![]() Even more recently, this concept has extended further into a new conceptual framework called “network physiology,” which focuses on the coordination and network interactions among diverse organ systems and subsystems as a hallmark of physiologic state and function ( Bartsch et al., 2015). Within this context, the characterisation of functional brain networks in different normal and pathological states from neuroimaging data has become an exciting and promising field in brain research ( Fornito et al., 2015 Bassett and Sporns, 2017). There is a growing body of evidence supporting the theory of large-scale networks of highly specialised and segregated areas within the brain. More recently, the same concepts have progressively entered the field of neuroscience and have lead to a new research field, referred to as “network neuroscience” ( Seth et al., 2015 Hassan and Wendling, 2018). One of the leading concepts for the detection of directional interactions, Granger causality, has been widely used in economics in an attempt to identify the driving and responding constituents within an economic environment ( Pasquale, 2007 Beyzatlar et al., 2012 Plíhal, 2016). Many scientific fields are interested in detecting causal relationships between simultaneously observed signals, as they reveal the interplay between different processes and how they are linked within a larger system. The lag estimation results show absence of a relationship between connectivity strength and estimated lag values, which contradicts the line of thinking in connectivity shaped by the neuron doctrine. The combined knowledge from the causality measures and insights from the simulations, on how these measures perform under different circumstances and when to use which one, allow us to recreate a plausible network of the seizure propagation that supports previous observations of desynchronisation and synchronisation during seizure progression. As a clinical application, the same methods are also applied on an intracranial recording of an epileptic seizure. However, only the latter was able to maintain its performance in the case of non-linear interactions. One of the autoregressive methods and the one based on information theory were able to reliably identify the correct lag value in different simulated systems. We propose three new methods for lag estimation in multivariate time series, based on autoregressive modelling and information theory. They are however often not taken into account and we lack proper tools to estimate them. Furthermore, lags between coupled variables are inherent to real-world systems and could hold essential information on the network dynamics. ![]() The varying performance depending on the system characteristics warrants the use of multiple measures and comparing their results to avoid errors. The performance of the causality metrics is evaluated on a set of simulation models with distinct characteristics, to assess how well they work in- as well as outside of their “comfort zone.” PDC and DTF perform best on systems with frequency-specific connections, while PMIME is the only one able to detect non-linear interactions. To correct for noise-related spurious connections, each measure (except PMIME) is tested for statistical significance based on surrogate data. ![]() In this work we consider some of the best-known causality measures i.e., cross-correlation, (conditional) Granger causality index (CGCI), partial directed coherence (PDC), directed transfer function (DTF), and partial mutual information on mixed embedding (PMIME). However, an extensive evaluation study is missing. ![]() Over the years different causality measures have been developed, each with their own advantages and disadvantages. The detection of causal effects among simultaneous observations provides knowledge about the underlying network, and is a topic of interests in many scientific areas. 2EEG and Epilepsy Unit, University Hospitals and Faculty of Medicine, University of Geneva, Geneva, Switzerland.1Medical Image and Signal Processing (MEDISIP), Department of Electronics and Information Systems (ELIS), Ghent University, Ghent, Belgium.Jolan Heyse 1 *, Laurent Sheybani 2, Serge Vulliémoz 2 and Pieter van Mierlo 1
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