A new type of model-based Roentgen stereophotogrammetric analysis for solving the occluded marker problem

Roentgen stereophotogrammetric analysis (RSA) measures micromotion of an orthopaedic implant with respect to its surrounding bone. A problem in RSA is that the markers are sometimes overprojected by the implant itself. This study describes the so-called Marker Configuration Model-based RSA (MCM-based RSA) that is able to measure the pose of a rigid body in situations where less than three markers could be detected in both images of an RSA radiograph. MCM-based RSA is based on fitting a Marker Configuration model (MC-model) to the projection lines from the marker projection positions in the image to their corresponding Roentgen foci. An MC-model describes the positions of markers relative to each other and is obtained using conventional RSA. We used data from 15 double examinations of a clinical study of total knee prostheses and removed projections of the three tibial component markers, simulating occlusion of markers. The migration of the tibial component with respect to the bone, which should be zero, for the double examination is a measure of the accuracy of algorithm. With the new algorithm, it is possible to estimate the pose of a rigid body of which one or two markers are occluded in one of the images of the RSA radiograph with high accuracy as long as a proper MC-model of the markers in the rigid body is available. The new algorithm makes RSA more robust for occlusion of markers. This improves the results of clinical RSA studies because the number of lost RSA follow-up moments is reduced.