Concerning the Mathematical Description of the Oculomotor System Based on Neurophysiological Experiments in the Alert Monkey

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Summary Single unit data from the Oculomotor nucler in alert monkeys were analyzed for periods of spontaneous eye movements and conditioned smooth pursuit movements. The presented results lead to the conclusion that the nypothesis for a mathematical description of the “final common pathway” by means of a single linear first order differential equation(Robinsun, 1970) can be replaced now by pairs of differential equations for each functional state of the system(e.g. fixation or tracking movements) for the following reasons: 1 During fixation there exist two linear characteristics for the impulse rate(IR) versus eye position because of the static hysteresis(Eckmiller, 1974), which describes the IR-difference between positions reached in the agonist phase(IR-increase) and those reached in the antagonist phase(IR-decrease). 2 Changes from fixation to visual tracking movements lead to changes in the impulse rate level at a given eye position (Eckmiller, 1975). Therefore a mathematical description must take these changes into account. 3 During visual tracking movements there exist different slopes in the characteristics for IR versus eye velocity in the agonist phase compared to the antagonist phase (Eckmiller, Mackeben, 1976). A model is presented which explains the measured characteristics for IR versus eye position and velocity for these oculomotor motoneurons in terms of a supra-nuclear and a nuclear superposition of eye position and velocity signals. This model makes use of recent findings by Keller(1974).