Study on Mathematical Description of Human Knee Joint Surface and Its Application

For describing free-formed surfaces mathematically, parameterized polynomial function was proposed in our previous study. By using our parameterized polynomial, the artificial knee joint surfaces were described in detail and the results were found to be superior to the established practices. However, this polynomial function has some problem for reconstructing human knee joint surface with minute undulation. In the present study, to overcome this problem, an additional application of Fourier series approximation was employed. First, the global shape of objective surface was described by our polynomial function. Then, minute undulation was approximated with Fourier series function. Finally, two sets of approximated surface were superimposed to reproduce the original surface in a complete fashion. Our newly proposed method was applied to the swine knee joint and human knee joint model surfaces. Curvature analysis was performed for two surfaces.