Physiologically based calculation of steady-state evoked potentials and cortical wave velocities

Steady-state evoked potentials (SSEPs) elicited by sinusoidal stimuli are predicted from a physiologically-based model, including bielectrode and volume conduction effects. Comparison with visual SSEPs yields constraints on phase and latency of the retinothalamic transfer function that are consistent with experiment. Predictions of phase velocities measured as SSEPs cross the cortex are consistent with low values measured for slow waves in sleep, while resonant behavior induced by corticothalamic loops, especially near the alpha peak, contributes to wide scatter in waking-state phase velocity measurements comparable to effects from volume conduction. The common use of bielectrode derivations to compensate for volume conduction effects is examined and shown to be incomplete, tending to lead to underestimates of phase velocity, especially at low frequencies and near the alpha peak, due to incorrect elimination of true long-wavelength contributions to the SSEP.

Mean field model of acetylcholine mediated dynamics in the cerebral cortex

A recent continuum model of the large scale electrical activity of the cerebral cortex is generalized to include cholinergic modulation. In this model, dynamic modulation of synaptic strength acts over the time scales of nicotinic and muscarinic receptor action. The cortical model is analyzed to determine the effect of acetylcholine (ACh) on its steady states, linear stability, spectrum, and temporal responses to changes in subcortical input. ACh increases the firing rate in steady states of the system. Changing ACh concentration does not introduce oscillatory behavior into the system, but increases the overall spectral power. Model responses to pulses in subcortical input are affected by the tonic level of ACh concentration, with higher levels of ACh increasing the magnitude firing rate response of excitatory cortical neurons to pulses of subcortical input. Numerical simulations are used to explore the temporal dynamics of the model in response to changes in ACh concentration. Evidence is seen of a transition from a state in which intracortical inputs are emphasized to a state where thalamic afferents have enhanced influence. Perturbations in ACh concentration cause changes in the firing rate of cortical neurons, with rapid responses due to fast acting facilitatory effects of nicotinic receptors on subcortical afferents, and slower responses due to muscarinic suppression of intracortical connections. Together, these numerical simulations demonstrate that the actions of ACh could be a significant factor modulating early components of evoked response potentials.

Laboratory evidence for stochastic plasma-wave growth

The first laboratory confirmation of stochastic growth theory is reported. Floating potential fluctuations are measured in a vacuum arc centrifuge using a Langmuir probe. Statistical analysis of the energy density reveals a lognormal distribution over roughly 2 orders of magnitude, with a high-field nonlinear cutoff whose spatial dependence is consistent with the predicted eigenmode profile. These results are consistent with stochastic growth and nonlinear saturation of a spatially extended eigenmode, the first evidence for stochastic growth of an extended structure.

Visual gamma oscillations: waves, correlations, and other phenomena, including comparison with experimental data

Mean-field theory of brain dynamics is applied to explain the properties of gamma (> or approximately 30 Hz) oscillations of cortical activity often seen during vision experiments. It is shown that mm-scale patchy connections in the primary visual cortex can support collective gamma oscillations with the correct frequencies and spatial structure, even when driven by uncorrelated inputs. This occurs via resonances associated with the the periodic modulation of the network connections, rather than being due to single-cell properties alone. Near-resonant gamma waves are shown to obey the Schrödinger equation, which enables techniques and insights from quantum theory to be used in exploring these classical oscillations. Resulting predictions for gamma responses to stimuli account in a unified way for a wide range of experimental results, including why oscillations and zero-lag synchrony are associated, and variations in correlation functions with time delay, intercellular distance, and stimulus features. They also imply that gamma oscillations may enable a form of frequency multiplexing of neural signals. Most importantly, it is shown that correlations reproduce experimental results that show maximal correlations between cells that respond to related features, but little correlation with other cells, an effect that has been argued to be associated with segmentation of a scene into separate objects. Consistency with infill of missing contours and increase in response with length of bar-shaped stimuli are discussed. Background correlations expected in the absence of stimulation are also calculated and shown to be consistent in form with experimental measurements and similar to stimulus-induced correlations in structure. Finally, possible links of gamma instabilities to certain classes of photically induced seizures and visual hallucinations are discussed.

Energy approach to rivalry dynamics, soliton stability, and pattern formation in neuronal networks

Hopfield's Lyapunov function is used to view the stability and topology of equilibria in neuronal networks for visual rivalry and pattern formation. For two neural populations with reciprocal inhibition and slow adaptation, the dynamics of neural activity is found to include a pair of limit cycles: one for oscillations between states where one population has high activity and the other has low activity, as in rivalry, and one for oscillations between states where both populations have the same activity. Hopfield's Lyapunov function is used to find the dynamical mechanism for oscillations and the basin of attraction of each limit cycle. For a spatially continuous population with lateral inhibition, stable equilibria are found for local regions of high activity (solitons) and for bound states of two or more solitons. Bound states become stable when moving two solitons together minimizes the Lyapunov function, a result of decreasing activity in regions between peaks of high activity when the firing rate is described by a sigmoid function. Lowering the barrier to soliton formation leads to a pattern-forming instability, and a nonlinear solution to the dynamical equations is found to be given by a soliton lattice, which is completely characterized by the soliton width and the spacing between neighboring solitons. Fluctuations due to noise create lattice vacancies analogous to point defects in crystals, leading to activity which is spatially inhomogeneous.

Spike-rate adaptation and neuronal bursting in a mean-field model of brain activity

Spike-rate adaptation is investigated within a mean-field model of brain activity. Two different mechanisms of negative feedback are considered; one involving modulation of the mean firing threshold, and the other, modulation of the mean synaptic strength. Adaptation to a constant stimulus is shown to take place for both mechanisms, and limit-cycle oscillations in the firing rate corresponding to bursts of neuronal activity are investigated. These oscillations are found to result from a Hopf bifurcation when the equilibrium lies between the local maximum and local minimum of a given nullcline. Oscillations with amplitudes significantly below the maximum firing rate are found over a narrow range of possible equilibriums.

Compact dynamical model of brain activity

A compact physiologically based mean-field formulation of brain dynamics is proposed to model observed brain activity and electroencephalographic (EEG) signals. In contrast to existing formulations, which are more detailed and complicated, our model is described by a single second-order delay differential equation that encapsulates salient aspects of the physiology. The model captures essential features of activity mediated by fast corticocortical connections and delayed feedbacks via extracortical pathways and external stimuli. In the linear regime, these features can be simply expressed by three coefficients derived from the properties of these physiological pathways and explicit nonlinear approximations are also derived. This compact model successfully reproduces the main features of experimental EEG's and the predictions of previous models, including resonance peaks in EEG spectra and nonlinear dynamics. As an illustration, key features of the dynamics of epileptic seizures are shown to be reproduced by the model. Due to its compact form, the model will facilitate insight into nonlinear brain dynamics via standard nonlinear techniques and will guide analysis and investigation of more complex models. It is thus a useful tool for analyzing complex brain activity, especially when it exhibits low-dimensional dynamics.

Transformation of arbitrary distributions to the normal distribution with application to EEG test-retest reliability

Many variables in the social, physical, and biosciences, including neuroscience, are non-normally distributed. To improve the statistical properties of such data, or to allow parametric testing, logarithmic or logit transformations are often used. Box-Cox transformations or ad hoc methods are sometimes used for parameters for which no transformation is known to approximate normality. However, these methods do not always give good agreement with the Gaussian. A transformation is discussed that maps probability distributions as closely as possible to the normal distribution, with exact agreement for continuous distributions. To illustrate, the transformation is applied to a theoretical distribution, and to quantitative electroencephalographic (qEEG) measures from repeat recordings of 32 subjects which are highly non-normal. Agreement with the Gaussian was better than using logarithmic, logit, or Box-Cox transformations. Since normal data have previously been shown to have better test-retest reliability than non-normal data under fairly general circumstances, the implications of our transformation for the test-retest reliability of parameters were investigated. Reliability was shown to improve with the transformation, where the improvement was comparable to that using Box-Cox. An advantage of the general transformation is that it does not require laborious optimization over a range of parameters or a case-specific choice of form.

The aggravating role of the ubiquitin–proteasome system in neurodegenerative disease

Intraneuronal inclusion bodies are key pathological features of most age-related neurodegenerative disorders including Parkinson's disease and Alzheimer's disease. These inclusions are commonly characterized both by the presence of ubiquitinated proteins and the sequestration of components of the UPS (ubiquitin–proteasome system). Unfortunately, as we age, the efficiency of the UPS declines, suggesting that the presence of ubiquitinated proteins and UPS components in inclusions may reflect unsuccessful attempts by the (failing) UPS to remove the aggregating proteins. Whether the physical presence of inclusions causes cell death or, conversely, whether they are non-toxic and their presence reflects a cellular protective mechanism remains highly controversial. Animal and in vitro model systems that allow detailed characterization of the inclusions and their effects on the cell have been developed by us and others. Identification of the mechanisms involved in inclusion formation is already aiding the development of novel therapeutic strategies to prevent or alleviate aggregate-associated neurodegenerative diseases.

Multielectrode electroencephalogram power spectra: theory and application to approximate correction of volume conduction effects

Using a physiologically based model of brain activity, electroencephalogram (EEG) power spectra are calculated for signals derived from general linear combinations of voltages from multiple electrodes, with and without filtering by volume conduction. Two simple methods of combining scalp measurements to estimate unfiltered EEG power spectra are then proposed and their accuracy and robustness are explored, using the model predictions as an illustration. It is found that these methods, including a case that uses just three electrodes, enable improved estimation of the underlying spectrum relative to each of several widely used combinations alone.

Numerical simulations of type-III solar radio bursts

The first numerical simulations are presented for type-III solar radio bursts in the inhomogeneous solar corona and interplanetary space, that include microscale quasilinear and nonlinear processes, intermediate-scale driven ambient density fluctuations, and large scale evolution of electron beams, Langmuir and ion sound waves, and fundamental and harmonic electromagnetic emission. Bidirectional coronal emission is asymmetric between the upward and downward directions, and harmonic emission dominates fundamental emission. In interplanetary space, fundamental and/or harmonic emission can be important. Langmuir and ion sound waves are bursty and the statistics of Langmuir wave energy agree well with the predictions of stochastic growth theory.

Patchy propagators, brain dynamics, and the generation of spatially structured gamma oscillations

Propagator theory of brain dynamics is generalized to incorporate a new class of patchy propagators that enable treatment of approximately periodic structures such as are seen in the visual cortex. Complex response fields are also incorporated to allow for features such as orientation preference and wave-number selectivity. The results are applied to the corticothalamic system associated with the primary visual cortex. It is found that this system can generate gamma ( > or = 30 Hz) oscillations during stimulation, whose properties are consistent with experimental findings on gamma frequency and bandwidth, and existence of fine-scale spatial structure. It is found that a potential resonance is associated with each reciprocal lattice vector corresponding to periodic modulations of the propagators. It is found that the lowest resonances are the most likely to give rise to noticeable spectral peaks and increases of correlation amplitude, length, and time, and that these aspects are prominent only if the system is close to marginal stability, in accord with previous measurements and discussions of cortical stability. These features also enable gamma resonances to be stimulus-evoked, with substantial resonance sharpening for relatively small changes in mean neural firing rate. The results also imply dependence of gamma frequency on stimulus features.

BOLD responses to stimuli: dependence on frequency, stimulus form, amplitude, and repetition rate

A quantitative theory is developed for the relationship between stimulus and the resulting blood oxygen level-dependent (BOLD) functional MRI signal. The relationship of stimuli to neuronal activity during evoked responses is inferred from recent physiology-based quantitative modeling of evoked response potentials (ERPs). A hemodynamic model is then used to calculate the BOLD response to neuronal activity having the form of an impulse, a sinusoid, or an ERP-like damped sinusoid. Using the resulting equations, the BOLD response is analyzed for different forms, frequencies, and amplitudes of stimuli, in contrast with previous research, which has mostly concentrated on sustained stimuli. The BOLD frequency response is found to be closely linear in the parameter ranges of interest, with the form of a low-pass filter with a weak resonance at approximately 0.07 Hz. An improved BOLD impulse response is systematically obtained which includes initial dip and post-stimulus undershoot for some parameter ranges. It is found that the BOLD response depends strongly on the precise temporal course of the evoked neuronal activity, not just its peak value or typical amplitude. Indeed, for short stimuli, the linear BOLD response is closely proportional to the time-integrated activity change evoked by the stimulus, regardless of amplitude. It is concluded that there can be widely differing proportionalities between BOLD and peak activity, that this is the likely reason for the low level of correspondence seen experimentally between ERP sources and BOLD measurements and that non-BOLD measurements, such as ERPs, can be used to correct for this effect to obtain improved activity estimates. Finally, stimulus sequences that optimize the signal-to-noise ratio in event-related BOLD fMRI (efMRI) experiments are derived using the hemodynamic transfer function.

A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis

The aim of this paper is to explain critical features of the human primary generalized epilepsies by investigating the dynamical bifurcations of a nonlinear model of the brain's mean field dynamics. The model treats the cortex as a medium for the propagation of waves of electrical activity, incorporating key physiological processes such as propagation delays, membrane physiology, and corticothalamic feedback. Previous analyses have demonstrated its descriptive validity in a wide range of healthy states and yielded specific predictions with regards to seizure phenomena. We show that mapping the structure of the nonlinear bifurcation set predicts a number of crucial dynamic processes, including the onset of periodic and chaotic dynamics as well as multistability. Quantitative study of electrophysiological data supports the validity of these predictions. Hence, we argue that the core electrophysiological and cognitive differences between tonic-clonic and absence seizures are predicted and interrelated by the global bifurcation diagram of the model's dynamics. The present study is the first to present a unifying explanation of these generalized seizures using the bifurcation analysis of a dynamical model of the brain.

Multiscale brain modelling

A central difficulty of brain modelling is to span the range of spatio-temporal scales from synapses to the whole brain. This paper overviews results from a recent model of the generation of brain electrical activity that incorporates both basic microscopic neurophysiology and large-scale brain anatomy to predict brain electrical activity at scales from a few tenths of a millimetre to the whole brain. This model incorporates synaptic and dendritic dynamics, nonlinearity of the firing response, axonal propagation and corticocortical and corticothalamic pathways. Its relatively few parameters measure quantities such as synaptic strengths, corticothalamic delays, synaptic and dendritic time constants, and axonal ranges, and are all constrained by independent physiological measurements. It reproduces quantitative forms of electroencephalograms seen in various states of arousal, evoked response potentials, coherence functions, seizure dynamics and other phenomena. Fitting model predictions to experimental data enables underlying physiological parameters to be inferred, giving a new non-invasive window into brain function that complements slower, but finer-resolution, techniques such as fMRI. Because the parameters measure physiological quantities relating to multiple scales, and probe deep structures such as the thalamus, this will permit the testing of a range of hypotheses about vigilance, cognition, drug action and brain function. In addition, referencing to a standardized database of subjects adds strength and specificity to characterizations obtained.

Biophysical modeling of tonic cortical electrical activity in attention deficit hyperactivity disorder

Psychophysiological theories characterize Attention Deficit Hyperactivity Disorder (ADHD) in terms of cortical hypoarousal and a lack of inhibition of irrelevant sensory input, drawing on evidence of abnormal electroencephalographic (EEG) delta-theta activity. To investigate the mechanisms underlying this disorder a biophysical model of the cortex was used to fit and replicate the EEGs from 54 ADHD adolescents and their control subjects. The EEG abnormalities in ADHD were accounted for by the model's neurophysiological parameters as follows: (i) dendritic response times were increased, (ii) intrathalamic activity involving the thalamic reticular nucleus (TRN) was increased, consistent with enhanced delta-theta activity, and (iii) intracortical activity was increased, consistent with slow wave (<1 Hz) abnormalities. The longer dendritic response time is consistent with the increase in the activity of inhibitory cells types, particularly in the TRN, and therefore reduced arousal. The increase in intracortical activity may also reflect an increase in background activity or cortical noise within neocortical circuits. In terms of neurochemistry, these findings may be accounted for by disturbances in the cholinergic and/or noradrenergic systems. To the knowledge of the authors, this is the first study to use a detailed biophysical model of the brain to elucidate the neurophysiological mechanisms underlying tonic abnormalities in ADHD.

Protection against Helicobacter pylori infection in the Mongolian gerbil after prophylactic vaccination

Vaccines against Helicobacter pylori could circumvent the problem of increasing antibiotic resistance. They would be particularly useful in developing countries, where re-infection rates are high following standard eradication regimes. The Mongolian gerbil is a good model for H. pylori infection, as the gastric pathology induced by infection is similar to that in humans. The H. pylori-induced inflammatory response in gerbils is considerably greater than in murine models. The aim of this study was to determine if gerbils could be vaccinated against H. pylori. Mongolian gerbils were vaccinated orally with an H. pylori whole cell sonicate preparation and cholera toxin adjuvant. Vaccinated gerbils and controls were challenged with the autologous H. pylori strain 42GX. All infection, and cholera toxin, control gerbils were H. pylori positive 6 weeks post-challenge. By contrast, a significant degree of protection was demonstrated in vaccinated gerbils. Only two of 10 of gerbils were H. pylori positive (P<0.001). Protection was associated with increased serum H. pylori IgG antibodies. Protected gerbils had histologically normal gastric mucosa and, in contrast to mice, no post-immunisation gastritis was evident. In the control groups, the degree of inflammation was variable, with some of the animals having corpus gastritis and corpus mucous metaplasia. The levels of gastric IL-12p40 and IFNgamma transcripts were significantly decreased in vaccinated animals compared to infection and cholera toxin controls (P<0.01). Gastric IL-10 and TGFbeta transcripts were found only at relatively low levels. These results demonstrate that Mongolian gerbils can be successfully vaccinated against H. pylori and protected from H. pylori-induced pathology.

Propagator theory of brain dynamics

A physiologically based continuum model of brain dynamics is extended to incorporate arbitrary numbers of structures and neural populations, multiple outgoing fields of activity from a single population of neurons to various targets, improved treatment of converging or diverging projections and mesoscopic structure, and generalized connections to quantities observable via electroencephalography and other methods. The results are applied to study the corticothalamic system, predicting an intracortical resonance that leads to enhancements of electroencephalographic activity in the gamma (>30 Hz) range. This resonance involves feedback loops incorporating slow, short-range inhibitory fibers.

Criticality in a Vlasov-Poisson system: a fermioniclike universality class

A model Vlasov-Poisson system is simulated close to the point of marginal stability, thus assuming only the wave-particle resonant interactions are responsible for saturation, and shown to obey the power-law scaling of a second-order phase transition. The set of critical exponents analogous to those of the Ising universality class is calculated and shown to obey the Widom and Rushbrooke scaling and Josephson's hyperscaling relations at the formal dimensionality d=5 below the critical point at nonzero order parameter. However, the two-point correlation function does not correspond to the propagator of Euclidean quantum field theory, which is the Gaussian model for the Ising universality class. Instead, it corresponds to the propagator for the fermionic vector field and to the upper critical dimensionality d(c) = 2. This suggests criticality of collisionless Vlasov-Poisson systems corresponds to a universality class analogous to that of critical phenomena of a fermionic quantum field description.

Stimulant drug action in attention deficit hyperactivity disorder (ADHD): inference of neurophysiological mechanisms via quantitative modelling

OBJECTIVE

To infer the neural mechanisms underlying tonic transitions in the electroencephalogram (EEG) in 11 adolescents diagnosed with attention deficit hyperactivity disorder (ADHD) before and after treatment with stimulant medication.

METHODS

A biophysical model was used to analyse electroencephalographic (EEG) measures of tonic brain activity at multiple scalp sites before and after treatment with medication.

RESULTS

It was observed that stimulants had the affect of significantly reducing the parameter controlling activation in the intrathalamic pathway involving the thalamic reticular nucleus (TRN) and the parameter controlling excitatory cortical activity. The effect of stimulant medication was also found to be preferentially localized within subcortical nuclei projecting towards frontal and central scalp sites.

CONCLUSIONS

It is suggested that the action of stimulant medication occurs via suppression of the locus coeruleus, which in turn reduces stimulation of the TRN, and improves cortical arousal. The effects localized to frontal and central sites are consistent with the occurrence of frontal delta-theta EEG abnormalities in ADHD, and existing theories of hypoarousal.

SIGNIFICANCE

To our knowledge, this is the first study where a detailed biophysical model of the brain has been used to estimate changes in neurophysiological parameters underlying the effects of stimulant medication in ADHD.

Conductance of photons in disordered photonic crystals

The conductance of photons in two-dimensional disordered photonic crystals is calculated using an exact multipole-plane wave method that includes all multiple scattering processes. Conductance fluctuations, the universal nature of which has been established for electrons in the diffusive regime, are studied for photons, in both principal polarizations and for varying disorder. Our simulations show that universal conductance fluctuations can be observed in H(||) (TE) polarization for weak and intermediate disorder while, for E(||) (TM) polarization, we show that the conductance variance is essentially independent of sample size but strongly dependent on disorder. The probability distribution of the conductance is also calculated in the diffusive and localized regimes, and also at their transition, for which the distributions for both polarizations are seen to be very similar.

New regimes of stochastic wave growth

Stochastic-growth theory (SGT) of bursty waves is generalized and it is shown that the previously separate theory of "elementary bursts" is a limiting case. New regimes of SG are found and elucidated, and results are compared with the first relevant simulations via quasilinear theory and a reduced-parameter model. Both display stochastic behavior with the expected properties--the first simulations to demonstrate SGT behavior explicitly. Reexamination of data and simulations previously analyzed using SGT or elementary burst theory also shows good agreement with the new predictions.

Analysis of the electroencephalographic activity associated with thalamic tumors

A physiologically based model of corticothalamic dynamics is used to investigate the electroencephalographic (EEG) activity associated with tumors of the thalamus. Tumor activity is modeled by introducing localized two-dimensional spatial non-uniformities into the model parameters, and calculating the resulting activity via the coupling of spatial eigenmodes. The model is able to reproduce various qualitative features typical of waking eyes-closed EEGs in the presence of a thalamic tumor, such as the appearance of abnormal peaks at theta ( approximately 3Hz) and spindle ( approximately 12Hz) frequencies, the attenuation of normal eyes-closed background rhythms, and the onset of epileptic activity, as well as the relatively normal EEGs often observed. The results indicate that the abnormal activity at theta and spindle frequencies arises when a small portion of the brain is forced into an over-inhibited state due to the tumor, in which there is an increase in the firing of (inhibitory) thalamic reticular neurons. The effect is heightened when there is a concurrent decrease in the firing of (excitatory) thalamic relay neurons, which are in any case inhibited by the reticular ones. This is likely due to a decrease in the responsiveness of the peritumoral region to cholinergic inputs from the brainstem, and a corresponding depolarization of thalamic reticular neurons, and hyperpolarization of thalamic relay neurons, similar to the mechanism active during slow-wave sleep. The results indicate that disruption of normal thalamic activity is essential to generate these spectral peaks. Furthermore, the present work indicates that high-voltage and epileptiform EEGs are caused by a tumor-induced local over-excitation of the thalamus, which propagates to the cortex. Experimental findings relating to local over-inhibition and over-excitation are discussed. It is also confirmed that increasing the size of the tumor leads to greater abnormalities in the observable EEG. The usefulness of EEG for localizing the tumor is investigated.

Unifying and interpreting the spectral wavenumber content of EEGs, ECoGs, and ERPs

A biological model of corticothalamic dynamics is used to investigate the spatial power spectrum (wavenumber spectrum) of electrical activity in the brain. The model provides a single framework for unifying different aspects of activity. Comparisons of the predicted spectra with published electrocorticographic, electroencephalographic, and evoked response potential data enable physiology and anatomy to be inferred, producing results which are complementary to those obtained from comparisons in the frequency domain; the inferred quantities are consistent with, and complementary to, direct physiological and anatomical measurements. We also use the model to quantify the interdependence of the wavenumber and frequency domains, and deduce that further experiments that cover large wavenumber and frequency ranges simultaneously would greatly increase our knowledge of brain function. We conclude that both the frequency and wavenumber domains should be studied in order to build the fullest picture of brain dynamics: the two domains are both complementary and interdependent.