Comparing dynamical systems concepts and techniques for biomechanical analysis

Abstract

Traditional biomechanical analyses of human movement are generally derived from linear mathematics. While these methods can be useful in many situations, they do not describe behaviors in human systems that are predominately nonlinear. For this reason, nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature. These analysis techniques have provided new insights into how systems (1) maintain pattern stability, (2) transition into new states, and (3) are governed by short- and long-term (fractal) correlational processes at different spatio-temporal scales. These different aspects of system dynamics are typically investigated using concepts related to variability, stability, complexity, and adaptability. The purpose of this paper is to compare and contrast these different concepts and demonstrate that, although related, these terms represent fundamentally different aspects of system dynamics. In particular, we argue that variability should not uniformly be equated with stability or complexity of movement. In addition, current dynamic stability measures based on nonlinear analysis methods (such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics, but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored. Finally, systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.

Postural Control Entropy Is Increased When Adopting an External Focus of Attention

“…The notion of self-organization in motor control is commonly examined by quantifying variability in movement profiles, which provides an indication of how changes in movement occurred over time (Hausdorff, 2007;Manor et al, 2010;Rhea & Kiefer, 2014;Stergiou & Decker, 2011;van Emmerik et al, 2016). Movement variability can be expressed in terms of magnitude (i.e., how much the movement changed over time) and/or structure (i.e., temporal organization of the changes in movement during the task).…”

“…To obtain a more finite understanding of motor control at the momentto-moment level, entropy analyses were adopted in the field (Newell & Vaillancourt, 2001;Slifkin & Newell, 1998). Research over the past two decades has linked entropy in motor control to the adaptive capacity (and potentially the health) of the motor control system (Manor et al, 2010;Rhea & Kiefer, 2014;Stergiou & Decker, 2011;van Emmerik, Ducharme, Amado, & Hamill, 2016). Specific to postural control, entropy has been shown to decrease (i.e., more repeating patterns) when neurological deficits are present, such as vision or somatosensory impairment (Manor et al, 2010), after a concussion Sosnoff, Broglio, Shin, & Ferrara, 2011), and in those with multiple sclerosis (Busa, Jones, Hamill, & van Emmerik, 2016).…”

Hand grip strength variability during serial testing as an entropic biomarker of aging: a Poincaré plot analysis

“…By analysing the geometric characteristics of the graphs plotted by the Poincaré method, it is possible to extract quantitative variables that help to characterize the dynamics of the systems taken into account [3]. Additionally, through complex statistical calculations, correlations across multiple spatiotemporal scales can be determined, which help to identify fractal dynamics [4]. Overall, using the proposed method, it is possible to achieve an entropy-based analysis of complex time series of data.…”

Effects of backpack loads and positions on the variability of gait spatiotemporal parameters in young adults

“…Gait variability performs an essential role in producing movement patterns that are adaptable and can be observed during transitions between different tasks; therefore, a gait variability increase is seen as either detrimental in some cases (end-point variability) or beneficial in others (coordinative variability) (Van Emmerik et al, 2016). Spatiotemporal parameters' variability relates to coordinative variability, whose increase implies a richer motor repertoire as an adaptive strategy to deal with perturbation during walking, as carrying a backpack load.…”