Headache: Chaos (Nonlinear Dynamics) and Migraine

Practical Pain Management. May 2010
by Lawrence Robbins, MD and Cameron Leith, PhD



The brain works primarily via synapses that interpret incoming inhibitory and excitatory impulses and nonlinear dynamics are involved in the feedback system of these complex neuronal systems. Physiologically, for energy conservation, it would make sense for living systems to utilize a nonlinear system, rather than random or simple linear dynamics. By utilizing a system where a tiny change in initial conditions may result in a major difference ‘downstream,’ a great deal of energy may be conserved. Chaos is a subset of nonlinear systems. Low-dimensional chaos theory may be the only way to explain how complex neurological systems are adaptable, efficient, versatile, and have effective feedback homeostasis. A large body of evidence has indicated that electrical activity of the brain, heart rhythms, blood glucose levels, and glycolysis are all governed, to some extent, by chaotic dynamics. Characteristics of chaotic systems include:



Extreme sensitivity to initial conditions; a tiny change upstream may lead to an enormous difference downstream. This would have major implications for headache therapies, as influencing the neuron’s initial conditions would require much less drug than attempting to affect all of the components later in the cascade.

The deterministic, not random, nature of chaotic dynamics. Chaotic output of a deterministic system, when plotted, mimics randomness but is not random and, in that sense, ‘chaos’ is a misnomer.

Chaotic systems possess a small number of independent variables, and the output is complex and deterministic.

The behavior of a system partially controlled by chaotic dynamics may change dramatically with a tiny change in the value of one parameter and is called a bifurcation.

The sequence of data in a chaotic system may be plotted and viewed as a phase space set.

To demonstrate chaotic mechanisms takes an enormous amount of data but this paper will simply describe the possible role of chaotic dynamics in headache pathophysiology.1,2