Stochastic resonance induced by exogenous noise in a model of a neuronal network

Effect of skin conductivity on the electric field induced by transcranial stimulation techniques in different head models

This study aims at quantifying the effect that using different skin conductivity values has on the estimation of the electric (E)-field distribution induced by transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (tDCS) in the brain of two anatomical models. The induced E-field was calculated with numerical simulations inside MIDA and Duke models, assigning to the skin a conductivity value estimated from a multi-layered skin model and three values taken from literature. The effect of skin conductivity variations on the local E-field induced by tDCS in the brain was up to 70%. In TMS, minor local differences, in the order of 20%, were obtained in regions of interest for the onset of possible side effects. Results suggested that an accurate model of the skin is necessary in all numerical studies that aim at precisely estimating the E-field induced during TMS and tDCS applications. This also highlights the importance of further experimental studies on human skin characterization, especially at low frequencies.

Revealing Spectrum Features of Stochastic Neuron Spike Trains

Power spectra of spike trains reveal important properties of neuronal behavior. They exhibit several peaks, whose shape and position depend on applied stimuli and intrinsic biophysical properties, such as input current density and channel noise. The position of the spectral peaks in the frequency domain is not straightforwardly predictable from statistical averages of the interspike intervals, especially when stochastic behavior prevails. In this work, we provide a model for the neuronal power spectrum, obtained from Discrete Fourier Transform and expressed as a series of expected value of sinusoidal terms. The first term of the series allows us to estimate the frequencies of the spectral peaks to a maximum error of a few Hz, and to interpret why they are not harmonics of the first peak frequency. Thus, the simple expression of the proposed power spectral density (PSD) model makes it a powerful interpretative tool of PSD shape, and also useful for neurophysiological studies aimed at extracting information on neuronal behavior from spike train spectra.

Influence of Anatomical Model and Skin Conductivity on the Electric Field Induced in the Head by Transcranial Magnetic Stimulation

Numerical evaluation of the electromagnetic (EM) quantities induced inside the brain during transcranial magnetic stimulation (TMS) applications is a fundamental step to obtain the optimization of the treatment in terms of coil position and current intensity. In this sense, the human head model considered and the electromagnetic properties used to characterize the tissues have an influence on the EM solution. Thus, the aim of this study is to evaluate how different skin conductivities and different computational head models, i.e. the ViP Duke and the MIDA, influence the electric field induced inside the brain by a typical TMS coil.

Stimulation Strategies for Tinnitus Suppression in a Neuron Model

Tinnitus is a debilitating perception of sound in the absence of external auditory stimuli. It may have either a central or a peripheral origin in the cochlea. Experimental studies evidenced that an electrical stimulation of peripheral auditory fibers may alleviate symptoms but the underlying mechanisms are still unknown. In this work, a stochastic neuron model is used, that mimics an auditory fiber affected by tinnitus, to check the effects, in terms of firing reduction, of different kinds of electric stimulations, i.e., continuous wave signals and white Gaussian noise. Results show that both white Gaussian noise and continuous waves at tens of kHz induce a neuronal firing reduction; however, for the same amplitude of fluctuations, Gaussian noise is more efficient than continuous waves. When contemporary applied, signal and noise exhibit a cooperative effect in retrieving neuronal firing to physiological values. These results are a proof of concept that a combination of signal and noise could be delivered through cochlear prosthesis for tinnitus suppression.

Noise-driven neuromorphic tuned amplifier

We study a simple stochastic model of neuronal excitatory and inhibitory interactions. The model is defined on a directed lattice and internodes couplings are modulated by a nonlinear function that mimics the process of synaptic activation. We prove that such a system behaves as a fully tunable amplifier: the endogenous component of noise, stemming from finite size effects, seeds a coherent (exponential) amplification across the chain generating giant oscillations with tunable frequencies, a process that the brain could exploit to enhance, and eventually encode, different signals. On a wider perspective, the characterized amplification process could provide a reliable pacemaking mechanism for biological systems. The device extracts energy from the finite size bath and operates as an out of equilibrium thermal machine, under stationary conditions.

Time resolved dosimetry of human brain exposed to low frequency pulsed magnetic fields

An accurate dosimetry is a key issue to understanding brain stimulation and related interaction mechanisms with neuronal tissues at the basis of the increasing amount of literature revealing the effects on human brain induced by low-level, low frequency pulsed magnetic fields (PMFs). Most literature on brain dosimetry estimates the maximum E field value reached inside the tissue without considering its time pattern or tissue dispersivity. Nevertheless a time-resolved dosimetry, accounting for dispersive tissues behavior, becomes necessary considering that the threshold for an effect onset may vary depending on the pulse waveform and that tissues may filter the applied stimulatory fields altering the predicted stimulatory waveform's size and shape. In this paper a time-resolved dosimetry has been applied on a realistic brain model exposed to the signal presented in Capone et al (2009 J. Neural Transm. 116 257-65), accounting for the broadband dispersivity of brain tissues up to several kHz, to accurately reconstruct electric field and current density waveforms inside different brain tissues. The results obtained by exposing the Duke's brain model to this PMF signal show that the E peak in the brain is considerably underestimated if a simple monochromatic dosimetry is carried out at the pulse repetition frequency of 75 Hz.

Restoring the encoding properties of a stochastic neuron model by an exogenous noise

Here we evaluate the possibility of improving the encoding properties of an impaired neuronal system by superimposing an exogenous noise to an external electric stimulation signal. The approach is based on the use of mathematical neuron models consisting of stochastic HH-like circuit, where the impairment of the endogenous presynaptic inputs is described as a subthreshold injected current and the exogenous stimulation signal is a sinusoidal voltage perturbation across the membrane. Our results indicate that a correlated Gaussian noise, added to the sinusoidal signal can significantly increase the encoding properties of the impaired system, through the Stochastic Resonance (SR) phenomenon. These results suggest that an exogenous noise, suitably tailored, could improve the efficacy of those stimulation techniques used in neuronal systems, where the presynaptic sensory neurons are impaired and have to be artificially bypassed.

The CNP signal is able to silence a supra threshold neuronal model

Several experimental results published in the literature showed that weak pulsed magnetic fields affected the response of the central nervous system. However, the specific biological mechanisms that regulate the observed behaviors are still unclear and further scientific investigation is required. In this work we performed simulations on a neuronal network model exposed to a specific pulsed magnetic field signal that seems to be very effective in modulating the brain activity: the Complex Neuroelectromagnetic Pulse (CNP). Results show that CNP can silence the neurons of a feed-forward network for signal intensities that depend on the strength of the bias current, the endogenous noise level and the specific waveforms of the pulses. Therefore, it is conceivable that a neuronal network model responds to the CNP signal with an inhibition of its activity. Further studies on more realistic neuronal networks are needed to clarify if such an inhibitory effect on neuronal tissue may be the basis of the induced analgesia seen in humans and the antinociceptive effects seen in animals when exposed to the CNP.

Numerical characterization of intraoperative and chronic electrodes in deep brain stimulation

An intraoperative electrode (microelectrode) is used in the deep brain stimulation (DBS) technique to pinpoint the brain target and to choose the best parameters for the electrical stimulus. However, when the intraoperative electrode is replaced with the chronic one (macroelectrode), the observed effects do not always coincide with predictions. To investigate the causes of such discrepancies, a 3D model of the basal ganglia has been considered and realistic models of both intraoperative and chronic electrodes have been developed and numerically solved. Results of simulations of the electric potential (V) and the activating function (AF) along neuronal fibers show that the different geometries and sizes of the two electrodes do not change the distributions and polarities of these functions, but rather the amplitudes. This effect is similar to the one produced by the presence of different tissue layers (edema or glial tissue) in the peri-electrode space. Conversely, an inaccurate positioning of the chronic electrode with respect to the intraoperative one (electric centers not coincident) may induce a completely different electric stimulation in some groups of fibers.

A numerical study to compare stimulations by intraoperative microelectrodes and chronic macroelectrodes in the DBS technique

Deep brain stimulation is a clinical technique for the treatment of parkinson's disease based on the electric stimulation, through an implanted electrode, of specific basal ganglia in the brain. To identify the correct target of stimulation and to choose the optimal parameters for the stimulating signal, intraoperative microelectrodes are generally used. However, when they are replaced with the chronic macroelectrode, the effect of the stimulation is often very different. Here, we used numerical simulations to predict the stimulation of neuronal fibers induced by microelectrodes and macroelectrodes placed in different positions with respect to each other. Results indicate that comparable stimulations can be obtained if the chronic macroelectrode is correctly positioned with the same electric center of the intraoperative microelectrode. Otherwise, some groups of fibers may experience a completely different electric stimulation.