Perturbation parameters associated with nonlinear responses of the head at small amplitudes

Abstract

The head-neck system has multiple degrees of freedom in both its control and response characteristics, but is often modeled as a single joint mechanical system. In this study, we have attempted to quantify the perturbation parameters that would elicit nonlinear responses in a single degree-of-freedom neuromechanical system at small amplitudes and velocities of perturbation. Twelve healthy young adults seated on a linear sled randomly received anterior-posterior sinusoidal translations with +/-15 mm and +/-25 mm peak displacements at 0.81, 1.76, and 2.25 Hz. Head angular velocity and angular position data were examined using a nonlinear phase-plane analysis. Poincare sections of the phase plane were computed and Lyapunov exponents calculated to measure divergence (chaotic behavior) or convergence (stable behavior) of system dynamics. Variability of head angular position and velocity across the entire phase plot was compared to that of the Poincare sections to quantify spatial-temporal irregularity. Multiple equilibrium points and positive Lyapunov exponents revealed chaotic behavior at 0.81 Hz at both amplitudes whereas responses at 1.76 and 2.25 Hz exhibited periodic oscillations, clustered phase points, and negative Lyapunov exponents. However, intersubject variability increased at the lowest frequency and a few subjects presented chaotic behavior at all frequencies. An inverted pendulum with position and velocity threshold nonlinearity was adopted as a simplistic model of the head and neck. Simulations with the model resulted in features similar to those observed in the experimental data. Our principal finding was that increasing the perturbation amplitude had a stabilizing effect on the behavior across frequencies. Nonlinear behaviors observed at the lowest stimulus frequency might be attributed to fluctuations in control between the multiple sensory inputs. Although this study has not conclusively pointed toward any single mechanism as responsible for the responses observed, it has revealed clear directions for further investigation. To examine if changing the sensory modalities would elicit a significant change in the nonlinear behaviors observed here, further experiments that target a patient population with some sort of sensory deficit are warranted.

Visual conflict and cognitive load modify postural responses to vibrotactile noise

“…We employed approximate entropy (ApEn) as a non-linear measure of the variability in the temporal structure of sway because of increasing evidence of non-linear control mechanisms for postural control [31,32]. It is not clear whether there is an optimal state of variability for functional movement, but it has been shown that biological systems that are either overly rigid or noisy are also unstable [33].…”

Stochastic Dynamics of Postural Sway Modeled by Double Ornstein Uhlenbeck Process

“…Followingly, the expression in Equation 1a keeps the variance bounded by confining the trajectories around a continuously updated stochastic process, θ t . Therefore, the system of SDEs is built in a way that the equilibrium point has been defined analogously to the rest length of a linear spring continuously updated by another mean reverting process, Ornstein Uhlenbeck (Equation 1a and 1b) against a static deadzone [45]. The second process involves a different mean reversion rate κ, volatility σ 2 and is driven by a new Wiener process W 2 t which is selected as independent from the first one, W 1 t for the sake of simplicity that is represented by ρ = 0 in Equation 1c as follows.…”

“…Because CoPx is simulated by X t , its distance to θ t then corresponds to the trembling component in dOU model. In this sense, θ t serves as the instant equilibrium point, which can be interpreted as the "rest length" of the elastic behavior (Figure 2d of [30]) observed in CoPx dynamics [36,45,53,54]. In this respect, the celebrated method proposed by Feldman, λ-threshold, handles the motor behavior at the joint level in which the equilibrium point of the joint is set at the motoneuron pool where the joint stabilization is dictated by the intrinsic Fig.…”

Developing a Human Balance Test System (DETES) in Order to Investigate Control Mechanisms of Human Erect Posture

“…Figures 4a and b show exemplar CoP x and CoP y time signals of an healthy subject collected at quiet stance and their related Fast Fouriér Transformations (FFT, see below paragraph for an explanation/ implication of FFT, Figures 4c and d). Figure 6a shows both CoP signals (CoP x and CoP y ) at the horizontal plane such that the path traced by CoP in time during a balance test presents complex dynamical characteristics (like an individual's signature), where nonlinear dynamical metrics can be computed about the information capacity, dynamical order, and the stability of the individual postural control system [18][19][20]. Neverthe-less path-length (Figures 4a and b), variability of the CoP x and CoP y signals and their velocities (variance of the CoP displacements and their On the other hand, Figures 5a and b show CoP x and CoP y time signals of a Bilateral Vestibular Loss patient (BVL) and its related FFTs.…”