The use of basis functions in modelling joint articular surfaces: application to the knee joint

This article introduces a new method to represent bone surface geometry for simulations of joint contact. The method uses the inner product of two basis functions to provide a mathematical representation of the joint surfaces. This method guarantees a continuous transition in the direction of the surface normals, an important property for computation of joint contact. Our formulation handles experimental data that are not evenly distributed, a common characteristic of digitized data of musculoskeletal morphologies. The method makes it possible to represent highly curved surfaces, which are encountered in many anatomical structures. The accuracy of this method is demonstrated by modeling the human knee joint. The mean relative percentage error in the representation of the patellar track surface was 0.25% (range 0–1.56%) which corresponded to an absolute error of 0.17 mm (range 0–0.16 mm).