인체관절의 회전중심 추정을 위한 구적합법의 비교

Abstract

The methods of fitting a circle to measured data, geometric fit and algebraic fit, have been studied profoundly in various areas of science. However, they have not been applied exactly to a biomechanics discipline for locating the center of rotation of a human joint. The purpose of this study was to generalize the methods to fitting spheres to the points in 3-dimension, and to estimate the center of rotation of a hip joint by three of geometric fit methods(Levenberg-Marquardt, Landau, and Sp<TEX>$\ddot{a}$</TEX>th) and four of algebraic fit methods(Delogne-K<TEX>${\aa}$</TEX>sa, Pratt, Taubin, and Hyper). 1000 times of simulation experiments for flexion/extension and ad/abduction at an artificial hip joint with four levels of range of motion(10, 15, 30, and <TEX>$60^{\circ</TEX><TEX>}$</TEX>) and three levels of angular velocity(30, 60, and <TEX>$90^{\circ}$</TEX>/s) were executed to analyze the responses of the estimated center of rotation. The results showed that the Sp<TEX>$\ddot{a}$</TEX>th estimate was very sensitive to the marker near the center of rotation. The bias of Delogne-K<TEX>${\aa}$</TEX>sa estimate existed in an even larger range of motion. The Levenberg-Marquardt algorithm of geometric fit and the Pratt of algebraic fit showed the best results. The combination of two methods, using the Pratt's estimate as initial values of the Levenberg-Marquardt algorithm, could be a candidate of more valid estimator.