Assessing complexity and causality in heart period variability through a model-free data-driven multivariate approach

Heart rate variability, that is, the spontaneous fluctuations of the inverse of heart period (HP) over time, is one of the most studied physiological time series. The key features of its success are: the relevance of the information encoded in it (Akselrod et al., 1981; Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology, 1996), thus making more and more clinically relevant HP variability assessment; and the richness of the observed dynamics (Goldberger, 1996), thus prompting for the application of virtually any tool for signal processing to it. Most of the approaches applied to HP variability are model-based, being spectral analysis grounded on autoregressive modeling of the most frequently exploited one in univariate applications (Pagani et al., 1986). Model-based approaches are largely utilized in multivariate applications as well (Xiao et al., 2005; Porta et al., 2006, 2009) to describe the influences of determinants driving HP fluctuations through well-known physiological pathways. Among the determinants of HP variability, systolic arterial pressure (SAP) variability and respiration (RESP) play a relevant role by contributing directly to HP oscillations through the baroreflex (Baselli et al., 1994; Mullen et al., 1997; Porta et al., 2000b) and the coupling between respiratory centers and vagal outflow (Baselli et al., 1994; Triedman et al., 1995; Eckberg, 2003; Porta et al., 2012b), respectively. While the univariate model-based approach allows the description of the time course and frequency content of HP variability (Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology, 1996), the multivariate model-based techniques permit the description of the relationship between HP variability and its determinants in terms of gain (Baselli et al., 1994; Patton et al., 1996), phase (Halamek et al., 2003; Porta et al., 2011), correlation (Porta et al., 2000b), degree of association along a given temporal direction (Porta et al., 2002; Nollo et al., 2005), and directionality of the interactions (Porta et al., 2012a, 2013b; Faes et al., 2013).