A Relaxation Oscillator Description of the Burst-Generating Mechanism in the Cardiac Ganglion of the Lobster, Homarus americanus

Abstract

Properties of the neural mechanism responsible for generating the periodic burst of spike potentials in the nine ganglion neurons were investigated by applying brief, single shocks to the four small cells with extracellular electrodes placed near the trigger zones of the small cells. The shock elicited a burst if presented during the latter portion of the silent period, terminated a burst during the latter portion of the burst period, and was followed by a newly initiated burst during the early portion of the burst period. The resultant changes in burst and silent period durations were quantitatively described by a secondorder non-linear differential equation similar to the van der Pol equation for a relaxation oscillator. The equation also qualitatively described changes in firing threshold of the small cells during the burst cycle. The first derivative of the solution to the equation is similar to slow transmembrane potentials in neurons that are involved in generation of burst activity in other crustacean cardiac ganglia.

Functional Organization of the Cardiac Ganglion of the Lobster, Homarus americanus

“…(Early work in both the Maine lobster, Homarus, and the spiny lobster, Panulirus, is reviewed in Maynard, 1960;Hagiwara, 1961. More recent works are Cooke, 1966;Hartline, 1967 a, b;Connor, 1969;Hartline and Cooke, 1969;Mayeri, 1969 a, b;Rao et al, 1969;Van der Kloot, 1970;Anderson and Cooke, 1971;Tazaki, 1971 a, b;Livengood and Kusano, 1972;Mayeri, 1973. ) Though the ganglion contains only nine neurons, its integrative mechanisms are complex.…”

Relationship between burst properties and sensitivity to input: A theoretical analysis

“…When the electric shock was applied during the latter part of the burst, it terminated the burst . Mayeri (1973) also measured the threshold (minimal shock duration needed to evoke a burst) during the quiescent period . He found that from the time where a burst could be evoked, the threshold declined throughout the quiescent period .…”

Computing with Biologically Inspired Neural Oscillators: Application to Colour Image Segmentation

“…Their famous system for which they obtained the Noble prize in "Physiology or Medicine" in 1963 (nobelprize.org) was later reduced to a system of two dynamic variables called Fitzhugh-Nagumo model [18,19] which represents a relaxation oscillator. A relaxation oscillator description of the burst-generating mechanism in the cardiac ganglion cells of the lobster was later developed by Mayeri [20]. Oscillations in cortical neurons were also modelled by Wilson-Cowan polynomial equations which model interactions between excitatory and inhibitory neurons [21][22][23][24].…”