This paper presents a phantom-based study for validating a newly developed 2D-3D reconstruction-based method for measuring implant migration after total hip arthroplasty (THA). Based on a mock-up setup, three different methods were used to determine the cup orientation with respect to the anterior pelvic plane (APP) of a plastic pelvis: (a) the optical tracking method; (b) the fiducial-based method; and (c) the 2D-3D reconstruction-based method. It was found that the incremental anteversion and inclination angles measured by the newly developed 2D-3D reconstruction-based method are comparable with those measured by the other two methods.
X-ray image acquisition: The acquisition started with the fixation of a calibration phantom to the pelvis. A pointer digitization based registration of the optical tracking space and the fiducails as well as the cup opening plane was performed. Next, 15 datasets were acquired. Each dataset was composed of three images (AP, outlet, 30° oblique). For each dataset the cup was oriented by hand with the help of the optical tracking software. All images were acquired with a standard clinical Philips X-ray machine. During acquisition, the orientation of the cup was tracked by the camera giving absolute readings for the anteversion and inclination angles at a rate of approx. 20 Hz. All positions recorded by the camera where stored to allow detailed analysis during evaluation. The images were stored in DICOM format for further processing.
Evaluation: The experimental setup provided three sources of measurements for the anteversion and inclination angles. (a) The optical tracking system provided a real time estimation of the angles using the optical tracking markers placed on the cup and the base frame. These values were stored onto hard disk. Measurements obtained by this method are labeled as ‘optical’. (b) Through a semi-automatic algorithm using Hough transform the X-rays where calibrated and a custom software was used to pick the markers on the X-ray’s and determine the 3D position of the markers. Next, these 3D points where used to determine the APP orientation. Since the plastic cup also contained a metal ring parallel to the cup plane it was used to determine the 3D orientation of the cup. (c) With the help of a SSM-based 2D-3D reconstruction algorithm [3] the pelvis was reconstructed for each dataset from the three calibrated X-ray images. The APP was then extracted based on four vertices determined on the mean model (see fig.2b). In the SSM-based 2D-3D reconstruction method four 3D points where determined from the reconstructed shape model using fixed vertices. The cup orientation was determined as in method (b). During the study 15 reconstructions where performed and the reconstructed surfaces where compared to a reference surface from a computer tomography (CT) scan of the used bone, the mean Hausdorff distance of the surfaces was 1.44 ± 0.15 mm. The anteversion and inclination angles between these planes are labeled ‘reconstructed’. 3
An extensive comparison of the incremental angles (difference of angle in a dataset to the angles of the first dataset) was conducted. The following plots show the correlation of the datases measured with the three different methods.
Correlation of anteversion (Absolute)
Optical Fiducial Optical 1 0.51 Fiducial ‐ 1 Reconstructed ‐ ‐ Correlation of inclination (Absolute)
Optical Fiducial Optical 1 0.96 Fiducial ‐ 1 Reconstructed ‐ ‐ Correlation of anteversion (Incremental)
Optical Fiducial Optical 1 0.93 Fiducial ‐ 1 Reconstructed ‐ ‐ Correlation of inclination (incremental)
Optical Fiducial Optical 1 0.96 Fiducial ‐ 1 Reconstructed ‐ ‐
Reconstructed 0.48 0.93 1 Reconstructed 0.95 0.92 1 Reconstructed 0.88 0.97 1 Reconstructed 0.94 0.96 1 As the main interest in this work is the migration of the cup, the absolute angles obtained by the three methods play a secondary role. The biggest focus is given to the incremental angles of each method. When comparing the absolute and the incremental angles of all three measurement types we noticed that the difference of the obtained results is smaller for the inclination than for the anteversion. Table 1 shows the differences between the incremental measurements. The difference between the reconstruction based method and the fiducial based method is smaller than the difference of the optical method to any of the two methods. When comparing the correlations of the incremental and absolute angles as shown in figure 3, we notice that reconstructed and fiducial based angles correlate very well, while the optical method do not always correlate. The reason for this is the calibration which is the basis of both the reconstructed and the fiducial measurement method. On one hand the size of the used calibration phantom limits the quality of the X-ray calibration. On the other hand the close correlation indicates that the error produced by the 2D-3D reconstruction is relatively small.
In this paper, we propose a method to determine the cup orientation from calibrated X-ray images and SSM based 2D3D reconstruction. From the results we conclude that the non-invasive SSM-based 2D-3D reconstruction method provides a valid method to determine the cup orientation as compared to fiducial based methods.
The main error contribution of our method at this point is the calibration of the X-ray images. Since the used phantom was originally designed for smaller scaled applications like C-arms, it needs to be redesigned in the future. For the determination of the cup orientation we used a metal ring inside the plastic cup instead of the initially implanted markers. While this method produced more repeatable results than using only the four markers it is also applicable in real surgical cases where the orientation of the cup in a planar x’ray may only be determined form the silhouette, but it also makes in plane rotation difficult to track.
Special thanks to Urs Rohrer (ISTB) and Patrick Moser (ISTB) for their help in developing the model frame. We would also like to thank the MTRA team from the Inselspital Bern under direction of Prof. Dr. Dr. J. T. Heverhagen for the access to the X-ray equipment.
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