We examined subjects' behavior when they tracked periodic oscillating targets moving along a randomly oriented ramp with the head free to move. This study focuses on the effect of target motion direction on pursuit performance and on head tracking strategies used by human subjects to coordinate eye and head movements. Our analyses revealed that the gaze tracking gain was modulated by both target oscillation frequency and target motion direction. We found that pursuit gain was modulated by the target motion direction: vertical pursuit being less accurate than horizontal pursuit. While gaze tracking was sensitive to target frequency and orientation, head behavior was less modulated by a change of target frequency than by a change of target motion direction. Additionally, subjects had two main strategies for moving their head: They oriented their head to favor rotations around either the head dorsoventral (target motion directions <20 deg) or mediolateral axis (target motion directions >70 deg). In between, the subjects did not choose a consistent rotation axis for identical target motion directions.

*X*-axis in text and figures) or perpendicular (

*Y*-axis) to the target motion. In this coordinate system, each target moved horizontally and started its movement to the right.

*f*

_{SGV}), and the phase shift between SGV and target velocity. To compute those parameters, we first fitted a sine wave to SGV. The fit was computed on the last 1.5 periods of pursuit to ensure that subjects were past the initiation phase of pursuit. To evaluate the pursuit gain, we computed the ratio between the amplitude of the velocity fit and the amplitude of target velocity. A second parameter used to evaluate the pursuit performances is the phase difference (or phase shift) between the target and gaze. This is not a simple task because target frequency and mean gaze frequency (estimated with the velocity fit) are closely related (see Equation 7 below) but not strictly equal. Thus, there is no constant time delay (and therefore no constant phase angle) between target and gaze displacements. Therefore, we computed the mean elapsed time between extrema of the target velocity and the corresponding extrema of the gaze fit for the last 1.5 periods of every trial (as a result, we had three extrema). Using this definition, a positive phase corresponds to a lead of gaze with respect to the target while a negative phase corresponds to a lag of gaze with respect to the target. A similar procedure was used on head velocity and head position to compute the equivalent parameters (gain, frequency, and phase shift) for the head movement.

*β*

_{1}and

*β*

_{2}are the intercepts of the regressions while

*α*

_{1}and

*α*

_{2}are their slopes.

*X*represents the dependent variable while

*Y*

_{1}and

*Y*

_{2}represent the independent variables. Equation 3 computes the

*t*value used to test the difference between the slopes

*α*

_{1}and

*α*

_{2}.

*SEM*in Equation 3 corresponds to the standard error.

*H*

_{Roll,1}=

*H*

_{Roll,4}in Figure 1) and in Situations 2 and 3 (

*H*

_{Roll,2}=

*H*

_{Roll,3}in Figure 1). Thus, studying the amplitude of the head roll could not discriminate between the two strategies.

*t*) (represented by the double-sided black arrows in Figure 1) at each instant. We also computed the vector that linked the two eyeballs (

*t*)). Then, we defined the strategy index as the magnitude of the cross product between the two vectors and called it

*δ*:

*t*) ×

*t*) corresponds to the cross product of

*t*) and

*t*) and ∥

*X*. Because this study focused on the maintenance of pursuit, we computed the mean value of

*δ*(

*t*) during the last period of tracking (

*g*

_{G}) and head (

*g*

_{H}) gains and target frequency (

*f*

_{T}; see Methods section for the computation of the gains). Linear regressions provided the following results:

*t*-test, as expressed in the Methods section, confirmed the steeper slope of the gaze regression (thus the bigger effect of target frequency on the gaze movement) compared to the slope of the head regression (one-tailed

*t*-test,

*t*(14) = 10.42,

*P*< 0.001).

*f*

_{T}) and gaze (

*f*

_{G}) and head (

*f*

_{H}) frequencies resulted in the following equations:

*t*-test did not show a statistical difference between the two regression slopes (two-tailed

*t*-test,

*t*(14) = 0.31,

*P*= 0.76).

*f*

_{T}) and head (

*φ*

_{H}) and gaze (

*φ*

_{G}) phases resulted in

*t*-test shows that the slope for the gaze phase was shallower than the slope for the head phase (one-tailed

*t*-test,

*t*(14) = 2.50,

*P*< 0.05). This result points toward a bigger effect of target frequency on the head phase than on the gaze phase.

*O*

_{T}=

*O*

_{T}mod

*π*(mod represents the modulo operator). We observed a modulation of both gaze and head pursuit gains when the orientation of the target was modified. To quantify this observation, we computed a non-linear fit between target motion direction and the gaze and head gains. Non-linear regressions resulted in

*O*

_{T}in Equations 11 and 12 represents target motion direction. Regressions (Equations 11 and 12) showed that the gain of the head movement is less sensitive to a change of the orientation than the gain of gaze movement (compare both the amplitude of the cosine regressions and the vafs of Equations 11 and 12). However, the frequency parameter of both fits (Equations 11 and 12) is similar. Those observations can be seen as evidence that both gaze and head share, at least partially, a common drive that modulates their response as a function of the orientation of the target.

*f*

_{T}< 0.75 Hz, 0.75 ≤

*f*

_{T}< 1.05 Hz, and

*f*

_{T}≥ 1.05 Hz). For each frequency bin, we computed the mean gaze and head pursuit gains for different target motion directions (bins of 5 deg). The lower row of Figure 3 shows that the head pursuit gain was insensitive to the target oscillation frequency (color curves are superimposed). In contrast, the upper row of Figure 3 shows that both target motion direction and target oscillation frequency influenced the gain of the gaze tracking system (color curves are separate).

*O*

_{T}−

*O*

_{H}) as a function of the orientation of the target. Then, we computed the mean of the difference between target and head orientations for 2.5-deg bins and represented it with the black solid line (

*SD*: dashed black lines).

*O*

_{T}≤ 30 deg)) = 0.22). For target motion directions larger than 60 deg, Figure 6 shows that subjects used head rotations around the mediolateral axis of the head (mean(

*O*

_{T}≥ 60 deg)) = 0.92). Similar to the results in Figure 5A, a transition zone was present between the two behaviors in Figure 6. Those areas are represented by a less dense concentration of the data in Figure 6, pointing toward a less defined strategy in which the subjects chose from among a wide range of combined head rotations.

*O*

_{T,A}) for which

*t*-tests (

*P*< 0.05). Second, we computed the first target motion orientation (

*O*

_{T,M}) for which

*t*-tests (

*P*< 0.05). The lower boundary (0.3) was estimated using the mean value plus two times the standard error of the head strategy index (all subjects pooled together) for target motion directions smaller than 20 deg. The higher boundary (0.89) was computed using the mean value minus two times the standard error of the head strategy index (all subjects pooled together) for target motion directions larger than 70 deg. Table 1 shows the two computed transition orientations (

*O*

_{T,M}and

*O*

_{T,A}) for each subject and for all data pooled across subjects. As shown in Table 1, the behavior was consistent across subjects. All of them started to significantly use combined rotations for target motion directions bigger than approximately 20 deg or smaller than approximately 70 deg. Finally, to test if subjects used a consistent head rotation axis during oblique movements, we computed the variance of the head strategy index for bins (width: 2 deg) of target motion orientations. A small variance corresponds to head rotations around a specific axis chosen consistently by subjects, whereas a large one arises when subjects choose different axes on each trial for the same target motion direction. We also computed the mean of the variances computed for each 2-deg bin of target motion direction for the three areas defined by Table 1 for each subject: dorsoventral rotations for 0 ≤

*O*

_{T}<

*O*

_{T,A}, combined rotations for

*O*

_{T,A}≤

*O*

_{T}≤

*O*

_{T,M}, and mediolateral rotations for

*O*

_{T,M}<

*O*

_{T}≤ 90. Those values are presented in columns two to four of Table 2. Finally, we used two-tailed

*t*-tests to see if the population of variances of either dorsoventral or mediolateral rotations was significantly different from the population of variances of the combined rotations. The

*P*-values of the

*t*-tests are presented in the fifth and sixth columns of Table 2. Table 2 shows that there is a significant increase of the variance of the strategy index for the combined rotations compared to either dorsoventral or mediolateral rotations. The broader distribution of

Subject no. | O _{T,A} (deg) | O _{T,M} (deg) |
---|---|---|

1 | 24 | 68 |

2 | 22 | 72 |

3 | 20 | 70 |

4 | 20 | 72 |

5 | 22 | 72 |

6 | 16 | 70 |

7 | 24 | 66 |

8 | 24 | 70 |

All | 22 | 69 |

Subject no. | μ(σ ^{2}(DV)) | μ(σ ^{2}(COMB)) | μ(σ ^{2}(ML)) | t(DV, COMB) | t(ML, COMB) |
---|---|---|---|---|---|

1 | 1.75 * 10^{−3} | 6.73 * 10^{−3} | 0.42 * 10^{−3} | P < 0.01 | P < 0.01 |

2 | 3.76 * 10^{−3} | 13.77 * 10^{−3} | 0.83 * 10^{−3} | P < 0.01 | P < 0.01 |

3 | 3.74 * 10^{−3} | 6.51 * 10^{−3} | 0.47 * 10^{−3} | P < 0.01 | P < 0.01 |

4 | 4.80 * 10^{−3} | 14.76 * 10^{−3} | 0.60 * 10^{−3} | P < 0.01 | P < 0.01 |

5 | 2.78 * 10^{−3} | 6.18 * 10^{−3} | 0.38 * 10^{−3} | P < 0.01 | P < 0.01 |

6 | 2.70 * 10^{−3} | 9.96 * 10^{−3} | 0.38 * 10^{−3} | P < 0.01 | P < 0.01 |

7 | 4.09 * 10^{−3} | 10.00 * 10^{−3} | 0.69 * 10^{−3} | P = 0.011 | P < 0.01 |

8 | 2.63 * 10^{−3} | 12.02 * 10^{−3} | 1.07 * 10^{−3} | P < 0.01 | P < 0.01 |

All | 4.74 * 10^{−3} | 13.53 * 10^{−3} | 1.56 * 10^{−3} | P < 0.01 | P < 0.01 |

*both*the frequency and the orientation of the target modulated the performance of gaze and head movements. Our analyses extended the observations of Collins and Barnes (1999) about head-unrestrained tracking of horizontal oscillating target to a condition where the target did not move only horizontally but explored a large range of possible target motion direction from horizontal to vertical directions. We found the same relationship between gaze pursuit gain, head pursuit gain, and target frequency as Collins and Barnes. However, our data revealed more variability of both gaze and head pursuit gains for a given frequency bin than the variability observed by them. Figure 3 demonstrated that the larger variability came from the larger range of orientations of the moving target in our experiments. As previously observed in head-restrained situations (Kettner et al., 1996; Leung & Kettner, 1997; Rottach et al., 1996), the gain of pursuit was smaller when the target moved vertically than when the target moved horizontally. Therefore, it appears that the variability of the gain as a function of the target motion direction is not a property of eye-only movements but is also present during head-unrestrained tracking. Finally, our regression analyses pointed toward a less sensitive gain of the head movement with respect to the orientation and the frequency of the target than the sensitivity of the gaze movement to the same parameters.

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