Abstract
The mechanism of the irregularity of R-R intervals and especially the genesis of the long R-R intervals in atrial fibrillation were clarified. From the point of view of the present study, the sequence of successive R-R intervals can be regarded as a stochastic process, and consequently mathematical analyses can be applied, and the following conclusion could be obtained: the stability of the data, mathematically called stationarity, is present in the sequence of R-R intervals, and these intervals are independently and identically distributed. The probability density function is an Erlangian distribution with phase k of 20 to 26. Namely, as soon as, on the average, 20 to 26 atrial excitatory stimuli have arrived at the AV node, a threshold value of the AV node is reached and ventricular activation is induced. However, if we examine the mathematical structure of the sequence of successive R-R intervals in more detail, the following results can be evidently obtained: during atrial fibrillation with rapid ventricular response, the sequence of R-R intervals is completely independent, but with intermediate or slow ventricular response the adjacent R-R intervals correclate with each other and these adjacent intervals have at least the first order Markov property, which seems to be caused by the concealed conduction. Because of this Markov property due to the prolongation of the refractory period of the AV node, slow ventricular response results.
