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 cerebellum influences the generation of saccades.1 In the head-restrained monkey, the unilateral inactivation of cFN by muscimol injection severely impairs the accuracy of all saccades. Horizontal saccades with a direction ipsilateral to the inactivated side are hypermetric, whereas contralesional saccades are hypometric. Vertical saccades are biased horizontally toward the inactivated side even though a horizontal displacement is not required.2–4 Despite the large amount of data showing an involvement of cFN in the control of saccade accuracy, there is no general consensus on how to incorporate this contribution into models of saccade generation (SG). Some of the few models that have included 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 vertical saccades and Quaia’s model does not account for the contralesional hypometria. To determine how the dysmetria after cFN inactivation fits into our current understanding of the saccadic system, we decided to use a generic local feedback-based saccade generator model (i.e., a model with the standard pulse generator, feedback integrator, etc. elements) and try to find which model parameters would need to be affected 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 differentiate the parameter values between the ipsi- and contralesional sides, we modeled the SG paths leading to the medial and lateral rectus (MR and LR) muscles separately as in Scudder7 and Gancarz and Grossberg.8 To incorporate the dynamical changes 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. [email protected] Ann. N.Y. Acad. Sci. 1004: 389–393 (2003). © 2003 New York Academy of Sciences. doi: 10.1196/annals.1303.038 389

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

relationship (equation 1), whereas all other SG elements were modeled as leaky integrators (equation 2). The leak time constants of the resetable feedback integrator and the pulse integrator were assumed to be infinite. Y(t) = B*[1/{1 + exp(−A (∑i [wi * Xi{t}] + C)}]

(1)

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

(2)

where Y[t] is the output at time t, L is the leak, wi is the connection weight of input i, 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 by Quaia and Optican.9 Simulations using other eye plant models yielded qualitatively similar results (not shown). To determine if specific changes in model parameters could qualitatively reproduce the effects of cFN inactivation, we focused on the following results that were observed by Goffart et al.4 (and in preparation). (1) Unilateral cFN inactivation causes horizontal deviation of vertical saccades toward the ipsilesional side. (2) Horizontal ipsiversive saccades are hypermetric and associated with a decrease in the deceleration rate (acceleration and maximum velocity are not affected). (3) Horizontal contraversive saccades are hypometric and associated with a decrease in maximum velocity, which is not completely compensated, by a decrease in deceleration rate. (4) The magnitude of the dysmetria increases with saccade size.

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RESULTS Horizontal Deviation toward Ipsilesional Side during Vertical Eye Movements To replicate this result with our SG model, we found that vertical saccades must be accompanied by an activation of the horizontal saccade generator. As long as the excitatory input from the ipsilateral pulse generator to the pulse integrator and motoneurons is just as strong as the inhibitory input from the contralateral pulse generator the signals cancel each other. Thus, a balanced bilateral activation of the LR and MR SG paths during vertical saccades will not lead to any horizontal displacement. The ipsilesional movement of the eye during saccades toward vertically displaced targets therefore indicates that lesioning the cFN increases the relative strength of the signals on the ipsilesional side for the signals on the contralesional side.

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

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Dysmetria of Horizontal Saccades Because the results in the Goffart et al. (this volume) study are caused by a unilateral cFN lesion, the changes in model parameters simulating the lesion should be restricted to the side that the lesioned part of the cFN projects to (i.e., the contralesional side). The effects of simulated lesions were as follows. (1) Changes to the pulse integrator and/or motoneurons of the contralesional side: Because the pulse integrator and motoneurons are involved in the acceleration of ipsilesional saccades, any change to the characteristics of the pulse integrator and/or motoneurons will also change the acceleration of ipsilateral saccades which is not in accordance with the experimental data. (2) Change in pulse generator: Because of the local feedback loop, this would not result in saccade dysmetria. It will, however, change the rate of acceleration and deceleration. (3) Change in the feedback integrator: Because the input to the contralesional side does not increase with larger ipsilesional saccades, changes in the feedback integrator would not cause ipsilesional hypermetria to increase for larger saccades. (4) Change in the input to the contralesional side: For the saccade dysmetria to increase with saccade size, the cFN lesion-induced change would 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 almost equivalent to a saccade duration-dependent offset. CONCLUSION An analysis of our simple model of the SG revealed that to successfully reproduce the 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 contralesional input (causing dysmetria that increases with saccade size and decreased deceleration rate of ipsilesional saccades), and we weaken the strength (wi) of the inhibitory connection from the contralesional to the ipsilesional pulse generator and the excitatory connection from the contralesional pulse generator to the contralesional pulse integrator and motoneurons (causing reduced acceleration and deceleration rates during contralesional saccades; FIG. 2). All of these parameter changes are static. They change neither during a saccade nor as function of saccade size. (To paraphrase Shakespeare,10 they are like true love which is an ever-fixed mark that does not alter when it alteration finds.) REFERENCES 1. ROBINSON, F.R. & A.F. FUCHS. 2001. The role of the cerebellum in voluntary eye movements. Annu. Rev. Neurosci. 24: 981–1004. 2. ROBINSON, F.R., A. STRAUBE & A.F. FUCHS. 1993. Role of the caudal fastigial nucleus in saccade generation. II. Effects of muscimol inactivation. J. Neurophysiol. 70: 1741–1758. 3. IWAMOTO, Y. & K. YOSHIDA. 2002. Saccadic dysmetria following inactivation of the primate fastigial oculomotor region. Neurosci. Lett. 325: 211–215. 4. GOFFART, L., L.L. CHEN & D.L. SPARKS. 2003. Saccade dysmetria during functional perturbation of the caudal fastigial nucleus in the monkey. Ann. N.Y. Acad. Sci. 1004: this volume.

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5. DEAN, P. 1995. Modelling the role of the cerebellar fastigial nuclei in producing accurate 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 by superior 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 the reticular formation. Neural Netw. 11: 1159–1174. 9. QUAIA, C. & L.M. OPTICAN. 1998. Commutative saccadic generator is sufficient to control a 3-D ocular plant with pulleys. J. Neurophysiol. 79: 3197–3215. 10. SHAKESPEARE, W. Sonnet CXVI.