Nonlinear systems identification: autocorrelation vs. autoskewness

Abstract

Sammon, Michel, and Frederick Curley. Nonlinear systems identification: autocorrelation vs. autoskewness. J. Appl. Physiol. 83(3): 975-993, 1997.-Autocorrelation function (C 1 ) or autoregressive model parameters are often estimated for temporal analysis of physiological measurements. However, statistical approximations truncated at linear terms are unlikely to be of sufficient accuracy for patients whose homeostatic control systems cannot be presumed to be stable local to a single equilibrium. Thus a quadratic variant of C 1 [autoskewness function (C 2 )] is introduced to detect nonlinearities in an output signal as a function of time delays. By use of simulations of nonlinear autoregressive models, C 2 is shown to identify only those nonlinearities that ''break'' the symmetry of a system, altering the mean and skewness of its outputs. Case studies of patients with cardiopulmonary dysfunction demonstrate a range of ventilatory patterns seen in the clinical environment; whereas testing of C 1 reveals their breath-by-breath minute ventilation to be significantly autocorrelated, the C 2 test concludes that the correlation is nonlinear and asymmetrically distributed. Higher-order functionals [e.g., autokurtosis (C 3 )] are necessary for global analysis of metastable systems that continuously ''switch'' between multiple equilibrium states and unstable systems exhibiting nonequilibrium dynamics. structural stability; metastability; symmetry breaking ; respiratory failure; congestive heart failure; nonlinear dynamics RECENT REVIEWS by Bruce and Daubenspeck (2, 3) on time-series analysis of respiratory measurements emphasized the issue of ''temporal scaling of respiratory pattern variability.'' This observation is indicative of the complexity and state dependence of the respiratory control system: metabolism, distribution of brain stem neurotransmitters, blood gas tensions, ventilatory dead space, sensations of dyspnea, cardiac output, pulmonary mechanics, and strength of respiratory muscles can vary with different time constants (4, 5, 7, 9, 10, 13-15, 17, 23, 24, 26-28, 30-32, 35-37). Under conditions of respiratory distress, highly complex ventilatory dynamics may unfold that would not be observable in the unstressed system. Thus comparative analyses of the ventilatory patterns of healthy adults and patients with cardiopulmonary disease are critical toward understanding mechanisms of respiratory failure.However, such analyses are complicated by the fact that various assumptions of classical linear statistics may not be valid when the control system is under duress and not operating locally to a single equilibrium state (a ventilatory ''set point'') (19,22,29). For example, many investigators have found that variables such as depth or rate of breathing exhibit a positive breath-to-breath autocorrelation (1,13,23,26,36), a result that has been interpreted as evidence of ''memory'' within the central pattern generator (1) or ''noise'' within the peripheral feedback control loop (23). Regardless of physiological interp...

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