Directional coupling detection through cross-distance vectors

Inferring the coupling direction from measured time series of complex systems is challenging. We propose a new state space based causality measure obtained from cross-distance vectors for quantifying interaction strength. It is a model-free noise-robust approach that requires only a few parameters. The approach is applicable to bivariate time series and is resilient to artefacts and missing values. The result is two coupling indices that quantify coupling strength in each direction more accurately than the already established state space measures. We test the proposed method on different dynamical systems and analyse numerical stability. As a result, a procedure for optimal parameter selection is proposed, circumventing the challenge of determining the optimal embedding parameters. We show it is robust to noise and reliable in shorter time series. Moreover, we show that it can detect cardiorespiratory interaction in measured data. A numerically efficient implementation is available at https://repo.ijs.si/mbresar/cd-vec

Multivariate assessment of linear and non-linear causal coupling pathways within the central-autonomic-network in patients suffering from schizophrenia

Im Bereich der Zeitreihenanalyse richtet sich das Interesse zunehmend darauf, wie Einblicke in die Interaktions- und Regulationsprozesse von pathophysiologischen- und physiologischen Zuständen erlangt werden können. Neuste Fortschritte in der nichtlinearen Dynamik, der Informationstheorie und der Netzwerktheorie liefern dabei fundiertes Wissen über Kopplungswege innerhalb (patho)physiologischer (Sub)Systeme. Kopplungsanalysen zielen darauf ab, ein besseres Verständnis dafür zu erlangen, wie die verschiedenen integrierten regulatorischen (Sub)Systeme mit ihren komplexen Strukturen und Regulationsmechanismen das globale Verhalten und die unterschiedlichen physiologischen Funktionen auf der Ebene des Organismus beschreiben. Insbesondere die Erfassung und Quantifizierung der Kopplungsstärke und -richtung sind wesentliche Aspekte für ein detaillierteres Verständnis physiologischer Regulationsprozesse. Ziel dieser Arbeit war die Charakterisierung kurzfristiger unmittelbarer zentral-autonomer Kopplungspfade (top-to-bottom und bottom to top) durch die Kopplungsanalysen der Herzfrequenz, des systolischen Blutdrucks, der Atmung und zentraler Aktivität (EEG) bei schizophrenen Patienten und Gesunden. Dafür wurden in dieser Arbeit neue multivariate kausale und nicht-kausale, lineare und nicht-lineare Kopplungsanalyseverfahren (HRJSD, mHRJSD, NSTPDC) entwickelt, die in der Lage sind, die Kopplungsstärke und -richtung, sowie deterministische regulatorische Kopplungsmuster innerhalb des zentralen-autonomen Netzwerks zu quantifizieren und zu klassifizieren. Diese Kopplungsanalyseverfahren haben ihre eigenen Besonderheiten, die sie einzigartig machen, auch im Vergleich zu etablierten Kopplungsverfahren. Sie erweitern das Spektrum neuartiger Kopplungsansätze für die Biosignalanalyse und tragen auf ihre Weise zur Gewinnung detaillierter Informationen und damit zu einer verbesserten Diagnostik/Therapie bei. Die Hauptergebnisse dieser Arbeit zeigen signifikant schwächere nichtlineare zentral-kardiovaskuläre und zentral-kardiorespiratorische Kopplungswege und einen signifikant stärkeren linearen zentralen Informationsfluss in Richtung des Herzkreislaufsystems auf, sowie einen signifikant stärkeren linearen respiratorischen Informationsfluss in Richtung des zentralen Nervensystems in der Schizophrenie im Vergleich zu Gesunden. Die detaillierten Erkenntnisse darüber, wie die verschiedenen zentral-autonomen Netzwerke mit paranoider Schizophrenie assoziiert sind, können zu einem besseren Verständnis darüber führen, wie zentrale Aktivierung und autonome Reaktionen und/oder Aktivierung in physiologischen Netzwerken unter pathophysiologischen Bedingungen zusammenhängen.In the field of time series analysis, increasing interest focuses on insights gained how the coupling pathways of regulatory mechanisms work in healthy and ill states. Recent advances in non-linear dynamics, information theory and network theory lead to a new sophisticated body of knowledge about coupling pathways within (patho)physiological (sub)systems. Coupling analyses aim to provide a better understanding of how the different integrated physiological (sub)systems, with their complex structures and regulatory mechanisms, describe the global behaviour and distinct physiological functions at the organism level. In particular, the detection and quantification of the coupling strength and direction are important aspects for a more detailed understanding of physiological regulatory processes. This thesis aimed to characterize short-term instantaneous central-autonomic-network coupling pathways (top-to-bottom and bottom to top) by analysing the coupling of heart rate, systolic blood pressure, respiration and central activity (EEG) in schizophrenic patients and healthy participants. Therefore, new multivariate causal and non-causal linear and non-linear coupling approaches (HRJSD, mHRJSD, NSTPDC) that are able to determine the coupling strength and direction were developed. Whereby, the HRJSD and mHRJSD approaches allow the quantification and classification of deterministic regulatory coupling patterns within and between the cardiovascular- the cardiorespiratory system and the central-autonomic-network were developed. These coupling approaches have their own unique features, even as compared to well-established coupling approaches. They expand the spectrum of novel coupling approaches for biosignal analysis and thus contribute in their own way to detailed information obtained, and thereby contribute to improved diagnostics/therapy. The main findings of this thesis revealed significantly weaker non-linear central-cardiovascular and central-cardiorespiratory coupling pathways, and significantly stronger linear central information flow in the direction of the cardiac- and vascular system, and a significantly stronger linear respiratory information transfer towards the central nervous system in schizophrenia in comparison to healthy participants. This thesis provides an enhanced understanding of the interrelationship of central and autonomic regulatory mechanisms in schizophrenia. The detailed findings on how variously-pronounced, central-autonomic-network pathways are associated with paranoid schizophrenia may enable a better understanding on how central activation and autonomic responses and/or activation are connected in physiology networks under pathophysiological conditions

Detection of synchronization from univariate data using wavelet transform

A method is proposed for detecting from univariate data the presence of synchronization of a self-sustained oscillator by external driving with varying frequency. The method is based on the analysis of difference between the oscillator instantaneous phases calculated using continuous wavelet transform at time moments shifted by a certain constant value relative to each other. We apply our method to a driven asymmetric van der Pol oscillator, experimental data from a driven electronic oscillator with delayed feedback and human heartbeat time series. In the latest case, the analysis of the heart rate variability data reveals synchronous regimes between the respiration and slow oscillations in blood pressure.Comment: 10 pages, 9 figure

Disclosing large-scale directed functional connections in MEG with the multivariate phase slope index.

Abstract The phase slope index (PSI) is a method to disclose the direction of frequency-specific neural interactions from magnetoencephalographic (MEG) time series. A fundamental property of PSI is that of vanishing for linear mixing of independent neural sources. This property allows PSI to cope with the artificial instantaneous connectivity among MEG sensors or brain sources induced by the field spread. Nevertheless, PSI is limited by being a bivariate estimator of directionality as opposite to the multidimensional nature of brain activity as revealed by MEG. The purpose of this work is to provide a multivariate generalization of PSI. We termed this measure as the multivariate phase slope index (MPSI). In order to test the ability of MPSI in estimating the directionality, and to compare the MPSI results to those obtained by bivariate PSI approaches based on maximizing imaginary part of coherency and on canonical correlation analysis, we used extensive simulations. We proved that MPSI achieves the highest performance and that in a large number of simulated cases, the bivariate methods, as opposed to MPSI, do not detect a statistically significant directionality. Finally, we applied MPSI to assess seed-based directed functional connectivity in the alpha band from resting state MEG data of 61 subjects from the Human Connectome Project. The obtained results highlight a directed functional coupling in the alpha band between the primary visual cortex and several key regions of well-known resting state networks, e.g. dorsal attention network and fronto-parietal network

Oscillating central motor networks in pathological tremors and voluntary movements: what makes the difference?

Parkinsonian tremor (PD), essential tremor (ET) and voluntarily mimicked tremor represent fundamentally different motor phenomena, yet, magnetoencephalographic and imaging data suggest their origin in the same motor centers of the brain. Using EEG–EMG coherence and coherent source analysis we found a different pattern of corticomuscular delays, time courses and central representations for the basic and double tremor frequencies typical for PD suggesting a wider range defective oscillatory activity. For the basic tremor frequency similar central representations in primary sensorimotor, prefrontal/premotor and diencephalic (e.g. thalamic) areas were reproduced for all three tremors. But renormalized partial directed coherence of the spatially filtered (source) signals revealed a mainly unidirectional flow of information from the diencephalon to cortex in voluntary tremor, e.g. a thalamocortical relay, as opposed to a bidirectional subcortico-cortical flow in PD and ET promoting uncontrollable, e.g. thalamocortical, loop oscillations. Our results help to understand why pathological tremors although originating from the physiological motor network are not under voluntary control and they may contribute to the solution of the puzzle why high frequency thalamic stimulation has a selective effect on pathological tremor leaving voluntary movement performance almost unaltered