Low dimensional model of bursting neurons.

A computationally efficient, biophysically-based model of neuronal behavior is presented; it incorporates ion channel dynamics in its two fast ion channels while preserving simplicity by representing only one slow ion current. The model equations are shown to provide a wide array of physiological dynamics in terms of spiking patterns, bursting, subthreshold oscillations, and chaotic firing. Despite its simplicity, the model is capable of simulating an extensive range of spiking patterns. Several common neuronal behaviors observed in vivo are demonstrated by varying model parameters. These behaviors are classified into dynamical classes using phase diagrams whose boundaries in parameter space prove to be accurately delineated by linear stability analysis. This simple model is suitable for use in large scale simulations involving neural field theory or neuronal networks.

Prediction and verification of nonlinear sleep spindle harmonic oscillations.

This paper examines nonlinear effects in a neural field model of the corticothalamic system to predict the EEG power spectrum of sleep spindles. Nonlinearity in the thalamic relay nuclei gives rise to a spindle harmonic visible in the cortical EEG. By deriving an analytic expression for nonlinear spectrum, the power in the spindle harmonic is predicted to scale quadratically with the power in the spindle oscillation. By isolating sleep spindles from background sleep in experimental EEG data, the spindle harmonic is directly observed.

Automated characterization of multiple alpha peaks in multi-site electroencephalograms.

The identification of alpha rhythm in the human electroencephalogram (EEG) is generally a laborious task involving visual inspection of the spectrum. Moreover the occurrence of multiple alpha rhythms is often overlooked. This paper seeks to automate the process of identifying alpha peaks and quantifying their frequency, amplitude and width as a function of position on the scalp. Experimental EEG was fitted with parameterized spectra spanning the alpha range, with results categorized by multi-site criteria into three distinct classes: no distinguishable alpha peak, a single alpha peak, and two alpha peaks. The technique avoids visual bias, integrates spatial information, and is automated. We show that multiple alpha peaks are a common feature of many spectra.

Mean field model of acetylcholine mediated dynamics in the thalamocortical system.

A recent continuum model of the large scale electrical activity of the thalamocortical system is generalized to include cholinergic modulation. The model is examined analytically and numerically to determine the effect of acetylcholine (ACh) on its steady states, linear stability, spectrum, and temporal responses. Changing the ACh concentration moves the system between zones of one, three, and five steady states, showing that neuromodulation of synaptic strength is a possible mechanism by which multiple steady states emerge in the brain. The lowest firing rate steady state is always stable, and subsequent fixed points alternate between stable and unstable. Increasing ACh concentration changes the form of the spectrum. Increasing the tonic level of ACh concentration increases the magnitudes of the N100 and P200 in the evoked response potential (ERP), without changing the timing of these peaks. Driving the system with a pulse of cholinergic activity results in a transient increase in the firing rate of cortical neurons that lasts over 10s. Step-like increases in cortical ACh concentration cause increases in the firing rate of cortical neurons, with rapid responses due to fast acting nicotinic receptors and slower responses due to muscarinic receptor suppression of intracortical connections.

Neural mechanisms of ERP change: combining insights from electrophysiology and mathematical modeling.

Using a standardized database of EEG data, recorded during the habituation and oddball paradigms, changes in the auditory event-related potential (ERP) are demonstrated on the time scale of seconds and minutes. Based on previous research and a mathematical model of neural activity, neural mechanisms that could account for these changes are proposed. When the stimulus tones are not relevant to a task, N100 magnitude decreases substantially for the first repetition of a stimulus pattern and increases in response to a variant tone. It is argued these short-term changes are consistent with the hypothesis that there is a refractory period in the neural elements underlying the ERP. In the oddball paradigm, when the stimulus tones are task-relevant, the magnitudes of both N100 and P200 for backgrounds decrease over the entire six-minute recording session. It is argued that these changes are mediated by a decreasing arousal level, and consistent with this, a subject's electrodermal activity (EDA) is shown to reduce over the recording session. By fitting ERPs generated by a biophysical model of neural activity, it is shown that the changes in the background ERPs over the recording session can be reproduced by changing the strength of connections between populations of cortical neurons. For ERPs elicited by infrequent stimuli, there is no corresponding trend in the magnitudes of N100 or P300 components. The effects of stimuli serial order on ERPs are also assessed, showing that the N100 for background ERPs and the N100 and P300 for target ERPs increases as the probability, and expectancy, of receiving a task relevant stimulus increases. Cortical neuromodulation by acetylcholine (ACh) is proposed as a candidate mechanism to mediate the ERP changes associated with attention and arousal.

Physiologically based arousal state estimation and dynamics.

A neural field model of the brain is used to represent brain states using physiologically based parameters rather than arbitrary, discrete sleep stages. Each brain state is represented as a point in a physiologically parametrized space. Over time, changes in brain state cause these points to trace continuous trajectories, unlike the artificial discrete jumps in sleep stage that occur with traditional sleep staging. The discrete Rechtschaffen and Kales sleep stages are associated with regions in the physiological parameter space based on their electroencephalographic features, which enables interpretation of traditional sleep stages in terms of physiological trajectories. Wake states are found to be associated with strong positive corticothalamic feedback compared to sleep. The existence of physiologically valid trajectories between brain states in the model is demonstrated. Actual trajectories for an individual can be determined by fitting the model using EEG alone, and enable analysis of the physiological differences between subjects.

Eye movements reflect impaired face processing in patients with schizophrenia.

BACKGROUND: Impaired processing of faces in patients with schizophrenia may underlie aspects of disturbance in their social interaction. This study examined patterns of eye fixation in subjects with schizophrenia and non-psychiatric controls, while processing a high resolution picture of a neutral face and a nonbiological complex geometric stimulus. METHODS: Ten-second sequences of eye movement were recorded video-oculographically (50 samples/sec) while subjects were "free-viewing" the stimuli. An essential element of the study was customized software that ensured stimulus presentation on a video display only after subjects were fixated upon a centre-screen cue, so that all subjects began stimulus processing from the same point. RESULTS: Compared with the control group, subjects with schizophrenia exhibited reduced scanpath lengths and a tendency toward fewer fixations for the face stimulus. They also showed an initial relative right spatial hemineglect (for the first voluntary fixation) when viewing the Rey figure, but not when viewing the face stimulus. Overall, there were no significant differences between the schizophrenia and control groups in the lateral distribution of subsequent fixations for either stimulus. CONCLUSIONS: Disturbed spatial and temporal patterns of eye movement in some people with schizophrenia may reflect sub-optimal processing of face stimuli, that may predispose these individuals to dysfunctional interpretation of facial communication cues.

Neurophysical modeling of brain dynamics.

A recent neurophysical model of brain electrical activity is outlined and applied to EEG phenomena. It incorporates single-neuron physiology and the large-scale anatomy of corticocortical and corticothalamic pathways, including synaptic strengths, dendritic propagation, nonlinear firing responses, and axonal conduction. Small perturbations from steady states account for observed EEGs as functions of arousal. Evoked response potentials (ERPs), correlation, and coherence functions are also reproduced. Feedback via thalamic nuclei is critical in determining the forms of these quantities, the transition between sleep and waking, and stability against seizures. Many disorders correspond to significant changes in EEGs, which can potentially be quantified in terms of the underlying physiology using this theory. In the nonlinear regime, limit cycles are often seen, including a regime in which they have the characteristic petit mal 3 Hz spike-and-wave form.

Simulated electrocortical activity at microscopic, mesoscopic, and global scales.

Simulation of electrocortical activity requires (a) determination of the most crucial features to be modelled, (b) specification of state equations with parameters that can be determined against independent measurements, and (c) explanation of electrical events in the brain at several scales. We report our attempts to address these problems, and show that mutually consistent explanations, and simulation of experimental data can be achieved for cortical gamma activity, synchronous oscillation, and the main features of the EEG power spectrum including the cerebral rhythms and evoked potentials. These simulations include consideration of dendritic and synaptic dynamics, AMPA, NMDA, and GABA receptors, and intracortical and cortical/subcortical interactions. We speculate on the way in which Hebbian learning and intrinsic reinforcement processes might complement the brain dynamics thus explained, to produce elementary cognitive operations.

Dynamics of large-scale brain activity in normal arousal states and epileptic seizures.

Links between electroencephalograms (EEGs) and underlying aspects of neurophysiology and anatomy are poorly understood. Here a nonlinear continuum model of large-scale brain electrical activity is used to analyze arousal states and their stability and nonlinear dynamics for physiologically realistic parameters. A simple ordered arousal sequence in a reduced parameter space is inferred and found to be consistent with experimentally determined parameters of waking states. Instabilities arise at spectral peaks of the major clinically observed EEG rhythms-mainly slow wave, delta, theta, alpha, and sleep spindle-with each instability zone lying near its most common experimental precursor arousal states in the reduced space. Theta, alpha, and spindle instabilities evolve toward low-dimensional nonlinear limit cycles that correspond closely to EEGs of petit mal seizures for theta instability, and grand mal seizures for the other types. Nonlinear stimulus-induced entrainment and seizures are also seen, EEG spectra and potentials evoked by stimuli are reproduced, and numerous other points of experimental agreement are found. Inverse modeling enables physiological parameters underlying observed EEGs to be determined by a new, noninvasive route. This model thus provides a single, powerful framework for quantitative understanding of a wide variety of brain phenomena.

Nonuniform corticothalamic continuum model of electroencephalographic spectra with application to split-alpha peaks.

Recent theoretical work has successfully predicted electroencephalographic spectra from physiology using a model corticothalamic system with spatially uniform parameters. The present work incorporates parameter nonuniformities into this model via the coupling they induce between spatial eigenmodes. Splitting of the spectral alpha peak, an effect seen in a small percentage of the normal population, is investigated as an illustrative special case. It is confirmed that weak splitting can arise from mode structure if the peak is sufficiently sharp, even for uniform parameters. However, it is further demonstrated that greater splitting can result from nonuniformities, and it is argued that this mechanism for split alpha is better able to account quantitatively for this effect than previously suggested alternatives of pacemakers or purely cortical resonances. On introducing nonuniformities in corticothalamic loop time delays, we find that the alpha frequency also varies as one moves from the front to the back of the head, in accord with observations, and that analogous (but less distinct) variations are seen in the beta peak. Analysis shows realistic variations of around +/-10 ms relative to the mean loop delay of approximately 80 ms can account for observed splittings of about 1 Hz. It is also suggested that subjects who display clear alpha splitting form the tail of a distribution of magnitude of cortical inhomogeneity, rather than a separate population.

Prediction of electroencephalographic spectra from neurophysiology.

A recent neurophysical model of propagation of electrical waves in the cortex is extended to include a physiologically motivated subcortical feedback loop via the thalamus. The electroencephalographic spectrum when the system is driven by white noise is then calculated analytically in terms of physiological parameters, including the effects of filtering of signals by the cerebrospinal fluid, skull, and scalp. The spectral power at low frequencies is found to vary as f(-1) when awake and f(-3) when asleep, with a breakpoint to a steeper power-law tail at frequencies above about 20 Hz in both cases; the f(-1) range concurs with recent magnetoencephalographic observations of such a regime. Parameter sensitivities are explored, enabling a model with fewer free parameters to be proposed, and showing that spectra predicted for physiologically reasonable parameter values strongly resemble those observed in the laboratory. Alpha and beta peaks seen near 10 Hz and twice that frequency, respectively, in the relaxed wakeful state are generated via subcortical feedback in this model, thereby leading to predictions of their frequencies in terms of physiological parameters, and of correlations in their occurrence. Subcortical feedback is also predicted to be responsible for production of anticorrelated peaks in deep sleep states that correspond to the occurrence of theta rhythm at around half the alpha frequency and sleep spindles at 3/2 times the alpha frequency. An additional positively correlated waking peak near three times the alpha frequency is also predicted and tentatively observed, as are two new types of sleep spindle near 5/2 and 7/2 times the alpha frequency, and anticorrelated with alpha. These results provide a theoretical basis for the conventional division of EEG spectra into frequency bands, but imply that the exact bounds of these bands depend on the individual. Three types of potential instability are found: one at zero frequency, another in the theta band at around half the alpha frequency, and a third at the alpha frequency itself.

Modal analysis of corticothalamic dynamics, electroencephalographic spectra, and evoked potentials.

The effects of cortical boundary conditions and resulting modal aspects of continuum corticothalamic electrodynamics are explored, including feedbacks. Dispersion relations, electroencephalographic spectra, and stimulus response functions are calculated from the underlying physiology, and the effects of discrete mode structure are determined. Conditions under which modal effects are important are obtained, along with estimates of the point at which modal series can be truncated, and the limit in which only a single globally uniform mode need be retained. It is found that for physiologically plausible parameters only the lowest cortical spatial eigenmode together with the set of next-lowest modes can produce distinct modal structure in spectra and response functions, and then only at frequencies where corticothalamic resonances reduce dissipation to the point where the spatial eigenmodes are weakly damped. The continuum limit is found to be a good approximation, except at very low frequencies and, under some circumstances, near the alpha resonance. It is argued that the major electroencephalographic rhythms result from corticothalamic feedback resonances, but that cortical modal effects can contribute to weak substructure in the alpha resonance. This mechanism is compared and contrasted with purely cortical and pacemaker-based alternatives and testable predictions are formulated to enable experimental discrimination between these possibilities.

Toward an integrated continuum model of cerebral dynamics: the cerebral rhythms, synchronous oscillation and cortical stability.

Continuum models of cerebral cortex with parameters derived from physiological data, provide explanations of the cerebral rhythms, synchronous oscillation, and autonomous cortical activity in the gamma frequency range, and suggest possible mechanisms for dynamic self-organization in the brain. Dispersion relations and derivations of power spectral response for the models, show that a low frequency resonant mode and associated travelling wave solutions of the models' equations of state can account for the predominant 1/f spectral content of the electroencephalogram (EEG). Large scale activity in the alpha, beta, and gamma bands, is accounted for by thalamocortical interaction, under regulation by diffuse cortical excitation. System impulse responses can be used to model Event-Related Potentials. Further classes of local resonance may be generated by rapid negative feedbacks at active synapses. Activity in the gamma band around 40 Hz, associated with large amplitude oscillations of pulse density, appears at higher levels of cortical activation, and is unstable unless compensated by synaptic feedbacks. Control of cortical stability by synaptic feedbacks offers a partial account of the regulation of autonomous activity within the cortex. Synchronous oscillation occurs between concurrently excited cortical sites, and can be explained by analysis of wave motion radiating from each of the co-active sites. These models are suitable for the introduction of learning rules-most notably the coherent infomax rule.

Scoliosis and uterine torsion in a pregnant sea otter (Enhydra lutris) from California.

Scoliosis and uterine torsion are described in a pregnant adult sea otter (Enhydra lutris) tagged 3 yr prior to death. Apparently, severe scoliosis in sea otters can be compatible with good nutritional status and a life-span measured in years. No causal correlation of this condition with the animal's death was established.

Observations of vaginal calculi in dolphins.

Vaginal calculi have been described from the common (Delphinus delphis), Pacific white-sided (Lagenorhynchus obliquidens) and spotted (Stenella attenuata) dolphins. We describe additional calculi found in six sexually mature D. delphis from southern California. Three calculi were large (ca. 7 x 5 cm), exhibited concentric layer crystallization, and were unique from previously published descriptions. One calculus described previously and one in our sample appeared to be a fetal skeleton and skull respectively. Using CAT scans of a first trimester northern right whale dolphin (Lissodelphis borealis) and of a near term Delphinus delphis, we discuss the potential origin and development of vaginal calculi through analysis of ossification in embryonic delphinids. We hypothesize that the calculi represented spontaneous incomplete abortion with retention of part or all of the fetus in the distal reproductive tract. The form of the calculus relates to the degree of skeletal development at the time of fetal death. Calculi from a pregnant dolphin provided one measure of residence time.

Experimental observation of a theoretically predicted nonlinear sleep spindle harmonic in human EEG.

OBJECTIVE: To investigate the properties of a sleep spindle harmonic oscillation previously predicted by a theoretical neural field model of the brain. METHODS: Spindle oscillations were extracted from EEG data from nine subjects using an automated algorithm. The power and frequency of the spindle oscillation and the harmonic oscillation were compared across subjects. The bicoherence of the EEG was calculated to identify nonlinear coupling. RESULTS: All subjects displayed a spindle harmonic at almost exactly twice the frequency of the spindle. The power of the harmonic scaled nonlinearly with that of the spindle peak, consistent with model predictions. Bicoherence was observed at the spindle frequency, confirming the nonlinear origin of the harmonic oscillation. CONCLUSIONS: The properties of the sleep spindle harmonic were consistent with the theoretical modeling of the sleep spindle harmonic as a nonlinear phenomenon. SIGNIFICANCE: Most models of sleep spindle generation are unable to produce a spindle harmonic oscillation, so the observation and theoretical explanation of the harmonic is a significant step in understanding the mechanisms of sleep spindle generation. Unlike seizures, sleep spindles produce nonlinear effects that can be observed in healthy controls, and unlike the alpha oscillation, there is no linearly generated harmonic that can obscure nonlinear effects. This makes the spindle harmonic a good candidate for future investigation of nonlinearity in the brain.

Model-based analysis and quantification of age trends in auditory evoked potentials.

OBJECTIVE: The physiological basis for the changes in auditory evoked potentials (AEPs) during development and aging is currently unknown. This study investigates age- and task-related changes via a mathematical model of neuronal activity, which allows a number of physiological changes to be inferred. METHODS: A quantitative, physiology-based model of activity in cortical and thalamic neurons was used to analyze oddball AEPs recorded from 1498 healthy subjects aged 6-86 years. RESULTS: Differences between standard and target responses can be largely explained by differences in connection strengths between thalamic and cortical neurons. The time it takes signals to travel between the thalamus and cortex decreases during development and increases during aging. Strong age trends are also seen in intracortical and thalamocortical neuronal connection strengths. CONCLUSIONS: Changes in AEP latency can be attributed to changes in the thalamocortical signal propagation time. Large changes in the connection strengths between neuronal populations occur during development, resulting in increased thalamocortical inhibition and decreased thalamocortical excitation. Standard and target parameters are similar in children but diverge during adolescence, due to changes in thalamocortical loop activity. SIGNIFICANCE: Model-based AEP analysis links age-related changes in brain electrophysiology to underlying changes in brain anatomy and physiology, and yields quantitative predictions of several currently unknown physiological and anatomical properties of the brain.

Age trends and sex differences of alpha rhythms including split alpha peaks.

OBJECTIVE: To investigate age trends, sex differences, and splitting of alpha peaks of the EEG spectrum in the healthy population. METHODS: An automated multi-site algorithm was used to parametrize the alpha rhythm in 1498 healthy subjects aged 6-86 years. Alpha peaks identified from multiple electrode sites were organized into clusters of similar frequencies whose sex differences and age trends were investigated. RESULTS: Significant age-related trends were observed for frequency, position, and amplitude of dominant alpha peaks. Occipital sites had alpha clusters of higher average frequency, higher power, and greater presence across the scalp. Frequency and power differences were found between the sexes. CONCLUSION: Observed increases in alpha frequency in children and decreases in the elderly were consistent with those from earlier studies. A large fraction of participants (≈ 44%) showed multiple distinct alpha rhythm thus investigations which only examine the alpha frequency with the highest peak power can produce misleading results. The strong dependence of alpha frequency on age and anterior-posterior position indicates use of a fixed alpha frequency band is insufficient to capture the full characteristics of the alpha rhythm. SIGNIFICANCE: This study establishes alpha rhythm parameter ranges (including power and frequency) in the healthy population, and quantifies the variation in alpha frequency across the scalp. The automated characterization enables objective evaluations of alpha band activities over large samples. These findings are potentially useful in testing theories of alpha generation, where splitting of the alpha rhythm has been theoretically predicted to occur in individuals with large differences in axon length between anterior and posterior corticothalamic loops.

Neurophysiological changes with age probed by inverse modeling of EEG spectra.

OBJECTIVE: To investigate age-associated changes in physiologically-based EEG spectral parameters in the healthy population. METHODS: Eyes-closed EEG spectra of 1498 healthy subjects aged 6-86 years were fitted to a mean-field model of thalamocortical dynamics in a cross-sectional study. Parameters were synaptodendritic rates, cortical wave decay rates, connection strengths (gains), axonal delays for thalamocortical loops, and power normalizations. Age trends were approximated using smooth asymptotically linear functions with a single turning point. We also considered sex differences and relationships between model parameters and traditional quantitative EEG measures. RESULTS: The cross-sectional data suggest that changes tend to be most rapid in childhood, generally leveling off at age 15-20 years. Most gains decrease in magnitude with age, as does power normalization. Axonal and dendritic delays decrease in childhood and then increase. Axonal delays and gains show small but significant sex differences. CONCLUSIONS: Mean-field brain modeling allows interpretation of age-associated EEG trends in terms of physiological processes, including the growth and regression of white matter, influencing axonal delays, and the establishment and pruning of synaptic connections, influencing gains. SIGNIFICANCE: This study demonstrates the feasibility of inverse modeling of EEG spectra as a noninvasive method for investigating large-scale corticothalamic dynamics, and provides a basis for future comparisons.