A new Frequency Domain Measure of Causality based on Partial Spectral Decomposition of Autoregressive Processes and its Application to Cardiovascular Interactions

Abstract

We present a new method to quantify in the frequency domain the strength of directed interactions between linear stochastic processes. This issue is traditionally addressed by the directed coherence (DC), a popular causality measure derived from the spectral representation of vector autoregressive (AR) processes. Here, to overcome intrinsic limitations of the DC when it needs to be objectively quantified within specific frequency bands, we propose an approach based on spectral decomposition, which allows to isolate oscillatory components related to the pole representation of the vector AR process in the Z-domain. Relating the causal and non-causal power content of these components we obtain a new spectral causality measure, denoted as pole-specific spectral causality (PSSC). In this study, PSSC is compared with DC in the context of cardiovascular variability analysis, where evaluation of the spectral causality from arterial pressure to heart period variability is of interest to assess baroreflex modulation in the low frequency band (0.04-0-15 Hz). Using both a theoretical example in which baroreflex interactions are simulated, and real cardiovascular variability series measured from a group of healthy subjects during a postural challenge, we show that – compared with DC– PSSC leads to a frequency-specific evaluation of spectral causality which is more objective and more focused on the frequency band of interest.