Previously Unrecognized Source of Error in the Change in Maximum Total Point Motion to Determine Continuous Migration of Unstable Tibial Baseplates

Abstract

In radiostereometric analysis (RSA), continuous migration denoted as ΔMTPM is the difference between maximum total point motion (MTPM) at 2 years relative to time zero and MTPM at 1 year relative to time zero. Continuous migration has been used to diagnose tibial baseplates as stable versus unstable when compared to a specified stability limit (i.e., value of ΔMTPM). If the same point experiences MTPM at 2 years and at 1 year (usually the case for marker-based RSA), then an implicit assumption is that the migration path between 2 years and 1 year is the same as the path between 1 year and time zero. This article uses vector analysis to demonstrate a source of error in ΔMTPM not previously recognized and estimates the magnitude of error based on the interplay of independent variables which affect the error. The two independent variables which affect the error are the angle between the two migration vectors (i.e., MTPM between time zero and 2 years and MTPM between time zero and 1 year) and the difference in magnitude of the two vectors. The relative error increased in an absolute sense as the angle between the vectors increased and decreased for larger differences in the magnitudes of the two vectors. For magnitude ratios ranging from 1.25 to 2, relative errors ranged from –21% to –3% at 10 deg and from –78% to –42% at 60 deg, respectively. Knowledge of these errors highlights a limitation in the use of ΔMTPM not previously recognized.