Norbert Wiener (1894-1964) and Arturo Rosenblueth (1900-1970)

Norbert Wiener (top image) and Arturo Rosenblueth (bottom image)

The work of Norbert Wiener and Arturo Rosenblueth on "The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle" (Wiener and Rosenblueth, 1946) was the starting point of theoretical research in this field. Their paper seemingly deals with cardiac arrythmia and its mathematical formulation. However, the authors made right in the beginning the connection to the brain: "Nervous elements and cardiac and other striate muscle fibers are excitable. [...] The laws which apply to the muscle fibers are also applicable to the nerve fibers"

First page of the paper from Wiener and Rosenblueth (1941). This copy is from 1970 and belongs to Art Winfree, a leading theoretical biologist who made major contributions to the field of mathematical biology.

A comparison between brain and muscle cell activity may be valid on a very basic cellular level. For example, both can generate action potentials. But a connection between the pathophysiology of migraine aura and cardiac arrhythmia seems far fetched. Nevertheless, from a mathematical point of view the two phenomena share the same formulation. Just like sound waves and electromagnetic waves share the same mathematical formulation, and therefore support the same phenomena, for example, interference and diffraction, migraine attacks and cardiac arrhythmia are based on the same nonlinear wave equation. However, they are far separated in the parameter window of this equation (Dahlem and Müller, 2004).

In fact, Norbert Wiener and Arturo Rosenblueth most likely thought already about the particular connection to migraine. A few years before Rosenblueth wrote the paper with Wiener, he was one of the supervisors of a young Brazilian PhD student, Aristides A. P. Leão, who worked in the department of Physiology at Harvard Medical School (Somjen, 2005).

Leão's task was to use the newly developed 6-channel EEG apparatus for investigations of the spread of epileptic discharges. As a keen observer, he was the first who payed attention to an unexpected flatlined EEG signal occurring after an artificial epileptic seizure. The depression started close to his stimulation electrode and spread over all 6 subsequent recording sites. The obtained velocity was about 3 mm/min. After several minutes−quite surprisingly−the EEG amplitude increased again and nothing unnormal seems to remain. Leão named the phenomenon Cortical Spreading Depression (CSD). CSD is today discussed as the likely mechanism for the migraine aura (Teive et al.., 2005).

The model of Wiener and Rosenblueth describes the propagation of an excitable wave. It considers the motion of curves with free ends representing the wave front. The attractive feature of this kinematic model is that it perfectly mimics biophysical reaction-diffusion equations of waves in excitable media in the parameter window of weak excitability (Brazhnik et al., 1988; Mikhailov et al., 1994). The kinematic theory of wave propagation attempts to follow the spatial and temporal aspects based only on the fundamental underlying biophysical processes. It can predict differences between the spatio-temporal aura pattern caused by a neural phenomena (CSD) and those caused by a vascular phenomena (TIA) (see here).

References

Brazhnik PK, Davydov VA, Mikhailov AS. Kinematical approach to description of autowave processes. Theor Math Phys 1988; 74: 300-306.
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.
Mikhailov AS, Davydov VA, Zykov VS. Complex dynamics of spiral waves and motion of curves. Physica D 1994; 70: 1-39.
Somjen GG. Aristides Leao's discovery of cortical spreading depression. J Neurophysiol 2005; 94: 2-4.
Teive HA, Kowacs PA, Maranhao Filho P, Piovesan EJ, Werneck LC. Leao's cortical spreading depression: from experimental "artifact" to physiological principle. Neurology 2005; 65: 1455-9145.
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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