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).