Ординатура / Офтальмология / Английские материалы / Eye Movements A Window on Mind and Brain_Van Gompel_2007

a downward saccade and the right column shows the 3D recording when the patient makes an upward saccade.

The patient fixated targets at different eccentricities, which are shown on the left of Figure 5. Mean 3D eye position during fixation to all targets is summarized at the right of Figure 5. The bars drawn to the black dots represent the mean torsion at that particular eccentric position. The fitted Listing’s plane in 3D is also shown by the projections on the top and at the right. The orientation of Listing’s plane is listed by the angle and the vector n. Also shown in the Figure 5 is the value of the SD of eye movements representing the thickness of Listing’s plane. In this case for the right eye this thickness is about 3 5 . This is much larger than has been measured in the normal control subjects. These results imply that CN patient’s eye movements do not obey Listing’s law.

To explain the non-Listing behaviour by anatomical factors in patients with CN, the dynamical model of Raphan was used. Only a signal in the horizontal direction was put into the model to generate the CN. The neural innervation r (Figure 6) of this input signal was a superposition of a sinusoid and a repetitive phase-locked saccade. To avoid drift, the total integral of this signal was 0. Comparison of the CN waveform in the horizontal plane between the actual recording of the patient shown in Figure 4 and the simulated shown in Figure 7 demonstrates that there is a close resemblance.

To simulate a pattern of CN containing also a vertical and torsional component as has been observed in the actual recordings (Figure 4) with the same input signal, two important adjustments had to be made in the model. First, Listing’s plane had to be displaced with respect to the fronto-parallel plane, and secondly, the pulley structures for the horizontal recti had to be displaced with respect to the pulley structures for the vertical recti.

The left panel of Figure 7 shows the result of the simulation with only a displaced pulley for the horizontal recti. A value of ky = 0 5 means that there is optimal position of the pulleys for the vertical pulleys. A value of kz = 0 3 means that the horizontal pulleys are located more backwards than the vertical pulleys and they do not fully compensate for non-commutativity. The right panel of Figure 7 depicts the result of the simulation when Listing’s plane is also displaced from the fronto-parallel plane. The angle and amplitude vector n listed on the top of the panel represent the rotation vector associated with this displacement. The resemblance of this simulation shown in the right panel of Figure 7 with the actual recording of the right eye shown in Figure 4 is evident. After the vertical saccade a shift in the torsional plane can be seen which is clockwise with a downward saccade and anti-clockwise with an upward saccade. In addition, the decrease of the jerk left amplitude in the torsional plane with the downward saccade and the increase of the jerk left amplitude in the torsional plane with the upward saccade is both observed in the actual recording as in the simulation.

6. Discussion

As has been demonstrated by other studies (Straumann et al., 1996; Tweed et al., 1990), Listing’s law holds for saccadic eye movements and the thickness of this plane does not

rω horizontal

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rω vertical

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Figure 6. Neural velocity commands to simulate CN in the horizontal plane, that is, a pendular movement and a repetitive jerk left, and a saccade in the vertical plane, that is, a velocity pulse.

exceed an SD of approximately 1 . This is also found in our normal control subjects. However, Listing’s plane does not necessarily have to lie parallel to the fronto-parallel plane and may be rotated even when a distant target is fixated (Bruno and Van den Berg, 1997; Mok, Cadera, Crawford, & Vilis, 1992; Van Rijn and Van den Berg, 1993). The analysis of recordings of 3D eye movements in a patient with CN showed a remarkably large SD from Listing’s plane, namely three to four degrees. Moreover, on average there was a larger deviation from the fronto-parallel plane than in the control subjects. By means of a dynamical model (Fetter, 1997; Raphan, 1997; Schanbolk and Raphan, 1994) it was examined whether both deviations originated from aberrations from the optimal anatomy of the ocular motor plant, including the eye-globe muscles and surrounding tissue. Particular attention was paid to the function of the so-called “muscle pulleys”,

of the eye. The amplitude and direction of the fast phase of CN in the torsional plane appeared to be dependent on vertical gaze. This was also found in the experimental data recorded in the CN patient. Torsional components of CN are not uncommon (AverbuchHeller, 2002); however, they are thought to originate in the central nervous system. Our study shows that there is no need to postulate a neural torsional generator to account for CN. Torsional components of CN can be explained by keeping the effects of specific anatomical structures into account. Patients with CN, particularly albinos, very often have strabismus, which may cause an imbalance in the horizontal recti and, therefore, the pulley effect may have changed in the horizontal plane (Oh et al., 2002). Moreover, albinos do have impaired binocular vision (Apkarian and Reits, 1989), which may lead to an insufficient neural drive to the extra-ocular muscles. It has also been demonstrated that patients with strabismus may have misplaced pulleys (Clark et al., 1997, 1998, 2000).

Some remarks have to be made about the model used for simulations. For instance, in the model the muscle torque is considered as a result of three muscle pairs. As has been pointed out by Schnabolk and Raphan (1994), the gain of the muscle pairs is not equal for each pair and the differences should be incorporated in the model. According to the Robinson model (1975), Quaia and Optican (2003) implemented these unequal forces of the six extraocular muscles into their model. This has not been implemented in our simulations, however, considering the effect of this adjustment to the model on the simulations in the paper of Quaia and Optican (2003), the effect on our type of eye-movement simulation should only be minor and it is not expected to influence our main conclusions. The presence of a vertical component of CN in the data, which is absent in the model simulations, probably finds its origin in the misalignment between the horizontal plane of the experimental set-up and the horizontal plane of the pulling direction of the horizontal recti: it does not change essentially in amplitude and direction as a function of gaze.

Furthermore, the role of the connective tissue still is not fully clear. Histological data show that there is evidence for both intermuscular and musculo-orbital coupling. The original model contains only intermuscular coupling, which yields approximately correct simulations for small angles. To sort out how large the pulley effect really is, in vivo experiment have been performed to determine the functional position of the pulleys (Demer et al., 2005). However, there is still a debate how the pulley effect is accomplished and whether the anatomical pulley structures really have a functional purpose (Van den Bedem et al., 2005).

As a general remark, it has to be stated that the impact of simulation results with this dynamical model should not be overestimated. Mathematically there are still several uncertain factors. For instance, for = 0 there is a singularity and the model becomes unstable. Therefore, has to be given a starting value that is unequal to zero.

Despite the aforementioned shortcomings, adjustment of the model to overcome these inaccuracies would not yield qualitatively different results. Hence, the effects found in the simulations can be compared to in vivo experimental data and the current dynamical eyemovement model may be used as a predictor for eye movements. Our simulations have demonstrated that the dynamical model gives a qualitative description of the observed

eye movements, despite the uncertainties about its exact dynamical behaviour. Certainly, simulations with a model of the dynamics of eye movements can be of practical clinical use and may help in a better understanding of strabismus and CN.

Acknowledgement

The authors thank Dr. P. Apkarian and Dr. H van der Steen for data acquisition of the CN patient and for many helpful discussions of the experimental results.

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