Inference of a Nonlinear Stochastic Model of the Cardiorespiratory Interaction

We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.

Figure 1

(a) Power spectrum of the BP data after Butterworth filtration: low-pass of the fourth order, with a cutoff frequency of 3 Hz, and high-pass of the second order with cutoff frequency of 0.03 Hz. (b) Summary of the main combinatorial frequencies of the cardiac and respiratory components. Correspondences between the nonlinear interaction terms of the model (1) and the observed frequencies are shown by arrows.

Figure 2

(a) Power spectra of cardiac oscillations obtained from measured data (black line) and from the synthesized model signal (green line). Arrows summarize combinational frequencies recovered in our analysis, corresponding to the nonlinear cardiorespiratory interaction. (b) Limit cycles of the cardiac oscillations $[x_c(n),y_c(n)]$ obtained from measured data (black line) and the synthesized signal (green line).