State Space Correspondence and Cross-Entropy Methods in the Assessment of Bidirectional Cardiorespiratory Coupling in Heart Failure

Abstract The complex interplay between the cardiac and the respiratory systems, termed cardiorespiratory coupling (CRC), is a bidirectional phenomenon that can be affected by pathologies such as heart failure (HF). In the present work, the potential changes in strength of directional CRC were assessed in HF patients classified according to their cardiac rhythm via two measures of coupling based on k-nearest neighbor (KNN) estimation approaches, cross-entropy (CrossEn) and state space correspondence (SSC), applied on the heart period (HP) and respiratory (RESP) variability series, while also accounting for the complexity of the cardiac and respiratory rhythms. We tested the measures on 25 HF patients with sinus rhythm (SR, age: 58.9 ± 9.7 years; 23 males) and 41 HF patients with ventricular arrhythmia (VA, age 62.2 ± 11.0 years; 30 males). A predominant directionality of interaction from the cardiac to the respiratory rhythm was observed in both cohorts and using both methodologies, with similar statistical power, while a lower complexity for the RESP series compared to HP series was observed in the SR cohort. We conclude that CrossEn and SSC can be considered strictly related to each other when using a KNN technique for the estimation of the cross-predictability markers. Keywords: cardiorespiratory coupling; cross-entropy; cross-predictability; heart failure; information theory; k-nearest neighbors.