RESUMEN
The increasing availability of time series data depicting the evolution of physical system properties has prompted the development of methods focused on extracting insights into the system behavior over time, discerning whether it stems from deterministic or stochastic dynamical systems. Surrogate data testing plays a crucial role in this process by facilitating robust statistical assessments. This ensures that the observed results are not mere occurrences by chance, but genuinely reflect the inherent characteristics of the underlying system. The initial process involves formulating a null hypothesis, which is tested using surrogate data in cases where assumptions about the underlying distributions are absent. A discriminating statistic is then computed for both the original data and each surrogate data set. Significantly deviating values between the original data and the surrogate data ensemble lead to the rejection of the null hypothesis. In this work, we present various surrogate methods designed to assess specific statistical properties in random processes. Specifically, we introduce methods for evaluating the presence of autodependencies and nonlinear dynamics within individual processes, using Information Storage as a discriminating statistic. Additionally, methods are introduced for detecting coupling and nonlinearities in bivariate processes, employing the Mutual Information Rate for this purpose. The surrogate methods introduced are first tested through simulations involving univariate and bivariate processes exhibiting both linear and nonlinear dynamics. Then, they are applied to physiological time series of Heart Period (RR intervals) and respiratory flow (RESP) variability measured during spontaneous and paced breathing. Simulations demonstrated that the proposed methods effectively identify essential dynamical features of stochastic systems. The real data application showed that paced breathing, at low breathing rate, increases the predictability of the individual dynamics of RR and RESP and dampens nonlinearity in their coupled dynamics.
RESUMEN
OBJECTIVE: Coupling in multiple electroencephalogram (EEG) signals provides a perspective tool to understand the mechanism of brain communication. In this study, we propose a method based on permutation cross-mutual information (PCMI) to investigate whether or not the coupling between EEG series can be used to quantify the effect of specific anesthetic drugs (isoflurane and remifentanil) on brain activities. METHODS: A Rössler-Lorenz system and surrogate analysis was first employed to compare histogram-based mutual information (HMI) and PCMI for estimating the coupling of two nonlinear systems. Then, the HMI and the PCMI indices of EEG recordings from two sides of the forehead of 12 patients undergoing combined remifentanil and isoflurane anesthesia were demonstrated for tracking the effect of drug on the coupling of brain activities. Performance of all indices was assessed by the correlation coefficients (Rij) and relative coefficient of variation (CV). RESULTS: The PCMI can track the coupling strength of two nonlinear systems, and it is sensitive to the phase change of the coupling systems. Compared to the HMI, the PCMI has a better correlation with the coupling strength in nonlinear systems. The PCMI could track the effect of anesthesia and distinguish the consciousness state from the unconsciousness state. Moreover, at the embedding dimension m=4 and lag τ=1, the PCMI had a better performance than HMI in tracking the effect of anesthesia drugs on brain activities. CONCLUSIONS: As a measure of coupling, the PCMI was able to reflect the state of consciousness from two EEG recordings. SIGNIFICANCE: The PCMI is a promising new coupling measure for estimating the effect of isoflurane and remifentanil anesthetic drugs on the brain activity.
