An index related to the autocorrelation function of RR intervals for the analysis of heart rate variability

Heart rate variability (HRV) is concerned with analysis of the variations in the intervals between heartbeats, known as RR intervals. Commonly used HRV indices may be insensitive in detecting some dynamic changes related to complex autocorrelation functions of the RR intervals. For example, indices SD1 and SD2 of the Poincaré plot can be expressed by the variance and first auto-covariance of the signal. The acceleration change index is related to the autocorrelation functions of the series only at the first three lags. We extend the idea of characterizing the sign of differences of a time series to propose a new index called VRL, which is the variance of the run length of the sign of the lagged differentiated time series. The theoretical study shows that VRL is directly related to the autocorrelation functions of the RR series at larger lags. Simulated data are used to validate the theoretical results and assess the power of testing group differences measured with VRL and other HRV indices. The performance of VRL is also evaluated for classifying subjects with normal sinus rhythm and congestive heart failure using the RR intervals taken from the PhysioNet database. We apply the index to RR intervals from an animal study of long-term exposure to particulate matter. The VRL values for the young mice susceptible to atherosclerosis in the control and exposure groups decreased gradually with different slopes after several weeks of exposure. The exposure effect changes in this HRV index estimated by fitting a generalized additive model are significant after 7 weeks of exposure.