Mutual information and phase dependencies: measures of reduced nonlinear cardiorespiratory interactions after myocardial infarction

The heart rate variability (HRV) is related to several mechanisms of the complex autonomic functioning such as respiratory heart rate modulation and phase dependencies between heart beat cycles and breathing cycles. The underlying processes are basically nonlinear. In order to understand and quantitatively assess those physiological interactions an adequate coupling analysis is necessary. We hypothesized that nonlinear measures of HRV and cardiorespiratory interdependencies are superior to the standard HRV measures in classifying patients after acute myocardial infarction. We introduced mutual information measures which provide access to nonlinear interdependencies as counterpart to the classically linear correlation analysis. The nonlinear statistical autodependencies of HRV were quantified by auto mutual information, the respiratory heart rate modulation by cardiorespiratory cross mutual information, respectively. The phase interdependencies between heart beat cycles and breathing cycles were assessed basing on the histograms of the frequency ratios of the instantaneous heart beat and respiratory cycles. Furthermore, the relative duration of phase synchronized intervals was acquired. We investigated 39 patients after acute myocardial infarction versus 24 controls. The discrimination of these groups was improved by cardiorespiratory cross mutual information measures and phase interdependencies measures in comparison to the linear standard HRV measures. This result was statistically confirmed by means of logistic regression models of particular variable subsets and their receiver operating characteristics.