Gaze displacement and inter-segmental coordination during large whole body voluntary rotations

Abstract

Displacements of the visual axis and multi-segmental (eye-to-foot) coordination in the yaw plane were studied in ten human subjects (Ss) during voluntary reorientations to illuminated targets of eccentricities up to 180°. We also investigated how knowledge of target location modifies the movement pattern. Eccentric targets (outbound trials) elicited eye, head, trunk and foot movements at latencies ca. 0.5, 0.6, 0.7 and 1.1 s, respectively. Knowledge of target location (return trials) reduced latencies for foot and trunk (but not eye and head) thus eye, head and trunk moved more en bloc. In most trials, the initial gaze shift fell short of the target and more than 50% of the visual angle was covered by the sum of vestibular nystagmic fast phases and head-in-space displacement, until target fixation. This indicates that during large gaze shifts the ‘anticompensatory’ role of the vestibulo-ocular reflex in target acquisition is prominent. During some predictable trials Ss acquired targets with a single large gaze shift, shortening target acquisition time by more than 200 ms. In these, gaze velocity (trunk-in-space + head-on-trunk + eye-in-orbit) remained often fairly constant for durations of up to 500 ms, suggesting that gaze velocity is a controlled parameter. Such pattern occurred during trunk mobilization, thus eye velocity co-varied with head-in-space rather than head-on-trunk velocity. Foot rotations were stereotyped and of constant frequency, suggesting they are generated by locomotor pattern generators. However, knowledge of target location reduced foot latencies indicating that local and supraspinal mechanisms interact for foot control. We propose that a single controller is responsible for the coupling of the multiple body segments and gaze velocity control during gaze shifts.

Appendix

PCA and artificial data simulations

Generally, PCA explores whether a set of variable data (herewith eye or head-in-space velocity, c.f. “Results”), stemming from the repetition of an experimental condition upon an event (‘trial’), can be thought to represent variations of an underlying function (‘system’). Variability levels might be maximal in case of a random pattern generating function while low variability levels might reflect stability of the process. Thus, a high degree of correlation among the output reiterations implies the existence of common patterns. PCA computes these patterns (called ‘principal components’, PCs) and the percentage of variation they account for (Chatfield and Collins 1980). Having a set of k-correlated traces X ₁,…,X _k , all assigned to the same channel, PCA creates a new set of orthogonal vectors Y ₁,…,Y _k called PCs). PCs are derived in decreasing order of importance so that the first PC (Y ₁) explains most of the variance of the original data. Percentage of variance explained by the jth PC $Y_{j} = X \cdot z_{j}$ (j = 1,…,k) is equal to the ω _j eigenvalue $\left( {\omega_{1} > \omega_{2} > \cdots > \omega_{k} > 0,\quad \sum\limits_{j = 1}^{k} {\omega_{j} = 1} } \right)$ of the covariance matrix $\sigma = X^{\text{T}} \cdot X$ with corresponding eigenvector z _j : $\left( {\sigma - \omega_{j} \cdot I} \right)z_{j} = 0$ and $\left| {\sigma - \omega_{i} \cdot I} \right| = 0$, where I is the k × k unique matrix, X = [X ₁,…,X _k ] and T is for transpose. Eigenvalues and eigenvectors were computed by using the MATLAB™ function eig.

The idea of working with PCA is: having a set of traces derived from repetitive trials, i.e., head velocity, we expect similarities in the trajectories, if we assume that the same function produces them. However, each trajectory may still be perturbed by randomly time-varying external sources. These sources produce non-systematic infrequent disturbances which appear in PCs of lower order of importance (with percentage of variance explained less than 1%). In contrast, the systematic, recurring parts of the trajectory are contained into the first and second PCs. Two useful properties of PCA as applied to our experiments with a multi-segmental control system are that: (1) the system’s degree of linearity is positively related to the proportion of the variability accounted for by the first PC and (2) the system’s degrees of freedom (dimensions) are the number of PCs that account for more than 1% of the system’s variability. One function is enough to describe all trials if the proportion of variability accounted for by the first PC approaches 100%; two functions (signals) would be necessary if the variability accounted for by the second PC and third PC is greater and less than 1%, respectively. Accordingly, a totally random configuration of a signal from trial to trial would require a system of n dimensions, equal to the number n of trials used for analysis (Chatfield and Collins 1980).

A disadvantage of PCA is that it requires data curves of equal length, and since trial duration may be variable, the number of trials included in the analysis will depend on the selection of an appropriate time interval. Simulations with artificial data were carried out to test these issues, before applying this analysis to our raw velocity data from the single-step gaze shifts. Specifically, we considered a time-varying Markov process for generating a red noise signal r: $r_{i} = \xi \cdot r_{i - 1} + g_{i} ,\quad r_{0} = 0,\;i = 1, \ldots ,n$ where 0 < ξ < 1 is the Markov index of variability and g _i is taken from a Gaussian white noise distribution. m = 27 different red noise signals r ⁽¹⁾,…,r ^(m) were thus generated and each was added to a ramp-step function x (Fig. 11) producing m correlated traces$X_{j} = x + a \cdot r^{(j)} ,\quad j = 1, \ldots ,m,\;0 < a < 1$, of n = 100 points each. PCA was then applied on signals X ₁,…,X _m , showing that the first PC, can in fact reveal the pattern of the original ramp-step signal, in spite of the biasing effects of the red noise (Fig. 11).

Fig. 11

Artificial data simulations. With dashes is represented the ramp-step signal (thick gray) when biased by red noise (in a ξ = 0.97 and α = 0.05; in b ξ = 0.75 and α = 0.05). The variance of the system (spanned by the m = 27 correlated traces) accounted for by the first PC (thin solid) is 97.3% in a and 99.4% in b (Euclidean error distance from the ramp-step signal is 0.53 and 0.30, respectively). In both examples all other PCs account for less than 1% of variability. Note that the ramp-step signal is very well approximated by the first PC