Markus Dahlem

I develop neural network models of visual cortex to model the neurological symptoms of migraine in terms of functional cortical organization. Combined with nonlinear wave dynamics this approach can help to explain what happens to the brain during a migraine attack. Computer models of the process are helping to understand this complex phenomenon. I hope that this provides a route from aura morphology to migraine etiology.

Scotoma propagation

A typical temporal development of a migraine scotoma in the visual hemi-field, as shown above, was modeled based on the assumption that a nonlinear neural wave triggers this event. The model used a variant of the kinematic theory of wave propagation (Dahlem and Müller, 2003), which was originally proposed by Wiener and Rosenblueth (1946), the founders of cybernetics. Such a mathematical formalism predicts typical aura pattern caused by neural dynamics and distinguishes pattern caused by a vascular trigger.

Slowly spreading, i.e., in the range of a few millimeter per minute, neural waves can be caused by nonlinear dynamics. Their emergence is a feature of a particular parameter window in the mathematical formalism of reaction-diffusion systems. In fact, such waves are not even linked to a particular neural process. The same pattern can occur in a wide range of systems, e.g. in heart tissue, and aggregating colonies of slime mold. Even chemical and physical systems can exhibit the same behavior, e.g. the Belousov Zhabotinsky reaction and CO-oxidation on platinum surfaces, respectively.

All these systems share the property of excitability. Traveling waves, as they are often called, are just propagating reaction-diffusion structures and as such they depend on the existence of an excitable medium.

Visualizing the mechanism that leads to propagation in the neural model of migraine aura. The leftmost cell "explodes" and a trigger substance, sometimes called "activator" diffuses towards adjacent cells, where the same reaction is started. © 2007 Markus Dahlem

A vascular triggered aura would lack an excitable mechanism. The aura symptoms appear as being caused by a traveling wave, whereas in fact a cortical gradient merely coordinates wave-like behavior. Such pseudo-waves show rather different spatial dynamics.

With the help of this mathematical formalism, it could be shown that the spatio-temporal development of a typical aura pattern is governed by the dynamics in a small parameter region of excitable systems. This window is characterized by relatively low excitability (Dahlem and Müller, 2004).

Have you made records of the progression of visual migraine aura? The graph above shows the eccentricity of migraine phosphenes as an example of such data records. Please contact Markus Dahlem to contribute the observations of your migraine auras.

The disappearance of the visual symptoms after 15 to 45 minutes is also satisfactorily predicted by the assumption of weak excitability in the model. The cortical activation is limited in extent. The wave does not necessarily engulfs all of posterior cortex.

Schematic views of cortical activity in the human brain in the human brain. Top row is time series of CSD adapted from Lauritzen (1987) with permission. Bottom row is the same phenomenon assuming a much weaker excitability, i.e., lower susceptibility for CSD (Dahlem and Müller, 2003).

In summary, the form and temporal evolution of the scotoma predicted by the model are in striking correspondence to drawings and reports by migraine patients.

Model of zigzag pattern

To examine the positive symptoms of the typical fortification pattern, i.e., a scintillating zigzag pattern at the leading edge of the scotoma, I basically implemented the suggestion from Richards (1971). Namely that the fortification pattern may be explained with reference to the layout of functional domains in V1, i.e., the orientation map (Dahlem et al., 2000). Based on the responses of ensembles of neurons, a neural population vector (population code) was calculated. Each population was represented in the visual field by an edge with the orientation of the population vector. Population responses may overlap in the visual field, in which case the more dominant population displaces the weaker. This procedure results in a zigzag pattern very similar to those reported by migraine patients.

The static appearance of the zigzag is still inconclusive, as similar forms would result from orientation layouts that are arranged in linear parallel stripes. I next animated the zigzag pattern in the expectation that this would reveal further temporal details of the scintillating fortification. The animation was created from the sequence of visual impressions caused by the excitation pattern at subsequent cortical positions. It may be viewed here, but please note that this page include materials that flicker and so may not be suitable for users with migraine with aura or photosensitive epilepsy.

References

Dahlem MA, Chronicle EP. A computational perspective on migraine aura. Prog Neurobiol 2004; 74: 351-361.
Dahlem MA, Müller SC. Reaction-diffusion waves in neural tissue and the window of cortical excitability. Annalen der Physik 2004; 13: 442-449.
Dahlem MA, Müller SC. Migraine aura dynamics after reverse retinotopic mapping of weak excitation waves in the primary visual cortex. Biol Cybern 2003; 88: 419-424.
Dahlem MA, Engelmann R, Löwel S, Müller SC. Does the migraine aura reflect cortical organization? Eur J Neurosci 2000; 12: 767-770.
Lauritzen M. Cerebral blood flow in migraine and cortical spreading depression. Acta Neurol Scand Suppl. 1987; 113: 1-40.
Richards W. The fortification illusions of migraines. Sci Am 1971; 224: 88-96.
Wiener N, Rosenbluth A. The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle. Arch Inst Cardiol Mex 1946; 16: 205-265.

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http://www.migraine-aura.org/