Robust Nonlinear Causality Analysis of Nonstationary Multivariate Physiological Time Series

Goal: An important research area in biomedical signal processing is that of quantifying the relationship between simultaneously observed time series and to reveal interactions between the signals. Since biomedical signals are potentially nonstationary and the measurements may contain outliers and artifacts, we introduce a robust time-varying generalized partial directed coherence (rTV-gPDC) function. Methods: The proposed method, which is based on a robust estimator of the time-varying autoregressive (TVAR) parameters, is capable of revealing directed interactions between signals. By definition, the rTV-gPDC only displays the linear relationships between the signals. We therefore suggest to approximate the residuals of the TVAR process, which potentially carry information about the nonlinear causality by a piece-wise linear time-varying moving-average model. Results: The performance of the proposed method is assessed via extensive simulations. To illustrate the method's applicability to real-world problems, it is applied to a neurophysiological study that involves intracranial pressure, arterial blood pressure, and brain tissue oxygenation level (PtiO2) measurements. Conclusion and Significance: The rTV-gPDC reveals causal patterns that are in accordance with expected cardiosudoral meachanisms and potentially provides new insights regarding traumatic brain injuries. The rTV-gPDC is not restricted to the above problem but can be useful in revealing interactions in a broad range of applications.