Abstract
The objective of system identification methods is to construct a mathematical model of a dynamical system in order to describe adequately the input-output relationship observed in that system. Over the past several decades, mathematical models have been employed frequently in the oculomotor field, and their use has contributed greatly to our understanding of how information flows through the implicated brain regions. However, the existing analyses of oculomotor neural discharges have not taken advantage of the power of optimization algorithms that have been developed for system identification purposes. In this article, we employ these techniques to specifically investigate the “burst generator” in the brainstem that drives saccadic eye movements. The discharge characteristics of a specific class of neurons, inhibitory burst neurons (IBNs) that project monosynaptically to ocular motoneurons, are examined. The discharges of IBNs are analyzed using different linear and nonlinear equations that express a neuron's firing frequency and history (i.e., the derivative of frequency), in terms of quantities that describe a saccade trajectory, such as eye position, velocity, and acceleration. The variance accounted for by each equation can be compared to choose the optimal model. The methods we present allow optimization across multiple saccade trajectories simultaneously. We are able to investigate objectively how well a specific equation predicts a neuron's discharge pattern as well as whether increasing the complexity of a model is justifiable. In addition, we demonstrate that these techniques can be used both to provide an objective estimate of a neuron's dynamic latency and to test whether a neuron's initial firing rate (expressed as an initial condition) is a function of a quantity describing a saccade trajectory (such as initial eye position).
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Baker R, Evinger R, McCrea RA (1981) Some thoughts about the three neurons in the vestibulo-ocular reflex. Ann. NY Acad. Sci. 374:171–188.
Caines PE (1988) Linear Stochastic Systems. John Wiley & Sons, Toronto.
Cannon SC, Robinson DA (1987) Loss of the neural integrator of the oculomotor system from brain stem lesions in monkey. J. Neurophysiol. 57:138–146.
Cheron G, Godaux E (1987) Disabling of the oculomotor neural integrator by kainic acid injections in the prepositus-vestibular complex of the cat. J. Physiol. Lond. 394:267–290.
Cheron G, Gilles P, Godaux E (1986a) Lesions in the cat prepositusvestibular complex: Effects on the optokinetic system. J. Physiol. Lond. 372:95–111.
Cheron G, Godaux E, Laune JM, Vanderkelen B (1986b) Lesions in the cat prepositus-vestibular complex: Effects on the vestibular ocular reflex and saccades. J. Physiol. Lond. 372:75–94.
Cullen KE, McCrea RA (1993) Firing behavior of brainstem neurons during voluntary cancellation of the horizontal vestibulo-ocular reflex. I. Secondary vestibular neurons. J. Neurophysiol. 70:828–855.
Cullen KE, Chen-Huang C, McCrea RA (1993) Firing behavior of brainstem neurons during voluntary cancellation of the horizontal vestibulo-ocular reflex. II. Eye movement related neurons. J. Neurophysiol. 70:844–856.
Devore JL (1982) Probability and Statistics for Engineering and the Sciences. Brooks/Cole, Monterey, CAL.
Escudero M, De La Cruz RR, Delgado-Garcia JM (1992) A comparative neurophysiological study of prepositus hypoglossi and vestibular neurons projecting to the abducens nucleus in the alert cat. J. Physiol. Lond. 458:539–560.
Fuchs AF, Kaneko CRS, Scudder CA (1985) Brainstem control of saccadic eye movements. Ann. Rev. Neuroscience 8:307–337.
Fuchs AF, Scudder CA, Kaneko CRS (1988) Discharge patterns and recruitment order of identified motor neurons and internuclear neurons in the monkey abducens nuclei. J. Neurophysiol. 60:1874–1895.
Galiana HL, Guitton D (1992) Central organization and modeling of eye-head coordination during orienting gaze shifts. In: B Cohen, DL Tomko, F Guedry, eds. Sensing and Controlling Motion. New York Academy of Sciences, New York. pp. 452–471.
Goldstein HP, Robinson DA (1984) A two-element oculomotor plant model solves problems inherent in a single-element plant model. Soc. Neurosci. Abstr. 10:909.
Grantyn A, Bertoz A (1985) Burst activity of identified tecto-reticulospinal neurons in the alert cat. Exp. Brain Res. 57:417–421.
Guitton D, Douglas RM, Volle M (1984) Eye-head coordination in cats. J. Neurophysiol. 52:427–459.
Harris CM, Wallman J, Scudder CA (1990) Fourier analysis of saccades in monkeys and humans. J. Neurophysiol. 63:877–886.
Hepp K, Henn V, Vilis T, Cohen B (1989) Brainstem regions related to saccade generation. In: RH Wurtz, ME Goldberg, eds. The Neurobiology of Saccadic Eye Movement. Elsevier North-Holland, Amsterdam, pp. 105–211.
Hikosaka O, Kawakami T (1977) Inhibitory neurons related to the quick phase of vestibular nystagmus their location and projection. Exp. Brain Res. 27:377–396.
Hikosaka O, Igusa Y, Nakao S, Shimazu H (1978) Direct inhibitory synaptic linkage of pontomedullary reticular burst neurons with abducens motoneurons in the cat. Exp. Brain Res. 33:337–352.
Igusa Y, Sasaki S, Shimazu H (1980) Excitatory premotor burst neurons in the cat pontine reticular formation related to the quick phase of vestibular nystagmus. Brain Res. 182:451–456.
Johansen TA, Foss BA (1993) Constructing NARMAX models using ARMAX models. Intl. J. of Control. 58:1125.
Jurgens R, Becker W, Kornhuber H (1981) Natural and drug-induced variations of velocity and duration of human saccadic eye movements: Evidence for the neural pulse generator by local feedback. Biol. Cybern. 39:87–96.
Kaneko CRS, Fuchs AF (1981) Inhibitory burst neurons in alert trained cats: Comparison with excitatory burst neurons and functional implications. In: AF Fuchs, W Becker, eds. Progress in Oculomotor Research. Elsevier North-Holland, Amsterdam, pp. 63–70.
Keller EL (1973) Accommodative vergence in the alert monkey: Motor unit analysis. Vision Res. 13:1565–1575.
Kuo BC (1992) Digital Control Systems, Saunders College Publishing, Orlando FL.
Ljung L (1987). System Identification: Theory for the User. Prentice-all, Englewood Cliffs, NJ.
Lopez-Barneo J, Darlot C, Bertoz A, Baker R (1982) Neural activity in prepositus nucleus correlated with eye movements in the alert cat. J. Neurophysiol. 47:329–352.
Mathworks Inc. (1987) System Identification Toolbox. Natick Massachussettes. Copyright by the Mathworks.
McFarland JL, Fuchs AF (1992) Discharge patterns of nucleus prepositus hypoglossi and adjacent vestibular nucleus during horizontal eye movement in behaving macaques. J. Neurophysiol. 68:319–332.
Mettens P, Godaux E, Cheron G, Galiana HL (1994) Effect of Muscimol microinjections into the prepositus hypoglossi and medial vestibular nuclei on cat eye movements. J. Neurophysiol. 72:785–802.
Munoz DP, Guitton D, Pelisson D (1991) Control of orienting gaze shifts by the tectoreticulospinal system in the head-free cat. III. Spatiotemporal characteristics of phasic motor discharges. J. Neurophysiol. 66:1642–1666.
Optican LM, Miles FA (1985) Visually induced adaptive changes in primate saccadic oculomotor control signals. J. Neurophysiol. 54:940–958.
Pare M, Guitton D (1990) Gaze-related activity of brainstem omnipause neurons during combined eye-head gaze shifts in the alert cat. Exp. Brain Res. 83:210–214.
Pintelon R, Kollar I (1991) Exact discrete time representation of continuous time systems. Proceedings 9th IFAC/IFORS Symposium in Identification and System Parameter Estimation, pp. 1628–1633.
Rey CG (1992) New algorithms for the classification and identification of the vestibulo-ocular reflex. Ph.D. Thesis, McGill University.
Rey CG, Galiana HL (1993) Transient analysis of vestibular nystagmus. Biol. Cybern. 69:395–405.
Richmond BJ, Optican LM, Podell M, Spitzer H (1987) Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. I. Response characteristics. J. Neurophysiol. 57:132–146.
Robinson DA (1964) The mechanics of human saccadic eye movement. J. Physiol. Lond. 174:245–264.
Robinson DA (1970) Oculomotor unit behavior in the monkey. J. Neurophysiol. 33:393–404.
Robinson DA (1975) Oculomotor control signals. In: G Lennerstrand, P Bach-y-Rita, eds. Basic Mechanisms of Ocular Motility and their Clinical Implications. Pergamon, Oxford. pp. 337–374.
Sales KR, Billings SA (1990) Self-tuning control of non-linear ARMAX models. Intl. J. of Control. 51:753.
Sanderson AC, Kobler B (1976) Sequential interval histogram analysis of non-stationary neural spike trains. Biol. Cybern. 22:61–71.
Sasaki S, Shimazu H (1981) Reticulovestibular organization participating in the generation of horizontal fast eye movement. Ann. NY Acad. Sci. 374:130–143.
Schwarz G (1978) Estimating the dimension of a model. Ann. Statist. 6:461–464.
Scudder CA (1988) A new local feedback model of the saccadic burst generator. J. Neurophysiol. 59:1455–1475.
Scudder CA, Fuchs AF (1992) Physiological and behavioral indentification of vestibular nucleus neurons mediating the horizontal vestibuloocular reflex in trained Rhesus monkeys. J. Neurophysiol. 69:244–264.
Scudder CA, Fuchs AF, Langer TP (1988) Characteristics and functional identification of saccadic inhibitory burst neurons in the alert monkey. J. Neurophysiol. 59:1430–1454.
Silverman BW (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.
Strassman A, Highstein SM, McCrea RA (1986a) Anatomy and physiology of saccadic burst neurons in the alert Squirrel monkey. I. Excitatory burst neurons. J. Comp. Neurol. 249:337–357.
Strassman A, Highstein SM, McCrea RA (1986b) Anatomy and physiology of saccadic burst neurons in the alert Squirrel monkey. II. Inhibitory burst neurons. J. Comp. Neurol. 249:358–380.
Van Gisbergen JAM, Robinson DA, Gielen S (1981), A quantitative analysis of generation of saccadic eye movements by burst neurons. J. Neurophysiol. 45:417–442.
Van Opstal AJ, Van Gisbergen JAM, Eggermont JJ (1985) Reconstruction of neural control signals for saccades based on and inverse method. Vision Res. 25:789–801.
Vijayan R, Poor HV, Moore JB, Goodwin GC (1991) A Levinson type algorithm for modeling fast sampled data. IEEE Trans. on Automatic Control. 36(3):314–321.
Yoshida K, Berthoz A, Vidal PP, McCrea RA (1982) Morphological and physiological characteristics of inhibitory burst neurons controlling rapid eye movements on the alert cat. J. Neurophysiol. 48:761–784.
Zellner A (1984) Posterior odds ratios for regression hypotheses: General implications and some specific results. In: Basic Issues in Econometrics. University of Chicago Press, Chicago, pp. 275–305.
Zuber BL, Semmlow JL, Stark L (1968) Frequency characteristics of the saccadic eye movement. Biophysical J. 8:1288–1298.
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Cullen, K.E., Rey, C.G., Guitton, D. et al. The use of system identification techniques in the analysis of oculomotor burst neuron spike train dynamics. J Comput Neurosci 3, 347–368 (1996). https://doi.org/10.1007/BF00161093
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DOI: https://doi.org/10.1007/BF00161093