Adaptive computation of approximate entropy and its application in integrative analysis of irregularity of heart rate variability and intracranial pressure signals

The present study introduces an adaptive calculation of approximate entropy (ApEn) by exploiting sample-by-sample construction and update of nearest neighborhoods in an n-dimensional space. The algorithm is first validated with a standard numerical test set. It is then applied to electrocardiogram R wave interval (RR) and beat-to-beat intracranial pressure signals recorded from 12 patients undergoing normal pressure hydrocephalus diagnosis. The ApEn time series are further processed using the causal coherence analysis to study the interaction between ICP and RR interval. Numerical validation demonstrates that the proposed algorithm reproduces the known time-varying patterns in the test set and better tracks abrupt signal changes. It is also demonstrated that occurrences of large-amplitude ICP oscillation are associated with decreased ICP ApEn and RR ApEn for all 12 patients. The causal coherence analysis of ApEn time series shows that coherence between RR ApEn and ICP ApEn, after mathematically decoupling RR effect on ICP, is enhanced for the oscillatory ICP state and so is the amplitude of transfer function between ICP and RR interval. However, no enhanced coherence is observed after mathematically decoupling ICP effect on RR interval. In conclusion, the adaptive ApEn algorithm can be used to track nonstationary signal characteristics. Furthermore, interactions between dynamic systems could be studied by using ApEn time series of the direct observations of systems.