Human movement variability, nonlinear dynamics, and pathology: is there a connection?

Abstract

Fields studying movement generation, including robotics, psychology, cognitive science, and neuroscience utilize concepts and tools related to the pervasiveness of variability in biological systems. The concept of variability and the measures for nonlinear dynamics used to evaluate this concept open new vistas for research in movement dysfunction of many types. This review describes innovations in the exploration of variability and their potential importance in understanding human movement. Far from being a source of error, evidence supports the presence of an optimal state of variability for healthy and functional movement. This variability has a particular organization and is characterized by a chaotic structure. Deviations from this state can lead to biological systems that are either overly rigid and robotic or noisy and unstable. Both situations result in systems that are less adaptable to perturbations, such as those associated with unhealthy pathological states or absence of skillfulness.

Fig. 1

Complementary linear and nonlinear measures from different signals; six signals are displayed, with the respective values for range and largest Lyapunov Exponent (LyE). The first two time series are periodic and have been generated using the sine function 15sin(t/24) and the cosine function 40cos(t/24). The following two time series are chaotic and have been generated using the Rössler and Lorenz systems, respectively. The final two time series are random and correspond to uniformly and Gaussian distributed white noise, respectively. All time series contain 4000 data points. The figure demonstrates that signals can have the same range but differ in terms of temporal structure (LyE) or they can have different ranges but the same LyE

Fig. 2

Periodic, chaotic, and random time series and their corresponding three-dimensional phase space plots. The phase space plot is obtained by plotting the original time series and its time delayed copies. This figure provides with an illustration of a chaotic signal and how is different from other signals.

Fig. 3

Theoretical model of optimal movement variability illustrated using the signals from Fig. 2. For clarification purposes, the signals presented (“Periodic”, “Chaotic”, and “Random”) are not the only three possibilities. Behavior in terms of variability should be viewed in a continuum as being more or less predictable (on the X-axis) or exhibiting or not chaos (on the Y-axis). Thus, there are many other possibilities.