Inferring a simple mechanism for alpha-blocking by fitting a neural population model to EEG spectra.

Alpha blocking, a phenomenon where the alpha rhythm is reduced by attention to a visual, auditory, tactile or cognitive stimulus, is one of the most prominent features of human electroencephalography (EEG) signals. Here we identify a simple physiological mechanism by which opening of the eyes causes attenuation of the alpha rhythm. We fit a neural population model to EEG spectra from 82 subjects, each showing a different degree of alpha blocking upon opening of their eyes. Though it has been notoriously difficult to estimate parameters by fitting such models, we show how, by regularizing the differences in parameter estimates between eyes-closed and eyes-open states, we can reduce the uncertainties in these differences without significantly compromising fit quality. From this emerges a parsimonious explanation for the spectral differences between states: Changes to just a single parameter, pei, corresponding to the strength of a tonic excitatory input to the inhibitory cortical population, are sufficient to explain the reduction in alpha rhythm upon opening of the eyes. We detect this by comparing the shift in each model parameter between eyes-closed and eyes-open states. Whereas changes in most parameters are weak or negligible and do not scale with the degree of alpha attenuation across subjects, the change in pei increases monotonically with the degree of alpha blocking observed. These results indicate that opening of the eyes reduces alpha activity by increasing external input to the inhibitory cortical population.

Parameter estimation and identifiability in a neural population model for electro-cortical activity.

Electroencephalography (EEG) provides a non-invasive measure of brain electrical activity. Neural population models, where large numbers of interacting neurons are considered collectively as a macroscopic system, have long been used to understand features in EEG signals. By tuning dozens of input parameters describing the excitatory and inhibitory neuron populations, these models can reproduce prominent features of the EEG such as the alpha-rhythm. However, the inverse problem, of directly estimating the parameters from fits to EEG data, remains unsolved. Solving this multi-parameter non-linear fitting problem will potentially provide a real-time method for characterizing average neuronal properties in human subjects. Here we perform unbiased fits of a 22-parameter neural population model to EEG data from 82 individuals, using both particle swarm optimization and Markov chain Monte Carlo sampling. We estimate how much is learned about individual parameters by computing Kullback-Leibler divergences between posterior and prior distributions for each parameter. Results indicate that only a single parameter, that determining the dynamics of inhibitory synaptic activity, is directly identifiable, while other parameters have large, though correlated, uncertainties. We show that the eigenvalues of the Fisher information matrix are roughly uniformly spaced over a log scale, indicating that the model is sloppy, like many of the regulatory network models in systems biology. These eigenvalues indicate that the system can be modeled with a low effective dimensionality, with inhibitory synaptic activity being prominent in driving system behavior.

Four dimensional chaos and intermittency in a mesoscopic model of the electroencephalogram.

The occurrence of so-called four dimensional chaos in dynamical systems represented by coupled, nonlinear, ordinary differential equations is rarely reported in the literature. In this paper, we present evidence that Liley's mesoscopic theory of the electroencephalogram (EEG), which has been used to describe brain activity in a variety of clinically relevant contexts, possesses a chaotic attractor with a Kaplan-Yorke dimension significantly larger than three. This accounts for simple, high order chaos for a physiologically admissible parameter set. Whilst the Lyapunov spectrum of the attractor has only one positive exponent, the contracting dimensions are such that the integer part of the Kaplan-Yorke dimension is three, thus giving rise to four dimensional chaos. A one-parameter bifurcation analysis with respect to the parameter corresponding to extracortical input is conducted, with results indicating that the origin of chaos is due to an inverse period doubling cascade. Hence, in the vicinity of the high order, strange attractor, the model is shown to display intermittent behavior, with random alternations between oscillatory and chaotic regimes. This phenomenon represents a possible dynamical justification of some of the typical features of clinically established EEG traces, which can arise in the case of burst suppression in anesthesia and epileptic encephalopathies in early infancy.

Effect of embedded optical fibres on the mechanical properties of cochlear electrode arrays.

Incorporating optical fibres in cochlear electrode arrays has been proposed to provide sensors to help minimise insertion trauma and also for the delivery of light in optical nerve stimulation applications. However, embedding an optical fibre into an electrode array may change its stiffness properties, which can affect the level of trauma during insertion. This report uses measurements of buckling and deflection force to compare the stiffness properties of a range of cochlear electrode arrays (Nucleus straight array, rat array, cat array and guinea pig array) with custom arrays containing an embedded optical fibre. The cladding diameters of the optical fibres tested were 125 µm, 80 µm and 50 µm. The results show that the stiffness of the optical-fibre-embedded arrays is related to the diameter of the optical fibre. Comparison with wired arrays suggests optical fibres with a diameter of 50 µm could be embedded into an electrode array without significantly changing the stiffness properties of the array.

Extensive Four-Dimensional Chaos in a Mesoscopic Model of the Electroencephalogram.

BACKGROUND: In a previous work (Dafilis et al. in Chaos 23(2):023111, 2013), evidence was presented for four-dimensional chaos in Liley's mesoscopic model of the electroencephalogram. The study was limited to one parameter set of the model equations. FINDINGS: In this report we expand that result by presenting evidence for the extension of four-dimensional chaotic behavior to a large area of the biologically admissible parameter space. A two-parameter bifurcation analysis highlights the complexity of the dynamical landscape involved in the creation of such chaos. CONCLUSIONS: The extensive presence of high-order chaos in a well-established physiological model of electrorhythmogenesis further emphasizes the applicability and relevance of mean field mesoscopic models in the description of brain activity at theoretical, experimental, and clinical levels.

Drug-induced modification of the system properties associated with spontaneous human electroencephalographic activity.

The benzodiazepine (BZ) class of minor tranquilizers are important modulators of the gamma-amino butyric acid (GABA(A))/BZ receptor complex that are well known to affect the spectral properties of spontaneous electroencephalographic activity. While it is experimentally well established that the BZs reduce total alpha band (8-13 Hz) power and increase total beta band (13-30 Hz) power, it is unclear what the physiological basis for this effect is. Based on a detailed theory of cortical electrorhythmogenesis it is conjectured that such an effect is explicable in terms of the modulation of GABAergic neurotransmission within locally connected populations of excitatory and inhibitory cortical neurons. Motivated by this theory, fixed order autoregressive moving average (ARMA) models were fitted to spontaneous eyes-closed electroencephalograms recorded from subjects before and approximately 2 h after the oral administration of a single 1 mg dose of the BZ alprazolam. Subsequent pole-zero analysis revealed that BZs significantly transform the dominant system pole such that its frequency and damping increase. Comparisons of ARMA derived power spectra with fast Fourier transform derived spectra indicate an enhanced ability to identify benzodiazepine induced electroencephalographic changes. This experimental result is in accord with the theoretical predictions implying that alprazolam enhances inhibition acting on inhibitory neurons more than inhibition acting on excitatory neurons. Further such a result is consistent with reported cortical neuronal distributions of the various GABA(A) receptor pharmacological subtypes. Therefore physiologically specified fixed order ARMA modeling is expected to become an important tool for the systematic investigation and modeling of a wide range of cortically acting compounds.

Robust chaos in a model of the electroencephalogram: Implications for brain dynamics.

Various techniques designed to extract nonlinear characteristics from experimental time series have provided no clear evidence as to whether the electroencephalogram (EEG) is chaotic. Compounding the lack of firm experimental evidence is the paucity of physiologically plausible theories of EEG that are capable of supporting nonlinear and chaotic dynamics. Here we provide evidence for the existence of chaotic dynamics in a neurophysiologically plausible continuum theory of electrocortical activity and show that the set of parameter values supporting chaos within parameter space has positive measure and exhibits fat fractal scaling. (c) 2001 American Institute of Physics.

Laser exposure of gold nanorods can induce intracellular calcium transients.

Uncoated and poly(styrene sulphonate) (PSS)-coated gold nanorods were taken up by NG108-15 neuronal cells. Exposure to 780 nm laser light at the plasmon resonance wavelength of the gold nanorods was found to induce intracellular Ca(2+) transients. The higher Ca(2+) peaks were observed at lower laser doses, with the highest levels obtained at a radiant exposure of 0.33 J/cm(2) . In contrast, the cells without nanoparticles showed a consistently small response, independent of the laser dose. These initial results open up new opportunities for peripheral nerve regeneration treatments and for more efficient optical stimulation techniques.

Modeling of the temporal effects of heating during infrared neural stimulation.

A model of infrared neural stimulation (INS) has been developed to allow the temporal characteristics of different stimulation parameters and geometries to be better understood. The model uses a finite element approach to solve the heat equation and allow detailed analysis of heat during INS with both microsecond and millisecond laser pulses. When compared with experimental data, the model provides insight into the mechanisms behind INS. In particular, the analysis suggests that there may be two broad regimes of INS: the process tends to be limited by the total pulse energy for pulse lengths below 100 µs, while the temperature gradient with respect to time becomes more important above 100 µs.

Temporal stability of regression-based electrooculographic correction coefficients.

A means of accounting for ocular artifact in the electroencephalograph (EEG) is to subtract portions (Bs) of ocular voltage measured by the electrooculograph (EOG) from the EEG. Some such EOG correction methods calculate Bs at one time and use these to correct data recorded at a different time; these require information about the temporal stability of the Bs. This study investigated the stability of Bs over a 2-hr EEG recording session. Participants performed 5 eye movement tasks, each separated by 30 min. Four EOG correction methods were then used to calculate Bs from each of the 5 data sets, resulting in VEOG, HEOG, and REOG (where appropriate) Bs for each methods at each of the 5 time points. We did not find evidence that Bs changed over the 2-hr period, nor of any difference in temporal stability between the methods. This study suggests that it is appropriate to employ Bs calculated from calibration trials to correct data recorded within at least a 2-hr time window.

A test of four EOG correction methods using an improved validation technique.

A group of methods that are employed for removing ocular artifact from the electroencephalogram (EEG) is referred to as electrooculogram (EOG) correction methods. These use least-square linear regression, and the relative success of these is yet to be established. Improving on previous EOG correction validation studies, we present a new validation technique (with greater face validity) and use it to compare four commonly employed EOG correction methods. Data consisted of ERP traces to auditory stimuli that were embedded in up, down, left and right eye movements (EMs), recorded from 24 subjects. A 'Peak Difference' validation measure was employed, which determined the magnitude of the difference of two auditory N100 peaks (those associated with EMs with opposing polarities). All correction methods produced data that was better than not correcting at all. EOG correction methods that accounted for vertical EM, horizontal EM and blink artifact separately using separate EOG channels, produced the best corrections, with some further advantage in methods that enhanced signal (EOG) to noise (EEG) ratios when calculating correction coefficients.

Is ocular voltage propagation to the electroencephalogram frequency dependent?

Conventional eye correction methods subtract portions (propagation coefficients; Bs) of electrooculogram (EOG) voltages from the electroencephalogram (EEG). The frequency domain approach (FDA) uses different Bs for different frequencies whereas the time domain approach (TDA) uses the same Bs. To determine whether measured Bs are dependent on frequency and whether one should employ frequency-dependent methods, 20 min of EEG from eye movement (EM) and blink data (24 participants) were recorded, and Bs were calculated for eye movement ERPs of differing signal-to-noise ratios for frequency bands ranging from 0 to 40 Hz and compared. At high signal to noise, EM Bs for different frequency bands did not differ, for both vertical and horizontal EOG, at all scalp sites tested. There were small differences in blink Bs for different bands, but smaller than the margin of error of this analysis. This indicates that TDA may be more appropriate than FDA.

A spatially continuous mean field theory of electrocortical activity.

A set of nonlinear continuum field equations is presented which describes the dynamics of neural activity in cortex. These take into account the most pertinent anatomical and physiological features found in cortex with all parameter values obtainable from independent experiment. Derivation of a white noise fluctuation spectrum from a linearized set of equations shows the presence of strong resonances that correspond to electroencephalographically observed 0.3-4 Hz (mammalian delta), 4-8 Hz (mammalian theta), 8-13 Hz (mammalian alpha) and >13 Hz (mammalian beta) activity. Numerical solutions of a full set of one-dimensional nonlinear equations include properties analogous to cortical evoked potentials, travelling waves at experimentally observed velocities, threshold type spike activity and limit cycle, chaotic and noise driven oscillations at the frequency of the mammalian alpha rhythm. All these types of behaviour are generated with parameters that are within ranges reported experimentally. The strong dependence of the phenomena observed on inhibitory-inhibitory interactions is demonstrated. These results suggest that the classically described alpha may be instantiated in a number of qualitatively distinct dynamical regimes, all of which depend on the integrity of inhibitory-inhibitory population interactions.