Synergistic information in a dynamical model implemented on the human structural connectome reveals spatially distinct associations with age.

We implement the dynamical Ising model on the large-scale architecture of white matter connections of healthy subjects in the age range 4-85 years, and analyze the dynamics in terms of the synergy, a quantity measuring the extent to which the joint state of pairs of variables is projected onto the dynamics of a target one. We find that the amount of synergy in explaining the dynamics of the hubs of the structural connectivity (in terms of degree strength) peaks before the critical temperature, and can thus be considered as a precursor of a critical transition. Conversely, the greatest amount of synergy goes into explaining the dynamics of more central nodes. We also find that the aging of structural connectivity is associated with significant changes in the simulated dynamics: There are brain regions whose synergy decreases with age, in particular the frontal pole, the subcallosal area, and the supplementary motor area; these areas could then be more likely to show a decline in terms of the capability to perform higher order computation (if structural connectivity was the sole variable). On the other hand, several regions in the temporal cortex show a positive correlation with age in the first 30 years of life, that is, during brain maturation.

Consensus clustering approach to group brain connectivity matrices.

A novel approach rooted on the notion of consensus clustering, a strategy developed for community detection in complex networks, is proposed to cope with the heterogeneity that characterizes connectivity matrices in health and disease. The method can be summarized as follows: (a) define, for each node, a distance matrix for the set of subjects by comparing the connectivity pattern of that node in all pairs of subjects; (b) cluster the distance matrix for each node; (c) build the consensus network from the corresponding partitions; and (d) extract groups of subjects by finding the communities of the consensus network thus obtained. Different from the previous implementations of consensus clustering, we thus propose to use the consensus strategy to combine the information arising from the connectivity patterns of each node. The proposed approach may be seen either as an exploratory technique or as an unsupervised pretraining step to help the subsequent construction of a supervised classifier. Applications on a toy model and two real datasets show the effectiveness of the proposed methodology, which represents heterogeneity of a set of subjects in terms of a weighted network, the consensus matrix.

Information transfer and criticality in the Ising model on the human connectome.

We implement the Ising model on a structural connectivity matrix describing the brain at two different resolutions. Tuning the model temperature to its critical value, i.e. at the susceptibility peak, we find a maximal amount of total information transfer between the spin variables. At this point the amount of information that can be redistributed by some nodes reaches a limit and the net dynamics exhibits signature of the law of diminishing marginal returns, a fundamental principle connected to saturated levels of production. Our results extend the recent analysis of dynamical oscillators models on the connectome structure, taking into account lagged and directional influences, focusing only on the nodes that are more prone to became bottlenecks of information. The ratio between the outgoing and the incoming information at each node is related to the the sum of the weights to that node and to the average time between consecutive time flips of spins. The results for the connectome of 66 nodes and for that of 998 nodes are similar, thus suggesting that these properties are scale-independent. Finally, we also find that the brain dynamics at criticality is organized maximally to a rich-club w.r.t. the network of information flows.

Functional and effective connectivity in EEG alpha and beta bands during intermittent flash stimulation in migraine with and without aura.

OBJECTIVES: This research was a case-control study to evaluate functional and effective connectivity patterns in ongoing electroencephalography (EEG) under repetitive photic stimulation in the interictal phase of migraine patients with and without aura compared to nonmigraine controls. METHODS: EEG was recorded by six scalp electrodes from 19 migraine without aura patients (MO), 19 migraine with aura patients (MA) and 11 healthy subjects (control group (N)). Flash stimuli were presented at 9-27 Hz frequencies. Phase synchronization after Hilbert transform and Granger causality were evaluated filtering the EEG in alpha and beta bands. RESULTS: Phase synchronization increased in alpha band in MO, and decreased in beta band in MA, with respect to controls. The intensity of directed interactions in beta band, revealed by Granger causality, increased in MA compared to both MO patients and controls. DISCUSSION: There were clear differences in ongoing EEG under visual stimulation, which emerged between the two forms of migraine, probably subtended by increased cortical activation in migraine with aura, and compensatory phenomena of reduced connectivity and functional networks segregation, occurring in patients not experiencing aura symptoms. Further investigation may confirm whether the clinical manifestation of aura symptoms is subtended by a peculiar neuronal connectivity pattern.

Information flow in networks and the law of diminishing marginal returns: evidence from modeling and human electroencephalographic recordings.

We analyze simple dynamical network models which describe the limited capacity of nodes to process the input information. For a proper range of their parameters, the information flow pattern in these models is characterized by exponential distribution of the incoming information and a fat-tailed distribution of the outgoing information, as a signature of the law of diminishing marginal returns. We apply this analysis to effective connectivity networks from human EEG signals, obtained by Granger Causality, which has recently been given an interpretation in the framework of information theory. From the distributions of the incoming versus the outgoing values of the information flow it is evident that the incoming information is exponentially distributed whilst the outgoing information shows a fat tail. This suggests that overall brain effective connectivity networks may also be considered in the light of the law of diminishing marginal returns. Interestingly, this pattern is reproduced locally but with a clear modulation: a topographic analysis has also been made considering the distribution of incoming and outgoing values at each electrode, suggesting a functional role for this phenomenon.

Kernel method for nonlinear granger causality.

Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.

Multiscale analysis of short term heart beat interval, arterial blood pressure, and instantaneous lung volume time series.

MOTIVATIONS: Physiological systems are ruled by mechanisms operating across multiple temporal scales. A recently proposed approach, multiscale entropy analysis, measures the complexity at different time scales and has been successfully applied to long term electrocardiographic recordings. The purpose of this work is to show the applicability of this methodology, rooted on statistical physics ideas, to short term time series of simultaneously acquired samples of heart rate, blood pressure and lung volume, from healthy subjects and from subjects with chronic heart failure. In the same spirit, we also propose a multiscale approach, to evaluate interactions between time series, by performing a multivariate autoregressive (AR) modeling of the coarse grained time series. METHODS: We apply the multiscale entropy analysis to our data set of short term recordings. Concerning the multiscale version of the multivariate AR approach, we apply it to the four dimensional time series so as to detect scale dependent patterns of interactions between the physiological quantities. RESULTS: Evaluating the complexity of signals at the multiple time scales inherent in physiologic dynamics, we find new quantitative indicators which are statistically correlated with the pathology. Our results show that multiscale entropy calculated on all the measured quantities significantly differs (P<10(-2) and less) in patients and control subjects, and confirms the complexity-loss theory of aging and disease. Also applying the multiscale autoregressive approach significant differences were found between controls and patients; in the sight of finding a possible diagnostic tools, satisfactory results came also from a receiver-operating-characteristic curve analysis (with some values above 0.8). CONCLUSIONS: The multiscale entropy analysis can give useful information also when only short term physiological recordings are at disposal, thus enlarging the applicability of the methodology. Also the proposed multiscale version of the multivariate regressive analysis, applied to short term time series, can shed light on patterns of interactions between cardiorespiratory variables.

Effects of levetiracetam vs topiramate and placebo on visually evoked phase synchronization changes of alpha rhythm in migraine.

OBJECTIVE: Recent theories about migraine pathogenesis have outlined an abnormal central processing of sensory signals, also suggested by an abnormal pattern of EEG hyper-synchronization under visual stimulation. The aim of the present study was to test the efficacy of topiramate and levetiracetam vs placebo in a double blind project observing the effects of the three treatments on the EEG synchronization in the alpha band under sustained flash stimulation. METHODS: Forty-five migraine without aura outpatients (MO) were selected and randomly assigned to 100mg topiramate, 1000 mg levetiracetam or placebo treatment. In addition, 24 non-migraine healthy controls were submitted to EEG analysis. The EEG was recorded by 19 channels: flash stimuli with a luminosity of 0.2J were delivered, in a frequency range from 3 to 30 Hz. We evaluated the phase synchronization index, that we previously applied in migraine, after EEG signals filtering in the alpha band. Our approach was based on the Hilbert transform. RESULTS: Both levetiracetam and topiramate significantly decreased migraine frequency, compared with placebo. MO patients displayed increased alpha-band phase synchronization as an effect of stimulus frequency; on the other hand the stimuli had an overall desynchronizing effect on control subjects. The phase synchronization index separates the two stages, before and after the treatment, only for levetiracetam, at stimulus frequencies of 9, 18, 24 and 27 Hz. CONCLUSIONS: An abnormal alpha band synchronization under visual stimuli was confirmed in migraine; this phenomenon was reversed by levetiracetam preventive treatment. SIGNIFICANCE: These results confirmed in humans the inhibiting action of levetiracetam on neuronal hyper-synchronization.

Nonlinear parametric model for Granger causality of time series.

The notion of Granger causality between two time series examines if the prediction of one series could be improved by incorporating information of the other. In particular, if the prediction error of the first time series is reduced by including measurements from the second time series, then the second time series is said to have a causal influence on the first one. We propose a radial basis function approach to nonlinear Granger causality. The proposed model is not constrained to be additive in variables from the two time series and can approximate any function of these variables, still being suitable to evaluate causality. Usefulness of this measure of causality is shown in two applications. In the first application, a physiological one, we consider time series of heart rate and blood pressure in congestive heart failure patients and patients affected by sepsis: we find that sepsis patients, unlike congestive heart failure patients, show symmetric causal relationships between the two time series. In the second application, we consider the feedback loop in a model of excitatory and inhibitory neurons: we find that in this system causality measures the combined influence of couplings and membrane time constants.

Visually evoked phase synchronization changes of alpha rhythm in migraine: correlations with clinical features.

OBJECTIVE: This study aimed to compute phase synchronization of the alpha band from a multichannel electroencephalogram (EEG) recorded under repetitive flash stimulation from migraine patients without aura. This allowed examination of ongoing EEG activity during visual stimulation in the pain-free phase of migraine. METHODS: Flash stimuli at frequencies of 3, 6, 9, 12, 15, 18, 21, 24, and 27 Hz were delivered to 15 migraine patients without aura and 15 controls, with the EEG recorded from 18 scalp electrodes, referred to the linked earlobes. The EEG signals were filtered in the alpha (7.5-13 Hz) band. For all stimulus frequencies that we evaluated, the phase synchronization index was based on the Hilbert transformation. RESULTS: Phase synchronization separated the patients and controls for the 9, 24 and 27 Hz stimulus frequencies; hyper phase synchronization was observed in patients, whereas healthy subjects were characterized by a reduced phase synchronization. These differences were found in all regions of the scalp. CONCLUSIONS: During migraine, the brain synchronizes to the idling rhythm of the visual areas under certain photic stimulations; in normal subjects however, brain regions involved in the processing of sensory information demonstrate desynchronized activity. Hypersynchronization of the alpha rhythm may suggest a state of cortical hypoexcitability during the interictal phase of migraine. SIGNIFICANCE: The employment of non-linear EEG analysis may identify subtle functional changes in the migraine brain.

Steady-state visual evoked potentials in the low frequency range in migraine: a study of habituation and variability phenomena.

Previous studies have revealed that migraine patients display an increased photic driving to flash stimuli in the medium frequency range. The aim of this study was to perform a topographic analysis of steady-state visual evoked potentials (SVEPs) in the low frequency range (3-9 Hz), evaluating the temporal behaviour of the F1 amplitude by investigating habituation and variability phenomena. The main component of SVEPs, the F1, demonstrated an increased amplitude in several channels at 3 Hz. Behaviour of F1 amplitude was rather variable over time, and the wavelet-transform standard deviation was increased in migraine patients at a low stimulus rate. The discriminative value of the F1 mean amplitude and variability index, tested by both an artificial neural network classifier and a support vector machine, were high according to both methods. The increased photic driving in migraine should be subtended by a more generic abnormality of visual reactivity instead of a selective impairment of a visual subsystem. Temporal behaviour of SVEPs is not influenced by a clear tendency to habituation, but the F1 amplitude seemed to change in a complex way, which is better described by variability phenomena. An increased variability in response to flicker stimuli in migraine patients could be interpreted as an overactive regulation mechanism, prone to instability and consequently to headache attacks, whether spontaneous or triggered.