A comparison of stability metrics based on inverted pendulum models for assessment of ramp walking

Abstract

Maintaining balance on ramps is important for mobility. However, balance is commonly assessed using inverted pendulum-based metrics (e.g., margin of stability), which may not be appropriate for assessment of human walking on non-level surfaces. To investigate this, we analyzed stability on ramps using four different inverted pendulum models: extrapolated center of mass (XCOM), foot placement estimate (FPE), foot placement estimate neglecting angular momentum (FPENoH), and capture point (CAP). We analyzed experimental data from 10 able-bodied individuals walking on a ramp at 0°, ±5°, and ±10°. Contrary to our hypothesis that the magnitude of differences between metrics would be greatest at ±10°, we observed the greatest magnitude of differences between metrics at 0°. In general, the stability metrics were bounded by FPE and CAP at each slope, consistent with prior studies of level walking. Our results also suggest that clinical providers and researchers should be aware that assessments that neglect angular momentum (e.g., margin of stability, XCOM) may underestimate stability in the sagittal-plane in comparison to analyses which incorporate angular momentum (e.g., FPE). Except for FPENoH-CAP (r = 0.82), differences between metrics were only moderately correlated (|r|≤0.65) with violations of leg length assumptions in the underlying inverted pendulum models. The differences in FPENoH relative to FPE and CAP were strongly correlated with body center of mass vertical velocity (max |r| = 0.92), suggesting that model representations of center of mass motion influence stability metrics. However, there was not a clear overall relationship between model inputs and differences in stability metrics. Future sensitivity analyses may provide additional insight into model characteristics that influence stability metrics.

Fig 1. Inverted pendulum model diagrams.

Diagrams illustrating the models used for calculating stability metrics: the extrapolated center of mass (XCOM, a), foot placement estimate (FPE, b), and capture point (CAP, c). The ramp angle and the angle of the leg relative to the vertical have been exaggerated for clarity. A summary of key model characteristics is given below each diagram.

Fig 2. Stability metric values.

Mean (±SD) stability metrics, computed as the distance between the toe marker and extrapolated center of mass (XCOM, black diamonds), foot placement estimate (FPE, red squares), foot placement estimate with no angular momentum (FPE_NoH, green circles) and capture point (CAP, blue triangles) at heel strike, normalized to percent static (i.e., standing) leg length. Positive values are defined as “stable” (toe anterior to stability location), and negative values are “unstable” (toe posterior to stability location) by the metric definitions.

Fig 3. Mean (±SD) differences between stability metrics.

Mean (±SD) signed differences between each pair of stability metrics at each of the slope angles investigated. Comparisons were made between extrapolated center of mass (XCOM), foot placement estimate (FPE), foot placement estimate with no angular momentum (FPE_NoH) and capture point (CAP). Differences were computed by subtracting one metric from the other, e.g., XCOM-FPE denotes that the FPE metric was subtracted from the XCOM metric. Each metric was normalized to percent static (i.e., standing) leg length. Lines connecting data points are solely intended as a visual aid.

Fig 4. Mean (±SD) magnitude of differences between stability metrics.

Mean (±SD) magnitude (i.e., absolute value) of differences between each pair of stability metrics at each of the slope angles investigated. Comparisons were made between extrapolated center of mass (XCOM), foot placement estimate (FPE), foot placement estimate with no angular momentum (FPE_NoH) and capture point (CAP). Each metric was normalized to percent static (i.e., standing) leg length. Lines connecting data points are solely intended as a visual aid.

Fig 5. Correlation between differences in stability metrics and model inputs.

Correlation between the signed differences between each pair of stability metrics and various inputs that affect model predictions. Effective leg length is the distance from the body center of mass (COM) to the ankle joint center at the instant of heel strike. Foot placement refers to the horizontal (i.e., anteroposterior) distance between the body COM and toe marker at the instant of heel strike. Each stability metric was normalized to percent static (i.e., standing) leg length. Mean values for each subject are plotted for each ramp angle: -10° (red circles), -5° (red squares), 0° (black triangles), +5° (blue crosses), and +10° (blue diamonds). Pearson correlation coefficients (r) and p-values are given for each subfigure. Statistically significant correlations are indicated by *.