Causality in physiological signals.

Health is one of the most important non-material assets and thus also has an enormous influence on material values, since treating and preventing diseases is expensive. The number one cause of death worldwide today originates in cardiovascular diseases. For these reasons the aim of understanding the functions and the interactions of the cardiovascular system is and has been a major research topic throughout various disciplines for more than a hundred years. The purpose of most of today's research is to get as much information as possible with the lowest possible effort and the least discomfort for the subject or patient, e.g. via non-invasive measurements. A family of tools whose importance has been growing during the last years is known under the headline of coupling measures. The rationale for this kind of analysis is to identify the structure of interactions in a system of multiple components. Important information lies for example in the coupling direction, the coupling strength, and occurring time lags. In this work, we will, after a brief general introduction covering the development of cardiovascular time series analysis, introduce, explain and review some of the most important coupling measures and classify them according to their origin and capabilities in the light of physiological analyses. We will begin with classical correlation measures, go via Granger-causality-based tools, entropy-based techniques (e.g. momentary information transfer), nonlinear prediction measures (e.g. mutual prediction) to symbolic dynamics (e.g. symbolic coupling traces). All these methods have contributed important insights into physiological interactions like cardiorespiratory coupling, neuro-cardio-coupling and many more. Furthermore, we will cover tools to detect and analyze synchronization and coordination (e.g. synchrogram and coordigram). As a last point we will address time dependent couplings as identified using a recent approach employing ensembles of time series. The scope of this review, as opposed to various other excellent reviews like (Hlaváčková-Schindler et al Phys. Rep. 441 1-46, Kramer et al 2004 Phys. Rev. E 70 1-10, Lombardi 2000 Circulation 101 8-10, Porta et al 2000 Am. J. Physiol.: Heart and Circulatory Physiol. 279 H2558-67, Schelter et al 2006 J. Neurosci. Methods 152 210-9), is to give a broader overview over existing coupling measures and where to look to find the most appropriate tool for a given situation. The review will comprise a test of one representative of the most important coupling measure groups using a simple toy model to illustrate some essential features of the tools. At the end we will summarise the performance of each measure and offer some advice on when to use which method.