The electrical activity of neurons depends on the physiological conditions in the nervous system. An electromagnetic field, for example, can significantly affect the dynamics of individual neural ...cells, and it also affects their collective dynamics. It is therefore of interest to study the neuronal dynamics under such an influence in various setups. We thus study the firing patterns in two coupled neurons by considering three different types of synapses, namely electrical, chemical, and electrochemical. We use the Hindmarsh–Rose mathematical model as the basis of neuronal dynamics, and we also introduce an electromagnetic field effect. We conduct extensive calculations of the firing patterns, and we determine the bifurcation diagrams for constant and periodic external currents. The results show that the different synaptic connections evoke different firing patterns and that in general electrochemical synapses can show richer variety of dynamical behavior than electrical or chemical synapses.
Transitions from one dynamical regime to another one are observed in many complex systems, especially biological ones. It is possible that even a slight perturbation can cause such a transition. It ...is clear that this can happen to an object when it is close to a tipping point. There is a lot of interest in finding ways to recognize that a tipping point (in which a bifurcation occurs) is near. There is a possibility that in complex systems, a phenomenon known as “critical slowing down” may be used to detect the vicinity of a tipping point. In this paper, we propose Lyapunov exponents as an indicator of “critical slowing down.”
Esophageal squamous cell carcinoma is the most predominant malignancy of the esophagus. Its histological precursors (dysplasia) emerge in the esophageal epithelium that their progression into the ...underlying layers leads to cancer. The epithelium is the origin of many solid cancers and, accordingly, the focus of numerous computational models. In this work, we proposed a framework to establish a two-dimensional, globally coupled map to model the epithelium dynamics. The model aims at diagnosing the early stage of dysplasia based on microscopic images of endoscopic biopsies. We used the logistic map as a black-box model for the epithelial cells. By relating between the structure and dynamic of the epithelium, we defined the coupling function and proposed a case-dependent model in which the parameters were adjusted based on fractal geometry of each pathological image. Thus, by assigning different attractors to the cells’ behavior, the lattice dynamic was investigated by the Lyapunov exponent. The decreasing pattern of Lyapunov exponent variations across the epithelium thickness had reasonable performance in diagnosing the normal specimens from the low-grade dysplasia ones. The results showed that there could be a direct relationship between the structural complexity of this system and its uncertainty of dynamics.
Graphical abstract
The modeling process of the esophageal epithelium to classify the experimental data at normal and LGD stages.
Detection of epileptic seizures is a major challenge of these days. There are lots of papers which pay their attention to this subject. Recently, some dynamical disease with attacks such as epilepsy ...are considered as a system in which critical slowing down can be seen before their attacks (seizure). Although there are not many researches on the prediction of seizures using this phenomenon. Recently P. Milanowski, P. Suffczynski, Int. J. Neural Syst.
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, 1650053 (2016) have investigated the application of critical slowing down indicators and surprisingly they found that only in 8% of nearby 300 epileptic patients have the evidence of critical slowing down before seizures. The main goal of this paper is finding the answer of the important question “can we trust that epileptic seizures are bifurcations in the neural system”. In order to find the answer, different studies on the prediction of seizure are investigated and we prove that features which are used in those papers are critical slowing down indicators although they are not aware of it. So we present some reasons for the occurrence of critical slowing down before the seizure. We hope that this study will be a motivation of future studies on the application of critical slowing down indicators for predicting epileptic seizures.
The use of chaos theory in modeling biological signals is becoming increasingly common, especially in EEG signal processing for predicting and detecting different brain states. However, the chaotic ...nature of the sleep EEG signal remains a challenging debate, and the use of nonlinear techniques such as Correlation Dimension, which is a common method for measuring a system's complexity, may lead to erroneous results in non-chaotic systems. To address this issue, in the present study, we attempt to provide an analysis to demonstrate the chaoticity of sleep EEG. The goals of this study are to model and detect the strange attractor of sleep and its stages. We model changes in the sleep attractor dynamics in phase space by exponential regression. Our model indicates that the sleep attractor is the sleep cycle attractor, whose size shrinks during successive cycles, by presenting a new definition of the sleep cycle. We study the EEG dynamics of different sleep stages by introducing two new features based on phase space properties and identify unique chaotic attractors for each sleep stage. We model the geometric changes of these attractors during successive sleep cycles. Our model achieves an accuracy, sensitivity, and specificity of 88.75%, 85.34%, and 83.64% in classifying sleep stages.
Background: Electrical activity of the brain, resulting from electrochemical signaling between neurons, is recorded by electroencephalogram (EEG). The neural network has complex behavior at different ...levels that strongly confirms the nonlinear nature of interactions in the human brain. This study has been designed and implemented with the aim of determining the effects of religious beliefs and the effect of listening to Holy Quran on electrical activity of the brain of the Iranian Persian-speaking Muslim volunteers. Methods: The brain signals of 47 Persian-speaking Muslim volunteers while listening to the Holy Quran consciously, and while listening to the Holy Quran and the Arabic text unconsciously were used. Therefore, due to the nonlinear nature of EEG signals, these signals are studied using approximate entropy, sample entropy, Hurst exponent, and Detrended Fluctuation Analysis. Results: Statistical analysis of the results has shown that listening to the Holy Quran consciously increases approximate entropy and sample entropy, and decreases Hurst Exponent and Detrended Fluctuation Analysis compared to other cases. Conclusion: Consciously listening to the Holy Quran decreases self-similarity and correlation of brain signal and instead increases complexity and dynamicity in the brain.
•A map-based model of a neuron is proposed based on interpretation in phase space.•The model is formulated with the help of the multi-criteria functions.•Various neural behaviors can be generated ...with small structural changes.
Computational models play an essential role in studying and predicting the behavior of a bio-system. Discrete dynamical models, usually known as maps, are important, especially when it comes to the mathematical study of the behavior of the neurons and neural network. Map-based neural models are simple, yet powerful and computationally efficient tools to study complex dynamical systems. In this paper, a one-dimensional map-based neuron model is proposed for which various dynamical behaviors are investigated using phase-space interpretation. In order to reproduce the behaviors observed in the real neurons such as action potential (AP), spike, burst, chaotic burst and, myocardial AP, different multi-criteria functions are formulated. In our proposed model, all the mentioned dynamical behaviors can be obtained only by changing the respective parameter. Therefore, though being simple, in terms of both analytical solutions and numerical calculations, our model is perfectly capable of demonstrating complex behaviors. In this study, the response of the model to various stimuli (excitation current) is explored. The time series analysis, phase-space and cobweb plot are provided as well for each multi-criteria function. Also, the bifurcation analysis with respect to different parameters of the model is carried out.
•Two topological approaches (fractal dimension and persistent homology) based on HRV phase space geometry was suggested to replicate the changes in AF progression.•A new feature based on the initial ...and end Čech radius of each barcode in β1, is defined as “Time of Life” (TOL) to classify AF stages qualitatively.•A neural network was implemented to prove the effectiveness of both TOL and fractal dimension as classification features.•The classification performance was accomplished as 93% accuracy of datasets.•TOL could be used as a tool to predict AF rhythm in patients, who have asymptomatic paroxysmal AF episodes.
In recent years, atrial fibrillation (AF) development from paroxysmal to persistent or permanent forms has become an important issue in cardiovascular disorders. Information about AF pattern of presentation (paroxysmal, persistent, or permanent) was useful in the management of algorithms in each category. This management is aimed at reducing symptoms and stopping severe problems associated with AF. AF classification has been based on time duration and episodes until now. In particular, complexity changes in Heart Rate Variation (HRV) may contain clinically relevant signals of imminent systemic dysregulation. A number of nonlinear methods based on phase space and topological properties can give more insight into HRV abnormalities such as fibrillation. Aiming to provide a nonlinear tool to qualitatively classify AF stages, we proposed two geometrical indices (fractal dimension and persistent homology) based on HRV phase space, which can successfully replicate the changes in AF progression. The study population includes 38 lone AF patients and 20 normal subjects, which are collected from the Physio-Bank database. “Time of Life (TOL)” is proposed as a new feature based on the initial and final Čech radius in the persistent homology diagram. A neural network was implemented to prove the effectiveness of both TOL and fractal dimension as classification features. The accuracy of classification performance was 93%. The proposed indices provide a signal representation framework useful to understand the dynamic changes in AF cardiac patterns and to classify normal and pathological rhythms.
It is proposed a nonlinear system to model highly complex states of rhythms, whose patterns of activity seem irregular. A non-autonomous system which takes into account both exogenous and endogenous ...influences. The dynamic behaviors of its stroboscopic map are investigated, by using triangular systems. The model provides a theoretical framework for addressing cyclic transitions between chaotic sets. The analysis underlines the role of the parameters in the structure and shape of the attractors, so to be in agreement with experimental data.
According to such paradigm, each stimulus would tend to lead the system to its own “liquid-like attractor” which is different from the other one. Compared to other alternative multi-agent modeling ...tools (such as artificial neural networks), in CA the researcher is able to determine the local behavior of individuals as well as their interaction rules and connectivity patterns, both locally and globally in space. ...future studies on this area may be able to demonstrate how perceptual deficits commonly observed in clinical practice (such as face recognition deficits in autistic patients) may be represented by a change in the basic parameters of CA models of visual representation.
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