Characterization of the disruption of neural control strategies for dynamic fingertip forces from attractor reconstruction

Abstract

The Strength-Dexterity (SD) test measures the ability of the pulps of the thumb and index finger to compress a compliant and slender spring prone to buckling at low forces (<3N). We know that factors such as aging and neurodegenerative conditions bring deteriorating physiological changes (e.g., at the level of motor cortex, cerebellum, and basal ganglia), which lead to an overall loss of dexterous ability. However, little is known about how these changes reflect upon the dynamics of the underlying biological system. The spring-hand system exhibits nonlinear dynamical behavior and here we characterize the dynamical behavior of the phase portraits using attractor reconstruction. Thirty participants performed the SD test: 10 young adults, 10 older adults, and 10 older adults with Parkinson’s disease (PD). We used delayed embedding of the applied force to reconstruct its attractor. We characterized the distribution of points of the phase portraits by their density (number of distant points and interquartile range) and geometric features (trajectory length and size). We find phase portraits from older adults exhibit more distant points (p = 0.028) than young adults and participants with PD have larger interquartile ranges (p = 0.001), trajectory lengths (p = 0.005), and size (p = 0.003) than their healthy counterparts. The increased size of the phase portraits with healthy aging suggests a change in the dynamical properties of the system, which may represent a weakening of the neural control strategy. In contrast, the distortion of the attractor in PD suggests a fundamental change in the underlying biological system, and disruption of the neural control strategy. This ability to detect differences in the biological mechanisms of dexterity in healthy and pathological aging provides a simple means to assess their disruption in neurodegenerative conditions and justifies further studies to understand the link with the physiological changes.

Sex differences in leg dexterity are not present in elite athletes

“…The detailed rationale and methodology for this nonlinear analysis are provided in detail elsewhere[29] and in[6], and therefore, are only described briefly below. It is based on the theory of nonlinear dynamical systems, where the time evolution of a system is defined in a phase space or state space .…”

“…The embedding parameters τ and m must be properly chosen to accurately reconstruct the attractor. Several approaches have been proposed to choose the optimal embedding delay, and for this analysis we focus on and employ the first minimum of the mutual information function[29, 36]. The embedding delay τ must be large enough so that the information gained from measuring the value of y i+ τ is significantly different from the information already known from the previous point, y i .…”

“…The embedding delay τ must be large enough so that the information gained from measuring the value of y i+ τ is significantly different from the information already known from the previous point, y i . Furthermore, τ should not be so large that memory about the system’s initial condition is lost[29, 36]. …”

“…Given a time series with a minimal embedding dimension, m 0 , the reconstructed attractor in m 0 - dimensional space is a one-to-one image of the attractor in the original phase space. If the attractor is embedded in an m -dimensional space where m is greater than m 0 , the topological structure is no longer preserved and points are projected into neighborhoods of other points to which they would not belong in higher dimensions (such points are called false neighbors)[29]. For example, if the attractor is a circle, a 1-dimensional (1-D) manifold embedded in 2-D, then points in opposite sides of circle can be seen as adjacent (i.e., false neighbors) if seen sideways in 3-D.…”

“…Unfortunately, the fact that subjects can reliably control the spring at the edge of instability only for the few seconds produces timeseries that are not well suited for many classical nonlinear dynamical measures (i.e, maximal Lyapunov Exponent, Correlation Dimension) that require longer time series[13, 43]. We recently showed that a nonlinear dynamical approach to the analysis of the time-varying compression forces at the edge of instability is more robust than traditional linear analyses (e.g., mean compression force, and root-mean square (RMS)) to quantify sensorimotor processing for finger dexterity, and can even distinguish the effects of healthy aging from those of mild-to-moderate degenerative neurologic conditions such as Parkinson’s disease[29]. Here we extend that work and apply the delayed embedding theorem (Takens’ theorem[37]), to reconstruct the phase portraits from time series of foot forces collected during the leg dexterity test from both elite (highly-skilled) and recreational (moderately-skilled) athletes.…”