Many experiments demonstrate that the synchrony of neurons is a hallmark in epileptic seizure and the dynamical process of the epilepsy is complex with new oscillations born. In fact, epileptic seizure is very complicated relating to many factors so that it can't be understood thoroughly only in some special aspect. Based on the previous work on synchronous oscillations of electrically coupled abnormal neurons, a theoretical effort is carried out to further investigate the chaos by Lyapunov exponent and phase portrait and degree of complexity by approximate entropy in the dynamical activities. It is concluded that the synchronous activities are chaotic and complex with new oscillations born and the values of Lyapunov exponent and approximate entropy are different with the electrical coupling strength. It is also found that the trend of approximate entropy is same as that of Lyapunov exponent in the study at the dynamical activity of the two electrical coupling neurons. In the synchrony of 2-D neuronal network, the values of Lyapunov exponent are almost much greater than that of the two electrical coupling neurons. The values of approximate entropy of the different neurons in the 2-D network have almost the same trend but approximate entropy of neuron in synchrony is greater than that of neuron in non-synchrony. It is indicated that the neurons in synchrony have greater ability to produce new oscillations than that in non-synchrony. The theoretical work is helpful to understand the pathological mechanism of new oscillations born in epilepsy from a nonlinear point of view.
Many electrophysiological experiments have shown that epileptic seizures often originate from the synchronous activities of abnormally excitable neurons. The dynamic process of epilepsy is very complex, and characterized by a seemingly rapid and dramatic birth of new oscillations, essentially leading to a propagation and amplification of the original aberrant activity. It is very difficult to thoroughly understand the mechanism from a theoretical standpoint, however some special work can prove helpful. Here we present a theoretical framework to investigate chaos and complexity in the synchrony of excitable neurons in an effort to study the collective oscillations within a neural network. As endogenous rhythms, oscillations arise because most cellular processes contain feedback. The Chay model of excitable neurons is chosen because the model describes the abnormal process, where spiking can be transformed into bursting via bifurcation. In our study, the Chay model is regarded as an abnormal oscillator and coupled via a resistor representing the effect of gap junctions (electrical synapses). In this paper, we present some models developed from the original Chay model, for the synchrony of two cells and a 2D neural network. Lyapunov exponent and phase portrait are utilized to evaluate the chaotic dynamics. Finally, approximate entropy is utilized to measure its complexity. Our results show that the synchrony of abnormal oscillations can occur when the coupling strength of the gap junction is sufficiently large. It is also found that the concentration of Ca 2+ ions does not synchronize. In the 2D network, approximate entropies of different oscillations with strong coupling strength are greater than those with weak coupling strength. It is indicated that synchronous neurons have greater ability to produce new oscillations than asynchronous ones. This work shows that nonlinear analytical methods may prove useful in elucidating the mechanisms of pathologic conditions, where new oscillations are born and propagated, such as in epilepsy.
The main goal of this study was to evaluate the possible effects of electromagnetic field (EMF) of transmission lines exposure on testis tissue of mice. Forty adult BALB/c mice were divided into two groups. One group (twenty mice) has been done by daily exposures of 24 hours, and the other sham-exposed group (twenty mice) served as the control. After seven weeks of exposure, two groups of the mice were sacrificed. The testis tissue was assessed by serum biochemical assay, histopathological examination and flow cytometric analysis (FCM). EMF exposure did not significantly affect the distribution of DNA ploidy (1n, 2n and 4n cells), but significantly decreased the S phase fraction and the Proliferation Index of testis germ cells.
The synchrony of abnormally excitable neurons is a hallmark in epileptic seizure. In order to study the nonlinear oscillations in two neurons coupled via gap junction in epilepsy, the model of a pair of neurons is derived from Chay model that gives many kinds of abnormal oscillations in excitable neurons by three nonlinear variables dynamics equations. The synchrony between two electrically coupled excitable neurons is found and a theoretical effort is carried out to investigate the chaos in the synchronous oscillations of the membrane potentials by the Lyapunov exponent and the phase portrait. It is shown that synchronous abnormal oscillations of membrane potentials can occur when the coupling strength of gap junction is large enough and the concentration of Ca/sup 2/ ions does not synchronize while the membrane potentials are synchronous and the coupling mechanism is chaotic. It is concluded that the synchrony and the chaos make birth to the new oscillations while disorder process such as epileptic seizure. The theoretical analysis may be helpful to investigate the mechanism of synchrony and the relationship between abnormal oscillations and gap junctions from nonlinear oscillatory points of view.
The relationships of epileptiform waves caused by abnormal neurons are studied and it is an important basis work to investigate the properties of neural disease such as epilepsy. In our work, two Chay neurons and 2-D network models and their chaotic characters are computed in order to study the effect of gap junction on the dynamics of neuron population. The numerical results of nonlinear oscillation are analyzed when neurons are coupled in different states. These states are: repetitive spike neuron and bursting chaotic neuron; bursting chaotic neuron and single bursting neuron; abnormal neuron and resting neuron; neurons randomly distributed in 2-D network. The phase diagram and the dynamic feature of Ca/sup 2+/ concentration are also used to learn the synchronous activities. Our work is helpful to our further research for the mechanism of epileptic waves propagation and the effect of gap junction on 3-D network.
The biological effects of irradiation by magnetic field on the proliferation and apoptosis of the liver cells in mice are studied. BALB/C mice were irradiated by 50 Hz homogeneous ferromagnetic field(0.097 T) and divided into four irradiation groups: 5 min., 30 min., 60 min., and 120 min.. Proliferation and apoptosis of the liver cells were analyzed with the flow cytometry (FCM) and DNA agarose gel electrophoresis. The FCM test results showed that different irradiation time of magnetic field could induce apoptosis of murine liver cells. The percentage of apoptosis in irradiation groups are 9.55%/spl plusmn/0.82%, 12.07%/spl plusmn/2.96%, 13.66%/spl plusmn/1.90% and 16.22%/spl plusmn/2.64% respectively and significantly higher than that in control group. In the interval of 5 min-120 min, the percentage of apoptosis of liver cells increased as the irradiation time prolonged (r=0.78, P<0.05), but FCM results showed that 50 Hz homogeneous ferromagnetic field have no effects on proliferation of murine liver cells. We concluded that irradiation of 50 Hz homogeneous ferromagnetic field could induce and promote apoptosis of murine liver cells in time-effects manner.
To study how the epileptiform waves are mutually affected is meaningful for the research of neural disease. And to investigate synchronous properties of coupling neurons is an important basis. The bursting dynamics of chay neuron model coupled by gap junction with different strength were observed and the chaotic characteristics were displayed. The numerical results of non-linear oscillation under different states of coupling neurons were analyzed, such as: pacemaker neuron and chaotic burst neuron, chaotic burst neuron and single burst neuron, abnormal neuron and resting neuron. Some phase portraits of coupling neurons and its dynamic features of Ca~(2+) concentration change were provided. The work is helpful to our further research for the mechanism of epileptic seizure, epileptic wave propagation and control.
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