A Pharmacokinetics-Neural Mass Model (PK-NMM) for the Simulation of EEG Activity during Propofol Anesthesia

Modeling the effects of anesthetic drugs on brain activity is very helpful in understanding anesthesia mechanisms. The aim of this study was to set up a combined model to relate actual drug levels to EEG dynamics and behavioral states during propofol-induced anesthesia. We proposed a new combined theoretical model based on a pharmacokinetics (PK) model and a neural mass model (NMM), which we termed PK-NMM—with the aim of simulating electroencephalogram (EEG) activity during propofol-induced general anesthesia. The PK model was used to derive propofol effect-site drug concentrations (C _eff) based on the actual drug infusion regimen. The NMM model took C _eff as the control parameter to produce simulated EEG-like (sEEG) data. For comparison, we used real prefrontal EEG (rEEG) data of nine volunteers undergoing propofol anesthesia from a previous experiment. To see how well the sEEG could describe the dynamic changes of neural activity during anesthesia, the rEEG data and the sEEG data were compared with respect to: power-frequency plots; nonlinear exponent (permutation entropy (PE)); and bispectral SynchFastSlow (SFS) parameters. We found that the PK-NMM model was able to reproduce anesthesia EEG-like signals based on the estimated drug concentration and patients’ condition. The frequency spectrum indicated that the frequency power peak of the sEEG moved towards the low frequency band as anesthesia deepened. Different anesthetic states could be differentiated by the PE index. The correlation coefficient of PE was 0.80±0.13 (mean±standard deviation) between rEEG and sEEG for all subjects. Additionally, SFS could track the depth of anesthesia and the SFS of rEEG and sEEG were highly correlated with a correlation coefficient of 0.77±0.13. The PK-NMM model could simulate EEG activity and might be a useful tool for understanding the action of propofol on brain activity.     

Specific Entrainment of Mitral Cells during Gamma Oscillation in the Rat Olfactory Bulb

Local field potential (LFP) oscillations are often accompanied by synchronization of activity within a widespread cerebral area. Thus, the LFP and neuronal coherence appear to be the result of a common mechanism that underlies neuronal assembly formation. We used the olfactory bulb as a model to investigate: (1) the extent to which unitary dynamics and LFP oscillations can be correlated and (2) the precision with which a model of the hypothesized underlying mechanisms can accurately explain the experimental data. For this purpose, we analyzed simultaneous recordings of mitral cell (MC) activity and LFPs in anesthetized and freely breathing rats in response to odorant stimulation. Spike trains were found to be phase-locked to the gamma oscillation at specific firing rates and to form odor-specific temporal patterns. The use of a conductance-based MC model driven by an approximately balanced excitatory-inhibitory input conductance and a relatively small inhibitory conductance that oscillated at the gamma frequency allowed us to provide one explanation of the experimental data via a mode-locking mechanism. This work sheds light on the way network and intrinsic MC properties participate in the locking of MCs to the gamma oscillation in a realistic physiological context and may result in a particular time-locked assembly. Finally, we discuss how a self-synchronization process with such entrainment properties can explain, under experimental conditions: (1) why the gamma bursts emerge transiently with a maximal amplitude position relative to the stimulus time course; (2) why the oscillations are prominent at a specific gamma frequency; and (3) why the oscillation amplitude depends on specific stimulus properties. We also discuss information processing and functional consequences derived from this mechanism.     

Neural field theory of synaptic plasticity

Plasticity is crucial to neural development, learning, and memory. In the common in vivo situation where postsynaptic neural activity results from multiple presynaptic inputs, it is shown that a widely used class of correlation-dependent and spike-timing dependent plasticity rules can be written in a form that can be incorporated into neural field theory, which enables their system-level dynamics to be investigated. It is shown that the resulting plasticity dynamics depends strongly on the stimulus spectrum via overall system frequency responses. In the case of perturbations that are approximately linear, explicit formulas are found for the dynamics in terms of stimulus spectra via system transfer functions. The resulting theory is applied to a simple model system to reveal how collective effects, especially resonances, can drastically modify system-level plasticity dynamics from that implied by single-neuron analyses. The simplified model illustrates the potential relevance of these effects in applications to brain stimulation, synaptic homeostasis, and epilepsy.     

Photic and nonphotic circadian phase resetting in a diurnal primate, the common marmoset

Despite the considerable literature on circadian entrainment, there is little information on this subject in diurnal mammals. Contributing to this lack of understanding is the problem of separating photic from nonphotic (behavioral) phase-resetting events in diurnal species. In the present study, photic phase resetting was obtained in diurnal common marmosets held under constant dim light (DimDim; <0.5 lx) by using a 20-s pulse of bright light to minimize time available for behavioral arousal. This stimulus elicited phase advances at circadian time (CT) 18-22 and phase delays at CT9-12. Daily presentation of these 20-s pulses produced entrainment with a phase angle of approximately 11 h (0 h = activity onset). Nonphotic phase resetting was obtained under DimDim with the use of a 1-h-induced activity pulse, consisting of intermittent cage agitation and water sprinkling, delivered in total darkness to minimize photic effects. This stimulus caused phase delays at CT20-24, and entrainment to a scheduled daily regimen of these pulses occurred with a phase angle of approximately 0 h. These results indicate that photic and nonphotic phase-response curves (PRCs) of marmosets are similar to those of nocturnal rodents and that nonphotic PRCs are keyed to the phase of the suprachiasmatic nucleus pacemaker, not to the phase of the activity-rest cycle.     

Neural organization of the circadian system of the cockroach Leucophaea maderae

The cockroach Leucophaea maderae was the first animal in which lesion experiments localized an endogenous circadian clock to a particular brain area, the optic lobe. The neural organization of the circadian system, however, including entrainment pathways, coupling elements of the bilaterally distributed internal clock, and output pathways controlling circadian locomotor rhythms are only recently beginning to be elucidated. As in flies and other insect species, pigment-dispersing hormone (PDH)-immunoreac- tive neurons of the accessory medulla of the cockroach are crucial elements of the circadian system. Lesions and transplantation experiments showed that the endogeneous circadian clock of the brain resides in neurons associated with the accessory medulla. The accessory medulla is organized into a nodular core receiving photic input, and into internodular and peripheral neuropil involved in efferent output and coupling input. Photic entrainment of the clock through compound eye photoreceptors appears to occur via parallel, indirect pathways through the medulla. Light-like phase shifts in circadian locomotor activity after injections of γ-aminobutyric acid (GABA)- or Mas-allatotropin into the vicinity of the accessory medulla suggest that both substances are involved in photic entrainment. Extraocular, cryptochrome-based photoreceptors appear to be present in the optic lobe, but their role in photic entrainment has not been examined. Pigment-dispersing hormone-immunoreactive neurons provide efferent output from the accessory medulla to several brain areas and to the peripheral visual system. Pigment-dispersing hormone-immunoreactive neurons, and additional heterolateral neurons are, furthermore, involved in bilateral coupling of the two pacemakers. The neuronal organization, as well as the prominent involvement of GABA and neuropeptides, shows striking similarities to the organization of the suprachiasmatic nucleus, the circadian clock of the mammalian brain.     

Conditioning in the Orcadian System

Light is the dominant environmental cue for entrainment of circadian rhythms. In mammals, light entrains rhythms by resetting the phase of a circadian pacemaker located in the hypothalamic suprachiasmatic nucleus (SCN). Until recently, the mechanism responsible for pacemaker resetting by light was thought to be exclusively sensitive to photic cues. New experiments indicate, however, that this mechanism is more plastic than once thought; is amenable to conditioned stimulus control; and is capable of acquiring, through conditioning, new response capabilities. These experiments showed that, in rats, a neutral stimulus paired with light in Pavlovian conditioning trials is capable of eliciting cellular and behavioral effects characteristic of circadian clock phase resetting by light, expression of Fos protein in the ventrolateral region of the SCN, and phase shifts of free-running rhythms. These novel results open up a previously unappreciated perspective on photic phase resetting and entrainment of circadian rhythms. Specifically, they suggest that the process normally initiated by light to reset the clock can be modified by learning and events in the environment that reliably precede the onset of light can assume the resetting function of light.     

Modulation of Hydra attenuata rhythmic activity: phase response curve.

We investigated the effect of photic stimulation on the frequency of Hydra attenuata column contractions. We used positive or negative abrupt light transitions, single or repetitive light or darkness pulses, and alternation of light and darkness periods. The main results are: (a) The frequency of the contraction pulse trains (CPTs) varies transiently in response to an abrupt variation of the light intensity. (b) CPTs in progress can be inhibited by different types of photic stimuli. (c) The response time to a single photic stimulus varies during the inter-CPT interval and depends also on the polarity of the stimulus. (d) The CPTs are entrainable with repetitive light stimulation of various frequencies. (e) Long-lasting variations of the frequency of CPTs occur after the end of a repetitive light stimulation. We suggest that the mechanism responsible for the rhythym of column contractions is quite similar to that on which other biological rhythmic phenomena are based.     

Tales from the crypt(ochromes)

Cryptochromes are a family of flavoproteins found in organisms ranging from Arabidopsis to man. Across phylogeny, these proteins have been used for pleiotropic functions ranging from blue-light-dependent development in plants and blue-light-mediated phase shifting of the circadian clock in insects to a core circadian clock component in mammals. Review of the roles of cryptochromes in model organisms reveals several common themes: Multiple cryptochrome family members within individual organisms have redundant functions; cryptochromes used in photic entrainment pathways of the circadian clock are partially redundant with other photopigments; and cryptochromes may function in circadian phototransduction and core clock mechanisms in the same organism, with different functions in different tissues. The present review summarizes recent research on the functions of cryptochrome in the circadian timekeeping and photic entrainment pathways.     

Brain rhythms reveal a hierarchical network organization

Recordings of ongoing neural activity with EEG and MEG exhibit oscillations of specific frequencies over a non-oscillatory background. The oscillations appear in the power spectrum as a collection of frequency bands that are evenly spaced on a logarithmic scale, thereby preventing mutual entrainment and cross-talk. Over the last few years, experimental, computational and theoretical studies have made substantial progress on our understanding of the biophysical mechanisms underlying the generation of network oscillations and their interactions, with emphasis on the role of neuronal synchronization. In this paper we ask a very different question. Rather than investigating how brain rhythms emerge, or whether they are necessary for neural function, we focus on what they tell us about functional brain connectivity. We hypothesized that if we were able to construct abstract networks, or "virtual brains", whose dynamics were similar to EEG/MEG recordings, those networks would share structural features among themselves, and also with real brains. Applying mathematical techniques for inverse problems, we have reverse-engineered network architectures that generate characteristic dynamics of actual brains, including spindles and sharp waves, which appear in the power spectrum as frequency bands superimposed on a non-oscillatory background dominated by low frequencies. We show that all reconstructed networks display similar topological features (e.g. structural motifs) and dynamics. We have also reverse-engineered putative diseased brains (epileptic and schizophrenic), in which the oscillatory activity is altered in different ways, as reported in clinical studies. These reconstructed networks show consistent alterations of functional connectivity and dynamics. In particular, we show that the complexity of the network, quantified as proposed by Tononi, Sporns and Edelman, is a good indicator of brain fitness, since virtual brains modeling diseased states display lower complexity than virtual brains modeling normal neural function. We finally discuss the implications of our results for the neurobiology of health and disease.     

Addition of a non-photic component to a light-based mathematical model of the human circadian pacemaker

Mathematical models have become vital to the study of many biological processes in humans due to the complexity of the physiological mechanisms underlying these processes and systems. While our current mathematical representation of the human circadian pacemaker has proven useful in many experimental situations, it uses as input only a direct effect of light on the circadian pacemaker. Although light (a photic stimulus) has been shown to be the primary synchronizer of the circadian pacemaker across a number of species, studies in both animals and humans have confirmed the existence of non-photic effects that also contribute to phase shifting and entrainment. We modified our light-based circadian mathematical model to reflect evidence from these studies that the sleep-wake cycle and/or associated behaviors have a non-photic effect on the circadian pacemaker. In our representation, the sleep-wake cycle and its associated behaviors provides a non-photic drive on the circadian pacemaker that acts both independently and concomitantly with light stimuli. Further experiments are required to validate fully our model and to understand the exact effect of the sleep-wake cycle as a non-photic stimulus for the human circadian pacemaker.     

Light pulses suppress responsiveness within the mouse photic entrainment pathway

We have characterized a decrease in photic responsiveness of the mammalian circadian entrainment pathway caused by light stimulation. Phase delays of the running-wheel activity rhythm were used to quantify the photic responsiveness of the circadian system in mice (C57BL/6J). In an initial experiment, the authors measured the responsiveness to single "saturating" light pulses ("white" fluorescent light; approximately 1876 [microW; 15 min). In two additional experiments, the authors measured responses to this stimulus at several time points following a saturating pulse at CT 14 or CT 16. Data from these experiments were analyzed in two manners. Experiment 2 was analyzed assuming that the phase of the circadian pacemaker was unchanged by an initial pulse, and Experiment 3 was analyzed assuming that the initial pulse induced an instantaneous phase delay. Results reveal a significant reduction in responsivity to light that persists for at least 2 h and possibly up to 4 h after the initial stimulus. Immediately after the stimulus, the responsiveness of the photic entrainment pathway was reduced to levels < or = 12% of normal. After 2 h, the responsiveness was < or = 42% of normal, and by 4 h, responsiveness had recovered to levels that were < or = 60% of normal (levels not statistically different from controls). By the following circadian cycle, responsiveness was more completely recovered, although the magnitude of some phase delays remained < or = 85% of normal. These major reductions in the magnitude of phase delays (and phase response curve amplitude) caused by saturating light pulses confound interpretations of two-pulse experiments designed to measure the rate of circadian phase delays. In addition, the time course for this reduced responsiveness may reflect the time course of cellular and molecular events that underlie light-induced resetting of the mammalian circadian pacemaker.     

Steady-state visual evoked potentials can be explained by temporal superposition of transient event-related responses

Background

One common criterion for classifying electrophysiological brain responses is based on the distinction between transient (i.e. event-related potentials, ERPs) and steady-state responses (SSRs). The generation of SSRs is usually attributed to the entrainment of a neural rhythm driven by the stimulus train. However, a more parsimonious account suggests that SSRs might result from the linear addition of the transient responses elicited by each stimulus. This study aimed to investigate this possibility.

Methodology/Principal Findings

We recorded brain potentials elicited by a checkerboard stimulus reversing at different rates. We modeled SSRs by sequentially shifting and linearly adding rate-specific ERPs. Our results show a strong resemblance between recorded and synthetic SSRs, supporting the superposition hypothesis. Furthermore, we did not find evidence of entrainment of a neural oscillation at the stimulation frequency.

Conclusions/Significance

This study provides evidence that visual SSRs can be explained as a superposition of transient ERPs. These findings have critical implications in our current understanding of brain oscillations. Contrary to the idea that neural networks can be tuned to a wide range of frequencies, our findings rather suggest that the oscillatory response of a given neural network is constrained within its natural frequency range.     

Photic and nonphotic inputs to the diurnal circadian clock

Diurnal animals occupy a different temporal niche from nocturnal animals and are consequently exposed to different amounts of light as well as different dangers. Accordingly, some variation exists in the way that diurnal animals synchronize their internal circadian clock to match the external 24-hour daily cycle. First, though the brain mechanisms underlying photic entrainment are very similar among species with different daily activity patterns, there is evidence that diurnal animals are less sensitive to photic stimuli compared to nocturnal animals. Second, stimuli other than light that synchronize rhythms (i.e. nonphotic stimuli) can also entrain and phase shift daily rhythms. Some of the rules that govern nonphotic entrainment in nocturnal animals as well as the brain mechanisms that control nonphotic influences on rhythms do not appear to apply to diurnal animals, however. Some evidence supports the idea that arousal or activity plays an important role in entraining rhythms in diurnal animals, either during the light (active) or dark (inactive) phases, though no consistent pattern is seen. GABAergic stimulation induces phase shifts during the subjective day in both diurnal and nocturnal animals. In diurnal Arvicanthis niloticus (Nile grass rats), SCN GABA_A receptor activation at this time results in phase delays while in nocturnal animals phase advances are induced. It appears that the effect of GABA at this circadian phase results from the inhibition of period gene expression in both diurnal and nocturnal animals. Nonetheless, the resulting phase shifts are in opposite directions. It is not known what stimuli or behaviours ultimately induce changes in GABA activity in the SCN that result in alterations of circadian phase in diurnal grass rats. Taken together, studies such as these suggest that it may be problematic to apply the principles governing nocturnal nonphotic entrainment and its underlying mechanisms to diurnal species including humans.     

A fly's eye view of circadian entrainment

The Drosophila circadian clock is an ideal model system for teasing out the molecular mechanisms of circadian behavior and the means by which animals synchronize to day-night cycles. The clock that drives behavioral rhythms, located in the lateral neurons in the central brain, consists of a feedback loop of the circadian genes period (per) and timeless (tim). The molecular cycle, roughly 24 h long, is constantly reset by the environment. This review focuses on the main input pathways of the dominant circadian zeitgeber, light. Light acts directly on the clock primarily through cryptochrome (cry), a deep brain blue-light photoreceptor. CRY activation causes rapid TIM degradation, which is a predicted means of resetting the clock both on a daily basis at dawn and on an acute basis following an entraining light pulse during the night hours. In the absence of cry, the clock can still be driven by photic input through the visual system, though the mechanisms underlying this entrainment are unclear. Temperature can also entrain the clock, although the mechanisms by which this occurs are also unclear.     

Formal analysis of resonance entrainment by central pattern generator

The neuronal circuit controlling the rhythmic movements in animal locomotion is called the central pattern generator (CPG). The biological control mechanism appears to exploit mechanical resonance to achieve efficient locomotion. The objective of this paper is to reveal the fundamental mechanism underlying entrainment of CPGs to resonance through sensory feedback. To uncover the essential principle, we consider the simplest setting where a pendulum is driven by the reciprocal inhibition oscillator. Existence and properties of stable oscillations are examined by the harmonic balance method, which enables approximate but insightful analysis. In particular, analytical conditions are obtained under which harmonic balance predicts existence of an oscillation at a frequency near the resonance frequency. Our result reveals that the resonance entrainment can be maintained robustly against parameter perturbations through two distinct mechanisms: negative integral feedback and positive rate feedback.     

Modeling the role of mid-wavelength cones in circadian responses to light

Nonvisual responses to light, such as photic entrainment of the circadian clock, involve intrinsically light-sensitive melanopsin-expressing ganglion cells as well as rod and cone photoreceptors. However, previous studies have been unable to demonstrate a specific contribution of cones in the photic control of circadian responses to light. Using a mouse model that specifically lacks mid-wavelength (MW) cones we show that these photoreceptors play a significant role in light entrainment and in phase shifting of the circadian oscillator. The contribution of MW cones is mainly observed for light exposures of short duration and toward the longer wavelength region of the spectrum, consistent with the known properties of this opsin. Modeling the contributions of the various photoreceptors stresses the importance of considering the particular spectral, temporal, and irradiance response domains of the photopigments when assessing their role and contribution in circadian responses to light.     

A phase dynamics model of human circadian rhythms

Nonphotic entrainment of an overt sleep-wake rhythm and a circadian pacemaker-driving temperature/melatonin rhythm suggests existence of feedback mechanisms in the human circadian system. In this study, the authors constructed a phase dynamics model that consisted of two oscillators driving temperature/melatonin and sleep-wake rhythms, and an additional oscillator generating an overt sleep-wake rhythm. The feedback mechanism was implemented by modifying couplings between the constituent oscillators according to the history of correlations between them. The model successfully simulated the behavior of human circadian rhythms in response to forced rest-activity schedules under free-run situations: the sleep-wake rhythm is reentrained with the circadian pacemaker after release from the schedule, there is a critical period for the schedule to fully entrain the sleep-wake rhythm, and the forced rest-activity schedule can entrain the circadian pacemaker with the aid of exercise. The behavior of human circadian rhythms was reproduced with variations in only a few model parameters. Because conventional models are unable to reproduce the experimental results concerned here, it was suggested that the feedback mechanisms included in this model underlie nonphotic entrainment of human circadian rhythms.     

Avalanches in Self-Organized Critical Neural Networks: A Minimal Model for the Neural SOC Universality Class

The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting that this homeostasis of brain activity could occur even without a central regulator, via self-organization on the level of neurons and their interactions, alone. Such physical mechanisms from the class of self-organized criticality exhibit characteristic dynamical signatures, similar to seismic activity related to earthquakes. Measurements of cortex rest activity showed first signs of dynamical signatures potentially pointing to self-organized critical dynamics in the brain. Indeed, recent more accurate measurements allowed for a detailed comparison with scaling theory of non-equilibrium critical phenomena, proving the existence of criticality in cortex dynamics. We here compare this new evaluation of cortex activity data to the predictions of the earliest physics spin model of self-organized critical neural networks. We find that the model matches with the recent experimental data and its interpretation in terms of dynamical signatures for criticality in the brain. The combination of signatures for criticality, power law distributions of avalanche sizes and durations, as well as a specific scaling relationship between anomalous exponents, defines a universality class characteristic of the particular critical phenomenon observed in the neural experiments. Thus the model is a candidate for a minimal model of a self-organized critical adaptive network for the universality class of neural criticality. As a prototype model, it provides the background for models that may include more biological details, yet share the same universality class characteristic of the homeostasis of activity in the brain.     

Energy-based stochastic control of neural mass models suggests time-varying effective connectivity in the resting state

Several studies posit energy as a constraint on the coding and processing of information in the brain due to the high cost of resting and evoked cortical activity. This suggestion has been addressed theoretically with models of a single neuron and two coupled neurons. Neural mass models (NMMs) address mean-field based modeling of the activity and interactions between populations of neurons rather than a few neurons. NMMs have been widely employed for studying the generation of EEG rhythms, and more recently as frameworks for integrated models of neurophysiology and functional MRI (fMRI) responses. To date, the consequences of energy constraints on the activity and interactions of ensembles of neurons have not been addressed. Here we aim to study the impact of constraining energy consumption during the resting-state on NMM parameters. To this end, we first linearized the model, then used stochastic control theory by introducing a quadratic cost function, which transforms the NMM into a stochastic linear quadratic regulator (LQR). Solving the LQR problem introduces a regime in which the NMM parameters, specifically the effective connectivities between neuronal populations, must vary with time. This is in contrast to current NMMs, which assume a constant parameter set for a given condition or task. We further simulated energy-constrained stochastic control of a specific NMM, the Wilson and Cowan model of two coupled neuronal populations, one of which is excitatory and the other inhibitory. These simulations demonstrate that with varying weights of the energy-cost function, the NMM parameters show different time-varying behavior. We conclude that constraining NMMs according to energy consumption may create more realistic models. We further propose to employ linear NMMs with time-varying parameters as an alternative to traditional nonlinear NMMs with constant parameters.