Improvement of depth position in 2-D/3-D registration of knee implants using single-plane fluoroscopy

Two-dimensional (2-D)/three-dimensional (3-D) registration techniques using single-plane fluoroscopy are highly important for analyzing 3-D kinematics in applications such as total knee arthroplasty (TKA) implants. The accuracy of single-plane fluoroscopy-based techniques in the determination of translation perpendicular to the image plane (depth position), however, is relatively poor because a change in the depth position causes only small changes in the 2-D silhouette. Accuracies achieved in depth position using conventional 2-D/3-D registration techniques are insufficient for clinical applications. Therefore, we propose a technique for improving the accuracy of depth position determination in order to develop a system for analyzing knee kinematics over the full six degrees of freedom (6 DOF) using single-plane fluoroscopy. In preliminary experiments, the behaviors of errors for each free variable were quantified as evaluation curves by examining changes in cost function with variations in the free variable. The evaluation curve for depth position was more jagged, and the curve peak less pointy, compared to the evaluation curves of the other five variables, and the curve was found to behave differently. Depth position is therefore optimized independently of the other variables, using an approximate evaluation curve of depth position prepared after initial registration. Accuracy of the proposed technique was evaluated by computer simulation and in vitro tests, with validation of absolute position and orientation performed for each knee component. In computer simulation tests, root-mean-square error (RMSE) in depth position was improved from 2.6 mm (conventional) to 0.9 mm (proposed), whereas for in vitro tests, RMSE improved from 3.2 mm to 1.4 mm. Accuracy of the estimation of the remaining two translational and three rotational variables was found to be almost the same as that obtained by conventional techniques. Results of in vivo tests are also described in which the possibility of full 6 DOF kinematic analysis of TKA implants is shown.