Study Design and Protocol of a Randomized Controlled Trial of the Efficacy of a Smartphone-Based Therapy of Migraine (SMARTGEM)

Background

Digitalization and electronic health (eHealth) offer new treatment approaches for patients with migraine. Current smartphone applications (apps) for migraine patients include a wide spectrum of functions ranging from digital headache diaries to app-based headache treatment by, among others, analysis of the possible triggers, behavioral therapy approaches and prophylactic non-drug treatment methods with relaxation therapy or endurance sport. Additional possibilities arise through the use of modern, location-independent communication methods, such as online consultations. However, there is currently insufficient evidence regarding the benefits and/or risks of these electronic tools for patients. To date, only few randomized controlled trials have assessed eHealth applications.

Methods

SMARTGEM is a randomized controlled trial assessing whether the provision of a new digital integrated form of care consisting of the migraine app M-sense in combination with a communication platform (with online consultations and medically moderated patient forum) leads to a reduction in headache frequency in migraine patients, improving quality of life, reducing medical costs and work absenteeism (DRKS-ID: DRKS00016328).

Discussion

SMARTGEM constitutes a new integrated approach for migraine treatment, which aims to offer an effective, location-independent, time-saving and cost-saving treatment. The design of the study is an example of how to gather high quality evidence in eHealth. Results are expected to provide insightful information on the efficacy of the use of electronic health technology in improving the quality of life in patients suffering from migraine and reducing resource consumption.

Determining the Evolution of Headache Among Regular Users of a Daily Electronic Diary via a Smartphone App: Observational Study

Background

Smartphone-based apps represent a major development in health care management. Specifically in headache care, the use of electronic headache diaries via apps has become increasingly popular. In contrast to the soaring volume of available data, scientific use of these data resources is sparse.

Objective

In this analysis, we aimed to assess changes in headache and migraine frequency, headache and migraine intensity, and use of acute medication among people who showed daily use of the headache diary as implemented in the freely available basic version of the German commercial app, M-sense.

Methods

The basic version of M-sense comprises an electronic headache diary, documentation of lifestyle factors with a possible impact on headaches, and evaluation of headache patterns. This analysis included all M-sense users who had entered data into the app on a daily basis for at least 7 months.

Results

We analyzed data from 1545 users. Mean MHD decreased from 9.42 (SD 5.81) at baseline to 6.39 (SD 5.09) after 6 months (P<.001; 95% CI 2.80-3.25). MMD, AMD, and migraine intensity were also significantly reduced. Similar results were found in 985 users with episodic migraine and in 126 users with chronic migraine.

Conclusions

Among regular users of an electronic headache diary, headache and migraine frequency, in addition to other headache characteristics, improved over time. The use of an electronic headache diary may support standard headache care.

Validation of an algorithm for automated classification of migraine and tension-type headache attacks in an electronic headache diary

Background

This study evaluates the accuracy of an automated classification tool of single attacks of the two major primary headache disorders migraine and tension-type headache used in an electronic headache diary.

Methods

One hundred two randomly selected reported headache attacks from an electronic headache-diary of patients using the medical app M-sense were classified by both a neurologist with specialisation in headache medicine and an algorithm, constructed based on the ICHD-3 criteria for migraine and tension-type headache. The level of agreement between the headache specialist and the algorithm was compared by using a kappa statistic. Cases of disagreement were analysed in a disagreement validity assessment.

Result

The neurologist and the algorithm classified migraines with aura (MA), migraines without aura (MO), tension-type headaches (TTH) and non-migraine or non-TTH events. Of the 102 headache reports, 86 cases were fully agreed on, and 16 cases not, making the level of agreement unweighted kappa 0.74 and representing a substantial level of agreement. Most cases of disagreement (12 out of 16) were due to inadvertent mistakes of the neurologist identified in the disagreement validity assessment. The second most common reason (3 out of 16) was insufficient information for classification by the neurologist.

Conclusions

The substantial level of agreement indicates that the classification tool is a valuable instrument for automated evaluation of electronic headache diaries, which can thereby support the diagnostic and therapeutic clinical processes. Based on this study’s results, additional diagnostic functionalities of primary headache management apps can be implemented. Finally, future research can use this classification algorithm for large scale database analysis for epidemiological studies.

Control of Spreading Depression with Electrical Fields

Spreading depression or depolarization is a large-scale pathological brain phenomenon related to migraine, stroke, hemorrhage and traumatic brain injury. Once initiated, spreading depression propagates across gray matter extruding potassium and other active molecules, collapsing the resting membrane electro-chemical gradient of cells leading to spike inactivation and cellular swelling, and propagates independently of synaptic transmission. We demonstrate the modulation, suppression and prevention of spreading depression utilizing applied transcortical DC electric fields in brain slices, measured with intrinsic optical imaging and potassium dye epifluorescence. We experimentally observe a surface-positive electric field induced forcing of spreading depression propagation to locations in cortex deeper than the unmodulated propagation path, whereby further propagation is confined and arrested even after field termination. The opposite surface-negative electric field polarity produces an increase in propagation velocity and a confinement of the wave to more superficial layers of cortex than the unmodulated propagation path. These field polarities are of opposite sign to the polarity that blocks neuronal spiking and seizures, and are consistent with biophysical models of spreading depression. The results demonstrate the potential feasibility of electrical control and prevention of spreading depression.

Heterogeneous propagation of spreading depolarizations in the lissencephalic and gyrencephalic brain

In the recently published article, "Heterogeneous incidence and propagation of spreading depolarizations," it is shown, in vivo and in vitro, how KCl-induced spreading depolarizations in mouse and rat brains can be highly variable, and that they are not limited, as once thought, to a concentric, isotropic, or homogenous depolarization wave in space or in time. The reported results serve as a link between the different species, and this paper contributes to changing the way in which SD expansion is viewed in the lissencephalic brain. Here, we discuss their results with our previous observations made in the gyrencephalic swine brain, in computer simulations, and in the human brain.

Recording, analysis, and interpretation of spreading depolarizations in neurointensive care: Review and recommendations of the COSBID research group

Spreading depolarizations (SD) are waves of abrupt, near-complete breakdown of neuronal transmembrane ion gradients, are the largest possible pathophysiologic disruption of viable cerebral gray matter, and are a crucial mechanism of lesion development. Spreading depolarizations are increasingly recorded during multimodal neuromonitoring in neurocritical care as a causal biomarker providing a diagnostic summary measure of metabolic failure and excitotoxic injury. Focal ischemia causes spreading depolarization within minutes. Further spreading depolarizations arise for hours to days due to energy supply-demand mismatch in viable tissue. Spreading depolarizations exacerbate neuronal injury through prolonged ionic breakdown and spreading depolarization-related hypoperfusion (spreading ischemia). Local duration of the depolarization indicates local tissue energy status and risk of injury. Regional electrocorticographic monitoring affords even remote detection of injury because spreading depolarizations propagate widely from ischemic or metabolically stressed zones; characteristic patterns, including temporal clusters of spreading depolarizations and persistent depression of spontaneous cortical activity, can be recognized and quantified. Here, we describe the experimental basis for interpreting these patterns and illustrate their translation to human disease. We further provide consensus recommendations for electrocorticographic methods to record, classify, and score spreading depolarizations and associated spreading depressions. These methods offer distinct advantages over other neuromonitoring modalities and allow for future refinement through less invasive and more automated approaches.

The continuum of spreading depolarizations in acute cortical lesion development: Examining Leão's legacy

A modern understanding of how cerebral cortical lesions develop after acute brain injury is based on Aristides Leão's historic discoveries of spreading depression and asphyxial/anoxic depolarization. Treated as separate entities for decades, we now appreciate that these events define a continuum of spreading mass depolarizations, a concept that is central to understanding their pathologic effects. Within minutes of acute severe ischemia, the onset of persistent depolarization triggers the breakdown of ion homeostasis and development of cytotoxic edema. These persistent changes are diagnosed as diffusion restriction in magnetic resonance imaging and define the ischemic core. In delayed lesion growth, transient spreading depolarizations arise spontaneously in the ischemic penumbra and induce further persistent depolarization and excitotoxic damage, progressively expanding the ischemic core. The causal role of these waves in lesion development has been proven by real-time monitoring of electrophysiology, blood flow, and cytotoxic edema. The spreading depolarization continuum further applies to other models of acute cortical lesions, suggesting that it is a universal principle of cortical lesion development. These pathophysiologic concepts establish a working hypothesis for translation to human disease, where complex patterns of depolarizations are observed in acute brain injury and appear to mediate and signal ongoing secondary damage.

How does spreading depression spread? Physiology and modeling

Spreading depression (SD) is a wave phenomenon in gray matter tissue. Locally, it is characterized by massive redistribution of ions across cell membranes. As a consequence, there is sustained membrane depolarization and tissue polarization that depress any normal electrical activity. Despite these dramatic events, SD remains difficult to observe in humans noninvasively, which, for long, has slowed advances in this field. The growing appreciation of its clinical importance in migraine and stroke is therefore consistent with an increasing need for computational methods that tackle the complexity of the problem at multiple levels. In this review, we focus on mathematical tools to investigate the question of spread and its two complementary aspects: What are the physiological mechanisms and what is the spatial extent of SD in the cortex? This review discusses two types of models used to study these two questions, namely, Hodgkin-Huxley type and generic activator-inhibitor models, and the recent advances in techniques to link them.

The Role of Cell Volume in the Dynamics of Seizure, Spreading Depression, and Anoxic Depolarization

Cell volume changes are ubiquitous in normal and pathological activity of the brain. Nevertheless, we know little of how cell volume affects neuronal dynamics. We here performed the first detailed study of the effects of cell volume on neuronal dynamics. By incorporating cell swelling together with dynamic ion concentrations and oxygen supply into Hodgkin-Huxley type spiking dynamics, we demonstrate the spontaneous transition between epileptic seizure and spreading depression states as the cell swells and contracts in response to changes in osmotic pressure. Our use of volume as an order parameter further revealed a dynamical definition for the experimentally described physiological ceiling that separates seizure from spreading depression, as well as predicted a second ceiling that demarcates spreading depression from anoxic depolarization. Our model highlights the neuroprotective role of glial K buffering against seizures and spreading depression, and provides novel insights into anoxic depolarization and the relevant cell swelling during ischemia. We argue that the dynamics of seizures, spreading depression, and anoxic depolarization lie along a continuum of the repertoire of the neuron membrane that can be understood only when the dynamic ion concentrations, oxygen homeostasis,and cell swelling in response to osmotic pressure are taken into consideration. Our results demonstrate the feasibility of a unified framework for a wide range of neuronal behaviors that may be of substantial importance in the understanding of and potentially developing universal intervention strategies for these pathological states.

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.

Analyzing critical propagation in a reaction-diffusion-advection model using unstable slow waves

The effect of advection on the propagation and in particular on the critical minimal speed of traveling waves in a reaction-diffusion model is studied. Previous theoretical studies estimated this effect on the velocity of stable fast waves and predicted the existence of a critical advection strength below which propagating waves are not supported anymore. In this paper, an analytical expression for the advection-velocity relation of the unstable slow wave is derived. In addition, the critical advection strength is calculated taking into account the unstable slow wave solution. We also analyze a two-variable reaction-diffusion-advection model numerically in a wide parameter range. Due to the new control parameter (advection) we can find stable wave propagation in the otherwise non-excitable parameter regime, if the advection strength exceeds a critical value. Comparing theoretical predictions to numerical results, we find that they are in good agreement. Theory provides an explanation for the observed behaviour.

Dynamics from seconds to hours in Hodgkin-Huxley model with time-dependent ion concentrations and buffer reservoirs

The classical Hodgkin-Huxley (HH) model neglects the time-dependence of ion concentrations in spiking dynamics. The dynamics is therefore limited to a time scale of milliseconds, which is determined by the membrane capacitance multiplied by the resistance of the ion channels, and by the gating time constants. We study slow dynamics in an extended HH framework that includes time-dependent ion concentrations, pumps, and buffers. Fluxes across the neuronal membrane change intra- and extracellular ion concentrations, whereby the latter can also change through contact to reservoirs in the surroundings. Ion gain and loss of the system is identified as a bifurcation parameter whose essential importance was not realized in earlier studies. Our systematic study of the bifurcation structure and thus the phase space structure helps to understand activation and inhibition of a new excitability in ion homeostasis which emerges in such extended models. Also modulatory mechanisms that regulate the spiking rate can be explained by bifurcations. The dynamics on three distinct slow times scales is determined by the cell volume-to-surface-area ratio and the membrane permeability (seconds), the buffer time constants (tens of seconds), and the slower backward buffering (minutes to hours). The modulatory dynamics and the newly emerging excitable dynamics corresponds to pathological conditions observed in epileptiform burst activity, and spreading depression in migraine aura and stroke, respectively.

Understanding migraine using dynamic network biomarkers

Background

Mathematical modeling approaches are becoming ever more established in clinical neuroscience. They provide insight that is key to understanding complex interactions of network phenomena, in general, and interactions within the migraine-generator network, in particular.

Purpose

In this study, two recent modeling studies on migraine are set in the context of premonitory symptoms that are easy to confuse for trigger factors. This causality confusion is explained, if migraine attacks are initiated by a transition caused by a tipping point.

Conclusion

We need to characterize the involved neuronal and autonomic subnetworks and their connections during all parts of the migraine cycle if we are ever to understand migraine. We predict that mathematical models have the potential to dismantle large and correlated fluctuations in such subnetworks as a dynamic network biomarker of migraine.

Radial, spiral and reverberating waves of spreading depolarization occur in the gyrencephalic brain

OBJECTIVES

The detection of the hemodynamic and propagation patterns of spreading depolarizations (SDs) in the gyrencephalic brain using intrinsic optical signal imaging (IOS).

METHODS

The convexity of the brain surface was surgically exposed in fourteen male swine. Within the boundaries of this window, brains were immersed and preconditioned with an elevated K(+) concentration (7 mmol/l) in the standard Ringer lactate solution for 30-40 min. SDs were triggered using 3-5 μl of 1 mol/l KCl solution. Changes in tissue absorbency or reflection were registered with a CCD camera at a wavelength of 564 nm (14 nm FWHM), which was mounted 25 cm above the exposed cortex. Additional monitoring by electrocorticography and laser-Doppler was used in a subset of animals (n=7) to validate the detection of SD.

RESULTS

Of 198 SDs quantified in all of the experiments, 187 SDs appeared as radial waves that developed semi-planar fronts. The morphology was affected by the surface of the gyri, the sulci and the pial vessels. Other SD patterns such as spirals and reverberating waves, which have not been described before in gyrencephalic brains, were also observed. Diffusion gradients created in the cortex surface (i.e., KCl concentrations), sulci, vessels and SD-SD interactions make the gyrencephalic brain prone to the appearance of irregular SD waves.

CONCLUSION

The gyrencephalic brain is capable of irregular SD propagation patterns. The irregularities of the gyrencephalic brain cortex may promote the presence of re-entrance waves, such as spirals and reverberating waves.

Linking a genetic defect in migraine to spreading depression in a computational model

Familial hemiplegic migraine (FHM) is a rare subtype of migraine with aura. A mutation causing FHM type 3 (FHM3) has been identified in SCN1A encoding the Nav1.1 Na⁺ channel. This genetic defect affects the inactivation gate. While the Na⁺ tail currents following voltage steps are consistent with both hyperexcitability and hypoexcitability, in this computational study, we investigate functional consequences beyond these isolated events. Our extended Hodgkin–Huxley framework establishes a connection between genotype and cellular phenotype, i.e., the pathophysiological dynamics that spans over multiple time scales and is relevant to migraine with aura. In particular, we investigate the dynamical repertoire from normal spiking (milliseconds) to spreading depression and anoxic depolarization (tens of seconds) and show that FHM3 mutations render gray matter tissue more vulnerable to spreading depression despite opposing effects associated with action potential generation. We conclude that the classification in terms of hypoexcitability vs. hyperexcitability is too simple a scheme. Our mathematical analysis provides further basic insight into also previously discussed criticisms against this scheme based on psychophysical and clinical data.

Migraine generator network and spreading depression dynamics as neuromodulation targets in episodic migraine

Migraine is a common disabling headache disorder characterized by recurrent episodes sometimes preceded or accompanied by focal neurological symptoms called aura. The relation between two subtypes, migraine without aura (MWoA) and migraine with aura (MWA), is explored with the aim to identify targets for neuromodulation techniques. To this end, a dynamically regulated control system is schematically reduced to a network of the trigeminal nerve, which innervates the cranial circulation, an associated descending modulatory network of brainstem nuclei, and parasympathetic vasomotor efferents. This extends the idea of a migraine generator region in the brainstem to a larger network and is still simple and explicit enough to open up possibilities for mathematical modeling in the future. In this study, it is suggested that the migraine generator network (MGN) is driven and may therefore respond differently to different spatio-temporal noxious input in the migraine subtypes MWA and MWoA. The noxious input is caused by a cortical perturbation of homeostasis, known as spreading depression (SD). The MGN might even trigger SD in the first place by a failure in vasomotor control. As a consequence, migraine is considered as an inherently dynamical disease to which a linear course from upstream to downstream events would not do justice. Minimally invasive and noninvasive neuromodulation techniques are briefly reviewed and their rational is discussed in the context of the proposed mechanism.

Towards dynamical network biomarkers in neuromodulation of episodic migraine

Computational methods have complemented experimental and clinical neurosciences and led to improvements in our understanding of the nervous systems in health and disease. In parallel, neuromodulation in form of electric and magnetic stimulation is gaining increasing acceptance in chronic and intractable diseases. In this paper, we firstly explore the relevant state of the art in fusion of both developments towards translational computational neuroscience. Then, we propose a strategy to employ the new theoretical concept of dynamical network biomarkers (DNB) in episodic manifestations of chronic disorders. In particular, as a first example, we introduce the use of computational models in migraine and illustrate on the basis of this example the potential of DNB as early-warning signals for neuromodulation in episodic migraine.

Transient localized wave patterns and their application to migraine

Transient dynamics is pervasive in the human brain and poses challenging problems both in mathematical tractability and clinical observability. We investigate statistical properties of transient cortical wave patterns with characteristic forms (shape, size, duration) in a canonical reaction-diffusion model with mean field inhibition. The patterns are formed by ghost behavior near a saddle-node bifurcation in which a stable traveling wave (node) collides with its critical nucleation mass (saddle). Similar patterns have been observed with fMRI in migraine. Our results support the controversial idea that waves of cortical spreading depression (SD) have a causal relationship with the headache phase in migraine and, therefore, occur not only in migraine with aura (MA), but also in migraine without aura (MO), i.e., in the two major migraine subtypes. We suggest a congruence between the prevalence of MO and MA with the statistical properties of the traveling waves' forms according to which two predictions follow: (i) the activation of nociceptive mechanisms relevant for headache is dependent upon a sufficiently large instantaneous affected cortical area; and (ii) the incidence of MA is reflected in the distance to the saddle-node bifurcation. We also observed that the maximal instantaneous affected cortical area is anticorrelated to both SD duration and total affected cortical area, which can explain why the headache is less severe in MA than in MO. Furthermore, the contested notion of MO attacks with silent aura is resolved. We briefly discuss model-based control and means by which neuromodulation techniques may affect pathways of pain formation.

Is spreading depolarization characterized by an abrupt, massive release of gibbs free energy from the human brain cortex?

In the evolution of the cerebral cortex, the sophisticated organization in a steady state far away from thermodynamic equilibrium has produced the side effect of two fundamental pathological network events: ictal epileptic activity and spreading depolarization. Ictal epileptic activity describes the partial disruption, and spreading depolarization describes the near-complete disruption of the physiological double Gibbs-Donnan steady state. The occurrence of ictal epileptic activity in patients has been known for decades. Recently, unequivocal electrophysiological evidence has been found in patients that spreading depolarizations occur abundantly in stroke and brain trauma. The authors propose that the ion changes can be taken to estimate relative changes in Gibbs free energy from state to state. The calculations suggest that in transitions from the physiological state to ictal epileptic activity to spreading depolarization to death, the cortex releases Gibbs free energy in a stepwise fashion. Spreading depolarization thus appears as a twilight state close to death. Consistently, electrocorticographic recordings in the core of focal ischemia or after cardiac arrest display a smooth transition from the initial spreading depolarization component to the later ultraslow negative potential, which is assumed to reflect processes in cellular death.

Interplay of time-delayed feedback control and temporally correlated noise in excitable systems

The interplay of time-delayed feedback and temporally correlated coloured noise in a single and two coupled excitable systems is studied in the framework of the FitzHugh-Nagumo (FHN) model. By using coloured noise instead of white noise, the noise correlation time is introduced as an additional time scale. We show that in a single FHN system the major time scale of oscillations is strongly influenced by the noise correlation time, which in turn affects the maxima of coherence with respect to the delay time. In two coupled FHN systems, coloured noise input to one subsystem influences coherence resonance and stochastic synchronization of both subsystems. Application of delayed feedback control to the coloured noise-driven subsystem is shown to change coherence and time scales of noise-induced oscillations in both systems, and to enhance or suppress stochastic synchronization under certain conditions.

Migraine aura: retracting particle-like waves in weakly susceptible cortex

Cortical spreading depression (SD) has been suggested to underlie migraine aura. Despite a precise match in speed, the spatio-temporal patterns of SD observed in animal cortex and aura symptoms mapped to the cortical surface ordinarily differ in aspects of size and shape. We show that this mismatch is reconciled by utilizing that both pattern types bifurcate from an instability point of generic reaction-diffusion models. To classify these spatio-temporal pattern we suggest a susceptibility scale having the value sigma = 1 at the instability point. We predict that human cortex is only weakly susceptible to SD (sigma<1), and support this prediction by directly matching visual aura symptoms with anatomical landmarks using fMRI retinotopic mapping. Moreover, we use retinal SD to give a proof of concept of the existence of this instability point and describe how cortical susceptibility to SD must be adjusted for migraine drug testing. Close to the instability point at sigma = 1 the dynamical repertoire of cortical tissue is increased. As a consequence, the picture of an engulfing SD that became paradigmatic for migraine with aura needs to be modified in most cases towards a more spatially confined pattern that remains within the originating major gyrus or sulcus. Furthermore, we discuss the resulting implications on migraine pharmacology that is hitherto tested in the regime (sigma>1), and potentially silent aura occurring below a second bifurcation point at sigma = 0 on the susceptible scale.

Time-delayed feedback in neurosystems

The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. A time delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic synchronization of instantaneously coupled neurons under the influence of white noise can be deliberately controlled by local time-delayed feedback. By appropriate choice of the delay time, synchronization can be either enhanced or suppressed. In delay-coupled neurons, antiphase oscillations can be induced for sufficiently large delay and coupling strength. The additional application of time-delayed self-feedback leads to complex scenarios of synchronized in-phase or antiphase oscillations, bursting patterns or amplitude death.

Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time-delayed feedback

The onset of pulse propagation is studied in a reaction-diffusion (RD) model with control by augmented transmission capability that is provided either along nonlocal spatial coupling or by time-delayed feedback. We show that traveling pulses occur primarily as solutions to the RD equations, while augmented transmission changes excitability. For certain ranges of the parameter settings, defined as weak susceptibility and moderate control, respectively, the hybrid model can be mapped to the original RD model. This results in an effective change in RD parameters controlled by augmented transmission. Outside moderate control parameter settings new patterns are obtained, for example, stepwise propagation due to delay-induced oscillations. Augmented transmission constitutes a signaling system complementary to the classical RD mechanism of pattern formation. Our hybrid model combines the two major signaling systems in the brain, namely, volume transmission and synaptic transmission. Our results provide insights into the spread and control of pathological pulses in the brain.

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.

Circles are different: The perception of Glass patterns modulates early event-related potentials

Glass patterns are randomized dot arrays that generate the perception of a global structure. They consist of correlated dot pairs which are generated by geometric transformations. The present study employed behavioral and event-related brain potential (ERP) measures to characterize the underlying neuronal processing when such patterns are perceived. Stimuli were circular, parallel, and randomized Glass patterns presented in two isoluminant colors using a choice reaction paradigm. Sixteen subjects were instructed to differentiate between colors with a button-press response. The N170 component increased in amplitude for circular patterns, and this effect was most pronounced bilaterally over occipito-temporal areas. The results suggest that the global perception of form generated by Glass patterns occurs at a stage of visual processing past area V1.

A computational perspective on migraine aura

The classical visual aura of migraine is characterized by a unilateral hallucination, composed of a zigzag fortification pattern followed by a trailing scotoma. This pattern usually starts in central vision, expands and spreads to the periphery, and then disappears. We review a number of historical attempts to explain the migraine aura in terms of brain events, then summarize recent theories of the pathophysiology of the aura. We describe an approach to the computational modeling of migraine aura, based on the principles of (a) cortical organization, and (b) active wave propagation in an excitable medium. We demonstrate correspondences between properties of the model system and aspects of the pathophysiology of the aura. The simulations produced by the model are in agreement with descriptions and drawings of visual aura from migraine patients. We outline several testable predictions stemming from the implementation of the model, and explain how model-based empirical research has the capacity to (a) improve recording of the phenomena of the visual aura, (b) improve understanding of the spatio-temporal dynamics of other types of aura, in particular somatosensory and dysphasic aurae, and (c) clarify the theoretical requirements for the initiation of aura in the brain.

Extracellular potassium alters frequency and profile of retinal spreading depression waves

The phenomenon of spreading depression (SD) was observed in chicken retina by means of optical registration via a microscope and a CCD camera applying modern methods of image processing for optimized evaluation of the wave profiles. The propagation dynamics of SD waves was investigated as a function of extracellular potassium. Two main findings were obtained. Firstly, the frequency of spontaneous wave generation increased with the increase of K+ concentration. Secondly, there was an effect of potassium on the wave profile. In particular, the recovery zone of SD waves was shortened at increased K+. This effect was not only due to the dispersion relation of waves in excitable media as shown by the result of the mechanically induced wave trains. Applying the basic principles of chemical excitability for the interpretation of the data led us to the conclusion that these potassium effects are due to perturbations of an autocatalytic reaction to be further explored.

Migraine aura dynamics after reverse retinotopic mapping of weak excitation waves in the primary visual cortex

Akinematical model for excitable wave propagation is analyzed to describe the dynamics of a typical neurological symptom of migraine. The kinematical model equation is solved analytically for a linear dependency between front curvature and velocity. The resulting wave starts from an initial excitation and moves in the medium that represents the primary visual cortex. Due to very weak excitability the wave propagates only across a confined area and eventually disappears. This cortical excitation pattern is projected onto a visual hemifield by reverse retinotopic mapping. Weak excitability explains the confined appearance of aura symptoms in time and sensory space. The affected area in the visual field matches in growth and form the one reported by migraine sufferers. The results can be extended from visual to tactile and to other sensory symptoms. If the spatiotemporal pattern from our model can be matched in future investigations with those from introspectives, it would allow one to draw conclusions on topographic mapping of sensory input in human cortex.

Image processing techniques applied to excitation waves in the chicken retina

Image processing techniques are described in detail that are used to gain information about the dynamics of wave propagation in excitable media. We focus on a phenomenon called spreading depression (SD) observed in the chicken retina, but the techniques described here concern a large variety of excitable systems. Despite the impressive progress both in SD research of the past 50 years and, during nearly the same period, in the theory of self-organization of wave patterns, there is still little mutual overlap. However, the increasing demands for understanding complex systems, like neuronal tissue, require such theoretical concepts. Arguments are given why the chicken retina is a nearly perfect experimental system for assessing and further developing these concepts.

Does the migraine aura reflect cortical organization?

Individuals suffering from classical migraine report an astonishing diversity of migraine auras. A frequently reported symptom is a visual hallucination known as fortification illusion (FI). Here we demonstrate that the typical zig-zag pattern of the FI can be reproduced using experimental data of orientation maps of the primary visual cortex (V1) assuming that a continuous excitation front propagates across V1. We put forward a model in which the cortical neurons within this excitation wave are activated sufficiently to contribute to conscious perception. It is shown that the discontinuous repetitive nature of the zig-zag pattern of the FI can reflect the specific layout of visual cortical orientation maps. Additionally, dynamic features of the FI are predicted based on our model.

Self-induced splitting of spiral-shaped spreading depression waves in chicken retina

Spreading depression (SD) of electroencephalographic activity is a dynamic wave phenomenon in the central nervous system (CNS). The retina, especially the isolated chicken retina, is an excellent constituent of the CNS in which to observe the dynamic behavior of the SD wave fronts, because it changes its optical properties during a SD attack. The waves become visible as milky fronts on a black background. It is still controversial what the basic mechanistic steps of SD are, but certainly SD belongs to the self-organization phenomena occurring in neuronal tissue. In this work, spiral-shaped wave fronts are analyzed using digital video imaging techniques. We report how the inner end of the wave front, the spiral tip, breaks away repeatedly. This separation process is associated with a Z-shaped trajectory (extension approximately 1.2 mm) that is described by the tip over one spiral revolution (period 2.45+/-0.1 min). The Z-shaped trajectory does not remain fixed, but performs a complex motion across the retina with each period. This is the first time, to our knowledge, that established imaging methods have been applied to the study of the two-dimensional features of SD wave propagation and to obtaining quantitative data of their dynamics. Since these methods do not interfere with the tissue, it is possible to observe the intrinsic properties of the phenomenon without any external influence.