Transient Localized Wave Patterns and Their Application to Migraine

@article{Dahlem2013TransientLW,
  title={Transient Localized Wave Patterns and Their Application to Migraine},
  author={Markus A. Dahlem and Thomas Isele},
  journal={Journal of Mathematical Neuroscience},
  year={2013},
  volume={3},
  pages={7 - 7}
}
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… 
Mathematical approaches to modeling of cortical spreading depression.
Migraine with aura (MwA) is a debilitating disease that afflicts about 25%-30% of migraine sufferers. During MwA, a visual illusion propagates in the visual field, then disappears, and is followed by
How does spreading depression spread? Physiology and modeling
TLDR
This review discusses two types of models used to study 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, and the recent advances in techniques to link them.
Computational Models for the Propagation of Spreading Depression Waves
TLDR
This work proposes extensions to a popular model for the wave spread to test whether structural connectivity could aid in stopping the wave and preventing it from engulfing larger portions of the brain.
Migraine generator network and spreading depression dynamics as neuromodulation targets in episodic migraine.
TLDR
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.
Migraines and Cortical Spreading Depression
  • M. Dahlem
  • Medicine
    Encyclopedia of Computational Neuroscience
  • 2014
Migraine is a headache disorder characterized by recurrent episodes of head pain, often throbbing and unilateral, sometimes preceded by neurological symptoms called aura. The known pathophysiologic
Cortical hot spots and labyrinths: why cortical neuromodulation for episodic migraine with aura should be personalized
TLDR
The numerical simulations suggest that these target structures for neuromodulation are like fingerprints, they are individual features of each migraine sufferer, and the goal in the future will be to provide individualized neural tissue simulations.
Patient‐specific computational modeling of cortical spreading depression via diffusion tensor imaging
TLDR
A distributed model for extracellular potassium concentration with patient‐specific diffusivity tensors derived locally from diffusion tensor imaging data is integrated.
Hot spots and labyrinths: Why neuromodulation devices for episodic migraine should be personalized
TLDR
The numerical simulations suggest that these target structures for neuromodulation are like fingerprints, they are individual features of each migraine sufferer, and the goal in the future will be to provide individualized neural tissue simulations.
Local Dynamics of Ion-Based Neuron Models for Cortical Spreading Depression, Stroke and Seizures
TLDR
The bifurcation analysis shows that a closed neuron system can only recover from FES if the rate of the ion pumps is extremely enhanced, and proves the coexistence of a physiological resting state and FES in a large number of reduced ion–based model variants.
Traveling Bumps and Their Collisions in a Two-Dimensional Neural Field
TLDR
It is shown through numerical experiments that localized traveling excitation patterns (traveling bumps) exist in a two-dimensional neural field with excitation and inhibition mechanisms and might shed light on how neurons in the brain are functionally organized.
...
1
2
3
...

References

SHOWING 1-10 OF 105 REFERENCES
Migraine Aura: Retracting Particle-Like Waves in Weakly Susceptible Cortex
TLDR
It is predicted that human cortex is only weakly susceptible to SD (σ<1), and this prediction is supported by directly matching visual aura symptoms with anatomical landmarks using fMRI retinotopic mapping and how cortical susceptibility to SD must be adjusted for migraine drug testing is described.
Migraine aura dynamics after reverse retinotopic mapping of weak excitation waves in the primary visual cortex
TLDR
A kinematical model for excitable wave propagation is analyzed to describe the dynamics of a typical neurological symptom of migraine and the spatiotemporal pattern from this model can be matched in future investigations with those from introspectives to allow one to draw conclusions on topographic mapping of sensory input in human cortex.
Efficient control of transient wave forms to prevent spreading depolarizations.
Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke.
TLDR
A mechanism for spreading depolarizations (SD) that rests upon a nonlocal or noninstantaneous feedback in a reaction-diffusion system is proposed and the optimization of this feedback is elaborated for different control schemes and ranges of control parameters.
Cortical spreading depression and migraine
TLDR
Current concepts of CSD and its potential roles in migraine are summarized, and ongoing studies aimed at a clearer understanding of this fundamental brain phenomenon are addressed.
Migraine generator network and spreading depression dynamics as neuromodulation targets in episodic migraine.
TLDR
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.
Interface dynamics in planar neural field models
TLDR
A linear stability analysis for the interface dynamics that allows us to understand the mechanisms of pattern formation that arise from instabilities of spots, rings, stripes and fronts is developed.
Mechanisms of migraine aura revealed by functional MRI in human visual cortex
TLDR
High-field functional MRI with near-continuous recording during visual aura in three subjects observed blood oxygenation level-dependent signal changes that strongly suggest that an electrophysiological event such as CSD generates the aura in human visual cortex.
Cortical Spreading Depression Triggers Migraine Attack: Pro
TLDR
The accumulated evidence supporting a causal relationship between SD and migraine aura and headache is reviewed, and the contested notion that SD may also be involved in migraine attacks without a “perceived” aura is discussed.
...
1
2
3
4
5
...