Phase entropy: a new complexity measure for heart rate variability

Abstract

Objective: Information entropy is generally employed for analysing the complexity of physiological signals. However, most definitions of entropy estimate the degree of compressibility and thus quantify the randomness. Physiological signals are very complex because of nonlinear relationships and interactions between various systems and subsystems of the body. Therefore, analysis of randomness may not be sufficient to describe this complexity. To analyse the complexity of heart rate variability (HRV), a new entropy method, phase entropy (PhEn), has been proposed as a quantification of two-dimensional phase space. Approach: The second-order difference plot (SODP), a two-dimensional phase space, provides a visual summary of the rate of variability. The distribution of scatter points in a SODP provides information about the dynamics of the underlying system. PhEn estimates the Shannon entropy of the weighted distribution in a coarse-grained SODP. Main results: The performance of PhEn has been evaluated using simulated signals, synthetic HRV signals and real HRV signals. PhEn shows a better discriminating power and stability than other entropy measures. It is computationally efficient. Moreover, it has the ability to assess temporal asymmetry of physiological signals. Significance: PhEn quantifies the multiplicity and rate of variability associated with physiological signals. It is sensitive to time irreversibility. Therefore, it appears to be a promising tool for analysing physiological signals such as HRV.