Nonlinear Time Domain Relation between Respiratory Phase and Timing of the First Heart Sound

The previous studies on respiratory physiology have indicated that inspiration and expiration have opposite effects on heart hemodynamics. The basic reason why these opposite hemodynamic changes cause regular timing variations in heart sounds is the heart sound generation mechanism that the acoustic vibration is triggered by heart hemodynamics. It is observed that the timing of the first heart sound has nonlinear relation with respiratory phase; that is, the timing delay with respect to the R-wave increases with inspiration and oppositely decreases with expiration. This paper models the nonlinear relation by a Hammerstein-Wiener model where the respiratory phase is the input and the timing is the output. The parameter estimation for the model is presented. The model is tested by the data collected from 12 healthy subjects in terms of mean square error and model fitness. The results show that the model can approximate the nonlinear relation very well. The average square error and the average fitness for all the subjects are about 0.01 and 0.94, respectively. The timing of the first heart sound related to respiratory phase can be accurately predicted by the model. The model has potential applications in fast and easy monitoring of respiration and heart hemodynamics induced by respiration.