How to Calculate Renyi Entropy from Heart Rate Variability, and Why it Matters for Detecting Cardiac Autonomic Neuropathy

Cardiac autonomic neuropathy (CAN) is a disease that involves nerve damage leading to an abnormal control of heart rate. An open question is to what extent this condition is detectable from heart rate variability (HRV), which provides information only on successive intervals between heart beats, yet is non-invasive and easy to obtain from a three-lead ECG recording. A variety of measures may be extracted from HRV, including time domain, frequency domain, and more complex non-linear measures. Among the latter, Renyi entropy has been proposed as a suitable measure that can be used to discriminate CAN from controls. However, all entropy methods require estimation of probabilities, and there are a number of ways in which this estimation can be made. In this work, we calculate Renyi entropy using several variations of the histogram method and a density method based on sequences of RR intervals. In all, we calculate Renyi entropy using nine methods and compare their effectiveness in separating the different classes of participants. We found that the histogram method using single RR intervals yields an entropy measure that is either incapable of discriminating CAN from controls, or that it provides little information that could not be gained from the SD of the RR intervals. In contrast, probabilities calculated using a density method based on sequences of RR intervals yield an entropy measure that provides good separation between groups of participants and provides information not available from the SD. The main contribution of this work is that different approaches to calculating probability may affect the success of detecting disease. Our results bring new clarity to the methods used to calculate the Renyi entropy in general, and in particular, to the successful detection of CAN.