A mathematical model for the mechanism of rapid eye movements induced by an anticholinesterase in the decerebrate cat.

The oculomotor pattern which appears in intact preparations during desynchronized sleep is characterized by the irregular occurrence of isolated ocular movements and bursts of rapid eye movements (REM). This complex oculomotor pattern results from the activity of two premotor structures which influence the extraocular motoneurons during this phase of sleep: one is located in the pontine reticular formation, the other in the vestibular nuclei. In the decerebrate preparation the intravenous injection of an anticholinesterase leads to the appearance of a typical pattern of oculomotor activity, which differs from that occurring during physiological sleep in so far as it consists quite exclusively of bursts of REM which appear at very regular intervals. Lesion experiments as well as unit recordings have shown that these bursts of REM depend in particular upon rhythmic discharges of the vestibular nuclear neurons. The underlying anatomical structures responsible for these bursts of REM are therefore the vestibular nuclei, the oculomotor nuclei and the oculo-orbital system. This mechanism is under the influence of cholinergic reticular neurons which generate the oculomotor rhythm. We have postulated the existence of a self-excitatory cholinergic system, located in the pontine reticular formation, whose steady discharge impinges upon an oscillatory neuronal system located in the dorso-lateral pontine tegmentum, which transforms the tonic input into a sinusoidal final output. We have assumed also that the periodic increases in the discharge frequency of this oscillatory system trigger a fast phase generator acting on the different components of the REM system, and that the behavior of each component follows a first-order differential equation. The state of excitation of the components of the system is defined as proportional to frequency of nerve impulses. Assuming ipsilateral and crossed connections, a pattern of oculomotor activity is obtained that simulates the experimental oculomotor output fairly well. The repetition of the eye jerks is described by a Fourier series. The model proposed in this paper may be taken as a first approach in describing the generation mechanism of REM, and as a theoretical guide to new experimental researches and the development of other more realistic models.