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The Derivation of Knee Joint Types from the Geometry of the Cruciate Ligament Four-bar System

Journal of Theoretical Biology
Publication Date
DOI: 10.1006/jtbi.1998.0719


Abstract 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 femoralarticulating surfaces (condyles) can be calculated starting from a flat or curved tibialarticulating surface and known bar-lengths (Menschik, 1974 Z. orthop. 112, 481–493; 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)≈(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°. 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°. Uniformly distributed sliding occurs within this range over an angle less than 90°. Theoretically derived, limiting requirements concerning maximum angulation range (Δγ max≤180°), stabilization (e.g. avoidance of a perpendicular position of the cruciate ligaments to the articulating surfaces; Δγ 78.5≥90°) and uniformly distributed sliding (Δγ s≥30°) lead to at least two different possibleknee joint shapes. These shapes closely correspond to the two realknee 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).

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