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Ann. N.Y. Acad. Sci. 1004: 389–393 (2003). © 2003 New York Academy of Sciences.doi: 10.1196/annals.1303.038

Accounting for Saccade Dysmetria after Cerebellar Lesion: A Modeling Approach

ANSGAR KOENE AND LAURENT GOFFART

INSERM U534, Bron, France

KEYWORDS: saccade; dysmetria; modeling; cerebellum; fastigial nucleus;lesion

INTRODUCTION

The caudal fastigial nucleus (cFN) is a major output nucleus by which the cere-bellum influences the generation of saccades.1 In the head-restrained monkey, theunilateral inactivation of cFN by muscimol injection severely impairs the accuracyof all saccades. Horizontal saccades with a direction ipsilateral to the inactivated sideare hypermetric, whereas contralesional saccades are hypometric. Vertical saccadesare biased horizontally toward the inactivated side even though a horizontal dis-placement is not required.2–4

Despite the large amount of data showing an involvement of cFN in the controlof saccade accuracy, there is no general consensus on how to incorporate this contri-bution into models of saccade generation (SG). Some of the few models that haveincluded the cFN input to the SG are the models proposed by Dean5 and Quaia et al.6

Unfortunately, Dean’s model does not consider the effect of cFN inactivation on ver-tical saccades and Quaia’s model does not account for the contralesional hypometria.

To determine how the dysmetria after cFN inactivation fits into our current un-derstanding of the saccadic system, we decided to use a generic local feedback-basedsaccade generator model (i.e., a model with the standard pulse generator, feedbackintegrator, etc. elements) and try to find which model parameters would need to beaffected by the cFN lesion to reproduce the postlesional saccade dysmetria.

METHODS

The saccade generator model used in this study is shown in FIGURE 1. To differ-entiate the parameter values between the ipsi- and contralesional sides, we modeledthe SG paths leading to the medial and lateral rectus (MR and LR) muscles separate-ly as in Scudder7 and Gancarz and Grossberg.8 To incorporate the dynamical chang-es in neural activity, we modeled the pulse generator with an S-function type I/O

Address for correspondence: Ansgar Koene, PhD, INSERM u534, 16 avenue Doyen Lépine,69500 Bron, France.

koene@lyon.inserm.fr

390 ANNALS NEW YORK ACADEMY OF SCIENCES

relationship (equation 1), whereas all other SG elements were modeled as leaky in-tegrators (equation 2). The leak time constants of the resetable feedback integratorand the pulse integrator were assumed to be infinite.

where Y(t) is the output at time t, B is maximum burst frequency, A determines thesteepness of the S-function, wi is the connection weight of input i, Xi{t} is the valueof the input i at time t, and C shifts the function so that Y(t) = 0 if ∑[wi*Xi{t}] = 0.

where Y[t] is the output at time t, L is the leak, wi is the connection weight of inputi, and Xi{t} is the input value at time t of input i.

The eye plant model that was used for the results shown here was the model byQuaia and Optican.9 Simulations using other eye plant models yielded qualitativelysimilar results (not shown).

To determine if specific changes in model parameters could qualitatively repro-duce the effects of cFN inactivation, we focused on the following results that wereobserved by Goffart et al.4 (and in preparation). (1) Unilateral cFN inactivation caus-es horizontal deviation of vertical saccades toward the ipsilesional side. (2) Horizon-tal ipsiversive saccades are hypermetric and associated with a decrease in thedeceleration rate (acceleration and maximum velocity are not affected). (3) Horizon-tal contraversive saccades are hypometric and associated with a decrease in maxi-mum velocity, which is not completely compensated, by a decrease in decelerationrate. (4) The magnitude of the dysmetria increases with saccade size.

Y(t) = B*[1/{1 + exp(−A (∑∑∑∑i [wi * Xi{t}] + C)}] (1)

Y(t) = ∫(L * Y[t] + ∑∑∑∑i [wi * Xi{t}])dt (2)

FIGURE 1. Generic saccade generator model. PG, pulse generator; RFI, resettablefeedback integrator; PI, pulse integrator; MN, motoneurons; LR/MR, lateral/medial rectusmuscles; OPN, omnipause neurons.

391KOENE & GOFFART: SACCADE DYSMETRIA

RESULTS

Horizontal Deviation toward Ipsilesional Side during Vertical Eye Movements

To replicate this result with our SG model, we found that vertical saccades mustbe accompanied by an activation of the horizontal saccade generator. As long as theexcitatory input from the ipsilateral pulse generator to the pulse integrator and mo-toneurons is just as strong as the inhibitory input from the contralateral pulse gener-ator the signals cancel each other. Thus, a balanced bilateral activation of the LR andMR SG paths during vertical saccades will not lead to any horizontal displacement.The ipsilesional movement of the eye during saccades toward vertically displacedtargets therefore indicates that lesioning the cFN increases the relative strength ofthe signals on the ipsilesional side for the signals on the contralesional side.

FIGURE 2. Simulation results of our saccade generator model with and without simu-lated cFN lesion. The top two panels show the velocity profiles for an 18° saccade to thecontralesional (left) and ipsilesional (right) side. The bottom left panel shows the positionprofile of a 10° vertical saccade (positive horizontal direction corresponds to ipsilesionalside). Bottom right panel shows the change in saccade dysmetria with saccade size (+ hy-permetria, – hypometria).

392 ANNALS NEW YORK ACADEMY OF SCIENCES

Dysmetria of Horizontal Saccades

Because the results in the Goffart et al. (this volume) study are caused by a uni-lateral cFN lesion, the changes in model parameters simulating the lesion should berestricted to the side that the lesioned part of the cFN projects to (i.e., the contrale-sional side).

The effects of simulated lesions were as follows. (1) Changes to the pulse inte-grator and/or motoneurons of the contralesional side: Because the pulse integratorand motoneurons are involved in the acceleration of ipsilesional saccades, anychange to the characteristics of the pulse integrator and/or motoneurons will alsochange the acceleration of ipsilateral saccades which is not in accordance with theexperimental data. (2) Change in pulse generator: Because of the local feedbackloop, this would not result in saccade dysmetria. It will, however, change the rate ofacceleration and deceleration. (3) Change in the feedback integrator: Because the in-put to the contralesional side does not increase with larger ipsilesional saccades,changes in the feedback integrator would not cause ipsilesional hypermetria to in-crease for larger saccades. (4) Change in the input to the contralesional side: For thesaccade dysmetria to increase with saccade size, the cFN lesion-induced changewould have to increase with saccade size. The simplest way to achieve this is a leak.A leak, causing the input signal to gradually reduce over time would be almostequivalent to a saccade duration-dependent offset.

CONCLUSION

An analysis of our simple model of the SG revealed that to successfully reproducethe qualitative effects of cFN lesion, we need only to introduce a fixed bilateral bias(for the horizontal deviation during vertical saccades) together with a leak in the con-tralesional input (causing dysmetria that increases with saccade size and decreaseddeceleration rate of ipsilesional saccades), and we weaken the strength (wi) of theinhibitory connection from the contralesional to the ipsilesional pulse generator andthe excitatory connection from the contralesional pulse generator to the contrale-sional pulse integrator and motoneurons (causing reduced acceleration and deceler-ation rates during contralesional saccades; FIG. 2). All of these parameter changesare static. They change neither during a saccade nor as function of saccade size. (Toparaphrase Shakespeare,10 they are like true love which is an ever-fixed mark thatdoes not alter when it alteration finds.)

REFERENCES

1. ROBINSON, F.R. & A.F. FUCHS. 2001. The role of the cerebellum in voluntary eyemovements. Annu. Rev. Neurosci. 24: 981–1004.

2. ROBINSON, F.R., A. STRAUBE & A.F. FUCHS. 1993. Role of the caudal fastigial nucleusin saccade generation. II. Effects of muscimol inactivation. J. Neurophysiol. 70:1741–1758.

3. IWAMOTO, Y. & K. YOSHIDA. 2002. Saccadic dysmetria following inactivation of theprimate fastigial oculomotor region. Neurosci. Lett. 325: 211–215.

4. GOFFART, L., L.L. CHEN & D.L. SPARKS. 2003. Saccade dysmetria during functionalperturbation of the caudal fastigial nucleus in the monkey. Ann. N.Y. Acad. Sci.1004: this volume.

393KOENE & GOFFART: SACCADE DYSMETRIA

5. DEAN, P. 1995. Modelling the role of the cerebellar fastigial nuclei in producing accu-rate saccades: the importance of burst timing. Neuroscience 68: 1059–1077.

6. QUAIA, C., P. LEFÈVRE & L.M. OPTICAN. 1999. Model of the control of saccades bysuperior colliculus and cerebellum. J. Neurophysiol. 92: 999–1018.

7. SCUDDER, C.A. 1988. A new local feedback model of the saccadic burst generator. J.Neurophysiol. 59: 1455–1475.

8. GANCARZ, G. & S. GROSSBERG. 1998. A neural model of the saccade generator in thereticular formation. Neural Netw. 11: 1159–1174.

9. QUAIA, C. & L.M. OPTICAN. 1998. Commutative saccadic generator is sufficient tocontrol a 3-D ocular plant with pulleys. J. Neurophysiol. 79: 3197–3215.

10. SHAKESPEARE, W. Sonnet CXVI.