Chaos (Nonlinear Dynamics) and Migraine
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
Chaos is a math-based, nonlinear dynamical theory. Chaos has been used to predict the behavior of ion flow, as well as neural and biosystems. Chaos is a misnomer, as it is deterministic, not random. A key property is extreme sensitivity to initial conditions so that a tiny change in initial conditions results in huge changes downstream. This has advantages for biosystems, particularly in conserving energy. Chaos has been shown to govern the beating of the heart, as well as the evolution of epileptic seizures.
Ionic flow is governed by either random, linear, or chaotic (nonlinear) controls. Chaotic control means that a small change in the channel protein results in a large change in the channel protein shape. This saves energy as compared to a simple linear control system. Ionic dynamics are crucial in cortical spreading depression (CSD). A tiny change in K+ efflux, or Ca+ influx, will result in a large effect downstream, with CSD and oligemia. Chaos has been demonstrated to play a role in K+, Ca+, and Na+ movements. Tiny perturbations—possibly brought about via weather, stress, or hormonal changes—in the hyperexcitable brain may result in CSD and eventually in plasma protein extravasation (PPE). Only chaotic dynamics could logically explain the cascade that leads from CSD to PPE.
The drugs that affect CSD may influence the membrane thru chaotic controls. Drugs that better control chaos may inhibit CSD. For instance, by affecting K+ efflux thru small effects upstream, we may prevent the events downstream that lead to headache. This has been demonstrated to be true with epileptic seizures. Peripherally, the familiar cascade of Mg++ binding to NMDA, with subsequent Ca+ influx, is very sensitive to initial conditions and changes. Drugs that work thru chaotic controls peripherally may be effective in very small concentrations.
With central sensitization (CS), wind-up is a typical system that is probably controlled by a nonlinear flexible system (chaos). Linear dynamics could not explain or control wind-up. Different aspects of CS are most likely under chaotic control, from NMDA activation to nitric oxide synthesis. Thalamic recruitment involved in expansion of the pain area is best explained by chaos. The pathological shift of homeostasis seen in chronic CS, with a loss of brainstem inhibition, may actually reflect a loss of chaotic control. This is similar to the loss of control in the heart, resulting in v-tachycardia. The brainstem periaqueductal grey (PAG)—important in migraine—has been shown to be under chaotic control thru P/Q-type Ca+ channels. Chaos may assert its most profound effects in the brainstem
Chaos and the Nervous System
Chaotic dynamics has been proven to function at a variety of levels in the nervous system. Both individual neurons (particularly in squid giant axons), as well as in neuronal systems, have been shown to be—at least some of the time—governed by nonlinear dynamics. Neuronal networks of thalamo-cortical circuits have their feedback loops managed by chaotic dynamics. Neural network models in analyzing thalamic networks have demonstrated the presence of chaos. In a person with epilepsy, when chaos fails and patterns become too regular, an epileptic seizure may result to return brain dynamics to a more normal (chaotic) state. By the very nature of generators of complex neural behaviors, they cannot be random but must be deterministic and nonlinear, at least some of the time. It is likely that neuronal dynamics vacillate and totter between random, linear, and chaotic dynamics.1
“Chaos theory may help us understand why a patient experiences a severe headache associated with a weather change or other headache triggers.”
Chaos at the Ionic Level
The flow of ions about the cell has been determined to be a combination of randomness, linear (deterministic) movements, and chaotic processes. Again, for energy saving, chaotic mechanisms are more efficient. Chaotic mechanisms in the brainstem may explain why tiny changes in weather or hormones may result in a migraine. Most neuronal activity in the brainstem involves postsynaptic inhibition that has been demonstrated to be governed by chaotic mechanisms. If we were dealing with a linear system, a tiny change in weather, stress, hormones or sleep would not lead to neuronal activity differences. Chaotic dynamics will turn tiny initial changes or perturbations into major events, possibly triggering cortical spreading depression. By altering the concentration of sodium outside of the cell, it has been demonstrated that the membrane response must be governed, at least in part, by chaos. Several studies have demonstrated chaos at the cellular level in the brain.3 By utilizing the “jumps” of ions through the energy barriers of the channel protein, maps have been constructed that reveal the chaotic controls. Numerical solutions and algorithms have been constructed revealing when the transition to chaotic dynamics occurs.1