Unified asymptotic theory for all partial directed coherence forms.

This paper presents a unified mathematical derivation of the asymptotic behaviour of the three main forms of partial directed coherence (PDC). Numerical examples are used to contrast PDC, gPDC (generalized PDC) and iPDC (information PDC) as to meaning and applicability and, more importantly, to show their essential statistical equivalence insofar as connectivity inference is concerned.

Thalamic bursting in rats during different awake behavioral states.

Thalamic neurons have two firing modes: tonic and bursting. It was originally suggested that bursting occurs only during states such as slow-wave sleep, when little or no information is relayed by the thalamus. However, bursting occurs during wakefulness in the visual and somatosensory thalamus, and could theoretically influence sensory processing. Here we used chronically implanted electrodes to record from the ventroposterior medial thalamic nucleus (VPM) and primary somatosensory cortex (SI) of awake, freely moving rats during different behaviors. These behaviors included quiet immobility, exploratory whisking (large-amplitude whisker movements), and whisker twitching (small-amplitude, 7- to 12-Hz whisker movements). We demonstrated that thalamic bursting appeared during the oscillatory activity occurring before whisker twitching movements, and continued throughout the whisker twitching. Further, thalamic bursting occurred during whisker twitching substantially more often than during the other behaviors, and a neuron was most likely to respond to a stimulus if a burst occurred approximately 120 ms before the stimulation. In addition, the amount of cortical area activated was similar to that during whisking. However, when SI was inactivated by muscimol infusion, whisker twitching was never observed. Finally, we used a statistical technique called partial directed coherence to identify the direction of influence of neural activity between VPM and SI, and observed that there was more directional coherence from SI to VPM during whisker twitching than during the other behaviors. Based on these findings, we propose that during whisker twitching, a descending signal from SI triggers thalamic bursting that primes the thalamocortical loop for enhanced signal detection during the whisker twitching behavior.

Partial directed coherence: a new concept in neural structure determination.

This paper introduces a new frequency-domain approach to describe the relationships (direction of information flow) between multivariate time series based on the decomposition of multivariate partial coherences computed from multivariate autoregressive models. We discuss its application and compare its performance to other approaches to the problem of determining neural structure relations from the simultaneous measurement of neural electrophysiological signals. The new concept is shown to reflect a frequency-domain representation of the concept of Granger causality.

Non-linear analysis of the rhythmic activity in rodent brains.

This paper discusses the employment of non-parametric non-linear prediction algorithms to investigate non-linear dynamics in the rhythmic brain activity of rats. Three algorithms (Sugihara-May Simplex, K-neighbour and Casdagli's) were tested yielding similar prediction results which--when subject to a suitable bootstrap based t-tests--revealed that the theta waves recorded in rat brains cannot have their intrinsic non-linearity dismissed at a significance of 0.05.

Using partial directed coherence to describe neuronal ensemble interactions.

This paper illustrates the use of the recently introduced method of partial directed coherence in approaching how interactions among neural structures change over short time spans that characterize well defined behavioral states. Central to the method is its use of multivariate time series modelling in conjunction with the concept of Granger causality. Simulated neural network models were used to illustrate the technique's power and limitations when dealing with neural spiking data. This was followed by the analysis of multi-unit activity data illustrating dynamical change in the interaction of thalamo-cortical structures in a behaving rat.

Sensorimotor encoding by synchronous neural ensemble activity at multiple levels of the somatosensory system.

Neural ensemble processing of sensorimotor information during behavior was investigated by simultaneously recording up to 48 single neurons at multiple relays of the rat trigeminal somatosensory system. Cortical, thalamic, and brainstem neurons exhibited widespread 7- to 12-hertz synchronous oscillations, which began during attentive immobility and reliably predicted the imminent onset of rhythmic whisker twitching. Each oscillatory cycle began as a traveling wave of neural activity in the cortex that then spread to the thalamus. Just before the onset of rhythmic whisker twitching, the oscillations spread to the spinal trigeminal brainstem complex. Thereafter, the oscillations at all levels were synchronous with whisker protraction. Neural structures manifesting these rhythms also exhibited distributed spatiotemporal patterns of neuronal ensemble activity in response to tactile stimulation. Thus, multilevel synchronous activity in this system may encode not only sensory information but also the onset and temporal domain of tactile exploratory movements.

Structural analysis of neural circuits using the theory of directed graphs.

A new approach to analysis of structural properties of biological neural circuits is proposed based on their representation in the form of abstract structures called directed graphs. To exemplify this methodology, structural properties of a biological neural network and randomly wired circuits (RC) were compared. The analyzed biological circuit (BC) represented a sample of 39 neural nuclei which are responsible for the control of the cardiovascular function in higher vertebrates. Initially, direct connections of both circuits were stored in a square matrix format. Then, standard algorithms derived from the theory of directed graphs were applied to analyze the pathways of the circuits according to their length (in number of synapses), degree of connectedness, and structural strength. Thus, the BC was characterized by the presence of short, reciprocal, and unidirectional pathways which presented a high degree of heterogeneity in their strengths. This heterogeneity was mainly due to the existence of a small cluster of reciprocally connected neural nuclei in the circuit that have access, through short pathways, to most of the network. On the other hand, RCs were characterized by the presence of long and mainly reciprocal pathways which showed lower and absolute homogeneous strengths. Through this study the proposed methodology was demonstrated to be a simple and efficient way to store, analyze, and compare basic neuroanatomical information.

Rhythmic bacterial susceptibility to antibiotics at a large hospital.

The in vitro susceptibility response of Staphylococcus aureus, Klebsiella pneumoniae, Escherichia coli, Proteus mirabilis and Pseudomonas aeruginosa to a set of antibiotics was investigated in a survey comprising 19,380 positive cultures over a period of 5 years in a large hospital environment. Four out of the five species (P. aeruginosa being the exception) presented a species-specific, drug-independent, rhythmic variation of their level of susceptibility to several antibiotics over the time of the study. The species-specific rhythmic responses were further characterized by spectral analysis, autocorrelation and cross-correlation functions. Through this analysis it was possible to rank the species according to their main period of oscillation. The longest period of oscillation was detected for S. aureus (38 months). K. pneumoniae and E. coli presented intermediate values (25 and 23 months respectively), and P. mirabilis the shortest period of oscillation (11 months). Species displaying long periods of oscillation tended to present very low levels of susceptibility, while species displaying short periods of oscillation usually presented the highest levels of susceptibility observed. Although some hospital environmental factors, such as drug consumption, were also analyzed, no correlation was found between them and the in vitro bacterial cyclic responses to antibiotics.

Structural characterization of the neural circuit responsible for control of cardiovascular functions in higher vertebrates.

A comparison of structural properties of a biological neural system responsible for cardiovascular function control in higher vertebrates with randomly connected networks was pursued using matrix representations of those circuits. The biological circuit was characterized by the presence of some heavily connected nuclei in contrast to the random networks that had equally distributed connections between their elements. This property of the analysed biological circuit was shown to account for a high logarithmic correlation found between two indexes defined to represent pointwise features of the nuclei and their global contribution to the whole network. The first index is obtained by the product of the number of inputs and of outputs of a nucleus and was called power index (PI). The second one, called occurrence index (OI), defines how many times a specific nucleus is crossed when all possible pathways joining two nuclei of the circuit are obtained. This PI-OI correlation was clearly dependent on the pathway length distribution (expressed in number of synapses), and was maximal considering pathways with a low number of synapses. When randomly connected circuits were analysed lower correlation was found between the same two indexes and only for much longer pathways. Therefore, it is proposed that the analysis of the PI-OI correlation can be useful to quantify structural differences between biological neural circuits as distinguished from randomly connected networks and also between neural systems at different levels of phylogenetic and ontogenetic development.

Time series analysis of rhythmic bacterial resistance development to antibiotics.

The sensitivity data of Staphylococcus aureus and Escherichia coli to a large set of antibiotics have undergone time series procedures of analysis in order to highlight possibly periodical behavior in time. These oscillational patterns have been characterized through the use of FFT and cross-correlational and variance analysis and were proved to be species-specific and drug-independent. S. aureus was shown to have a large period of oscillation (40 months) when compared to E. coli (from 7 to 11 months). A perfect species distinction was only possible through cross correlation. These results may reflect the influence of the local environment, since this finding was not referred to in the literature.