Computer Simulation of Errors in Migration Metrics Using Marker-Based and Model-Based Radiostereometric Analysis: Application to the Risk-Assessment of Tibial Baseplate Instability

Abstract

Background: Marker-based radiostereometric analysis (RSA) involves locating bone markers and implant markers on a series of biplanar radiographs to determine the relative motion (or migration) of the tibial baseplate following total knee arthroplasty. The long history of marker-based RSA enabled previous researchers to determine that short-term migration (within 2 years) can predict long-term baseplate stability and subsequently enabled the development of stability limits which accelerate the time required to assess the risk of new baseplate designs or surgical techniques. However, there are many barriers to successfully implementing a marker-based RSA study including regulatory restrictions on marking implants, loosening and/or occlusion of implant markers during imaging, or faulty migration measurements due to the relative motion between the insert and baseplate, all of which have led to the development of model-based RSA.

Model-based RSA differs from marker-based RSA in that there are no implant markers, but rather the position and orientation of the baseplate are determined by registering a 3D surface model onto the series of radiographs. Use of a surface model (i.e. thousands of points) in place of implant markers (i.e. typically 5 points) creates two distinctions between the two RSA methods: (1) the number of points considered for migration and (2) the registration error associated with each method, both of which may impact migration measurements.

Accordingly, previous researchers compared the bias (systematic error) and precision (random error) of model-based RSA to marker-based RSA for migration measurements in six degrees of freedom (3 translations and 3 rotations) and found no difference in bias, but worse precision for model-based RSA due to registration error. This difference in precision is noteworthy when considering that the stability limits used for risk assessment are not based on migration in six degrees of freedom, but rather are based on the maximum total point motion (MTPM), the largest movement of any point on the baseplate relative to the tibia, and on the change in MTPM (ΔMTPM) which may be impacted by the number of points and/or the registration error. The first stability limit diagnoses stable baseplates as those with a mean MTPM < 0.5 mm at 6 months and the second stability limit diagnoses stable baseplates as those with ΔMTPM < 0.2 mm between 1 to 2 years. Understanding how the number of points or the registration error associated with marker-based or model-based RSA affects the computation of MTPM or ΔMTPM is essential for determining whether the stability limits from marker-based RSA studies can be applied to model-based RSA studies.

Hence the objectives of Chapter 1 were to quantify the mean difference in MTPM when using 5 points versus all points, and evaluate the dependency of this difference on baseplate shape and size. The objectives of Chapter 2 were to quantify the bias and precision in MTPM for marker-based and model-based RSA and compare the bias to the 0.5 mm stability limit. The objectives of Chapter 3 were to quantify the bias and precision in ΔMTPM for marker-based and model-based RSA and compare the proportion of stable baseplate which fall above the 0.2 mm stability limit.

Methods: All analyses were performed by simulating baseplate migration in MATLAB. For Chapter 1, the difference in MTPM using 5 points and all points and error (i.e. difference in MTPM/stability limit) relative to the 0.5 mm stability limit were determined by applying a generated dataset of migrations at 6 months to four 3D models (two baseplate shapes and two baseplate sizes).

For Chapter 2, the bias and precision in MTPM relative to the 0.5 mm stability limit were determined for marker-based versus model-based RSA by applying registration errors associated with each method to a tibial baseplate under stationary and non-stationary conditions.

For Chapter 3, the bias and precision in ΔMTPM relative to the 0.2 mm stability limit were determined for marker-based versus model-based RSA by applying registration errors associated with each method to a tibial baseplate under stable conditions. Furthermore, the proportion of baseplates above the stability limit were computed.

Results: For Chapter 1, the pooled mean difference in MTPM using 5 points versus all points was 0.02 mm, or 4% relative to the 0.5 mm stability limit, and results were not affected by baseplate shape or size.

For Chapter 2, the bias error in MTPM relative to the 0.5 mm stability limit was three to four times greater for model-based RSA than for marker-based RSA (12%-27% vs. 3%-8%). The precision in MTPM for stable baseplates was two times greater for model-based RSA than for marker-based RSA (0.12-0.14 mm vs. 0.05-0.07mm).

For Chapter 3, there was no bias error in ΔMTPM; however, the precision of ΔMTPM was twice as large for model-based RSA than marker-based RSA, resulting in about 25% of stable baseplates falling above the 0.2 mm stability limit for model-based RSA.

Conclusion: The decision to use 5 points versus all points when computing MTPM for model-based RSA does not substantively affect the mean MTPM at 6 months. The author recommends using 5 points to maintain consistency with marker-based RSA. Furthermore, the 0.5 mm stability limit needs to be adjusted for application to model-based RSA studies to compensate for the larger bias error in MTPM and the author proposes a method for making this adjustment. Lastly, application of the 0.2 mm stability limit to model-based RSA studies is viable for group assessment, but questionable for individual patient assessment.