Effect of gap-filling technique and gap location on linear and nonlinear calculations of motion during locomotor activities.

Background: Marker occlusion during camera-based movement analysis is common. Different interpolation techniques are available for estimating location of missing marker trajectories.

Research Question: What is the effect of gap location and interpolation technique on linear and nonlinear measures for a given kinematic time series?

Methods: Kinematic data were recorded during motor-assisted elliptical training and treadmill walking. Gap-filling techniques (i.e., Cubic, Makima, Autoregressive, Nearest Neighbor, and No Interpolation) and gap locations experimentally applied to each cycle across initially complete time series (Gap 1: local minimum and maximum peaks; Gap 2: maximum peaks; Gap 3: maximum peaks at negative slope; Gap 4: random locations) were examined during linear (Maxima and Minima joint angles) and nonlinear [maximum Lyapunov exponent (LyE)] measures.

Results: Gap-filling technique and gap location influenced values calculated for linear and nonlinear measures of joint motions. When referenced to the gold standard (original data series without gaps), across all joints studied the average % error of Maxima and Minima joint angles and LyE % error were lower when applying Cubic, Makima, Autoregressive, and Nearest Neighbor techniques compared to No Interpolation (p < 0.0001). The % error of Maxima joint angles was lower for Gaps 1, 3, and 4 compared to Gap 2 (p = 0.0003), while % error of Minima joint angles was lower for Gaps 2 and 3, compared to Gaps 1 and 4 (p < 0.0001). An interaction between gap-filling technique and gap location was identified for LyE % error, in which Gap 4 % error was significantly greater during No Interpolation compared to other gap-filling techniques (p < 0.0001).

Significance: Findings can guide selection of appropriate techniques to manage missing kinematic data points in camera-based motion analysis time series. Gap-filling techniques significantly reduced error in calculating select linear and nonlinear measures of variability, with Cubic most consistently resulting in the greatest reduction in error.