Modelling a parasystolic rhythm in a heart-transplant patient

A parasystole from a heart-transplant patient is analysed using a beat-to-beat RR interval time series obtained from an electrocardiogram (ECG). The dysrhythmia, resulting from the co-existence of two pacemakers, the sinus node and an ectopic focus, presents distinctive regular patterns, with transitions from one pattern to another occurring abruptly. It is shown that the parasystolic rhythm can be simulated by a model involving two oscillators firing at fixed rates, under the restriction that neither is allowed to fire during the other's refractory period. It is found that the structure of the generated RR time series is essentially determined by the ratio of the periods of the two oscillators. In the case of a heart-transplant patient with a small heart-rate variability as a result of heart denervation, the model predicts the RR intervals with an error of less than 6% for an 80-beat sequence. From a physiological point of view, the results imply that the interaction between the two pacemakers in the heart is fairly weak, and hence the parasystole observed in the heart-transplant patient can be modelled as pure parasystole.