Applications of causal techniques to neural time series have increased extensively over last decades, including a wide and diverse family of methods focusing on electroencephalogram (EEG) analysis. Besides connectivity inferred in defined frequency bands, there is a growing interest in the analysis of cross-frequency interactions, in particular phase and amplitude coupling and directionality. Some studies show contradicting results of coupling directionality from high frequency to low frequency signal components, in spite of generally considered modulation of a high-frequency amplitude by a low-frequency phase. We have compared two widely used methods to estimate the directionality in cross frequency coupling: conditional mutual information (CMI) and phase slope index (PSI). The latter, applied to infer cross-frequency phase-amplitude directionality from animal intracranial recordings, gives opposite results when comparing to CMI. Both metrics were tested in a numerically simulated example of unidirectionally coupled Rössler systems, which helped to find the explanation of the contradictory results: PSI correctly estimates the lead/lag relationship which, however, is not generally equivalent to causality in the sense of directionality of coupling in nonlinear systems, correctly inferred by using CMI with surrogate data testing.
- MeSH
- elektroencefalografie * metody MeSH
- lidé MeSH
- modely neurologické MeSH
- mozek fyziologie MeSH
- nelineární dynamika * MeSH
- počítačová simulace MeSH
- počítačové zpracování signálu MeSH
- zvířata MeSH
- Check Tag
- lidé MeSH
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- srovnávací studie MeSH
The mechanism of seizure emergence and the role of brief interictal epileptiform discharges (IEDs) in seizure generation are two of the most important unresolved issues in modern epilepsy research. We found that the transition to seizure is not a sudden phenomenon, but is instead a slow process that is characterized by the progressive loss of neuronal network resilience. From a dynamical perspective, the slow transition is governed by the principles of critical slowing, a robust natural phenomenon that is observable in systems characterized by transitions between dynamical regimes. In epilepsy, this process is modulated by synchronous synaptic input from IEDs. IEDs are external perturbations that produce phasic changes in the slow transition process and exert opposing effects on the dynamics of a seizure-generating network, causing either anti-seizure or pro-seizure effects. We found that the multifaceted nature of IEDs is defined by the dynamical state of the network at the moment of the discharge occurrence.
- MeSH
- elektroencefalografie MeSH
- hipokampální oblast CA1 patofyziologie MeSH
- hipokampus patofyziologie MeSH
- lidé MeSH
- nervová síť patofyziologie MeSH
- potkani Sprague-Dawley MeSH
- potkani Wistar MeSH
- synapse fyziologie MeSH
- záchvaty patofyziologie MeSH
- zvířata MeSH
- Check Tag
- lidé MeSH
- mužské pohlaví MeSH
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
In this comparative study, six causality detection methods were compared, namely, the Granger vector autoregressive test, the extended Granger test, the kernel version of the Granger test, the conditional mutual information (transfer entropy), the evaluation of cross mappings between state spaces, and an assessment of predictability improvement due to the use of mixed predictions. Seven test data sets were analyzed: linear coupling of autoregressive models, a unidirectional connection of two Hénon systems, a unidirectional connection of chaotic systems of Rössler and Lorenz type and of two different Rössler systems, an example of bidirectionally connected two-species systems, a fishery model as an example of two correlated observables without a causal relationship, and an example of mediated causality. We tested not only 20000 points long clean time series but also noisy and short variants of the data. The standard and the extended Granger tests worked only for the autoregressive models. The remaining methods were more successful with the more complex test examples, although they differed considerably in their capability to reveal the presence and the direction of coupling and to distinguish causality from mere correlation.
- MeSH
- časové faktory MeSH
- kauzalita MeSH
- systémová analýza MeSH
- teoretické modely * MeSH
- Publikační typ
- práce podpořená grantem MeSH
- srovnávací studie MeSH
Using several methods for detection of causality in time series, we show in a numerical study that coupled chaotic dynamical systems violate the first principle of Granger causality that the cause precedes the effect. While such a violation can be observed in formal applications of time series analysis methods, it cannot occur in nature, due to the relation between entropy production and temporal irreversibility. The obtained knowledge, however, can help to understand the type of causal relations observed in experimental data, namely, it can help to distinguish linear transfer of time-delayed signals from nonlinear interactions. We illustrate these findings in causality detected in experimental time series from the climate system and mammalian cardio-respiratory interactions.
- Publikační typ
- časopisecké články MeSH
Nonparametric detection of coupling delay in unidirectionally and bidirectionally coupled nonlinear dynamical systems is examined. Both continuous and discrete-time systems are considered. Two methods of detection are assessed-the method based on conditional mutual information-the CMI method (also known as the transfer entropy method) and the method of convergent cross mapping-the CCM method. Computer simulations show that neither method is generally reliable in the detection of coupling delays. For continuous-time chaotic systems, the CMI method appears to be more sensitive and applicable in a broader range of coupling parameters than the CCM method. In the case of tested discrete-time dynamical systems, the CCM method has been found to be more sensitive, while the CMI method required much stronger coupling strength in order to bring correct results. However, when studied systems contain a strong oscillatory component in their dynamics, results of both methods become ambiguous. The presented study suggests that results of the tested algorithms should be interpreted with utmost care and the nonparametric detection of coupling delay, in general, is a problem not yet solved.
- MeSH
- algoritmy MeSH
- šíření informací MeSH
- systémová analýza MeSH
- teoretické modely * MeSH
- Publikační typ
- práce podpořená grantem MeSH
Identifying regions important for spreading and mediating perturbations is crucial to assess the susceptibilities of spatio-temporal complex systems such as the Earth's climate to volcanic eruptions, extreme events or geoengineering. Here a data-driven approach is introduced based on a dimension reduction, causal reconstruction, and novel network measures based on causal effect theory that go beyond standard complex network tools by distinguishing direct from indirect pathways. Applied to a data set of atmospheric dynamics, the method identifies several strongly uplifting regions acting as major gateways of perturbations spreading in the atmosphere. Additionally, the method provides a stricter statistical approach to pathways of atmospheric teleconnections, yielding insights into the Pacific-Indian Ocean interaction relevant for monsoonal dynamics. Also for neuroscience or power grids, the novel causal interaction perspective provides a complementary approach to simulations or experiments for understanding the functioning of complex spatio-temporal systems with potential applications in increasing their resilience to shocks or extreme events.
Functional connectivity (FC) analysis is a prominent approach to analyzing fMRI data, especially acquired under the resting state condition. The commonly used linear correlation FC measure bears an implicit assumption of Gaussianity of the dependence structure. If only the marginals, but not all the bivariate distributions are Gaussian, linear correlation consistently underestimates the strength of the dependence. To assess the suitability of linear correlation and the general potential of nonlinear FC measures, we present a framework for testing and estimating the deviation from Gaussianity by means of comparing mutual information in the data and its Gaussianized counterpart. We apply this method to 24 sessions of human resting state fMRI. For each session, matrix of connectivities between 90 anatomical parcel time series is computed using mutual information and compared to results from its multivariate Gaussian surrogate that conserves the correlations but cancels any nonlinearity. While the group-level tests confirmed non-Gaussianity in the FC, the quantitative assessment revealed that the portion of mutual information neglected by linear correlation is relatively minor-on average only about 5% of the mutual information already captured by the linear correlation. The marginality of the non-Gaussianity was confirmed in comparisons using clustering of the parcels-the disagreement between clustering obtained from mutual information and linear correlation was attributable to random error. We conclude that for this type of data, practical relevance of nonlinear methods trying to improve over linear correlation might be limited by the fact that the data are indeed almost Gaussian.
- MeSH
- algoritmy MeSH
- dospělí MeSH
- Fourierova analýza MeSH
- kyslík krev MeSH
- lidé MeSH
- lineární modely MeSH
- magnetická rezonanční tomografie MeSH
- mladý dospělý MeSH
- nervové dráhy fyziologie MeSH
- normální rozdělení MeSH
- odpočinek fyziologie MeSH
- shluková analýza MeSH
- software MeSH
- Check Tag
- dospělí MeSH
- lidé MeSH
- mladý dospělý MeSH
- mužské pohlaví MeSH
- ženské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
Recent findings indicate that changes in synchronization of neural activities underlying sensitization and kindling could be more comprehensively understood using nonlinear methods. With this aim we have examined local synchronization using novel measure of coarse-grained information rate (CIR) in 8 EEG signals recorded at different cortical areas in 44 patients with paranoid schizophrenia. The values of local synchronization that could reflect sensitization related changes in EEG activities of cortical sites were then related to psychometric measures of epileptic-like symptoms and positive and negative schizophrenia symptoms (PANSS). While no significant correlations between CIR and positive and negative symptoms have been found, statistically significant relationships described by Spearman correlation coefficients between CIR indices and results of LSCL-33 have been observed in 7 (of 8) EEG channels (r in the range from 0.307 to 0.374, p<0.05). Results of this study provide first supportive evidence for the relationship between local synchronization measured by CIR and epileptic-like symptoms in schizophrenia.
- MeSH
- dospělí MeSH
- elektroencefalografie metody MeSH
- epilepsie etiologie MeSH
- korová synchronizace MeSH
- lidé MeSH
- mladý dospělý MeSH
- paranoidní schizofrenie komplikace MeSH
- Check Tag
- dospělí MeSH
- lidé MeSH
- mladý dospělý MeSH
- mužské pohlaví MeSH
- ženské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
Oscillatory phenomena in the brain activity and their synchronization are frequently studied using mathematical models and analytic tools derived from nonlinear dynamics. In many experimental situations, however, neural signals have a broadband character and if oscillatory activity is present, its dynamical origin is unknown. To cope with these problems, a framework for detecting nonlinear oscillatory activity in broadband time series is presented. First, a narrow-band oscillatory mode is extracted from a broadband background. Second, it is tested whether the extracted mode is significantly different from linearly filtered noise, modelled as a linear stochastic process possibly passed through a static nonlinear transformation. If a nonlinear oscillatory mode is positively detected, further analysis using nonlinear approaches such as the phase synchronization analysis can potentially bring new information. For linear processes, however, standard approaches such as the coherence analysis are more appropriate and provide sufficient description of underlying interactions with smaller computational effort. The method is illustrated in a numerical example and applied to analyze experimentally obtained human EEG time series from a sleeping subject.
- MeSH
- biologické hodiny fyziologie MeSH
- časové faktory MeSH
- elektroencefalografie metody MeSH
- lidé MeSH
- modely neurologické MeSH
- mozek fyziologie MeSH
- nelineární dynamika MeSH
- počítačové zpracování signálu MeSH
- spánek fyziologie MeSH
- spektrální analýza MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- Klíčová slova
- entropie, rozlišování a variabilita srdeční frekvence,
- MeSH
- biomedicínský výzkum MeSH
- dospělí MeSH
- elektrokardiografie ambulantní metody využití MeSH
- entropie * MeSH
- lidé MeSH
- srdeční elektrofyziologie * metody přístrojové vybavení MeSH
- srdeční frekvence fyziologie MeSH
- srdeční zástava MeSH
- statistika jako téma MeSH
- studie případů a kontrol MeSH
- Check Tag
- dospělí MeSH
- lidé MeSH
- Publikační typ
- práce podpořená grantem MeSH
