Neural basis of postural instability identified by VTC and EEG

Abstract

In this study, we investigated the neural basis of virtual time to contact (VTC) and the hypothesis that VTC provides predictive information for future postural instability. A novel approach to differentiate stable pre-falling and transition-to-instability stages within a single postural trial while a subject was performing a challenging single leg stance with eyes closed was developed. Specifically, we utilized wavelet transform and stage segmentation algorithms using VTC time series data set as an input. The VTC time series was time-locked with multichannel (n = 64) EEG signals to examine its underlying neural substrates. To identify the focal sources of neural substrates of VTC, a two-step approach was designed combining the independent component analysis (ICA) and low-resolution tomography (LORETA) of multichannel EEG. There were two major findings: (1) a significant increase of VTC minimal values (along with enhanced variability of VTC) was observed during the transition-to-instability stage with progression to ultimate loss of balance and falling; and (2) this VTC dynamics was associated with pronounced modulation of EEG predominantly within theta, alpha and gamma frequency bands. The sources of this EEG modulation were identified at the cingulate cortex (ACC) and the junction of precuneus and parietal lobe, as well as at the occipital cortex. The findings support the hypothesis that the systematic increase of minimal values of VTC concomitant with modulation of EEG signals at the frontal-central and parietal–occipital areas serve collectively to predict the future instability in posture.

Appendix

It is important to note that both the conceptualization of the time-to-contact approach and computational differences may be the major reasons for discrepancies among recently published studies. In short, the one-dimensional constant velocity Lee’ tau method (originally developed for posture by Riccio 1993), adopted by Hertel et al. (2006) and Van Wegen et al. (2002), is conceptually different from our originally proposed virtual time-to-contact (VTC) method (Slobounov et al. 1997). Overall, unlike Lee’s tau method, the VTC takes into account the instantaneous position, velocity, and acceleration vectors with respect to two-dimensional stability boundary in computation of VTC. The use of different methodologies makes interpretation of time-to-contact data and comparisons between studies less than straightforward (Haddad et al. 2006). However, as mentioned in the “Discussion”, the VTC computation approach, using acceleration information similar to our originally proposed algorithm (Slobounov et al. 1997, outlined below), has provided the best predictor of taking a step when balance is in danger (Hasson et al. 2008).

VTC in this study was defined as the time taken by an object to reach the stability boundary, if the object were to move from the current position on its real trajectory, with instantaneous initial conditions and constant acceleration, along the virtual trajectory. To calculate the VTC value for each instantaneous measured position of the center of pressure (the object in our case), the real time was stopped at a current moment (t _i ) and the virtual motion of the object with constant acceleration was simulated. The resultant force, as well as acceleration $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {a} (t_{i} )$_, was considered to be constant while the object moved along its virtual trajectory from the current initial position $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {r}_{{}} (t_{i} )$ with instantaneous initial velocity $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {v} (t_{i} )$_, until it collided with the stability boundary (calculated here on a functional stability boundary as described earlier).

The position vector of the center of pressure on the virtual trajectory $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\rho }_{i} (\tau )$ started at the moment t _i as a function of time was obtained by double integration of constant acceleration $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {a} (\tau ) = \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {a} (t_{i} )$ with respect to virtual time parameter τ,

$$ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\rho }_{i} (\tau ) = \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {r} (t_{i} ) + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {v} (t_{i} )\tau + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {a} (t_{i} ){\frac{{\tau^{2} }}{2}}. $$

(5)

The same equation is written in terms of x and y components of the center of pressure with respect to the reference frame attached to the force platform as:

$$ x_{i} (\tau ) = r_{x} (t_{i} ) + v_{x} (t_{i} )\tau + a_{x} (t_{i} ){\frac{{\tau^{2} }}{2}}, $$

(6)

$$ y_{i} (\tau ) = r_{y} (t_{i} ) + v_{y} (t_{i} )\tau + a_{y} (t_{i} ){\frac{{\tau^{2} }}{2}} $$

(7)

where:

• r _x (t_i) and r _y (t_i) are components of instantaneous initial position vector;

• kj v _x (t_i) and r _y (t_i) are components of instantaneous initial velocity vector;

• and a _x (t_i) and a _x (t_i) are components of instantaneous initial acceleration vector.

• The virtual trajectory has a parabolic shape if the initial velocity and acceleration vectors are not co-linear. However, the virtual trajectory is linear if the initial velocity is linear.

Each boundary segment must be checked for crossing with the current virtual trajectory. The components of the position vector for crossing point (x _c ,y _c ) were determined by:

$$ x_{c} (\tau ) = r_{x} (t_{i} ) + v_{x} (t_{i} )\tau + a_{x} (t_{i} ){\frac{{\tau^{2} }}{2}} $$

(8)

and

$$ y_{c} (\tau ) = r_{y} (t_{i} ) + v_{y} (t_{i} )\tau + a_{y} (t_{i} ){\frac{{\tau^{2} }}{2}}. $$

(9)

For the case when the boundary segment had a vertical orientation, the value x _c  = x _b was substituted into Eq. 4 to obtain the value of the time parameter for the crossing point. For the case when the boundary segment had a horizontal orientation, the value y _c  = y _b was substituted into Eq. 5.

For all other possible orientations of the boundary line segment with two distinct end points, (x ₁ ,y ₁) and (x ₂ ,y ₂), the dependency between components of a crossing point is determined by:

$$ y_{c} = y_{1} + s(x_{c} - x_{1} ) $$

(10)

where

$s = (y_{2} - y_{1} )/(x_{2} - x_{1} )$ is the slope.

In this case, Eqs. 4 and 5 should substitute y _c and x _c, respectively, in Eq. 10 and form the resulting quadratic equation,

$$ A\tau^{2} + B\tau + C = 0 $$

(11)

where:

$$ A = {{[a_{y} (t_{i} ) - sa_{x} (t_{i} )]} \mathord{\left/ {\vphantom {{[a_{y} (t_{i} ) - sa_{x} (t_{i} )]} 2}} \right. \kern-\nulldelimiterspace} 2}; $$

$$ B = \left[ {v_{y} (t_{i} ) - sv_{x} (t_{i} )} \right]; $$

$$ C = \left[ {(r_{y} (t_{i} ) - y_{b} ) - s(r_{x} (t_{i} ) - x_{b} )} \right]. $$

In all three cases, the possible values of parameter τ were obtained by solving the corresponding resulting quadratic equation. If the equation did not have a solution, the infinity value was assigned to parameter τ. For each measured position of the center of pressure, this procedure was repeated until the time parameters for all possible crossing points of the simulated virtual trajectory with all boundary segments were computed. Then the minimum positive time parameter τ associated with the first crossing point was assigned to VTC. Please note that infinity is a legitimate value for VTC, which means that contact will never occur, and that the zero VTC value means that the object is in contact with the boundary.