Accurate determination of a joint rotation center based on the minimal amplitude point method

In many computer-assisted surgery procedures in the field of joint replacement a joint rotation center must be located. To this end, joints such as the hip or the shoulder are approximated as spherical joints, and the most commonly used numerical method is the sphere-fitting algorithm. However, this method has a numerical instability where there is a limited range of motion caused by, for example, joint impingement. The aim of the present study was to develop an alternative kinematic method called the minimal amplitude point method. This method estimates the localization of the rotation center and can easily be integrated into program codes of computer-assisted surgery modules. It mainly consists of identifying the point of a mobile segment that moves least in the reference coordinate system of an immobile segment using an optimization procedure (genetic algorithm). The point determined can then be assumed to be the rotation center of the joint. To compare results of the two methods, an experimental set-up of two rigid solids linked by a spherical joint with known geometry was used to compute the rotation center. In contrast to the sphere-fitting method, the minimal amplitude point method permits the evaluation of the rotation center with an error of less than 4.1 mm, having a range of motion (ROM) of 5 degrees. An equivalent accuracy for the sphere-fitting method requires an ROM of 45 degrees.