Separating Timing, Movement Conditions and Individual Differences in the Analysis of Human Movement

Abstract

A central task in the analysis of human movement behavior is to determine systematic patterns and differences across experimental conditions, participants and repetitions. This is possible because human movement is highly regular, being constrained by invariance principles. Movement timing and movement path, in particular, are linked through scaling laws. Separating variations of movement timing from the spatial variations of movements is a well-known challenge that is addressed in current approaches only through forms of preprocessing that bias analysis. Here we propose a novel nonlinear mixed-effects model for analyzing temporally continuous signals that contain systematic effects in both timing and path. Identifiability issues of path relative to timing are overcome by using maximum likelihood estimation in which the most likely separation of space and time is chosen given the variation found in data. The model is applied to analyze experimental data of human arm movements in which participants move a hand-held object to a target location while avoiding an obstacle. The model is used to classify movement data according to participant. Comparison to alternative approaches establishes nonlinear mixed-effects models as viable alternatives to conventional analysis frameworks. The model is then combined with a novel factor-analysis model that estimates the low-dimensional subspace within which movements vary when the task demands vary. Our framework enables us to visualize different dimensions of movement variation and to test hypotheses about the effect of obstacle placement and height on the movement path. We demonstrate that the approach can be used to uncover new properties of human movement.

Author Summary

When you move a cup to a new location on a table, the movement of lifting, transporting, and setting down the cup appears to be completely automatic. Although the hand could take continuously many different paths and move on any temporal trajectory, real movements are highly regular and reproducible. From repetition to repetition movements vary, and the pattern of variance reflects movement conditions and movement timing. If another person performs the same task, the movement will be similar. When we look more closely, however, there are systematic individual differences. Some people will overcompensate when avoiding an obstacle and some people will systematically move slower than others. When we want to understand human movement, all these aspects are important. We want to know which parts of a movement are common across people and we want to quantify the different types of variability. Thus, the models we use to analyze movement data should contain all the mentioned effects. In this work, we developed a framework for statistical analysis of movement data that respects these structures of movements. We showed how this framework modeled the individual characteristics of participants better than other state-of-the-art modeling approaches. We combined the timing-and-path-separating model with a novel factor analysis model for analyzing the effect of obstacles on spatial movement paths. This combination allowed for an unprecedented ability to quantify and display different sources of variation in the data. We analyzed data from a designed experiment of arm movements under various obstacle avoidance conditions. Using the proposed statistical models, we documented three findings: a linearly amplified deviation in mean path related to increase in obstacle height; a consistent asymmetric pattern of variation along the movement path related to obstacle placement; and the existence of obstacle-distance invariant focal points where mean trajectories intersect in the frontal and vertical planes.