Talar dome detection and its geometric approximation in CT: Sphere, cylinder or bi-truncated cone?

Objective The purpose of our study is to give a relatively objective definition of talar dome and its shape approximations to sphere (SPH), cylinder (CLD) and bi-truncated cone (BTC). Materials and methods The “talar dome” is well-defined with the improved Dijkstra's algorithm, considering the Euclidean distance and surface curvature. The geometric similarity between talar dome and ideal shapes, namely SPH, CLD and BTC, is quantified. 50 unilateral CT datasets from 50 subjects with no pathological morphometry of tali were included in the experiments and statistical analyses were carried out based on the approximation error. Results The similarity between talar dome and BTC was more prominent, with smaller mean, standard deviation, maximum and median of the approximation error (0.36 ± 0.07 mm, 0.32 ± 0.06 mm, 2.24 ± 0.47 mm and 0.28 ± 0.06 mm) compare with fitting to SPH and CLD. In addition, there were significant differences between the fitting error of each pair of models in terms of the 4 measurements (p-values < 0.05). The linear regression analyses demonstrated high correlation between CLD and BTC approximations (R² = 0.55 for median, R² > 0.7 for others). Color maps representing fitting error indicated that fitting error mainly occurred on the marginal regions of talar dome for SPH and CLD fittings, while that of BTC was small for the whole talar dome. Conclusion The successful restoration of ankle functions in displacement surgery highly depends on the comprehensive understanding of the talus. The talar dome surface could be well-defined in a computational way and compared to SPH and CLD, the talar dome reflects outstanding similarity with BTC.