Abstract
Introduction
The most common method for accurate kinematic analysis of the knee arthroplasty uses bi-planar fluoroscopy and model-based RSA. The main challenge is to have access to reverse-engineered CAD models of the implant components, if not provided by the company, making this method impractical for a clinical study involving many types or sizes of implants. An alternative could be to reconstruct the 3D primitive features of the implant, such as cylindrical pegs, flat surfaces and circular boundaries, based on their 2D projections. This method was applied by Kaptein et al. (2006) for hip implants. However, despite its broad potential, it has not yet been applied for studying TKA kinematics. This study develops a methodology for feature-based RSA of TKA and investigates the range of accuracies in comparison to model-based RSA.
Methods
Joint-3D software was developed in the MATLAB programming language to segment and fit elementary 2D features such as circles, lines, and ellipses to the edges of the parts on the radiographs (Figure 1). The software has the capability to reconstruct the 3D location and orientation of the components based on their 2D projections. To test the accuracy of the system a standard primary knee replacement system (Zimmer NexGen) was implanted on bone replica models, and positioned at 0° to 120° flexion at 30° intervals, simulating a lunge activity. For each pose, a multi-planar radiography system developed in our lab (Amiri et al., 2011) was used to take a sagittal and a 15° distally rotated radiograph (Figure 2a).
Figure 1 shows the features C, L, and E segmented on the tibia and femur. The 3D reconstruction is performed based on a number of functions: Functions ‘f’ and ‘g’ reconstruct a 3D point or line based on their 2D projections. Function ‘h’ finds the plane containing the 3D circular edge based on its two projection ellipses. Function ‘i’ finds the 3D location of a line based on one projection line, and a known 3D vector normal to the solution 3D line. Based on these, the coordinate systems of the components were reconstructed (Figure 2b):
Femur_Origin=f(C1A,C1B);
Femur_Anteroposterior=g(L1A, L1B);
Femur_Proximodistal=g(L2A,L2B);
Femur_Mediolateral=i(L,C1A–C1B),{L=L1: if flexion<45°; L=L2: if flexion>45°};
E_3D=h(E1A,E1B);
Tibia_Origin=f(E1A_Centre,E1B_Centre);
Tibia_Anteroposterior=g(L3A,L3B);
Tibia_Mediolateral=cross(E_3D, Tibia_Anteroposterior);
Tibia_Proximodistal=cross(Tibia_Anteroposterior, Tibia_Mediolateral)
To determine the errors, model-based RSA measures were used as the reference using the reverse-engineered models of the components in JointTrack software (University of Florida).
Results
The overall accuracies in terms of bias (the mean error) and precision (standard deviation of the errors) are shown in Figure 3. The bias was within 0.5–1 mm and 0.9–1.2°, and the calculated precision was in the range of 0.4–0.6 mm and 0.7–1.0°. The overall accuracy was 0.8±0.6 mm and 1±0.7°.
Discussion
The very good accuracies obtained show the practicality of the methodology. The methodology can be easily worked out for any type of implant based on the primitive geometric features at the bone-implant interface. This method can be extremely useful in a large clinical study by eliminating the need for having the 3D models of many types and sizes of the implant available.
