Design, Calibration and Validation of a Novel 3D Printed Instrumented Spatial Linkage that Measures Changes in the Rotational Axes of the Tibiofemoral Joint

An accurate axis-finding technique is required to measure any changes from normal caused by total knee arthroplasty in the flexion–extension (F–E) and longitudinal rotation (LR) axes of the tibiofemoral joint. In a previous paper, we computationally determined how best to design and use an instrumented spatial linkage (ISL) to locate the F–E and LR axes such that rotational and translational errors were minimized. However, the ISL was not built and consequently was not calibrated; thus the errors in locating these axes were not quantified on an actual ISL. Moreover, previous methods to calibrate an ISL used calibration devices with accuracies that were either undocumented or insufficient for the device to serve as a gold-standard. Accordingly, the objectives were to (1) construct an ISL using the previously established guidelines,(2) calibrate the ISL using an improved method, and (3) quantify the error in measuring changes in the F–E and LR axes. A 3D printed ISL was constructed and calibrated using a coordinate measuring machine, which served as a gold standard. Validation was performed using a fixture that represented the tibiofemoral joint with an adjustable F–E axis and the errors in measuring changes to the positions and orientations of the F–E and LR axes were quantified. The resulting root mean squared errors (RMSEs) of the calibration residuals using the new calibration method were 0.24, 0.33, and 0.15 mm for the anterior–posterior, medial–lateral, and proximal–distal positions, respectively, and 0.11, 0.10, and 0.09 deg for varus–valgus, flexion–extension, and internal–external orientations, respectively. All RMSEs were below 0.29% of the respective full-scale range. When measuring changes to the F–E or LR axes, each orientation error was below 0.5 deg; when measuring changes in the F–E axis, each position error was below 1.0 mm. The largest position RMSE was when measuring a medial–lateral change in the LR axis (1.2 mm). Despite the large size of the ISL, these calibration residuals were better than those for previously published ISLs, particularly when measuring orientations, indicating that using a more accurate gold standard was beneficial in limiting the calibration residuals. The validation method demonstrated that this ISL is capable of accurately measuring clinically important changes (i.e. 1 mm and 1 deg) in the F–E and LR axes.