Mathematical modeling of heart rate and blood pressure variations due to changes in breathing pattern

Analysis of the heart rate (HR) variation due to respiration, known as respiratory sinus arrhythmia (RSA), is a method to assess the autonomic nervous system (ANS) function. In this paper a physiologically-based mathematical model consisting of the cardiorespiratory system and ANS control has been used in order to study the cardiovascular response (mean arterial blood pressure and HR) to breathing with different respiration rates and tidal volumes. Simulation results show that RSA has its maximal amplitude at the respiration frequency of 0.12 Hz and that RSA amplitude varies linearly by tidal volume. These results are in agreement with real data from the literature. In addition, the amplitude of the variations of the simulated blood pressure (BP) in each respiratory cycle is maximum at almost the same respiratory rate as RSA.