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Research Highlights

Migraine Generator Network


This project attempts to integrate the expertise from a collaboration partner in Japan (K. Aihara) on dynamical network biomarkers with the our expertise on migraine modeling to establish the theoretical foundation for understanding the mechanisms of pain formation in migraine. We aim at identifying putative neural correlates of early-warning signs indicating the imminent transition to a state of pain during two distinct phases, namely the prodromal and the aura phase. The prodromal phase with subtle symptoms, e.g. extreme yawning, precedes the pain phase by 1 day; the aura phase with various sensory hallucinations lasts up to 1 hour and directly precedes or overlaps with the pain phase that can then last up to 3 days. Pain is caused by a yet unknown transition into a state in which the brain responds with largely increased sensitivity to normal stimuli from the cranial blood vessels (central sensitization). This transition into the pain phase will be analysed by the model-free theory of dynamical network biomarker (DNB), which has been developed by the group of Prof. Aihara. The goal is to identify the role of putative subnetworks by their speci.c ability to generate early-warning signals of this transition in form of correlated large  fluctuations.


Biomarkers and Neuromodulation


Towards new therapy, the most upstream events in an episode are believed to reveal root causes of migraine and in this particular quest human data  must replace speculative data coming from animal models.  The problem is that in most volunteers, natural triggers all fail and using pharmacological stimulants instead could significantly bias results and in the worst case render the advantage of a human over an animal migraine model useless. We addressed this question with mathematical migraine model and suggest a blurring of the boundary between triggers and symptoms explains this failure. This may seem a baffling solution,
yet a mechanism for this blurring of causality is well studied in the framework of complex systems theory. The central message from complex systems theory is that migraine is an inherently dynamical disease with a complex network of interdependent events.  Unlike in a linear course from upstream to downstream events and from triggers to symptoms, we should expect to a certain degree a blurring of these usually opposing distinctions.  The challenge is to make use of this and to translate nonlinear principles into therapy by fusing control theory to an integrated systems medicine approach.

See: M. A. Dahlem, S. Rode, A. May, N. Fujiwara, Y. Hirata, K. Aihara, J. Kurths, Towards dynamical network biomarkers in neuromodulation of episodic migraine, Translational Neuroscience, 4,282-294 (2013)

Patterns of spreading depression in migraine


Our understanding how spreading depression (SD) relates to migraine without aura (MO) may be limited by inappropriate small animal models.  We suggest that large--scale SD patterns (extending over up to 40 square centimeter) and cortical geometry are important. This is concluded from statistical properties of simulations of SD with a computer model.   The simulated spatio-temporal SD patterns fall into two groups characterized by continuous and discontinuous (broken) SD wave fronts. Both forms have been further quantified and can be distinguished by size and duration.  Discontinuous patterns are the less prevalent type and these patterns have been observed with fMRI in migraine with aura (MA) and are reported by patients as visual field defects.  Therefore, we suggest that the mechanism for this group provides a dynamical understanding of ictogenesis in MA. The model also supports the still controversial idea that MO and MA share the same headache mechanism caused by SD.  The more prevalent type of continuous SD fronts shares features with the less prevalent type. These features are likely to be relevant for pain formation.  In particular, we predict (i) that pain is mainly caused if a sufficiently large area (2.5square centimeter) is instantaneously affected by SD, which is observed in either type only during the ignition phase, and (ii) that in MO, SD does not break away.  The model provides a mechanistic explanation why initially large ictogenic foci hinder further propagation. As two corollaries the model predicts (iii) that only from a smaller ictogenic focus SD can break away; headaches would therefore on average be less severe in MA than in MO, and (iv) that in migraine with typical aura without headache (MX) a particular small ictogenic focus (<2.5 square centimeter) exits.  All predictions can be tested by non-invasive imaging.

See: M. A. Dahlem and Thomas Isele: Transient localized wave patterns and their application to migraine.  J. Math. Neurosci. 3,7 (2013)  open access.

Simulation of migraine based on individual MRI scans

Cooperation with Bernd Schmidt.


This project will allow us to customize and validate the nucleation of migraine aura pathophysiology  by uploading the patient's MRI scanner readings into our simulation tool box. The methods involve polygon mesh processing, finite element analysis, and reaction-diffusion simulations.



Two-dimensional Wave Patterns in the Brain

We investigated spatio-temporal characteristics of spreading depolarizations (SD) in two experimental systems: retracting SD wave segments observed with intrinsic optical signals in chicken retina, and spontaneously occurring re-entrant SD waves that repeatedly spread across gyrencephalic feline cortex observed by laser speckle flowmetry. A mathematical framework of reaction diffusion systems is developed to explain the emergence and transitions between these patterns. Our prediction is that the observed patterns are reaction diffusion patterns controlled and modulated by weak nonlocal coupling such as long-range, time-delayed, and global coupling. The described spatio-temporal characteristics of SD are of important clinical relevance under conditions of migraine and stroke. In stroke, the emergence of re-entrant SD waves is believed to worsen outcome. In migraine, retracting SD wave segments cause neurological symptoms and transitions to stationary SD wave patterns may cause persistent symptoms without evidence from noninvasive imaging of infarction.

  • M. A. Dahlem, R. Graf, A. J. Strong, J. P. Dreier, Y. A. Dahlem, M. Sieber, W. Hanke, K. Podoll, and E. Schöll: Two-dimensional wave patterns of spreading depolarization: retracting, re-entrant, and stationary waves, Physica D 239,889 (2010). DOI


Migraine and TMS

The emerging transient patterns of Spreading Depression and their classification according to size and duration offers a model-based analysis of phase-depended stimulation protocols for non-invasive neuromodulation devices, e.g. utilizing transcranial magnetic stimulation, to intelligently target migraine. Furthermore, the migraine generator theory, a central pattern generator located in dorsolateral pons within the brain stem, is currently investigated by mathematical models. The stimulation protocol of neuromodulatory devices can be optimized. This optimization can be done either empirically or quantitatively with model-based methods.  Simply said, given the hardware works well with the wetware, what is the optimal software? To answer this, we need mathematical models.

[work in progress]


Cortical Mapping of Visual Migraine Aura (fMRI study)

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. We predict that human cortex is only weakly susceptible, and support this prediction by directly matching visual aura symptoms with anatomical landmarks using fMRI retinotopic mapping. 

  • Dahlem MA, Hadjikhani N (2009) Migraine Aura: Retracting Particle-Like Waves in Weakly Susceptible Cortex. PLoS ONE 4(4): e5007. doi


Time-delay Feedback in Neural Systems


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.

  • Schöll E, Hiller G, Hövel P, Dahlem MA. Time-delayed feedback in neurosystems.  Philos Transact A Math Phys Eng Sci. 2009 Mar 28;367(1891):1079-96. DOI


Failure of Spatio-Temporal Feedback


During migraine and stroke, neurological symptoms occur representing pathological events that spread through the cerebral cortex. While these clinical observations have been known for a long time, only recently direct measurements were made. Two studies have revealed common spatio-temporal wave patterns, one using functional magnetic resonance imaging in a migraine patient and another using electrodes placed directly on the exposed cortical surface to record electrical activity in a stroke patient. The observed spatio-temporal patterns in the cortex constitute examples of excitable behavior that evidently emerges from pathological pathways. Spatial systems that exhibit the emergent property that activity
breaks away from a local stimulation site are called excitable media. The capacity to propagate pulses is the distinguishing feature of excitability in spatial systems. As a mechanism for shifting the onset of excitability in a reaction-diffusion system we propose failure of nonlocal or noninstantaneous feedback control.


  • Dahlem MA, Schneider FM, Schöll E. Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke. Chaos. 2008 Jun;18(2):026110. DOI
  • F. M. Schneider, E. Schöll, and M. A. Dahlem: Control of traveling waves in excitable media by nonlocal coupling and time-delayed feedback. Chaos 19, 015110 (2009). APS/AIP selected paper Virtual Journal of Biological Physics Research March 2009. DOI


Cortical Magnification Tensor and Migraine Aura


The cortical magnification matrix M is introduced founded on a notion similar to that of the scalar cortical magnification factor M. This matrix frame is suitable to describe anisotropy in cortical magnification, which is of particular interest in the highly gyrified human cerebral cortex. The advantage of this tensor method over other surface-based 3D methods to explore cortical morphometry is that M expresses cortical quantities in the corresponding sensory space frame. It allows us to investigate the spatial relation between sensory function and anatomical structure. To this end, we consider the calcarine sulcus (CS) as an anatomical landmark for the primary visual cortex (V1). We found that a stereotypically formed 3D model of V1 compared to a flat model explains an excess of cortical tissue for the representation of visual information coming from the horizon of the visual field. This suggests that the intrinsic geometry of this sulcus is adapted to encephalize a particular function along the horizon. Since visual functions are assumed to be M-scaled, cortical folding can serve as an anatomical basis for increased functionality on the horizon similar to a retinal specialization known as visual streak, which is found in animals with lower encephalization. Thus, the gain of surface area by cortical folding links anatomical structure to cortical function in a previously unrecognized way, which may guide sulci development. We apply the concept to visual hallucination in migraine.

[in revision]

Spiral Waves in the Brain


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.


  • Dahlem MA, Müller SC. Self-induced splitting of spiral-shaped spreading depression waves in chicken retina. Exp Brain Res. 1997 Jun;115(2):319-24. DOI
  • Dahlem MA, Müller SC. Image processing techniques applied to excitation waves in the chicken retina. Methods. 2000 Aug;21(4):317-23. DOI


Self-organizing Map with Curved Kohonen-Layer Using Centroidal Voronoi Tesselations

An artificial neural network in form of a self-organizing map (SOM) is used to predict human retinotopy on an intrinsically curved surface that takes the shape of the area V1, i.e., the primary visual cortex. The neural layer of the SOM algorithm is created by a novel approach to implement centroidal Voronoi tesselations on meshes. Realistic retinotopic maps are obtained by driving self-organization with training sets derived from commonly accepted cortical magnification principles. We found that the curved nature of the visual cortex guides the observed map orientation.


Propagation of Visual Hallucination in Migraine

A kinematical 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.

  • Dahlem MA, Müller SC. Migraine aura dynamics after reverse retinotopic mapping of weak excitation waves in the primary visual cortex. Biol Cybern. 2003 Jun;88(6):419-24. (DOI)


The Ghost of a Saddle-Node Bifurcation and Migraine Aura



The key to the genesis of migraine with aura (with or without headache phase) is a phenomenon called cortical spreading depression (SD). SD is a transient state that during its course massively perturbs the brain's ionic homoeostasis. A mechanism is presented by which localized SD wave segments are formed in the folded cortical surface. These patterns are long-lasting but are transient. They emerge in a subexcitable medium. In such a medium, the homogeneous steady state is a global attractor. Local perturbations of this state can develop into distinct transient wave forms caused by a ghost of a saddle-node bifurcation that leads certain perturbed states through a slow 'bottle-neck' passage. The location of the bottle-neck in phase space is associated with a characteristic form (shape, size) of the wave segment that also depends critically on the curvature of the medium, i.e., the anatomical landmarks of human cortex. Similar patterns have been observed with fMRI.

[work in progress]

Cortical Geometry and Nucleation


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