Digital templating with external calibration markers is the standard method for planning total hip arthroplasty. We determined the geometrical basis of the magnification effect, compared magnification with external and internal calibration markers, and examined the influence on magnification of the position of the calibration markers, patient weight, and body mass index (BMI). A formula was derived to calculate magnification with internal and external calibration markers, informed by 100 digital radiographs of the pelvis. Intraclass correlations between the measured and calculated values and the strength of relationships between magnification, position and distance of calibration markers and height, weight, and BMI were sought. There was a weak correlation between magnification of internal and external calibration markers (r = 0.297–0.361; p < 0.01). Intraclass correlations were 0.882–1.000 (p = 0.000) for all parameters. There were also weak correlations between magnification of internal and external calibration markers and weight and BMI (r = 0.420, p = 0.000; r = 0.428, p = 0.000, respectively). The correlation between external and internal calibration markers was poor, indicating the need for more accurate calibration methods. While weight and BMI weakly correlated with the magnification of markers, future studies should examine this phenomenon in more detail.

Abstract. We show that the fundamental group of the space of contact structures on the 3-torus (based at the standard contact structure) is isomorphic to the integers.