Combination of equiprobable symbolization and time reversal asymmetry for heartbeat interval series analysis

Abstract

Symbolic dynamics method and time reversal asymmetry analysis are both important approaches in the study of heartbeat interval series. However, there is limited research work reported on combining these two methods. We provide a method of time reversal asymmetry analysis which focuses on the differences between the forward and backward embedding "m words" after the operation of equiprobable symbolization. To investigate the total amplitude as well as the distribution features of the difference, four indices are proposed. Based on the application to simulation series, we found that these measures can successfully detect time reversal asymmetry in chaos series. With application to human heartbeat interval series (RR series), it is suggested that the distribution features of the forward-backward difference can sensitively capture the dynamical changes caused by diseases or aging. In particular, the index E(D), which reflects the random degree of the forward-backward difference distribution, can significantly discriminate healthy subjects from diseased ones. We conclude that RR series from healthy subjects show more asymmetry in temporal structure on the original time scale from the perspective of equiprobable symbolization, whereas diseases account for loss of this asymmetry.