A Model for Multi-site Pacing of Fibrillation Using Nonlinear Dynamics Feedback

Traditionally, cardiac defibrillation requires a strong electric shock. Many unwanted side effects of this shock could be eliminated if defibrillation were performed using weak stimuli applied to several locations throughout the heart. Such multi-site pacing algorithms have been shown to defibrillate both experimentally (Pak et al., Am J Physiol 285:H2704–H2711, 2003) and theoretically (Puwal and Roth, J Biol Systems 14:101–112, 2006). Gauthier et al. (Chaos, 12:952–961, 2002) proposed a method to pace the heart using an algorithm based on nonlinear dynamics feedback applied through a single electrode. Our study applies a related but simpler algorithm, which essentially configures each electrode as a demand pacemaker, to simulate the multi-site pacing of fibrillating cardiac tissue. We use the numerical model developed by Fenton et al. (Chaos, 12:852–892, 2002) as the reaction term in a reaction–diffusion equation that we solve over a two-dimensional sheet of tissue. The defibrillation rate after pacing for 3 s is about 30%, which is significantly higher than the spontaneous defibrillation rate and is higher than observed in previous experimental and theoretical studies. Tuning the algorithm period can increase this rate to 45%. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Periodicity and synchronization in blood-stage malaria infection

Malaria fever is highly periodic and is associated with the parasite replication cycles in red blood cells. The existence of periodicity in malaria infection demonstrates that parasite replication in different red blood cells is synchronized. In this article, rigorous mathematical analysis of an age-structured human malaria model of infected red blood cells (Rouzine and McKenzie, Proc Natl Acad Sci USA 100:3473–3478, 2003) is provided and the synchronization of Plasmodium falciparum erythrocytic stages is investigated. By using the replication rate as the bifurcation parameter, the existence of Hopf bifurcation in the age-structured malaria infection model is obtained. Numerical simulations indicate that synchronization with regular periodic oscillations (of period 48 h) occurs when the replication rate increases. Therefore, Kwiatkowski and Nowak’s observation (Proc Natl Acad Sci USA 88:5111–5113, 1991) that synchronization could be generated at modest replication rates is confirmed.     

Effects of spinal recurrent inhibition on motoneuron short-term synchronization

Spinal recurrent inhibition linking skeleto- motoneurons (α-MNs) via Renshaw cells (RCs) has been variously proposed to increase or decrease tendencies toward synchronous discharges between α-MNs. This controversy is not easy to settle experimentally in animal or human paradigms because RCs receive, in addition to excitatory input from α-MNs, many other modulating influences which may change their mode of operation. Computer simulations help to artificially isolate the recurrent inhibitory circuit and thus to study its effects on α-MN synchronization under conditions not achievable in natural experiments. We present here such a study which was designed to specifically test the following hypothesis. Since many α-MNs excite any particular Renshaw cell, which in turn inhibits many α-MNs, this convergence–divergence pattern establishes a random network whose random discharge patterns inject uncorrelated noise into α-MNs, and this noise counteracts any synchronization potentially arising from other sources, e.g., common inputs (Adam et al. in Biol Cybern 29:229–235, 1978). We investigated the short-term synchronization of α-MNs with two types of excitatory input signals to α-MNs (random and sinusoidally modulated random patterns). The main results showed that, while recurrent inhibitory inputs to different α-MNs were indeed different, recurrent inhibition (1) exerted rather small effects on the modulation of α-MN discharge, (2) tended to increase the short-term synchronization of α-MN discharge, and (3) did not generate secondary peaks in α-MN-α-MN cross-correlograms associated with α-MN rhythmicity.     

Desynchronization and synchronization of EEG related to stimuli triggering or forbidding sensory-motor reaction in adolescents: II. The peculiarities in case of the attention deficit and hyperactivity syndrome

Evoked desynchronization and synchronization of EEG in θ (4–7.5 Hz), α (7.5–14 Hz) and β (14–20 Hz) ranges were recorded by 19 electrodes in healthy volunteer adolescents and those with attention deficit hyperactivity syndrome in the modified GO/NO-GO test. Two stimuli (high and low tone) were presented in pairs with 1 s intervals inside the pair and 1.5 s intervals between the pairs. Test subjects had to push the button in response to presentation of a pair of high tones and to ignore other stimulus combinations. The components of evoked EEG synchronization in α-θ range that were revealed in the frontocentral and temporoparietal brain regions in connection with inhibition of action (inhibition of movements and making a decision to cancel sensory-motor task performance) were statistically significantly lower in subjects with attention deficit hyperactivity disorder compared with that in healthy subjects.     

Shaping bursting by electrical coupling and noise

Gap-junctional coupling is an important way of communication between neurons and other excitable cells. Strong electrical coupling synchronizes activity across cell ensembles. Surprisingly, in the presence of noise synchronous oscillations generated by an electrically coupled network may differ qualitatively from the oscillations produced by uncoupled individual cells forming the network. A prominent example of such behavior is the synchronized bursting in islets of Langerhans formed by pancreatic β-cells, which in isolation are known to exhibit irregular spiking (Sherman and Rinzel, Biophys J 54:411–425, 1988; Sherman and Rinzel, Biophys J 59:547–559, 1991). At the heart of this intriguing phenomenon lies denoising, a remarkable ability of electrical coupling to diminish the effects of noise acting on individual cells. In this paper, building on an earlier analysis of denoising in networks of integrate-and-fire neurons (Medvedev, Neural Comput 21 (11):3057–3078, 2009) and our recent study of spontaneous activity in a closely related model of the Locus Coeruleus network (Medvedev and Zhuravytska, The geometry of spontaneous spiking in neuronal networks, submitted, 2012), we derive quantitative estimates characterizing denoising in electrically coupled networks of conductance-based models of square wave bursting cells. Our analysis reveals the interplay of the intrinsic properties of the individual cells and network topology and their respective contributions to this important effect. In particular, we show that networks on graphs with large algebraic connectivity (Fiedler, Czech Math J 23(98):298–305, 1973) or small total effective resistance (Bollobas, Modern graph theory, Graduate Texts in Mathematics, vol. 184, Springer, New York, 1998) are better equipped for implementing denoising. As a by-product of the analysis of denoising, we analytically estimate the rate with which trajectories converge to the synchronization subspace and the stability of the latter to random perturbations. These estimates reveal the role of the network topology in synchronization. The analysis is complemented by numerical simulations of electrically coupled conductance-based networks. Taken together, these results explain the mechanisms underlying synchronization and denoising in an important class of biological models.     

Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks

We describe and analyze a model for a stochastic pulse-coupled neuronal network with many sources of randomness: random external input, potential synaptic failure, and random connectivity topologies. We show that different classes of network topologies give rise to qualitatively different types of synchrony: uniform (Erdős–Rényi) and “small-world” networks give rise to synchronization phenomena similar to that in “all-to-all” networks (in which there is a sharp onset of synchrony as coupling is increased); in contrast, in “scale-free” networks the dependence of synchrony on coupling strength is smoother. Moreover, we show that in the uniform and small-world cases, the fine details of the network are not important in determining the synchronization properties; this depends only on the mean connectivity. In contrast, for scale-free networks, the dynamics are significantly affected by the fine details of the network; in particular, they are significantly affected by the local neighborhoods of the “hubs” in the network.     

Synchronization of gallers with host plant phenology

In addition to various bottom-up effects, the synchronization of herbivores with their host plant phenology determines quality and quantity of food resources and affects the preference–performance linkage and abundance of herbivores. The synchronization has a more critical meaning for such short-lived galling insects as cecidomyiid adults and young aphid stem mothers than for other insects. This review, first, presents general information about gall midges and gall aphids, together with their life history patterns and some ecological attributes. Second, some important topics of galling insect–host plant relation are briefly reviewed. Then, synchronization patterns between gall midge emergence and host plant phenology are analyzed to discuss the adaptive strategies of gall midges and to show how the amount of available food resources is affected by the time lag in synchronization. The spatial distribution pattern and the preference–performance linkage of aphid stem mothers is also discussed in relation to synchronization. Received: October 2, 1998 / Accepted: July 3, 2000     

The response of a classical Hodgkin–Huxley neuron to an inhibitory input pulse

A population of uncoupled neurons can often be brought close to synchrony by a single strong inhibitory input pulse affecting all neurons equally. This mechanism is thought to underlie some brain rhythms, in particular gamma frequency (30–80 Hz) oscillations in the hippocampus and neocortex. Here we show that synchronization by an inhibitory input pulse often fails for populations of classical Hodgkin–Huxley neurons. Our reasoning suggests that in general, synchronization by inhibitory input pulses can fail when the transition of the target neurons from rest to spiking involves a Hopf bifurcation, especially when inhibition is shunting, not hyperpolarizing. Surprisingly, synchronization is more likely to fail when the inhibitory pulse is stronger or longer-lasting. These findings have potential implications for the question which neurons participate in brain rhythms, in particular in gamma oscillations.     

Effect of context on the plasticity of cognitive activity

The hypotheses that the plasticity or flexibility of cognitive activity substantially depends on the ability to replace the previous cognitive sets by new sets that are more appropriate to new conditions is substantiated. Working memory overload results in a decrease in set-shifting and, as a consequence, increased erroneous stimuli recognition. The plasticity of set-shifting is changed depending on the context of cognitive activity. On the basis of the data from the analysis of the coherence function and induced synchronization/desynchronization responses of potentials in the θ (4–7 Hz) and low-frequency α (8–10 Hz) bands, the roles of the tonic and phasic forms of activity of the cortico-hippocampal and fronto-thalamic functional systems of cerebral integration in changes of plasticity of cognitive functions are discussed.     

Dynamics of two electrically coupled chaotic neurons: Experimental observations and model analysis

Conductance-based models of neurons from the lobster stomatogastric ganglion (STG) have been developed to understand the observed chaotic behavior of individual STG neurons. These models identify an additional slow dynamical process – calcium exchange and storage in the endoplasmic reticulum – as a biologically plausible source for the observed chaos in the oscillations of these cells. In this paper we test these ideas further by exploring the dynamical behavior when two model neurons are coupled by electrical or gap junction connections. We compare in detail the model results to the laboratory measurements of electrically-coupled neurons that we reported earlier. The experiments on the biological neurons varied the strength of the effective coupling by applying a parallel, artificial synapse, which changed both the magnitude and polarity of the conductance between the neurons. We observed a sequence of bifurcations that took the neurons from strongly synchronized in-phase behavior, through uncorrelated chaotic oscillations to strongly synchronized – and now regular – out-of-phase behavior. The model calculations reproduce these observations quantitatively, indicating that slow subcellular processes could account for the mechanisms involved in the synchronization and regularization of the otherwise individual chaotic activities. Received: 28 June 1999 / Accepted in revised form: 30 June 2000     

Changes in emotional face expression recognition caused by an additional visuospatial task

Changes in the recognition of facial expression and spatial synchronization of the cortical electrical activity of the θ- and α-potentials caused by load on working memory were studied in healthy adults by introducing an additional semantic or visuospatial task into the context of experiment with a visual set. An increase in the number of erroneous recognitions of facial stimuli in the form of assimilative illusions was revealed in both types of the additional task. The analysis of the function of coherence of the low-frequency α-potentials indicates (8–10 Hz) a decrease in this situation in the number of connections in the frontal cortical divisions with other cortical zones, which is regarded as a lesser involvement of the frontal system of selective attention in set-forming and set-shifting for an emotionally negative facial expression. Spatial synchronization of the θ-activity (4–7 Hz) with an increase in the load on working memory changes ambiguously in different cortical structures: it decreases in the system of the fronto-temporal connections of the right hemisphere; in the other cortical areas, especially in the left hemisphere, and in the system of interhemispheric connections it substantially increases. The facts confirming the hypothesis that the fronto-thalamic and cortico-hippocampal systems are the two key formations involved in changes in the plasticity of cognitive sets for facial expression are discussed.     

Diapause development in the chestnut weevilCurculio elephas

Larval diapause development in the chestnut weevilCurculio elephas (Coleoptera, Curculionidae) was studied in the laboratory at different temperatures. The results proved that exposure to low temperatures (3–6°C) in the period December–February is not required to complete diapause. The diapause is terminated in December and from January on, the larvae can initiate post-diapause morphogenesis in the laboratory, if temperatures allow it. In the field developmental rates are negligible during winter cold (4–6°C) and only after March morphogenesis can proceed with no interruption until adult emergence. Diapause and post-diapause quiescence contribute to individual synchronization for initiation of development. The observed spread of adult emergence was 30 days in the laboratory. This variability produced during post-diapause development may be a response to annual variation in the phenology of the chestnuts.     

Proximate and Elemental Composition of <Emphasis Type="Italic">Chamelea gallina</Emphasis> from the Southern Coast of the Marmara Sea (Turkey)

The venerid clam Chamelea gallina is a popular and economic foodstuff around the Mediterranean countries especially in Italy, Spain, and France. The aim of this study is to evaluate the nutritional quality of striped venus of Southern Marmara. Samples were harvested seasonally at five stations and analyzed to determine meat yield, proximate, and elemental composition. According to the results, meat yield ranged from 20.24% to 29.94%. Means of water, protein, lipid, and ash content were 67%, 10.12%, 2.57%, and 1.66%, respectively. The mean concentrations (mg/kg wet weight) of elements in tissues are as follows: B: 2.37–4.24; Cr: 0–0.76; Co: 0–0.43; Cu: 0.71–5.30; Mn: 0.30–5.94; Zn: 13.08–77.76; Ni: 0–1.22; Fe: 2.46–114.22; Al: 1.23–75.49; Pb: 0.18–3.24; Ba: 0.66–15.97; Cd: 0.04–0.69. Among the reported metal levels, only Pb and Zn in two stations exceeded the maximum critical concentrations enforced by Turkish legislation and European Commission. Therefore, we report that striped venus from Southern Marmara Sea, in general, are safe for human consumption; nonetheless, Pb and Zn levels should be closely monitored in the future.     

Local lateral inhibition: a key to spike synchronization?

 Starting from the idea that neural group activity as such is unlikely to be immediately relevant for neural synchronization, we investigate mechanisms that act at the level of individual nerve impulses (spikes). Hence, we consider populations of formal spike-emitting ‘leaky integrate and fire’ neurons instead of networks built from non-spiking oscillators. After outlining the principle of synchronization for basic forms of recurrent impulse coupling by using a pair of simplified formal neurons, we show that local lateral inhibition results in robust impulse synchronization in networks with non-vanishing transmission delays. Received: 12 January 1994/Accepted in revised form: 25 April 1995     

Changes in the fluctuation of interbeat intervals in spontaneously beating cultured cardiac myocytes: experimental and modeling studies

 Isolated and cultured neonatal cardiac myocytes contract spontaneously and cyclically, and have the properties of a non-linear oscillator. In this study, we have analyzed the relationship between the fluctuation of contraction rhythm of spontaneously beating cultured cardiac myocytes, and the coupling strength among them. The coefficient of variation of contraction intervals increased transiently in the early stages of incubation, and then decreased almost monotonically with time. The contraction rhythm of the myocytes became synchronized in the late stage of the culture. The day on which synchronization occurred almost coincided with the day when the coefficient of variation reached its lowest value. In addition, we have performed a mathematical analysis using interacting Bonhoeffer–van der Pol oscillators to clarify the mechanisms underlying the changes in the fluctuation of contraction rhythm with time. As the coupling strength among oscillators increased, the coefficient of variation of oscillation periods increased temporarily, but then decreased rapidly when the oscillators showed synchronization. These results suggest that the changes in the fluctuation of beating rhythm result from the increase in strength of electrical coupling among spontaneously beating cardiac myocytes. Received: 10 August 2000 / Accepted in revised form: 19 August 2001     

Trace elements in aerial parts and rhizosphere of <Emphasis Type="Italic">Thymus pannonicus</Emphasis> All.

This paper brings out the results of the study on the levels of selected trace elements (Cu, Fe, Mn, Zn and Cr) in aerial parts of Thymus pannonicus All. (Lamiaceae) and rhizosphere soil from twelve locations in Serbia. Prior to assays by flame and flameless atomic absorption spectrometry, samples were subjected to microwave-assisted acid digestion. Real and potential acidity of soil samples were also measured. Obtained results for soil samples, although slightly higher for some elements (Cu: 12.38–45.18 mg/kg; Fe: 22102–46193 mg/kg; Mn: 776.95–4901.27 mg/kg; Zn: 62.27–214.02 mg/kg; Cr: 48.86–69.13 mg/kg), were found to fit into biogeochemical background. Element contents in plant samples differed depending on collecting site (Cu: 5.26–14.07 mg/kg; Fe: 25.92–1454.07 mg/kg; Mn: 89.29–278.25 mg/kg; Zn: 1.81–10.64 mg/kg; Cr: 1.11–3.51 mg/kg), which can be partly explainable by different nutrient availability influenced by soil acidity. Zinc levels in T. pannonicus were below expected and seem to be strongly influenced by plant physiological properties.     

A general linear framework for the comparison and evaluation of models of sensorimotor synchronization

Sensorimotor synchronization (SMS), the temporal coordination of a rhythmic movement with an external rhythm, has been studied most often in tasks that require tapping along with a metronome. Models of SMS use information about the timing of preceding stimuli and responses to predict when the next response will be made. This article compares the theoretical structure and empirical predictions of four two-parameter models proposed in the literature: Michon (Timing in temporal tracking, Van Gorcum, Assen, 1967), Hary and Moore (Br J Math Stat Psychol 40:109–124, 1987b), Mates (Biol Cybern 70:463–473, 1994a; Biol Cybern 70:475–484, 1994b), and Schulze et al. (Mus Percept 22:461–467, 2005). By embedding these models within a general linear framework, the mathematical equivalence of the Michon, Hary and Moore, and Schulze et al. models is demonstrated. The Mates model, which differs from the other three, is then tested empirically with new data from a tapping experiment in which the metronome alternated between two tempi. The Mates model predictions are found to be invalid for about one-third of the trials, suggesting that at least one of the model’s underlying assumptions is incorrect. The other models cannot be refuted as easily, but they do not predict some features of the data very accurately. Comparison of the models’ predictions in a training/test procedure did not yield any significant differences. The general linear framework introduced here may help in the formulation of new models that make better predictions.     

Transient synchronization following invasion: revisiting Moran’s model and a case study

Synchrony in forest insect outbreaks is important because the resulting regionalized outbreak dilutes the regulating effects of natural enemies, reduces the landscape’s ability to buffer the disturbance, exacerbates the economic burden on individual stakeholders, and overwhelms the logistical abilities of managers to suppress populations and mitigate impacts. Understanding the process of synchronization of dynamics is therefore a crucial aspect of understanding outbreak dynamics. We studied the second-order log-linear (autoregressive) model to ask what patterns of synchronization across invasion fronts may be expected from Moran’s model. Generally, we show that the time to synchronization in the log-linear model is a complex function of a number of parameters of which the overall strength of regulation, the strength of delayed statistical density dependence, and the relaxation time seem to be of particular importance. Interestingly, while environmental correlation is the crucial determinant of the magnitude of asymptotic synchrony, it does not appear to influence the transient process of synchronization. However, synchronization proceeds much more quickly among weakly periodic populations than among populations that are strongly periodic. As a case study, we investigate synchronization following colonization by gypsy moth (Lymantria dispar) populations located along the species’s expanding invasion front in northeastern USA. Data consisted of more than 100 years of county quarantine records and 30 years of detailed defoliation maps. We found that the dynamics of new populations tended to be initially out of synch with the broadly synchronized outbreaks within the established range. However, the outbreak dynamics of these new populations lock on to the regional patterns very quickly—within 10–15 years of invasion. Focusing on parameters that produce periodicity comparable to that seen in real gypsy moth populations, we discuss how the observed synchronization compares to that predicted by the log-linear model. While our results are equivocal, the synchronization appears to be surprisingly rapid, so more mechanistic models may be needed to explain the synchronization observed in this case study.

A comparative study of pattern synchronization detection between neural signals using different cross-entropy measures

Cross-approximate entropy (X-ApEn) and cross-sample entropy (X-SampEn) have been employed as bivariate pattern synchronization measures for characterizing interdependencies between neural signals. In this study, we proposed a new measure, cross-fuzzy entropy (X-FuzzyEn), to describe the synchronicity of patterns. The performances of three statistics were first quantitatively tested using five different coupled systems including both deterministic and stochastic models, i.e., coupled broadband noises, Lorenz–Lorenz, Rossler–Rossler, Rossler–Lorenz, and neural mass model. All the measures were compared with each other with respect to their ability to distinguish between different levels of coupling and their robustness against noise. The three measures were then applied to a real-life problem, pattern synchronization analysis of left and right hemisphere rat electroencephalographic (EEG) signals. Both simulated and real EEG data analysis results showed that the X-FuzzyEn provided an improved evaluation of bivariate series pattern synchronization and could be more conveniently and powerfully applied to different neural dynamical systems contaminated by noise.     

Computer vision analysis of somatic embryos of sweet potato [Ipomoea batatas (L.) Lam.] for assessing their ability to convert to plants

Apical and axial shoot tips of sweet potato were cultured to produce somatic embryos that mature and develop into plants in basal nutrient medium. However, the lack of high regeneration efficiency is an impediment to the use of somatic embryos to produce synthetic seeds. Conversion experiments with mature embryos over a 20-day period revealed that 80–90% of the embryos formed roots but only 40–50% formed shoots. Using computer vision and canonical or Fisher discriminant function (CDA) analysis along with conversion results, it was possible to correctly classify competent embryos 40–50% of the time based on size features, 50–60% of the time based on shape features, and 55–60% of the time based on color features. Non-competent embryos were correctly classified 65–75%, 55–60%, and 70–75% of the time based on size, shape, and color, respectively. These results can be used effectively to identify and select competent embryos for improved regeneration efficiency. Received: 2 January 1997 / Revision received: 21 January 1998 / Accepted: 12 February 1998