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Computational and Mathematical Methods in Medicine
Volume 2015 (2015), Article ID 410102, 7 pages
Research Article

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

1Department of Biomedical Engineering, Dalian University of Technology, No. 2 Linggong Road, Dalian 116024, China
2Department of Information and Communication Engineering, Yeungnam University, Dae-dong, Gyeongsan-si, Gyeongsangbuk-do 712749, Republic of Korea

Received 23 May 2015; Accepted 26 July 2015

Academic Editor: Feng Liu

Copyright © 2015 Hong Tang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.