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Lehnertz K. Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems. CHAOS (WOODBURY, N.Y.) 2024; 34:072102. [PMID: 38985967 DOI: 10.1063/5.0214733] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2024] [Accepted: 06/21/2024] [Indexed: 07/12/2024]
Abstract
Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in and are driven by temporally varying environments. Such systems can show multiple timescale and transient dynamics together with transitions to very different and, at times, even disastrous dynamical regimes. Since such critical transitions disrupt the systems' intended or desired functionality, it is crucial to understand the underlying mechanisms, to identify precursors of such transitions, and to reliably detect them in time series of suitable system observables to enable forecasts. This review critically assesses the various steps of investigation involved in time-series-analysis-based detection of critical transitions in real-world non-autonomous systems: from the data recording to evaluating the reliability of offline and online detections. It will highlight pros and cons to stimulate further developments, which would be necessary to advance understanding and forecasting nonlinear behavior such as critical transitions in complex systems.
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Bröhl T, Rings T, Pukropski J, von Wrede R, Lehnertz K. The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives. FRONTIERS IN NETWORK PHYSIOLOGY 2024; 3:1338864. [PMID: 38293249 PMCID: PMC10825060 DOI: 10.3389/fnetp.2023.1338864] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/15/2023] [Accepted: 12/19/2023] [Indexed: 02/01/2024]
Abstract
Epilepsy is now considered a network disease that affects the brain across multiple levels of spatial and temporal scales. The paradigm shift from an epileptic focus-a discrete cortical area from which seizures originate-to a widespread epileptic network-spanning lobes and hemispheres-considerably advanced our understanding of epilepsy and continues to influence both research and clinical treatment of this multi-faceted high-impact neurological disorder. The epileptic network, however, is not static but evolves in time which requires novel approaches for an in-depth characterization. In this review, we discuss conceptual basics of network theory and critically examine state-of-the-art recording techniques and analysis tools used to assess and characterize a time-evolving human epileptic brain network. We give an account on current shortcomings and highlight potential developments towards an improved clinical management of epilepsy.
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Affiliation(s)
- Timo Bröhl
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - Thorsten Rings
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - Jan Pukropski
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
| | - Randi von Wrede
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
- Interdisciplinary Center for Complex Systems, University of Bonn, Bonn, Germany
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Lehnertz K. Ordinal methods for a characterization of evolving functional brain networks. CHAOS (WOODBURY, N.Y.) 2023; 33:022101. [PMID: 36859225 DOI: 10.1063/5.0136181] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Accepted: 01/06/2023] [Indexed: 06/18/2023]
Abstract
Ordinal time series analysis is based on the idea to map time series to ordinal patterns, i.e., order relations between the values of a time series and not the values themselves, as introduced in 2002 by C. Bandt and B. Pompe. Despite a resulting loss of information, this approach captures meaningful information about the temporal structure of the underlying system dynamics as well as about properties of interactions between coupled systems. This-together with its conceptual simplicity and robustness against measurement noise-makes ordinal time series analysis well suited to improve characterization of the still poorly understood spatiotemporal dynamics of the human brain. This minireview briefly summarizes the state-of-the-art of uni- and bivariate ordinal time-series-analysis techniques together with applications in the neurosciences. It will highlight current limitations to stimulate further developments, which would be necessary to advance characterization of evolving functional brain networks.
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Affiliation(s)
- Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany; Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany; and Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53175 Bonn, Germany
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Network structure from a characterization of interactions in complex systems. Sci Rep 2022; 12:11742. [PMID: 35817803 PMCID: PMC9273794 DOI: 10.1038/s41598-022-14397-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Accepted: 06/06/2022] [Indexed: 11/29/2022] Open
Abstract
Many natural and man-made complex dynamical systems can be represented by networks with vertices representing system units and edges the coupling between vertices. If edges of such a structural network are inaccessible, a widely used approach is to identify them with interactions between vertices, thereby setting up a functional network. However, it is an unsolved issue if and to what extent important properties of a functional network on the global and the local scale match those of the corresponding structural network. We address this issue by deriving functional networks from characterizing interactions in paradigmatic oscillator networks with widely-used time-series-analysis techniques for various factors that alter the collective network dynamics. Surprisingly, we find that particularly key constituents of functional networks—as identified with betweenness and eigenvector centrality—coincide with ground truth to a high degree, while global topological and spectral properties—clustering coefficient, average shortest path length, assortativity, and synchronizability—clearly deviate. We obtain similar concurrences for an empirical network. Our findings are of relevance for various scientific fields and call for conceptual and methodological refinements to further our understanding of the relationship between structure and function of complex dynamical systems.
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Lehnertz K, Bröhl T, Rings T. The Human Organism as an Integrated Interaction Network: Recent Conceptual and Methodological Challenges. Front Physiol 2020; 11:598694. [PMID: 33408639 PMCID: PMC7779628 DOI: 10.3389/fphys.2020.598694] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2020] [Accepted: 11/30/2020] [Indexed: 12/30/2022] Open
Abstract
The field of Network Physiology aims to advance our understanding of how physiological systems and sub-systems interact to generate a variety of behaviors and distinct physiological states, to optimize the organism's functioning, and to maintain health. Within this framework, which considers the human organism as an integrated network, vertices are associated with organs while edges represent time-varying interactions between vertices. Likewise, vertices may represent networks on smaller spatial scales leading to a complex mixture of interacting homogeneous and inhomogeneous networks of networks. Lacking adequate analytic tools and a theoretical framework to probe interactions within and among diverse physiological systems, current approaches focus on inferring properties of time-varying interactions-namely strength, direction, and functional form-from time-locked recordings of physiological observables. To this end, a variety of bivariate or, in general, multivariate time-series-analysis techniques, which are derived from diverse mathematical and physical concepts, are employed and the resulting time-dependent networks can then be further characterized with methods from network theory. Despite the many promising new developments, there are still problems that evade from a satisfactory solution. Here we address several important challenges that could aid in finding new perspectives and inspire the development of theoretic and analytical concepts to deal with these challenges and in studying the complex interactions between physiological systems.
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Affiliation(s)
- Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
- Interdisciplinary Center for Complex Systems, University of Bonn, Bonn, Germany
| | - Timo Bröhl
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - Thorsten Rings
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
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Bröhl T, Rings T, Lehnertz K. Von Interaktionen zu Interaktionsnetzwerken: Zeitabhängige
funktionelle Netzwerke am Beispiel der Epilepsie. KLIN NEUROPHYSIOL 2020. [DOI: 10.1055/a-1195-9190] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Abstract
ZusammenfassungDas menschliche Gehirn ist ein komplexes Netzwerk aus interagierenden
nichtstationären Subsystemen (Netzwerk von Netzwerken), deren
komplizierte räumlich-zeitliche Dynamiken bis heute nur unzureichend
verstanden sind. Dabei versprechen aktuelle Entwicklungen im Bereich der
Zeitreihenanalyse sowie der Theorie komplexer Netzwerke neue und verbesserte
Einblicke in die Dynamiken von Hirnnetzwerken auf verschiedenen
räumlich-zeitlichen Skalen. Wir geben einen Überblick
über diese Entwicklungen und besprechen am Beispiel
zeitabhängiger epileptischer Hirnnetzwerke Fortschritte im
Verständnis von Hirndynamiken, die über multiple Skalen
hinweg variieren.
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Affiliation(s)
- Timo Bröhl
- Klinik und Poliklinik für Epileptologie,
Universitätsklinikum Bonn, Bonn
- Helmholtz Institut für Strahlen- und Kernphysik,
Bonn
| | - Thorsten Rings
- Klinik und Poliklinik für Epileptologie,
Universitätsklinikum Bonn, Bonn
- Helmholtz Institut für Strahlen- und Kernphysik,
Bonn
| | - Klaus Lehnertz
- Klinik und Poliklinik für Epileptologie,
Universitätsklinikum Bonn, Bonn
- Helmholtz Institut für Strahlen- und Kernphysik,
Bonn
- Interdisziplinäres Zentrum für komplexe Systeme,
Bonn
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Lopes MA, Zhang J, Krzemiński D, Hamandi K, Chen Q, Livi L, Masuda N. Recurrence quantification analysis of dynamic brain networks. Eur J Neurosci 2020; 53:1040-1059. [PMID: 32888203 DOI: 10.1111/ejn.14960] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2020] [Revised: 08/03/2020] [Accepted: 08/27/2020] [Indexed: 01/02/2023]
Abstract
Evidence suggests that brain network dynamics are a key determinant of brain function and dysfunction. Here we propose a new framework to assess the dynamics of brain networks based on recurrence analysis. Our framework uses recurrence plots and recurrence quantification analysis to characterize dynamic networks. For resting-state magnetoencephalographic dynamic functional networks (dFNs), we have found that functional networks recur more quickly in people with epilepsy than in healthy controls. This suggests that recurrence of dFNs may be used as a biomarker of epilepsy. For stereo electroencephalography data, we have found that dFNs involved in epileptic seizures emerge before seizure onset, and recurrence analysis allows us to detect seizures. We further observe distinct dFNs before and after seizures, which may inform neurostimulation strategies to prevent seizures. Our framework can also be used for understanding dFNs in healthy brain function and in other neurological disorders besides epilepsy.
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Affiliation(s)
- Marinho A Lopes
- Department of Engineering Mathematics, University of Bristol, Bristol, UK.,Cardiff University Brain Research Imaging Centre, School of Psychology, Cardiff University, Cardiff, UK
| | - Jiaxiang Zhang
- Cardiff University Brain Research Imaging Centre, School of Psychology, Cardiff University, Cardiff, UK
| | - Dominik Krzemiński
- Cardiff University Brain Research Imaging Centre, School of Psychology, Cardiff University, Cardiff, UK
| | - Khalid Hamandi
- Cardiff University Brain Research Imaging Centre, School of Psychology, Cardiff University, Cardiff, UK
| | - Qi Chen
- Center for Studies of Psychological Application and School of Psychology, South China Normal University, Guangzhou, China
| | - Lorenzo Livi
- Departments of Computer Science and Mathematics, University of Manitoba, Winnipeg, MB, Canada.,Department of Computer Science, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK
| | - Naoki Masuda
- Department of Engineering Mathematics, University of Bristol, Bristol, UK.,Department of Mathematics, University at Buffalo, State University of New York, Buffalo, NY, USA.,Computational and Data-Enabled Science and Engineering Program, University at Buffalo, State University of New York, Buffalo, NY, USA
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Stankovski T, Pereira T, McClintock PVE, Stefanovska A. Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2019; 377:20190039. [PMID: 31656134 PMCID: PMC6834002 DOI: 10.1098/rsta.2019.0039] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 08/13/2019] [Indexed: 06/10/2023]
Abstract
Dynamical systems are widespread, with examples in physics, chemistry, biology, population dynamics, communications, climatology and social science. They are rarely isolated but generally interact with each other. These interactions can be characterized by coupling functions-which contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how each interaction occurs. Coupling functions can be used, not only to understand, but also to control and predict the outcome of the interactions. This theme issue assembles ground-breaking work on coupling functions by leading scientists. After overviewing the field and describing recent advances in the theory, it discusses novel methods for the detection and reconstruction of coupling functions from measured data. It then presents applications in chemistry, neuroscience, cardio-respiratory physiology, climate, electrical engineering and social science. Taken together, the collection summarizes earlier work on coupling functions, reviews recent developments, presents the state of the art, and looks forward to guide the future evolution of the field. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.
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Affiliation(s)
- Tomislav Stankovski
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
- Faculty of Medicine, Ss Cyril and Methodius University, Skopje 1000, Macedonia
| | - Tiago Pereira
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK
- Institute of Mathematical and Computer Sciences, University of Sao Paulo, Sao Carlos 13566-590, Brazil
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Bröhl T, Lehnertz K. Centrality-based identification of important edges in complex networks. CHAOS (WOODBURY, N.Y.) 2019; 29:033115. [PMID: 30927842 DOI: 10.1063/1.5081098] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2018] [Accepted: 02/13/2019] [Indexed: 06/09/2023]
Abstract
Centrality is one of the most fundamental metrics in network science. Despite an abundance of methods for measuring centrality of individual vertices, there are by now only a few metrics to measure centrality of individual edges. We modify various, widely used centrality concepts for vertices to those for edges, in order to find which edges in a network are important between other pairs of vertices. Focusing on the importance of edges, we propose an edge-centrality-based network decomposition technique to identify a hierarchy of sets of edges, where each set is associated with a different level of importance. We evaluate the efficiency of our methods using various paradigmatic network models and apply the novel concepts to identify important edges and important sets of edges in a commonly used benchmark model in social network analysis, as well as in evolving epileptic brain networks.
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Affiliation(s)
- Timo Bröhl
- Department of Epileptology, University of Bonn Medical Centre, Sigmund-Freud-Straße 25, 53105 Bonn, Germany
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Sigmund-Freud-Straße 25, 53105 Bonn, Germany
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Sanz-Garcia A, Rings T, Lehnertz K. Impact of type of intracranial EEG sensors on link strengths of evolving functional brain networks. Physiol Meas 2018; 39:074003. [PMID: 29932428 DOI: 10.1088/1361-6579/aace94] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Objective and Approach: Investigating properties of evolving functional brain networks has become a valuable tool to characterize the complex dynamics of the epileptic brain. Such networks are usually derived from electroencephalograms (EEG) recorded with sensors implanted chronically into deeper structures of the brain and/or placed onto the cortex. It is still unclear, however, whether the use of different sensors for an identification of network nodes affects properties of functional brain networks. We address this question by investigating properties of links of such networks that we characterize by assessing interactions in multi-sensor, multi-day EEG data recorded from 49 epilepsy patients during presurgical evaluation. These data allow us to study the impact of different types of sensors together with the impact of various physiologic and pathophysiologic activities on the properties of links. MAIN RESULTS We observe that different types of sensors differently impact on spatial means and temporal fluctuations of link strengths. Moreover, the impact depends on the relative anatomical location of sensors with respect to location and extent of sources of the prevailing activities. SIGNIFICANCE Type and location of sensors should be considered when constructing networks.
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Affiliation(s)
- Ancor Sanz-Garcia
- Instituto de Investigacion Sanitaria, Hospital Universitario De La Princesa, C/Diego de Leon 62, 28006 Madrid, Spain
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