Statistical Complexity and Nontrivial Collective Behavior in Electroencephalografic Signals

📝 Abstract

We calculate a measure of statistical complexity from the global dynamics of electroencephalographic (EEG) signals from healthy subjects and epileptic patients, and are able to stablish a criterion to characterize the collective behavior in both groups of individuals. It is found that the collective dynamics of EEG signals possess relative higher values of complexity for healthy subjects in comparison to that for epileptic patients. To interpret these results, we propose a model of a network of coupled chaotic maps where we calculate the complexity as a function of a parameter and relate this measure with the emergence of nontrivial collective behavior in the system. Our results show that the presence of nontrivial collective behavior is associated to high values of complexity; thus suggesting that similar dynamical collective process may take place in the human brain. Our findings also suggest that epilepsy is a degenerative illness related to the loss of complexity in the brain.

💡 Analysis

We calculate a measure of statistical complexity from the global dynamics of electroencephalographic (EEG) signals from healthy subjects and epileptic patients, and are able to stablish a criterion to characterize the collective behavior in both groups of individuals. It is found that the collective dynamics of EEG signals possess relative higher values of complexity for healthy subjects in comparison to that for epileptic patients. To interpret these results, we propose a model of a network of coupled chaotic maps where we calculate the complexity as a function of a parameter and relate this measure with the emergence of nontrivial collective behavior in the system. Our results show that the presence of nontrivial collective behavior is associated to high values of complexity; thus suggesting that similar dynamical collective process may take place in the human brain. Our findings also suggest that epilepsy is a degenerative illness related to the loss of complexity in the brain.

📄 Content

arXiv:0901.0829v3 [nlin.AO] 7 May 2009 STATISTICAL COMPLEXITY AND NONTRIVIAL COLLECTIVE BEHAVIOR IN ELECTROENCEPHALOGRAPHIC SIGNALS M. ESCALONA-MOR´AN,1, 2, 3 M. G. COSENZA,4 R. L´OPEZ-RUIZ,5 and P. GARC´IA6 1Grupo de Ingenier´ıa Biom´edica, Facultad de Ingenier´ıa, Universidad de Los Andes, M´erida, Venezuela. 2Laboratoire Traitement du Signal et de l’Image (LTSI), Universit´e de Rennes 1, Campus Scientifique de Beaulieu, Bˆat. 22, 35042 Rennes Cedex, France. 3INSERM U642, LTSI, Bˆat. 22, 35042 Rennes Cedex, France 4Centro de F´ısica Fundamental, Universidad de Los Andes, M´erida, Venezuela. 5DIIS and BIFI, Facultad de Ciencias, Universidad de Zaragoza, E-50009 Zaragoza, Spain. 6Laboratorio de Sistemas Complejos, Departamento de F´ısica Aplicada, Facultad de Ingenier´ıa, Universidad Central de Venezuela, Caracas, Venezuela. 1 Abstract We calculate a measure of statistical complexity from the global dynamics of electroencephalo- graphic (EEG) signals from healthy subjects and epileptic patients, and are able to establish a criterion to characterize the collective behavior in both groups of individuals. It is found that the collective dynamics of EEG signals possess relative higher values of complexity for healthy subjects in comparison to that for epileptic patients. To interpret these results, we propose a model of a net- work of coupled chaotic maps where we calculate the complexity as a function of a parameter and relate this measure with the emergence of nontrivial collective behavior in the system. Our results show that the presence of nontrivial collective behavior is associated to high values of complexity; thus suggesting that similar dynamical collective process may take place in the human brain. Our findings also suggest that epilepsy is a degenerative illness related to the loss of complexity in the brain. PACS numbers: 05.45.-a, 05.45.Xt, 05.45.Ra 2 The concept of complex systems has become a new paradigm for the search of mecha- nisms and a unified interpretation of the processes of emergence of structures, organization and functionality in a variety of natural and artificial phenomena in different contexts [Badii & Politi, 1997; Mikhailov & Calenbuhr, 2002; Kaneko & Tsuda, 2000]. One common cri- terion for defining complexity is the emergent behavior: collective structures, patterns and functions that are absent at the local level arise from simple interaction rules between the constitutive elements in a system. Phenomena such as the spontaneous formation of struc- tures, organization, spatial patterns, chaos synchronization, collective oscillations, spiral waves, segregation and differentiation, formation and growth of domains, and social consen- sus, are examples of self-organizing processes that occur in various contexts such as physical, chemical, biological, physiological, social and economic systems. There has been much interest in the study of the phenomenon of emergence of nontrivial collective behavior in the context of systems of interacting chaotic elements [Kaneko, 1990; Chat´e & Manneville, 1992a, 1992b; Pikovsky & Kurths, 1994; Shibata & Kaneko, 1998; Cosenza, 1998; Cosenza & Gonz´alez, 1998; Cisneros et al., 2002; Manrubia et al., 2004]. Nontrivial collective behavior is characterized by a well defined evolution of macroscopic quantities coexisting with local chaos. Models based on coupled map networks have been widely used in the investigation of collective phenomena that appear in many complex systems [Kaneko & Tsuda, 2000]. In particular, networks of coupled chaotic maps can exhibit nontrivial collective behavior. A paradigmatic example of a complex system is provided by the human brain. It consists of a highly interconnected network of millions of neurons. The local dynamics of a neuron in general behaves as a non-linear excitable element [Herz et al., 2006]. From the signal of a single neuron it is not possible to understand the highly structured collective behavior and functions of the brain. In this paper we investigate the relative complexity of the human brain by considering the collective dynamics that arise from the local dynamics of groups of neurons, as manifested in electroencephalographic (EEG) signals. We calculate a measure of complexity from the global dynamics of EEG signals from healthy subjects and epileptic patients, and are able to establish a criterion to characterize the collective behavior in both groups of individuals. It is found that the collective dynamics of EEG signals possess relative higher values of complexity for healthy subjects in comparison to that for epileptic patients. Our results 3 support the view that epilepsy is characterized by a loss of complexity in the brain, as indicated by measurements of the dimension correlation [Babloyantz A. & Destexhe A., 1986], algorithmic complexity [Rapp et al., 1994], and anticipation of seizures [Martinerie et al., 1998]. In order to interpret our results, we propose a model of coupled chaotic maps where we

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