Synchronization of neuron population subject to steady DC electric field induced by magnetic stimulation

Topology of eeg wave fronts

Whenever one attempts to comb a hairy ball flat, there will always be at least one tuft of hair at one point on the ball. This seemingly worthless sentence is an informal description of the hairy ball theorem, an invaluable mathematical weapon that has been proven useful to describe a variety of physical/biological processes/phenomena in terms of topology, rather than classical cause/effect relationships. In this paper we will focus on the electrical brain field-electroencephalogram (EEG). As a starting point we consider the recently-raised observation that, when electromagnetic oscillations propagate with a spherical wave front, there must be at least one point of the tangential components of the vector fields where the electromagnetic field vanishes. We show how this description holds also for the electric waves produced by the brain and detectable by EEG. Once located these zero-points in EEG traces, we confirm that they are able to modify the electric wave fronts detectable in the brain. This sheds new light on the functional features of a nonlinear, metastable nervous system at the edge of chaos, based on the neuroscientific model of Operational Architectonics of brain-mind functioning. As an example of practical application of this theorem, we provide testable previsions, suggesting the proper location of transcranial magnetic stimulation's coils to improve the clinical outcomes of drug-resistant epilepsy.

Collective responses in electrical activities of neurons under field coupling

Synapse coupling can benefit signal exchange between neurons and information encoding for neurons, and the collective behaviors such as synchronization and pattern selection in neuronal network are often discussed under chemical or electric synapse coupling. Electromagnetic induction is considered at molecular level when ion currents flow across the membrane and the ion concentration is fluctuated. Magnetic flux describes the effect of time-varying electromagnetic field, and memristor bridges the membrane potential and magnetic flux according to the dimensionalization requirement. Indeed, field coupling can contribute to the signal exchange between neurons by triggering superposition of electric field when synapse coupling is not available. A chain network is designed to investigate the modulation of field coupling on the collective behaviors in neuronal network connected by electric synapse between adjacent neurons. In the chain network, the contribution of field coupling from each neuron is described by introducing appropriate weight dependent on the position distance between two neurons. Statistical factor of synchronization is calculated by changing the external stimulus and weight of field coupling. It is found that the synchronization degree is dependent on the coupling intensity and weight, the synchronization, pattern selection of network connected with gap junction can be modulated by field coupling.

The Effects of Medium Spiny Neuron Morphologcial Changes on Basal Ganglia Network under External Electric Field: A Computational Modeling Study

The damage of dopaminergic neurons that innervate the striatum has been considered to be the proximate cause of Parkinson's disease (PD). In the dopamine-denervated state, the loss of dendritic spines and the decrease of dendritic length may prevent medium spiny neuron (MSN) from receiving too much excitatory stimuli from the cortex, thereby reducing the symptom of Parkinson's disease. However, the reduction in dendritic spine density obtained by different experiments is significantly different. We developed a biological-based network computational model to quantify the effect of dendritic spine loss and dendrites tree degeneration on basal ganglia (BG) signal regulation. Through the introduction of error index (EI), which was used to measure the attenuation of the signal, we explored the amount of dendritic spine loss and dendritic trees degradation required to restore the normal regulatory function of the network, and found that there were two ranges of dendritic spine loss that could reduce EI to normal levels in the case of dopamine at a certain level, this was also true for dendritic trees. However, although these effects were the same, the mechanisms of these two cases were significant difference. Using the method of phase diagram analysis, we gained insight into the mechanism of signal degradation. Furthermore, we explored the role of cortex in MSN morphology changes dopamine depletion-induced and found that proper adjustments to cortical activity do stop the loss in dendritic spines induced by dopamine depleted. These results suggested that modifying cortical drive onto MSN might provide a new idea on clinical therapeutic strategies for Parkinson's disease.

Global asymptotic stability of complex-valued neural networks with additive time-varying delays

In this paper, we extensively study the global asymptotic stability problem of complex-valued neural networks with leakage delay and additive time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional and applying newly developed complex valued integral inequalities, sufficient conditions for the global asymptotic stability of proposed neural networks are established in the form of complex-valued linear matrix inequalities. This linear matrix inequalities are efficiently solved by using standard available numerical packages. Finally, three numerical examples are given to demonstrate the effectiveness of the theoretical results.

A new theoretical model for transmembrane potential and ion currents induced in a spherical cell under low frequency electromagnetic field

Time-varying electromagnetic fields (EMF) can induce some physiological effects in neuronal tissues, which have been explored in many applications such as transcranial magnetic stimulation. Although transmembrane potentials and induced currents have already been the subjects of many theoretical studies, most previous works about this topic are mainly completed by utilizing Maxwell's equations, often by solving a Laplace equation. In previous studies, cells were often considered to be three-compartment models with different electroconductivities in different regions (three compartments are often intracellular regions, membrane, and extracellular regions). However, models like that did not take dynamic ion channels into consideration. Therefore, one cannot obtain concrete ionic current changes such as potassium current change or sodium current change by these models. The aim of the present work is to present a new and more detailed model for calculating transmembrane potentials and ionic currents induced by time-varying EMF. Equations used in the present paper originate from Nernst-Plank equations, which are ionic current-related equations. The main work is to calculate ionic current changes induced by EMF exposure, and then transmembrane potential changes are calculated with Hodgkin-Huxley model. Bioelectromagnetics. 37:481-492, 2016. © 2016 Wiley Periodicals, Inc.

Computational modeling of neurostimulation in brain diseases

Neurostimulation as a therapeutic tool has been developed and used for a range of different diseases such as Parkinson's disease, epilepsy, and migraine. However, it is not known why the efficacy of the stimulation varies dramatically across patients or why some patients suffer from severe side effects. This is largely due to the lack of mechanistic understanding of neurostimulation. Hence, theoretical computational approaches to address this issue are in demand. This chapter provides a review of mechanistic computational modeling of brain stimulation. In particular, we will focus on brain diseases, where mechanistic models (e.g., neural population models or detailed neuronal models) have been used to bridge the gap between cellular-level processes of affected neural circuits and the symptomatic expression of disease dynamics. We show how such models have been, and can be, used to investigate the effects of neurostimulation in the diseased brain. We argue that these models are crucial for the mechanistic understanding of the effect of stimulation, allowing for a rational design of stimulation protocols. Based on mechanistic models, we argue that the development of closed-loop stimulation is essential in order to avoid inference with healthy ongoing brain activity. Furthermore, patient-specific data, such as neuroanatomic information and connectivity profiles obtainable from neuroimaging, can be readily incorporated to address the clinical issue of variability in efficacy between subjects. We conclude that mechanistic computational models can and should play a key role in the rational design of effective, fully integrated, patient-specific therapeutic brain stimulation.

An ephaptic transmission model of CA3 pyramidal cells: an investigation into electric field effects

Extracellular electric fields existing throughout the living brain affect the neural coding and information processing via ephaptic transmission, independent of synapses. A two-compartment whole field effect model (WFEM) of pyramidal neurons embedded within a resistive array which simulates the extracellular medium i.e. ephapse is developed to study the effects of electric field on neuronal behaviors. We derive the two linearized filed effect models (LFEM-1 and LFEM-2) from WFEM at the stable resting state. Through matching these simplified models to the subthreshold membrane response in experiments of the resting pyramidal cells exposed to applied electric fields, we not only verify our proposed model's validity but also found the key parameters which dominate subthreshold frequency response characteristic. Moreover, we find and give its underlying biophysical mechanism that the unsymmetrical properties of active ion channels results in the very different low-frequency response of somatic and dendritic compartments. Following, WFEM is used to investigate both direct-current (DC) and alternating-current field effect on the neural firing patterns by bifurcation analyses. We present that DC electric field could modulate neuronal excitability, with the positive field improving the excitability, the modest negative field suppressing the excitability, but interestingly, the larger negative field re-exciting the neuron back into spiking behavior. The neuron exposed to the sinusoidal electric field exhibits abundant firing patterns sensitive to the input frequency and intensity. In addition, the electrical properties of ephapse can modulate the efficacy of field effect. Our simulated results are qualitatively in line with the relevant experimental results and can explain some experimental phenomena. Furthermore, they are helpful to provide the predictions which can be tested in future experiments.

A linear model for characterization of synchronization frequencies of neural networks

The synchronization frequency of neural networks and its dynamics have important roles in deciphering the working mechanisms of the brain. It has been widely recognized that the properties of functional network synchronization and its dynamics are jointly determined by network topology, network connection strength, i.e., the connection strength of different edges in the network, and external input signals, among other factors. However, mathematical and computational characterization of the relationships between network synchronization frequency and these three important factors are still lacking. This paper presents a novel computational simulation framework to quantitatively characterize the relationships between neural network synchronization frequency and network attributes and input signals. Specifically, we constructed a series of neural networks including simulated small-world networks, real functional working memory network derived from functional magnetic resonance imaging, and real large-scale structural brain networks derived from diffusion tensor imaging, and performed synchronization simulations on these networks via the Izhikevich neuron spiking model. Our experiments demonstrate that both of the network synchronization strength and synchronization frequency change according to the combination of input signal frequency and network self-synchronization frequency. In particular, our extensive experiments show that the network synchronization frequency can be represented via a linear combination of the network self-synchronization frequency and the input signal frequency. This finding could be attributed to an intrinsically-preserved principle in different types of neural systems, offering novel insights into the working mechanism of neural systems.