A computational perspective on migraine aura

Interneuronal dynamics facilitate the initiation of spike block in cortical microcircuits

Pyramidal cell spike block is a common occurrence in migraine with aura and epileptic seizures. In both cases, pyramidal cells experience hyperexcitation with rapidly increasing firing rates, major changes in electrochemistry, and ultimately spike block that temporarily terminates neuronal activity. In cortical spreading depression (CSD), spike block propagates as a slowly traveling wave of inactivity through cortical pyramidal cells, which is thought to precede migraine attacks with aura. In seizures, highly synchronized cortical activity can be interspersed with, or terminated by, spike block. While the identifying characteristic of CSD and seizures is the pyramidal cell hyperexcitation, it is currently unknown how the dynamics of the cortical microcircuits and inhibitory interneurons affect the initiation of hyperexcitation and subsequent spike block.We tested the contribution of cortical inhibitory interneurons to the initiation of spike block using a cortical microcircuit model that takes into account changes in ion concentrations that result from neuronal firing. Our results show that interneuronal inhibition provides a wider dynamic range to the circuit and generally improves stability against spike block. Despite these beneficial effects, strong interneuronal firing contributed to rapidly changing extracellular ion concentrations, which facilitated hyperexcitation and led to spike block first in the interneuron and then in the pyramidal cell. In all cases, a loss of interneuronal firing triggered pyramidal cell spike block. However, preventing interneuronal spike block was insufficient to rescue the pyramidal cell from spike block. Our data thus demonstrate that while the role of interneurons in cortical microcircuits is complex, they are critical to the initiation of pyramidal cell spike block. We discuss the implications that localized effects on cortical interneurons have beyond the isolated microcircuit and their contribution to CSD and epileptic seizures.

Study on “Atypical” Migraine Auras in the Pediatric Age: The Role of Cortical Spreading Depression and the Physiopathogenetic Hypothesis Arising from Our Clinical Cases

Migraine is a complex neurologic disorder by which several systems of the central nervous system (autonomous system, affective, cognitive, sensory and motor system) may be affected on different levels. About a fourth of migraine patients have migraine auras. The most common aura is the visual aura followed by the sensorial aura but motor deficits, as well as deficits of higher cortical centers (disorders of thinking, orientation, coherence, or concentration), may occur as well. In analogy with a headache diary, an aura diary can deliver important help in the diagnostic process of rare migraine manifestations and prevent the under-diagnosis of unusual migraine manifestations. Complex migraine manifestations are a diagnosis of exclusion, and a broad diagnostic work-up is necessary in order to exclude dangerous neurologic pathologies. In addition, here, we discuss the atypical clinical presentation and possible physio-pathogenetic related aspects of these atypical migraine aura features in the developmental age. In addition, we wanted to stress and analyze the clinical aspects of our children/adolescents with atypical auras, which seem to be more difficult to frame with the mechanisms originally proposed to explain the physio-pathogenetic relationship between CSD and aura. Finally, we discuss in detail the complex aspects of this topic on the basis of available data and propose new terminology: “Multiple, Synchronous and Asynchronous, Cortical and Subcortical Spreading Depression”.

No Evidence of Reduced Contrast Sensitivity in Migraine-with-Aura for Large, Narrowband, Centrally Presented Noise-Masked Stimuli

Individuals with migraine aura show differences in visual perception compared to control groups. Measures of contrast sensitivity have suggested that people with migraine aura are less able to exclude external visual noise, and that this relates to higher variability in neural processing. The current study compared contrast sensitivity in migraine with aura and control groups for narrow-band grating stimuli at 2 and 8 cycles/degree, masked by Gaussian white noise. We predicted that contrast sensitivity would be lower in the migraine with aura group at high noise levels. Contrast sensitivity was higher for the low spatial frequency stimuli, and decreased with the strength of the masking noise. We did not, however, find any evidence of reduced contrast sensitivity associated with migraine with aura. We propose alternative methods as a more targeted assessment of the role of neural noise and excitability as contributing factors to migraine aura.

Migraine Visual Aura and Cortical Spreading Depression-Linking Mathematical Models to Empirical Evidence

This review describes the subjective experience of visual aura in migraine, outlines theoretical models of this phenomenon, and explores how these may be linked to neurochemical, electrophysiological, and psychophysical differences in sensory processing that have been reported in migraine with aura. Reaction-diffusion models have been used to model the hallucinations thought to arise from cortical spreading depolarisation and depression in migraine aura. One aim of this review is to make the underlying principles of these models accessible to a general readership. Cortical spreading depolarisation and depression in these models depends on the balance of the diffusion rate between excitation and inhibition and the occurrence of a large spike in activity to initiate spontaneous pattern formation. We review experimental evidence, including recordings of brain activity made during the aura and attack phase, self-reported triggers of migraine, and psychophysical studies of visual processing in migraine with aura, and how these might relate to mechanisms of excitability that make some people susceptible to aura. Increased cortical excitability, increased neural noise, and fluctuations in oscillatory activity across the migraine cycle are all factors that are likely to contribute to the occurrence of migraine aura. There remain many outstanding questions relating to the current limitations of both models and experimental evidence. Nevertheless, reaction-diffusion models, by providing an integrative theoretical framework, support the generation of testable experimental hypotheses to guide future research.

Cortical stimulation in aphasia following ischemic stroke: toward model-guided electrical neuromodulation

The aim of this paper is to integrate different bodies of research including brain traveling waves, brain neuromodulation, neural field modeling and post-stroke language disorders in order to explore the opportunity of implementing model-guided, cortical neuromodulation for the treatment of post-stroke aphasia. Worldwide according to WHO, strokes are the second leading cause of death and the third leading cause of disability. In ischemic stroke, there is not enough blood supply to provide enough oxygen and nutrients to parts of the brain, while in hemorrhagic stroke, there is bleeding within the enclosed cranial cavity. The present paper focuses on ischemic stroke. We first review accumulating observations of traveling waves occurring spontaneously or triggered by external stimuli in healthy subjects as well as in patients with brain disorders. We examine the putative functions of these waves and focus on post-stroke aphasia observed when brain language networks become fragmented and/or partly silent, thus perturbing the progression of traveling waves across perilesional areas. Secondly, we focus on a simplified model based on the current literature in the field and describe cortical traveling wave dynamics and their modulation. This model uses a biophysically realistic integro-differential equation describing spatially distributed and synaptically coupled neural networks producing traveling wave solutions. The model is used to calculate wave parameters (speed, amplitude and/or frequency) and to guide the reconstruction of the perturbed wave. A stimulation term is included in the model to restore wave propagation to a reasonably good level. Thirdly, we examine various issues related to the implementation model-guided neuromodulation in the treatment of post-stroke aphasia given that closed-loop invasive brain stimulation studies have recently produced encouraging results. Finally, we suggest that modulating traveling waves by acting selectively and dynamically across space and time to facilitate wave propagation is a promising therapeutic strategy especially at a time when a new generation of closed-loop cortical stimulation systems is about to arrive on the market.

The effects of cerebral curvature on cortical spreading depression

Neuronal activity evokes a localised increase in cerebral blood flow through neurovascular coupling (NVC), a communication system between a group of cells known as a neurovascular unit (NVU). Dysfunctional NVC can lead to pathologies such as cortical spreading depression (CSD), characterised by a slowly propagating wave of neuronal depolarisation and high extracellular potassium (K⁺) levels. CSD is associated with several neurological disorders such as migraine, stroke, and traumatic brain injury. Insight into the spatial dynamics of CSD in humans is mainly deduced from animal experiments on the smooth lissencephalic brain (in particular murine experiments), however the human cortex is gyrencephalic (highly folded) and is considered likely to exhibit different and more complex patterns of CSD. In this study a large scale numerical NVC model of multiple NVUs is coupled to a vascular tree simulating a two-dimensional cerebral tissue slice. This model is extended with a spatial Gaussian curvature mapping that can simulate the highly folded nature of the human cortex. For a flat surface comparable to a lissencephalic cortex the model can simulate propagating waves of high extracellular K⁺ travelling radially outwards from a stimulated area at approximately 6.7 mm/min, corresponding well with multiple experimental results. The high K⁺ concentration induces a corresponding wave of vasoconstriction (with decreased blood flow) then slight vasodilation, achieved through cellular communication within the NVU. The BOLD response decreases below baseline by approximately 10% followed by an increase of 1%. For a surface with spatially varied curvature comparable to a section of gyrencephalic cortex, areas of positive Gaussian curvature inhibit wave propagation due to decreased extracellular diffusion rate. Whereas areas of negative curvature promote propagation. Consequently extracellular K⁺ is observed travelling as wave segments (as opposed to radial waves) through flat or negatively curved "valleys" corresponding to folds (sulci) in the cortex. If the wave size (defined as the activated area of high K⁺ concentration) is too small or diffusion rate too low then wave segments can cease propagation. If the diffusion rate is high enough the wave segments can grow from open ends forming loose spiral waves. These results may provide some insight into the differences seen between human and animal experiments.

Alternating activity patterns and a chimeralike state in a network of globally coupled excitable Morris-Lecar neurons

Spatiotemporal chaos collapses to either a rest state or a propagating pulse in a ring network of diffusively coupled, excitable Morris-Lecar neurons. Adding global varying synaptic coupling to the ring network reveals complex transient behavior. Spatiotemporal chaos collapses into a transient pulse that reinitiates spatiotemporal chaos to allow sequential pattern switching until a collapse to the rest state. A domain of irregular neuron activity coexists with a domain of inactive neurons forming a transient chimeralike state. Transient spatial localization of the chimeralike state is observed for stronger synapses.

Transient chaos and associated system-intrinsic switching of spacetime patterns in two synaptically coupled layers of Morris-Lecar neurons

Spatiotemporal chaos collapses to either a rest state or a propagating pulse solution in a single layer of diffusively coupled, excitable Morris-Lecar neurons. Weak synaptic coupling of two such layers reveals system intrinsic switching of spatiotemporal activity patterns within and between the layers at irregular times. Within a layer, switching sequences include spatiotemporal chaos, erratic and regular pulse propagation, spontaneous network wide neuron activity, and rest state. A momentary substantial reduction in neuron activity in one layer can reinitiate transient spatiotemporal chaos in the other layer, which can induce a swap of spatiotemporal chaos with a pulse state between the layers. Presynaptic input maximizes the distance between propagating pulses, in contrast to pulse merging in the absence of synapses.

Objective Assessment of Cortical Excitability in Migraine With and Without Aura

Recent progress in the genetics of migraine has refocused attention on cortical dysfunction as an important component of the pathophysiology of this disorder. In previous work, we have demonstrated functional changes in the visual cortex of migraine patients, using an objective transcranial magnetic stimulation technique, termed magnetic suppression of perceptual accuracy (MSPA). This study aimed to replicate previous findings in migraine with aura (MA) and to use the technique to examine migraine without aura (MoA). Eight MA patients, 14 MoA patients and 13 migraine-free controls participated. MSPA assessments were undertaken using a standardized protocol in which computer-presented letter targets were followed at a variable delay interval by a single magnetic pulse delivered over the occiput. MSPA performance is expressed as a profile of response accuracy across target-pulse delay intervals. The profiles of migraine-free controls exhibited a normal U-shape. MA patients had significantly shallower profiles, showing little or no suppression at intermediate delay intervals. MoA patients had profiles that were similar to controls. Recent animal evidence strongly indicates that the U-shape of the normal MSPA function is caused by preferential activation of inhibitory neurons. Shallower MPSA profiles in MA patients are therefore likely to indicate a functional hyperexcitability caused by impaired inhibition. The finding of normal MPSA profiles in MoA patients is novel and will require further investigation.

Ophthalmological Assessment of OCT and Electrophysiological Changes in Migraine Patients

BACKGROUND

A cross-sectional study to investigate the morphological and functional changes of the visual pathway taking place in patients with migraine.

METHODS

Fifteen patients (14 female, 1 male) diagnosed with migraine with aura and 23 patients (21 female, 2 male) diagnosed with migraine without aura were compared with 20 healthy volunteers (18 female, 2 male). All the participants underwent optical coherence tomography scan, electroretinogram (ERG), visual evoked potentials, and multifocal electroretinogram (mf-ERG) recording.

RESULTS

Assessing ERG recordings, no significant differences in mean N1-P1 amplitudes were measured among the groups. The mean visual evoked potentials N80-P100 amplitudes were not significantly different among the three groups (one way analysis of variance: P = 0.075, F = 2.718). No significant difference was found in P100 latency times among groups. The mean retinal response density of mf-ERG in ring 1 was higher in healthy individuals compared with migraineurs, with statistical significance (Kruskal-Wallis analysis of variance and Dunn multiple comparisons test; P < 0.001, mean rank difference = -24.857 and P < 0.001, mean rank difference = -20.9, for migraine with aura-control and migraine without aura-control comparisons, respectively). In migraine with aura subjects, retinal nerve fiber layer thickness in superior and inferior quadrants was significantly decreased compared with healthy individuals, whereas in migraine without aura group, only the superior quadrant was significantly thinner compared with the control group.

CONCLUSIONS

Retinal response density in mfERG of all migraineurs was significantly lessened compared with healthy individuals. There was no significant difference in visual evoked potentials N80-P100 amplitudes or P100 latencies among the groups. Moreover, retinal nerve fiber layer thinning observed in patients with migraine compared with control subjects, appeared statistically significant in some quadrants. The authors may be able to defend the retinal blood flow decrease theory in migraine. The results also indicate that several levels of the visual pathway seem to be affected in migraineurs.

Effects of Glia in a Triphasic Continuum Model of Cortical Spreading Depression

Cortical spreading depression (SD) is a spreading disruption in brain ionic homeostasis during which neurons experience complete and prolonged depolarizations. SD is generally believed to be the physiological substrate of migraine aura and is associated with many other brain pathologies. Here, we perform simulations with a model of SD treating brain tissue as a triphasic continuum of neurons, glia and the extracellular space. A thermodynamically consistent incorporation of the major biophysical effects, including ionic electrodiffusion and osmotic water flow, allows for the computation of important physiological variables including the extracellular voltage (DC) shift. A systematic parameter study reveals that glia can act as both a disperser and buffer of potassium in SD propagation. Furthermore, we show that the timing of the DC shift with respect to extracellular [Formula: see text] rise is highly dependent on glial parameters, a result with implications for the identification of the propagating mechanism of SD.

Analytically tractable studies of traveling waves of activity in integrate-and-fire neural networks

In contrast to other large-scale network models for propagation of electrical activity in neural tissue that have no analytical solutions for their dynamics, we show that for a specific class of integrate and fire neural networks the acceleration depends quadratically on the instantaneous speed of the activity propagation. We use this property to analytically compute the network spike dynamics and to highlight the emergence of a natural time scale for the evolution of the traveling waves. These results allow us to examine other applications of this model such as the effect that a nonconductive gap of tissue has on further activity propagation. Furthermore we show that activity propagation also depends on local conditions for other more general connectivity functions, by converting the evolution equations for network dynamics into a low-dimensional system of ordinary differential equations. This approach greatly enhances our intuition into the mechanisms of the traveling waves evolution and significantly reduces the simulation time for this class of models.

Laminar Neural Field Model of Laterally Propagating Waves of Orientation Selectivity

We construct a laminar neural-field model of primary visual cortex (V1) consisting of a superficial layer of neurons that encode the spatial location and orientation of a local visual stimulus coupled to a deep layer of neurons that only encode spatial location. The spatially-structured connections in the deep layer support the propagation of a traveling front, which then drives propagating orientation-dependent activity in the superficial layer. Using a combination of mathematical analysis and numerical simulations, we establish that the existence of a coherent orientation-selective wave relies on the presence of weak, long-range connections in the superficial layer that couple cells of similar orientation preference. Moreover, the wave persists in the presence of feedback from the superficial layer to the deep layer. Our results are consistent with recent experimental studies that indicate that deep and superficial layers work in tandem to determine the patterns of cortical activity observed in vivo.

From chemical systems to systems chemistry: Patterns in space and time

We present a brief, idiosyncratic overview of the past quarter century of progress in nonlinear chemical dynamics and discuss what we view as the most exciting recent developments and some challenges and likely areas of progress in the next 25 years.

Changes in plasma PPARs levels in migraine patients

Background

The aim of this study was to observe the change in plasma PPARs (peroxisome proliferator-activated receptors) level during various periods and in different subtypes in migraine patients.

Material/Methods

We divided 227 patients with migraine into 2 main groups: the attack period group (n=98) and the attack-free period group (n=129). Patients were further divided into 4 subgroups according to whether they had aura symptoms. The control group consisted of 100 healthy subjects. We collected the clinical data of patients and measured the plasma levels of PPARs using enzyme-linked immunoassay (ELISA). We used SPSS software for statistical analysis.

Results

We found no significant difference in age, BMI, blood pressure, or blood lipid level among migraine patients during the headache attack period and during the headache-free period compared with the control group. The PPARα and PPARβ/δ levels during the headache attack period were significantly higher than during the headache free period and in healthy controls. The PPARγ levels during the headache attack period were significantly lower than those during the headache-free period and in the healthy control group. The PPARs levels during the headache attack period were significantly different from those during the headache-free period, regardless of presence or absence of aura. The PPARs levels during the headache-free period were not significantly different from those of the healthy control group. The level of PPARs has no significant differences between migraine with aura group and without aura group, regardless of whether headache attack.

Conclusions

PPARs involved in the pathogenesis of migraine. Presence of absence of aura had no obvious effect on PPARs level.

Cortical hot spots and labyrinths: why cortical neuromodulation for episodic migraine with aura should be personalized

Stimulation protocols for medical devices should be rationally designed. For episodic migraine with aura we outline model-based design strategies toward preventive and acute therapies using stereotactic cortical neuromodulation. To this end, we regard a localized spreading depression (SD) wave segment as a central element in migraine pathophysiology. To describe nucleation and propagation features of the SD wave segment, we define the new concepts of cortical hot spots and labyrinths, respectively. In particular, we firstly focus exclusively on curvature-induced dynamical properties by studying a generic reaction-diffusion model of SD on the folded cortical surface. This surface is described with increasing level of details, including finally personalized simulations using patient's magnetic resonance imaging (MRI) scanner readings. At this stage, the only relevant factor that can modulate nucleation and propagation paths is the Gaussian curvature, which has the advantage of being rather readily accessible by MRI. We conclude with discussing further anatomical factors, such as areal, laminar, and cellular heterogeneity, that in addition to and in relation to Gaussian curvature determine the generalized concept of cortical hot spots and labyrinths as target structures for neuromodulation. Our numerical simulations suggest that these target structures are like fingerprints, they are individual features of each migraine sufferer. The goal in the future will be to provide individualized neural tissue simulations. These simulations should predict the clinical data and therefore can also serve as a test bed for exploring stereotactic cortical neuromodulation.

The visual system in migraine: from the bench side to the office

BACKGROUND

Throughout history, migraine-associated visual symptoms have puzzled patients, doctors, and neuroscientists. The visual aspects of migraine extend far beyond the aura phenomena, and have several clinical implications.

METHODS

A narrative review was conducted, beginning with migraine mechanisms, then followed by pertinent aspects of the anatomy of visual pathways, clinical features, implications of the visual system on therapy, migraine on visually impaired populations, treatment of visual auras and ocular (retinal) migraine, effect of prophylactic migraine treatments on visual aura, visual symptoms induced by anti-migraine or anti-headache drugs, and differential diagnosis.

RESULTS

A comprehensive narrative review from both basic and clinical standpoints on the visual aspects of migraine was attained; however, the results were biased to provide any useful information for the clinician.

CONCLUSION

This paper achieved its goals of addressing and condensing information on the pathophysiology of the visual aspects of migraine and its clinical aspects, especially with regards to therapy, making it useful not only for those unfamiliar to the theme but to experienced physicians as well.

The ripple pond: enabling spiking networks to see

We present the biologically inspired Ripple Pond Network (RPN), a simply connected spiking neural network which performs a transformation converting two dimensional images to one dimensional temporal patterns (TP) suitable for recognition by temporal coding learning and memory networks. The RPN has been developed as a hardware solution linking previously implemented neuromorphic vision and memory structures such as frameless vision sensors and neuromorphic temporal coding spiking neural networks. Working together such systems are potentially capable of delivering end-to-end high-speed, low-power and low-resolution recognition for mobile and autonomous applications where slow, highly sophisticated and power hungry signal processing solutions are ineffective. Key aspects in the proposed approach include utilizing the spatial properties of physically embedded neural networks and propagating waves of activity therein for information processing, using dimensional collapse of imagery information into amenable TP and the use of asynchronous frames for information binding.

SPREADING DEPRESSION IN MAINLY LOCALLY CONNECTED CELLULAR AUTOMATON

A computational model based on cellular automaton (CA) is developed for studying the spreading depression (SD) phenomenon. CA cells correspond to neurons which are mainly locally connected. The influence of the parameter values in the spatiotemporal dynamics is investigated in order to obtain ways of reducing, or even preventing, occurrences of SD.

Self-terminating wave patterns and self-organized pacemakers in a phenomenological model of spreading depression

A simple reaction-diffusion model of spreading depression (SD) is presented. Its local dynamics are governed by two activator and two inhibitor variables that provide an extremely simplified description of the mutual interaction between the neurons and extracellular space. This interaction is realized by the substances in the extracellular space that are increasing excitability of the neurons that have released them and are diffusing to the neighboring neurons, thereby spreading this excitation. Typical dynamic patterns of simulated activity are presented. The focus is laid on the case where response of the extracellular medium is relatively fast, and retracting waves, spiral-shaped waves, and autonomous pacemakers are observed, which is in good agreement with experimental observations. The underlying mechanisms are found to be related to switching between the local bi-stable, excitable, and self-sustained dynamics in the simulated medium. This article is part of a Special Issue entitled: Neural Coding.

A model for the origin and properties of flicker-induced geometric phosphenes

We present a model for flicker phosphenes, the spontaneous appearance of geometric patterns in the visual field when a subject is exposed to diffuse flickering light. We suggest that the phenomenon results from interaction of cortical lateral inhibition with resonant periodic stimuli. We find that the best temporal frequency for eliciting phosphenes is a multiple of intrinsic (damped) oscillatory rhythms in the cortex. We show how both the quantitative and qualitative aspects of the patterns change with frequency of stimulation and provide an explanation for these differences. We use Floquet theory combined with the theory of pattern formation to derive the parameter regimes where the phosphenes occur. We use symmetric bifurcation theory to show why low frequency flicker should produce hexagonal patterns while high frequency produces pinwheels, targets, and spirals.

Perceptive aspects of visual aura

Visual aura is the most common feature associated with migraine, though it can occur separately. In both cases it often represents a dramatic event, especially for patients who experience it for the first time. Besides, its subjective characteristics may illuminate on the functional architecture of the visual cortex. Repetitive events of migraine and visual aura have been suggested to affect the visual system in the long run, both on the cortical and precortical level. In effect, objective investigation of visual functions in patients support the idea that a selective damage does occur, so that more attention to visual examination seems to be justified. In this paper, subjective and psychophysical aspects of visual aura are examined, lastly highlighting and discussing the interesting correlations found between this condition and normal-tension glaucoma.

The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression: a computational study

Experimental evidences point out the participation of nonsynaptic mechanisms (e.g., fluctuations in extracellular ions) in epileptiform bursting and spreading depression (SD). During these abnormal oscillatory patterns, it is observed an increase of extracellular potassium concentration [K(+)](o) and a decrease of extracellular calcium concentration [Ca(2+)](o) which raises the neuronal excitability. However, whether the high [K(+)](o) triggers and propagates these abnormal neuronal activities or plays a secondary role into this process is unclear. To better understand the influence of extracellular potassium dynamics in these oscillatory patterns, the experimental conditions of high [K(+)](o) and zero [Ca(2+)](o) were replicated in an extended Golomb model where we added important regulatory mechanisms of ion concentration as Na(+)-K(+) pump, ion diffusion and glial buffering. Within these conditions, simulations of the cell model exhibit seizure-like discharges (ictal bursting). The SD was elicited by the interruption of the Na(+)-K(+) pump activity, mimicking the effect of cellular hypoxia (an experimental protocol to elicit SD, the hypoxia-induced SD). We used the bifurcation theory and the fast-slow method to analyze the interference of K(+) dynamics in the cellular excitability. This analysis indicates that the system loses its stability at a high [K(+)](o), transiting to an elevated state of neuronal excitability. Effects of high [K(+)](o) are observed in different stages of ictal bursting and SD. In the initial stage, the increase of [K(+)](o) creates favorable conditions to trigger both oscillatory patterns. During the neuronal activity, a continuous growth of [K(+)](o) by outward K(+) flow depresses K(+) currents in a positive feedback way. At the last stage, due to the depression of K(+) currents, the Na(+)-K(+) pump is the main mechanism in the end of neuronal activity. Thus, this work suggests that [K(+)](o) dynamics may play a fundamental role in these abnormal oscillatory patterns.

Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke

The stability of cortical function depends critically on proper regulation. Under conditions of migraine and stroke a breakdown of transmembrane chemical gradients can spread through cortical tissue. A concomitant component of this emergent spatio-temporal pattern is a depolarization of cells detected as slow voltage variations. The propagation velocity of approximately 3 mm/min indicates a contribution of diffusion. We propose a mechanism for spreading depolarizations (SD) that rests upon a nonlocal or noninstantaneous feedback in a reaction-diffusion system. Depending upon the characteristic space and time scales of the feedback, the propagation of cortical SD can be suppressed by shifting the bifurcation line, which separates the parameter regime of pulse propagation from the regime where a local disturbance dies out. The optimization of this feedback is elaborated for different control schemes and ranges of control parameters.

Efficient control of transient wave forms to prevent spreading depolarizations

In various neurological disorders spatio-temporal excitation patterns constitute examples of excitable behavior emerging from pathological pathways. During migraine, seizure, and stroke an initially localized pathological state can temporarily spread indicating a transition from non-excitable to excitable behavior. We investigate these transient wave forms in the generic FitzHugh-Nagumo (FHN) system of excitable media. Our goal is to define an efficient control minimizing the volume of invaded tissue. The general point of such a therapeutic optimization is how to apply control theory in the framework of structures in differential geometry by regarding parameter plane M of the FHN system as a differentiable manifold endowed with a metric. We suggest to equip M with a metric given by pharmacokinetic-pharmacodynamic models of drug receptor interaction.

Saccade-Related Spread of Activity Across Superior Colliculus May Arise From Asymmetry of Internal Connections

The superior colliculus (SC) receives a retinotopic projection of the contralateral visual field in which the representation of the central field is expanded with respect to the peripheral field. The visual projection forms a nonlinear, approximately logarithmic, map on the SC. Models of the SC commonly assume that the function defining the strength of neuronal connections within this map (the kernel) depends only on the distance between two neurons, and is thus isotropic and homogeneous. However, if the connection strength is based on the distance between two stimuli in sensory space, the kernel will be asymmetric because of the nonlinear projection onto the brain map. We show, using a model of the SC, that one consequence of these asymmetric intrinsic connections is that activity initiated at one point spreads across the map. We compare this simulated spread with the spread observed experimentally around the time of saccadic eye movements with respect to direction of spread, differing effects of local and global inhibition, and the consequences of localized inactivation on the SC map. Early studies suggested that the SC spread was caused by feedback of eye displacement during a saccade, but subsequent studies were inconsistent with this feedback hypothesis. In our new model, the spread is autonomous, resulting from intrinsic connections within the SC, and thus does not depend on eye movement feedback. Other sensory maps in the brain (e.g., visual cortex) are also nonlinear and our analysis suggests that the consequences of asymmetric connections in those areas should be considered.

Computational neuropharmacology: dynamical approaches in drug discovery

Computational approaches that adopt dynamical models are widely accepted in basic and clinical neuroscience research as indispensable tools with which to understand normal and pathological neuronal mechanisms. Although computer-aided techniques have been used in pharmaceutical research (e.g. in structure- and ligand-based drug design), the power of dynamical models has not yet been exploited in drug discovery. We suggest that dynamical system theory and computational neuroscience--integrated with well-established, conventional molecular and electrophysiological methods--offer a broad perspective in drug discovery and in the search for novel targets and strategies for the treatment of neurological and psychiatric diseases.

Flicker-induced color and form: interdependencies and relation to stimulation frequency and phase

Our understanding of human visual perception generally rests on the assumption that conscious visual states represent the interaction of spatial structures in the environment and our nervous system. This assumption is questioned by circumstances where conscious visual states can be triggered by external stimulation which is not primarily spatially defined. Here, subjective colors and forms are evoked by flickering light while the precise nature of those experiences varies over flicker frequency and phase. What's more, the occurrence of one subjective experience appears to be associated with the occurrence of others. While these data indicate that conscious visual experience may be evoked directly by particular variations in the flow of spatially unstructured light over time, it must be assumed that the systems responsible are essentially temporal in character and capable of representing a variety of visual forms and colors, coded in different frequencies or at different phases of the same processing rhythm.