Wai-Lok Chan

Vibrational resonance in neuron populations

In this paper different topologies of populations of FitzHugh-Nagumo neurons have been introduce to investigate the effect of high-frequency driving on the response of neuron populations to a subthreshold low-frequency signal. We show that optimal amplitude of high-frequency driving enhances the response of neuron populations to a subthreshold low-frequency input and the optimal amplitude dependences on the connection among the neurons. By analyzing several kinds of topology (i.e., random and small world) different behaviors have been observed. Several topologies behave in an optimal way with respect to the range of low-frequency amplitude leading to an improvement in the stimulus response coherence, while others with respect to the maximum values of the performance index. However, the best results in terms of both the suitable amplitude of high-frequency driving and high stimulus response coherence have been obtained when the neurons have been connected in a small-world topology.

Chaotic phase synchronization in small-world networks of bursting neurons

We investigate the chaotic phase synchronization in a system of coupled bursting neurons in small-world networks. A transition to mutual phase synchronization takes place on the bursting time scale of coupled oscillators, while on the spiking time scale, they behave asynchronously. It is shown that phase synchronization is largely facilitated by a large fraction of shortcuts, but saturates when it exceeds a critical value. We also study the external chaotic phase synchronization of bursting oscillators in the small-world network by a periodic driving signal applied to a single neuron. It is demonstrated that there exists an optimal small-world topology, resulting in the largest peak value of frequency locking interval in the parameter plane, where bursting synchronization is maintained, even with the external driving. The width of this interval increases with the driving amplitude, but decrease rapidly with the network size. We infer that the externally applied driving parameters outside the frequency locking region can effectively suppress pathologically synchronized rhythms of bursting neurons in the brain.

Exploring how extracellular electric field modulates neuron activity through dynamical analysis of a two-compartment neuron model

To investigate how extracellular electric field modulates neuron activity, a reduced two-compartment neuron model in the presence of electric field is introduced in this study. Depending on neuronal geometric and internal coupling parameters, the behaviors of the model have been studied extensively. The neuron model can exist in quiescent state or repetitive spiking state in response to electric field stimulus. Negative electric field mainly acts as inhibitory stimulus to the neuron, positive weak electric field could modulate spiking frequency and spike timing when the neuron is already active, and positive electric fields with sufficient intensity could directly trigger neuronal spiking in the absence of other stimulations. By bifurcation analysis, it is observed that there is saddle-node on invariant circle bifurcation, supercritical Hopf bifurcation and subcritical Hopf bifurcation appearing in the obtained two parameter bifurcation diagrams. The bifurcation structures and electric field thresholds for triggering neuron firing are determined by neuronal geometric and coupling parameters. The model predicts that the neurons with a nonsymmetric morphology between soma and dendrite, are more sensitive to electric field stimulus than those with the spherical structure. These findings suggest that neuronal geometric features play a crucial role in electric field effects on the polarization of neuronal compartments. Moreover, by determining the electric field threshold of our biophysical model, we could accurately distinguish between suprathreshold and subthreshold electric fields. Our study highlights the effects of extracellular electric field on neuronal activity from the biophysical modeling point of view. These insights into the dynamical mechanism of electric field may contribute to the investigation and development of electromagnetic therapies, and the model in our study could be further extended to a neuronal network in which the effects of electric fields on network activity may be investigated.

Neuronal spike initiation modulated by extracellular electric fields.

Based on a reduced two-compartment model, the dynamical and biophysical mechanism underlying the spike initiation of the neuron to extracellular electric fields is investigated in this paper. With stability and phase plane analysis, we first investigate in detail the dynamical properties of neuronal spike initiation induced by geometric parameter and internal coupling conductance. The geometric parameter is the ratio between soma area and total membrane area, which describes the proportion of area occupied by somatic chamber. It is found that varying it could qualitatively alter the bifurcation structures of equilibrium as well as neuronal phase portraits, which remain unchanged when varying internal coupling conductance. By analyzing the activating properties of somatic membrane currents at subthreshold potentials, we explore the relevant biophysical basis of spike initiation dynamics induced by these two parameters. It is observed that increasing geometric parameter could greatly decrease the intensity of the internal current flowing from soma to dendrite, which switches spike initiation dynamics from Hopf bifurcation to SNIC bifurcation; increasing internal coupling conductance could lead to the increase of this outward internal current, whereas the increasing range is so small that it could not qualitatively alter the spike initiation dynamics. These results highlight that neuronal geometric parameter is a crucial factor in determining the spike initiation dynamics to electric fields. The finding is useful to interpret the functional significance of neuronal biophysical properties in their encoding dynamics, which could contribute to uncovering how neuron encodes electric field signals.

Impact of delays on the synchronization transitions of modular neuronal networks with hybrid synapses

The combined effects of the information transmission delay and the ratio of the electrical and chemical synapses on the synchronization transitions in the hybrid modular neuronal network are investigated in this paper. Numerical results show that the synchronization of neuron activities can be either promoted or destroyed as the information transmission delay increases, irrespective of the probability of electrical synapses in the hybrid-synaptic network. Interestingly, when the number of the electrical synapses exceeds a certain level, further increasing its proportion can obviously enhance the spatiotemporal synchronization transitions. Moreover, the coupling strength has a significant effect on the synchronization transition. The dominated type of the synapse always has a more profound effect on the emergency of the synchronous behaviors. Furthermore, the results of the modular neuronal network structures demonstrate that excessive partitioning of the modular network may result in the dramatic detriment of neuronal synchronization. Considering that information transmission delays are inevitable in intra- and inter-neuronal networks communication, the obtained results may have important implications for the exploration of the synchronization mechanism underlying several neural system diseases such as Parkinsons Disease.

EFFECTS OF EXTREMELY LOW-FREQUENCY MAGNETIC FIELDS ON THE RESPONSE OF A CONDUCTANCE-BASED NEURON MODEL

To provide insights into the modulation of neuronal activity by extremely low-frequency (ELF) magnetic field (MF), we present a conductance-based neuron model and introduce ELF sinusoidal MF as an additive voltage input. By analyzing spike times and spiking frequency, it is observed that neuron with distinct spiking patterns exhibits different response properties in the presence of MF exposure. For tonic spiking neuron, the perturbations of MF exposure on spike times is maximized at the harmonics of neuronal intrinsic spiking frequency, while it is maximized at the harmonics of bursting frequency for burst spiking neuron. As MF intensity increases, the perturbations also increase. Compared with tonic spiking, bursting dynamics are less sensitive to the perturbations of ELF MF exposure. Further, ELF MF exposure is more prone to perturb neuronal spike times relative to spiking frequency. Our finding suggests that the resonance may be one of the neural mechanisms underlying the modulatory effects of the low-intensity ELF MFs on neuronal activities. The results highlight the impacts of ELF MFs exposure on neuronal activity from the single cell level, and demonstrate various factors including ELF MF properties and neuronal spiking characteristics could determine the outcome of exposure. These insights into the mechanism of MF exposure may be relevant for the design of multi-intensity magnetic stimulus protocols, and may even contribute to the interpretation of MF effects on the central nervous systems.

Ordinal pattern based complexity analysis for EEG activity evoked by manual acupuncture in healthy subjects

Manual acupuncture (MA) is widely used in Traditional Chinese Medicine clinic for pain treatment and controlling stress. To investigate how MA modulates brain activities, electroencephalograph (EEG) signals are recorded with 20 channels by MA at ST36 of right leg in 11 healthy subjects during rest. Two novel nonlinear measures based on ordinal patterns of EEG series, i.e. permutation entropy (PE) and order index (OI), are adopted to investigate the nonlinear complexity characteristic in EEG data at different acupuncture states. It is observed that the recorded EEG series during and after MA have higher PE values and lower OI values compared to before MA. The results show that MA at ST36 can increase EEG complexity, which is especially obvious during MA. Our findings suggest that the PE and OI measures are promising methods to reveal EEG dynamical changes associated with MA stimulus, which could provide a potential for further exploring the interactions between acupuncture and brain activity. Moreover, these preliminary conclusions highlight the beneficial modulations of brain activity by MA, which could contribute to understanding the acupuncture effects on brain, as well as the neurophysiological mechanisms underlying MA.

Propagation of spiking regularity and double coherence resonance in feedforward networks

We investigate the propagation of spiking regularity in noisy feedforward networks (FFNs) based on FitzHugh-Nagumo neuron model systematically. It is found that noise could modulate the transmission of firing rate and spiking regularity. Noise-induced synchronization and synfire-enhanced coherence resonance are also observed when signals propagate in noisy multilayer networks. It is interesting that double coherence resonance (DCR) with the combination of synaptic input correlation and noise intensity is finally attained after the processing layer by layer in FFNs. Furthermore, inhibitory connections also play essential roles in shaping DCR phenomena. Several properties of the neuronal network such as noise intensity, correlation of synaptic inputs, and inhibitory connections can serve as control parameters in modulating both rate coding and the order of temporal coding.

A combined method to estimate parameters of the thalamocortical model from a heavily noise-corrupted time series of action potential

A combined method composing of the unscented Kalman filter (UKF) and the synchronization-based method is proposed for estimating electrophysiological variables and parameters of a thalamocortical (TC) neuron model, which is commonly used for studying Parkinsons disease for its relay role of connecting the basal ganglia and the cortex. In this work, we take into account the condition when only the time series of action potential with heavy noise are available. Numerical results demonstrate that not only this method can estimate model parameters from the extracted time series of action potential successfully but also the effect of its estimation is much better than the only use of the UKF or synchronization-based method, with a higher accuracy and a better robustness against noise, especially under the severe noise conditions. Considering the rather important role of TC neuron in the normal and pathological brain functions, the exploration of the method to estimate the critical parameters could have important implications for the study of its nonlinear dynamics and further treatment of Parkinsons disease.

The asymptotic structure of the Morris-Lecar model

In this paper, the asymptotic structure of the Morris-Lecar (ML) model in the concepts of slow manifold and fast foliation is analyzed based on the Tikhonovs theorem. The rationality of the well-known V, N reduced ML system is discussed, and a new V, N reduced ML system is derived from a more reasonable asymptotic structures of the original ML system, which we propose.