Many Attractors, Long Chaotic Transients, and Failure in Small-World Networks of Excitable Neurons

We study the dynamical states that emerge in a small-world network of recurrently coupled excitable neurons through both numerical and analytical methods. These dynamics depend in large part on the fraction of long-range connections or `short-cuts' and the delay in the neuronal interactions. Persistent activity arises for a small fraction of `short-cuts', while a transition to failure occurs at a critical value of the `short-cut' density. The persistent activity consists of multi-stable periodic attractors, the number of which is at least on the order of the number of neurons in the network. For long enough delays, network activity at high `short-cut' densities is shown to exhibit exceedingly long chaotic transients whose failure-times averaged over many network configurations follow a stretched exponential. We show how this functional form arises in the ensemble-averaged activity if each network realization has a characteristic failure-time which is exponentially distributed.Comment: 14 pages 23 figure

Relargage d’ions métalliques après l’arthroplastie de la hanche à grand diamètre avec couple de frottement métal sur métal

La dégénérescence articulaire sévère de la hanche est une pathologie fréquente et son traitement ultime est le remplacement prothétique. L’arthroplastie la plus répandue au monde est la prothèse totale de hanche (PTH) avec un couple de frottement métal-sur-polyéthylène (MPE). Cependant ce type d’intervention présente une longévité limitée à cause de l’usure de PE et ne convient pas aux patients actifs souffrant de coxarthrose sévère tôt dans leur vie. Afin de palier à ce problème, une nouvelle génération de surfaces de frottement métal-sur-métal (MM) est actuellement employée. Ces surfaces de frottement sont utilisées en PTH avec tête de 28 mm, en resurfaçage (RH) et avec la PTH à tête de grand diamètre. Alors qu’il y a beaucoup d’évidence à l’égard du bon fonctionnement des implants PTH 28 mm et du RH, les données quant aux performances in vivo des PTH MM à grand diamètre manquent. Malgré cela, ces implants sont utilisés à grande échelle. Dans un premier temps, l’objectif de ce travail de recherche était d’évaluer l’effet et de comparer les taux d’ions chrome (Cr) et cobalt (Co) chez des sujets porteurs de PTH MM à grand diamètre à ceux de 64 porteurs de RH, tous deux possédant des surfaces de frottement aux propriétés tribologiques identiques. Dans un deuxième temps, nous avons comparé les taux ioniques (Cr, Co et titane (Ti)) entre quatre PTH MM à grand diamètre provenant de fabricants différents (Zimmer, DePuy, Smith & Nephew et Biomet). Les mesures d’ions étaient effectuées dans le sang entier dans un laboratoire indépendant par la technique de spectrophotométrie de masse à haute résolution HR-ICP-MS, pour l’ensemble de ce travail de recherche. Les deux comparaisons ont démontré le rôle crucial joué par la modularité au niveau de la jonction tête-col des PTH MM à grand diamètre. En effet, des écarts considérables dans les concentrations ioniques de Co ont été retrouvés entre les RH et PTH Durom ayant un couple de frottement identique, ainsi qu’entre les 4 différents designs de PTH MM à grand diamètre comparés entre eux. La PTH MM à grand diamètre Durom était la moins favorable alors que celle de Biomet était la plus performante. Nos observations démontrent que des sources inattendues comme la jonction tête-col de certains implants PTH MM à grand diamètre peuvent contribuer au relargage ionique systémique. Une meilleure compréhension de ce phénomène est indispensable avant l’utilisation clinque de nouveaux implants de ce type.The treatment for advanced degenerative hip disease consists in replacing the native joint with artificial implants. This is a very common procedure and the type of arthroplasty most practiced worldwide is metal-on-polyethylene (MOPE) total hip replacement (THR). However, this type of bearing has limited lifespan and is not adapted for active patients struggling with hip osteoarthritis early in their lives. In order to increase implant longevity, new generation, metal-on–metal (MOM) bearing surfaces is used nowadays in this particular population. These MOM bearings are used in 28 mm THR, in resurfacing hip arthroplasty (RH) and in large diameter head THR. Although consistent results have been obtained with the 28 mm THR and RH, large diameter head THR are increasingly used despite lack of scientific data about their performances. The main purpose of our first paper was to compare chromium (Cr) and cobalt (Co) concentrations among patients implanted with large diameter head THR and with RH. In this case, both bearing surfaces presented identical tribological properties. In the second paper, we compared performances in terms of ion release (Cr, Co and titanium (Ti)) from four different manufacturers of large diameter head THR systems (Zimmer, DePuy, Smith & Nephew and Biomet). Whole blood was used for all samples and ion measurements were conducted by an independent laboratory in a blinded fashion, using high-resolution inductive coupled plasma mass spectrophotometry (HR-ICP-MS). Both papers have emphasized the crucial role played by modularity at the head-neck junction in metal ion release from large diameter THR MOM bearings. In fact, significant differences were found in Co ion concentration between large head THR and HRA as well as among the different designs of large head THRs. Briefly, the Durom large head THR system was the least favorable implant while the Biomet large head THR system showed the best results. Our results prove that systemic ion release might origin from surprising sources such as modularity at the head-neck junction in patients implanted with certain large head MOM THR systems. A better comprehension of head-neck junction biomechanics is necessary before clinical use of such new devices

Modeling extracellular field potentials and the frequency-filtering properties of extracellular space

Extracellular local field potentials (LFP) are usually modeled as arising from a set of current sources embedded in a homogeneous extracellular medium. Although this formalism can successfully model several properties of LFPs, it does not account for their frequency-dependent attenuation with distance, a property essential to correctly model extracellular spikes. Here we derive expressions for the extracellular potential that include this frequency-dependent attenuation. We first show that, if the extracellular conductivity is non-homogeneous, there is induction of non-homogeneous charge densities which may result in a low-pass filter. We next derive a simplified model consisting of a punctual (or spherical) current source with spherically-symmetric conductivity/permittivity gradients around the source. We analyze the effect of different radial profiles of conductivity and permittivity on the frequency-filtering behavior of this model. We show that this simple model generally displays low-pass filtering behavior, in which fast electrical events (such as Na$^+$-mediated action potentials) attenuate very steeply with distance, while slower (K$^+$-mediated) events propagate over larger distances in extracellular space, in qualitative agreement with experimental observations. This simple model can be used to obtain frequency-dependent extracellular field potentials without taking into account explicitly the complex folding of extracellular space.Comment: text (LaTeX), 6 figs. (ps

Implication of Kir4.1 Channel in Excess Potassium Clearance: An In Vivo Study on Anesthetized Glial-Conditional Kir4.1 Knock-Out Mice

The

The brain decade in debate: VII. Neurobiology of sleep and dreams

This article is a transcription of an electronic symposium held on February 5, 2001 by the Brazilian Society of Neuroscience and Behavior (SBNeC) during which eight specialists involved in clinical and experimental research on sleep and dreaming exposed their personal experience and theoretical points of view concerning these highly polemic subjects. Unlike most other bodily functions, sleep and dreaming cannot, so far, be defined in terms of definitive functions that play an ascribable role in maintaining the organism as a whole. Such difficulties appear quite clearly all along the discussions. In this symposium, concepts on sleep function range from a protective behavior to an essential function for maturation of the nervous system. Kleitman's hypothesis [Journal of Nervous and Mental Disease (1974), 159: 293-294] was discussed, according to which the basal state is not the wakeful state but sleep, from which we awake to eat, to protect ourselves, to procreate, etc. Dreams, on the other hand, were widely discussed, being considered either as an important step in consolidation of learning or simply the conscious identification of functional patterns derived from the configuration of released or revoked memorized information.Universidade de São Paulo Faculdade de Medicina Instituto de PsiquiatriaUniversity of Laval School of Medicine Department of PhysiologyRutgers State University Center for NeuroscienceUniversidade de São Paulo Instituto de Ciências Biomédicas Departamento de Fisiologia e BiofísicaUniversidade Federal de São Paulo (UNIFESP) Instituto do SonhoFacultad de Medicina de Montevideo Departamento de Fisiología NeurofisiologíaFlorida Atlantic University Center for Complex SystemsUniversidade de São Paulo Faculdade de Medicina Departamento de NeurologiaUNIFESP, Instituto do SonhoSciEL

Calcium Dynamics of Cortical Astrocytic Networks In Vivo

Large and long-lasting cytosolic calcium surges in astrocytes have been described in cultured cells and acute slice preparations. The mechanisms that give rise to these calcium events have been extensively studied in vitro. However, their existence and functions in the intact brain are unknown. We have topically applied Fluo-4 AM on the cerebral cortex of anesthetized rats, and imaged cytosolic calcium fluctuation in astrocyte populations of superficial cortical layers in vivo, using two-photon laser scanning microscopy. Spontaneous [Ca(2+)](i) events in individual astrocytes were similar to those observed in vitro. Coordination of [Ca(2+)](i) events among astrocytes was indicated by the broad cross-correlograms. Increased neuronal discharge was associated with increased astrocytic [Ca(2+)](i) activity in individual cells and a robust coordination of [Ca(2+)](i) signals in neighboring astrocytes. These findings indicate potential neuron–glia communication in the intact brain

Topography of slow sigma power during sleep is associated with processing speed in preschool children

Cognitive development is influenced by maturational changes in processing speed, a construct reflecting the rapidity of executing cognitive operations. Although cognitive ability and processing speed are linked to spindles and sigma power in the sleep electroencephalogram (EEG), little is known about such associations in early childhood, a time of major neuronal refinement. We calculated EEG power for slow (10-13 Hz) and fast (13.25-17 Hz) sigma power from all-night high-density electroencephalography (EEG) in a cross-sectional sample of healthy preschool children (n = 10, 4.3 ± 1.0 years). Processing speed was assessed as simple reaction time. On average, reaction time was 1409 ± 251 ms; slow sigma power was 4.0 ± 1.5 μV²; and fast sigma power was 0.9 ± 0.2 μV². Both slow and fast sigma power predominated over central areas. Only slow sigma power was correlated with processing speed in a large parietal electrode cluster (p \u3c 0.05, r ranging from -0.6 to -0.8), such that greater power predicted faster reaction time. Our findings indicate regional correlates between sigma power and processing speed that are specific to early childhood and provide novel insights into the neurobiological features of the EEG that may underlie developing cognitive abilities

Large-Scale Cortical Dynamics of Sleep Slow Waves

Slow waves constitute the main signature of sleep in the electroencephalogram (EEG). They reflect alternating periods of neuronal hyperpolarization and depolarization in cortical networks. While recent findings have demonstrated their functional role in shaping and strengthening neuronal networks, a large-scale characterization of these two processes remains elusive in the human brain. In this study, by using simultaneous scalp EEG and intracranial recordings in 10 epileptic subjects, we examined the dynamics of hyperpolarization and depolarization waves over a large extent of the human cortex. We report that both hyperpolarization and depolarization processes can occur with two different characteristic time durations which are consistent across all subjects. For both hyperpolarization and depolarization waves, their average speed over the cortex was estimated to be approximately 1 m/s. Finally, we characterized their propagation pathways by studying the preferential trajectories between most involved intracranial contacts. For both waves, although single events could begin in almost all investigated sites across the entire cortex, we found that the majority of the preferential starting locations were located in frontal regions of the brain while they had a tendency to end in posterior and temporal regions

Robust Off- and Online Separation of Intracellularly Recorded Up and Down Cortical States

BACKGROUND: The neuronal cortical network generates slow (<1 Hz) spontaneous rhythmic activity that emerges from the recurrent connectivity. This activity occurs during slow wave sleep or anesthesia and also in cortical slices, consisting of alternating up (active, depolarized) and down (silent, hyperpolarized) states. The search for the underlying mechanisms and the possibility of analyzing network dynamics in vitro has been subject of numerous studies. This exposes the need for a detailed quantitative analysis of the membrane fluctuating behavior and computerized tools to automatically characterize the occurrence of up and down states. METHODOLOGY/PRINCIPAL FINDINGS: Intracellular recordings from different areas of the cerebral cortex were obtained from both in vitro and in vivo preparations during slow oscillations. A method that separates up and down states recorded intracellularly is defined and analyzed here. The method exploits the crossover of moving averages, such that transitions between up and down membrane regimes can be anticipated based on recent and past voltage dynamics. We demonstrate experimentally the utility and performance of this method both offline and online, the online use allowing to trigger stimulation or other events in the desired period of the rhythm. This technique is compared with a histogram-based approach that separates the states by establishing one or two discriminating membrane potential levels. The robustness of the method presented here is tested on data that departs from highly regular alternating up and down states. CONCLUSIONS/SIGNIFICANCE: We define a simple method to detect cortical states that can be applied in real time for offline processing of large amounts of recorded data on conventional computers. Also, the online detection of up and down states will facilitate the study of cortical dynamics. An open-source MATLAB toolbox, and Spike 2-compatible version are made freely available