Nonlinear multivariable modeling and analysis of sleep apnea time series

This paper investigates the modeling and analysis of physiological data recorded from a 49-year-old male and are composed of three time series: blood oxygen saturation, heart rate and respiration. In particular, it is desired to verify if the models estimated from data can distinguish between the dynamics underlying two different breathing patterns (normal breathing and apnea). The estimated models are nonlinear autoregressive, moving average with exogenous inputs (NARMAX) and the regressors used to compose such models are carefully chosen, among hundreds of candidates, by an automatic procedure. The results discussed in this paper suggest that the dynamics underlying the data are nonlinear and basically deterministic. Using estimated models it seems to be possible to quantify the stability of the fixed point in phase space reconstructed using the blood oxygen time series. This, as discussed, could be the basis of an algorithmic monitoring system.