regression analysis ("type R") has a relatively small femoral condyle and an angulation range of about 174 degrees. Uniformly distributed sliding occurs with this range over an angle less than 90 degrees. Theoretically derived, limiting requirements concerning maximum angulation range (delta gamma max < or = 180 degrees), stabilization (e.g. avoidance of a perpendicular position of the cruciate ligaments to the articulating surfaces; delta gamma 78.5 max > or = 90 degrees) and uniformly distributed sliding (delta gamma s > or = 30 degrees) lead to at least two different possible knee joint shapes. These shapes correspond to the two real knee joint shapes found from the statistical analysis mentioned above. This was verified by studying quantitative characteristics obtained from the derivation of knee joint shapes from the bar lengths and vice versa. The bird (Ardea) possessed a knee joint shape, very different from the shapes described above (i.e. f > t, type D1).