The Lotka-Volterra equations, a possible model for the rhythmogenesis of respiration: an experimental and simulation study (author's transl)

Abstract

The aim of the present study was to simulate respiratory responses to vagal stimulation using theLotka-Volterra model, a system of two simultaneous non-linear differential equations. The experiments were carried out on vagotomized, artificially ventilated rabbits. Low-threshold, fast-conducting vagal afferent fibres were stimulated with relatively high frequencies (100---200 cps) at various stages of the respiratory cycle. The phrenic activity was recorded in order to analyze the latency and duration of exspiratory reactions with regard to the time relation between stimulatory and respiratory phase. The onset of the stimulatory phase was progressively delayed with regard to the onset of the inspiratory or expiratory phase, stimulation ceasing at the onset of the ensuing respiratory cycle. Real-time simulation was carried out on a hybrid computer. The vagal stimulation was imitated by altering the values of one of the system parameters. The onset of parameter changes was progressively delayed with regard to the onset of the inspiratory or expiratory phase of the model, and the parameters were reset to the initial values as soon as the following respiratory phase began. Comparison of experimental and model data revealed satisfactory agreement between the time-dependent system properties of both respiratory centre and model. The results are discussed with regard to the central nervous processes underlying the genesis of respiratory rhythm. Further light is also thrown on the central processing of afferent vagal input subserving inspiratory inhibitory reactions.