Mathematical modeling of cardiovascular coupling: Central autonomic commands and baroreflex control

The cross-correlation function (CCF) yields the correlation coefficient between spontaneous fluctuations of heart period and blood pressure as a function of the time shift between these variables. Two CCF patterns occur in humans: I) positive correlation between heart period and previous pressure values; II) negative correlation between heart period and subsequent pressure values. These patterns may result from the baroreflex and central autonomic commands (CAC), respectively. The aim of this study was to test this interpretation with a non-linear mathematical model of the human cardiovascular system. CAC were modeled as either phasic changes or random fluctuations of vagal and sympathetic activities with opposite sign. CCF pattern I resulted from baroreflex buffering of blood pressure changes elicited by vascular resistance fluctuations. When cardiac baroreflex control was absent or outweighed by CAC to the heart, simulations resulted in CCF pattern II only. In intermediate conditions when cardiac baroreflex interacted with CAC to the heart, CCF patterns I and II coexisted because the coupling between heart period and blood pressure varied with time. CAC to the heart decreased in magnitude the correlation coefficient and lengthened the time shift of CCF pattern I, thus apparently slowing and blunting baroreflex effects. Conversely, the baroreflex decreased in magnitude the correlation coefficient of CCF pattern II, thus blunting CAC effects. These results provide theoretical evidence in favor of application of the CCF analysis to investigate the balance between central autonomic and baroreflex cardiac control.