Identifying Sources Of Error In Computer Navigated Total Knee Arthroplasties Using A Metric On SE(3) and Sensitivity Analyses

Throughout the procedure of a computer-navigated total knee arthroplasty (TKA), there are many opportunities for sources of error to be introduced. Identifying these errors can improve surgical outcomes. There is also a lack of accessible methods in available literature for clinicians to perform research in this area using engineering analysis techniques. This thesis aims to provide a greater understanding of the sources of error that can occur pre-bone cut. Possible sources of error include the bony landmark selections and the placement of the cut guide. Using artificial bone models and a 3D point capture system concurrently with a computer-navigation system, the data points collected during the procedure are mimicked. It was found that variability of point selection varied between landmarks with some being more precise than others. Bone reference frames can be calculated using these landmark points. By painting the surface of the saw blade, the cut plane values, and a reference frame for the cuts, can also be estimated. These frames are easily represented with homogeneous transformation matrices. One method of comparing transformation matrices is with a metric on SE(3), simplified in this thesis to be the Frobenius norm. It was found that bone reference frames with the highest metric were the ones with the highest error in femur or tibia center points. It was also found that there was no clear correlation between the bone reference frame error and cut plane error, implying that other sources must be taken into account. Sensitivity analyses were performed to observe the outcome error of the bone reference frame and cut plane in regards to error in the landmark selection. The results from this support other results in this thesis: that landmark points used for the origin of the reference frames have the greatest effect on the system output. The methods in this thesis can easily be applied to other computer-navigated systems for analysis