Predicting tibiotalar and subtalar joint angles from skin-marker data with dual-fluoroscopy as a reference standard

Abstract

Evidence suggests that the tibiotalar and subtalar joints provide near six degree-of-freedom (DOF) motion. Yet, kinematic models frequently assume one DOF at each of these joints. In this study, we quantified the accuracy of kinematic models to predict joint angles at the tibiotalar and subtalar joints from skin-marker data. Models included 1 or 3 DOF at each joint. Ten asymptomatic subjects, screened for deformities, performed 1.0m/s treadmill walking and a balanced, single-leg heel-rise. Tibiotalar and subtalar joint angles calculated by inverse kinematics for the 1 and 3 DOF models were compared to those measured directly in vivo using dual-fluoroscopy. Results demonstrated that, for each activity, the average error in tibiotalar joint angles predicted by the 1 DOF model were significantly smaller than those predicted by the 3 DOF model for inversion/eversion and internal/external rotation. In contrast, neither model consistently demonstrated smaller errors when predicting subtalar joint angles. Additionally, neither model could accurately predict discrete angles for the tibiotalar and subtalar joints on a per-subject basis. Differences between model predictions and dual-fluoroscopy measurements were highly variable across subjects, with joint angle errors in at least one rotation direction surpassing 10° for 9 out of 10 subjects. Our results suggest that both the 1 and 3 DOF models can predict trends in tibiotalar joint angles on a limited basis. However, as currently implemented, neither model can predict discrete tibiotalar or subtalar joint angles for individual subjects. Inclusion of subject-specific attributes may improve the accuracy of these models.

Keywords: Ankle; Dynamic imaging; Hindfoot; Inverse kinematics; Motion capture.

Figure 1

Flowchart of experimental and computational methods. (A) For each subject, experimental skin-marker data and dual-fluoroscopy data were simultaneously collected. Note, at the foot and ankle, the skin-marker set included markers on the medial and lateral malleoli, calcaneal tuberosity, dorsal aspects of the second and fifth phalanxes, dorsal web space between the fourth and fifth metatarsals, and the dorsal-medial aspect of the first metatarsal head. (B) Using only the skin-marker data, tibiotalar and subtalar joint angles were predicted from inverse kinematic simulations using the 1 DOF and 3 DOF models. (C) Independently, tibiotalar and subtalar joint angles were measured using dual-fluoroscopy. The joint angles predicted from skin-marker data were then compared to those measured using dual-fluoroscopy.

Figure 2

Motion of (A) tibiotalar and (B) subtalar joints during the heel-strike and toe-off activities. Joint angles calculated using the 1 DOF model (green) and the 3 DOF model (purple) are plotted separately to facilitate comparison with the joint angles calculated using the experimental dual-fluoroscopy (DF) data (black). Solid lines represent average across subjects. Given that the length of trials varied across subjects, averages were calculated for any region for which data existed for at least 5 subjects. Shaded regions represent one standard deviation. All joint angles are plotted versus the percentage of the stance phase of gait, where 0% represents heel-strike of the imaged foot and 100% represents toe-off of the imaged foot. Dorsiflexion, inversion, and internal rotation are defined as positive.

Figure 3

Root mean square (RMS) errors of the (A) tibiotalar and (B) subtalar joints during each activity. For each model, the RMS errors were calculated between joint angles predicted by the models versus measured experimentally using dual-fluoroscopy. The RMS errors are displayed separately for the 1 DOF (green) and 3 DOF (purple) models. Bars represent average across subjects. Error bars represent one standard deviation, thereby illustrating across subject variability. Asterisks (*) and displayed p-values indicate a significant difference between the RMS errors for the 1 and 3 DOF models.

Figure 4

Bland-Altman plots of (A) tibiotalar and (B) subtalar joint motion during the heelstrike and toe-off activities. Differences between motions predicted by the models versus measured experimentally using dual-fluoroscopy (DF) are displayed separately for the (i) 1 DOF and (ii) 3 DOF models. Within each trial (unique points) and subject (unique colors), differences were calculated across all collected time points and then averaged. All calculated differences are model minus experimental, thus positive values represent an overestimation by the model. Solid lines represent mean difference (i.e., bias). Dotted lines represent 95% limits of agreement. Dorsiflexion, inversion, and internal rotation are defined as positive.

Figure 5

Motion of (A) tibiotalar and (B) subtalar joints during four separate walking trials (two heel-strike and two toe-off) from a single subject. The displayed subject demonstrated some of the largest tibiotalar joint angle errors, as evidenced in the Bland-Altman analysis (plotted color chosen to be consistent with Bland-Altman plots in Fig. 4). Joint angles calculated using the models (dotted lines) are plotted separately for the (i) 1 DOF and (ii) 3 DOF models to facilitate comparison with the joint angles calculated using the experimental dual-fluoroscopy (DF) data (solid lines). All joint angles are plotted versus the percentage of the stance phase of gait, where 0% represents heel-strike of the imaged foot and 100% represents toe-off of the imaged foot. Dorsiflexion, inversion, and internal rotation are defined as positive.