OBJECTIVES
This paper will describe in detail the probable connection between chaos theory and migraine pathophysiology.

BACKGROUND
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; 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.

METHODS
To demonstrate chaos in the brain, it takes 3 to 5 billion data points; therefore, this paper will interpret and expand upon what is known about chaos and migraine.

RESULTS
Ionic flow is governed by 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, versus 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 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.

CONCLUSION
The physical dynamics involved at the neuronal level, both intra and extracellular, are too complex to be explained via random, or even linear, dynamics. Chaotic dynamics certainly play a role, at least some of the time. It has been demonstrated that chaotic dynamics help to govern individual neurons, as well as neural systems. One fundamental principal of chaotic dynamics, unlike simple linear systems, is that a tiny change in initial conditions may lead to a profound difference later in the process. Only chaotic dynamics may explain why a tiny change in weather, stress, hormones, or sleep may result in a migraine. Chaos has been demonstrated to be involved in heart rhythms; chaotic dynamics may explain why a PFO may result, upstream, in an increase in CSD and headache. It is possible that, by utilizing and affecting chaotic controls, new therapies may be employed that utilize less drug than is currently required.

INTRODUCTION
The brain works primarily via synapses that interpret incoming inhibitory and excitatory impulses. 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, and versatile, with effective feedback homeostasis. A large body of evidence has indicated that electrical activity of the brain, heart rhythms, blood glucose levels, and glycolysis are governed, to some extent, by chaotic dynamics. Characteristics of chaotic systems include: 1. 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; 2.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; 3. Chaotic systems possess a small number of independent variables, and the output is complex and deterministic; 4. The behavior of a system partially controlled by chaotic dynamics may change dramatically with a tiny change in the value of one parameter; this is called a bifurcation; 5. The sequence of data in a chaotic system may be plotted and viewed as a phase space set. To demonstrate chaotic mechanisms, it takes an enormous amount of data; this paper will simply describe the possible role of chaotic dynamics in headache pathophysiology.^1,2

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, 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, returning brain dynamics to a more normal (chaotic) state. The nature of generators of complex neural behaviors cannot be random; it 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 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. 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, which 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

Ion channel kinetics, partially controlled by chaotic dynamics, play a crucial role in cortical spreading depression, and in brainstem inhibition. A small change in the channel protein will result, thru chaos, in a major difference in the shape of the protein. Neurons in the cortex fire with irregular patterns. Part of what governs the spiking patterns is the balance between excitatory and inhibitory inputs. The spiking patterns have been proven to be governed by chaotic dynamics, at least some of the time.

CHAOS AT THE NEURONAL LEVEL
Single neurons, as well as groups, fire in a variety of patterns, from regular oscillating patterns to bursts (and everything in between). Neurons, and neuronal systems, undergo transitions that carry them between diverse states. 4 Chaotic dynamics partially govern both individual neurons, as well as groups of neurons. The chaotic dynamics switch the neurons from one firing pattern to another. In the presence of low concentrations of serotonin, neuronal firing patterns change, with an increase in ‘beating’ periods, all of which follows chaotic dynamics. The synchronized dynamics of groups of neurons take the form, at times, of low dimensional chaos. The presence of chaos has been proven to be a factor in the inhibitory synaptic noise of certain types of neurons. Experimental studies have shown that chaos is involved in the dynamics of central dopaminergic neuronal systems, particularly in the substantia nigra.⁵

CORTICAL SPREADING DEPRESSION AND CHAOS
Cortical spreading depression (CSD) induces calcium and sodium influx, with potassium efflux, and P-Q calcium channels are involved. It is much too delicate and complex to be run by a random mechanism, or simple linear kinetics. Chaotic controls have been demonstrated to be involved with these channel ionic movements. Chaos would aid in explaining some of the properties of CSD. The initiation of CSD may be brought about by a very tiny change in potassium, with an activation of receptors, resulting in a large change downstream, with the resulting CSD and oligemia. With the potassium efflux under (partial) chaotic control, the chaos probably helps to regulate the increased cortical hyperactivity inherent in the brain of some migraineurs. There is evidence that the PAG may be partially controlled by chaotic dynamics.

A tiny cortical input may result in activation of the trigeminal nucleus caudalis, with resultant release of pro-inflammatory peptides, and a release of glutamate. CSD leads to plasma protein extravasation, with a very small perturbation upstream leading to this cascade. Only chaotic dynamics may explain how this sequence may be possible. The drugs that affect CSD (topiramate, amitriptyline, sodium valproate) may influence chaotic dynamics through membrane effects. It requires significantly less drug to influence the system if chaos is involved, versus if the system is primarily governed by linear (or random) dynamics. As is the situation with epileptic seizures, preventing the propagation of impulses upstream, through tiny ionic changes, may lead to less of the headache cascade downstream.

SENSITIZATION
The pathological shift of homeostasis that is observed with chronic central sensitization, with a loss of brainstem inhibitory activity, may actually reflect a loss of chaotic control; this is similar to a loss of chaotic controls in the heart, leading to certain arrhythmias, or with a loss of chaos, leading to a seizure.

Glutamate is the most prevalent excitatory neurotransmitter in the brain, and along with calcium is crucial in positive feedback processes. Glutamate has been shown to be directly involved in bi-directional communications between neurons and astrocytes. Research has demonstrated that glutamate feedback processes are critical in the generation of complex bursting oscillations in astrocytes. These glutamate-mediated events are likely to be involved in memory storage, epilepsy, and migraine. The control of this feedback process may well be, at least partially, enacted through chaotic control. Peripherally, the familiar cascade of magnesium binding to NMDA, with subsequent calcium influx, is very sensitive to minute initial changes. 6 Chaotic controls would help to explain the dynamics of peripheral sensitization. Drugs that may influence chaotic dynamics could work peripherally, in very low concentrations.

Simple nonlinear dynamics could not possibly explain the phenomenon of wind-up. NMDA receptor activation, as well as thalamic recruitment, would best be explained if they were controlled by nonlinear membrane/ionic dynamics.

CONTROLLING CHAOTIC DYNAMICS
By utilizing and influencing chaotic dynamics, significantly less drug would have to be employed, versus the amount required to affect a linear system. Brain-derived neurotrophic factor (BDNF) is a neurotropin that modulates the excitability of neuronal membranes. One study utilized BDNF to affect hippocampal neurons. It has been demonstrated that the patterns of electrical activity in hippocampal neurons are governed, in part, by chaotic dynamics. The hippocampal electrical system is a deterministic, chaotic one, with a few degrees of freedom. This ‘neuronal chaos’ may be sensitive to change by the application of small amounts of materials, such as BDNF, that influence temporal spiking. In this study, the application of BDNF to cultured hippocampal neurons enhanced the reliability of spike timing, and resulted in more stereotyped firing patterns. It was felt that BDNF influenced chaos through effects on sodium at the membrane level. BDNF enhanced membrane conductance, therefore stabilizing the membrane. The application of BDNF affected the switching between periodic and aperiodic neuronal oscillations. BDNF has been linked to modulation of neuroplasticity. The BDNF application decreased irregularity of firing patterns, by modulating neuronal outputs as well as inputs. The result was a BDNF-induced chaos stabilization. This experiment with BDNF was the first one to demonstrate a pharmacological stabilization of chaos, at the neuronal level.⁷

PRACTICAL APPLICATIONS
In several areas of medicine, practical applications for chaos type mathematical models are beginning to emerge. One company, Vicor Technologies, Inc., is utilizing a device (the PD2i) to identify patients at high risk for sudden cardiac death. This unit employs chaos theory to determine risk. In addition, the company is developing a similar device, using chaotic dynamics, to evaluate the health of the autonomic nervous system in patients with diabetic neuropathy.

Chaos theory may help us understand why a patient experiences a severe headache associated with a weather change, or due to other headache triggers. Tiny perturbations in a migraineur’s delicate autonomic nervous system may lead, after the familiar cascade of migrainous physiological events,to a migraine.

A number of studies have been done to identify the role, if any of patent foramen ovale (PFO) in migraine. There may be an association, not yet clinically proven, between PFO and migraine. Two current headache trials, in Europe and North America("Premium" and "Prima"), are blinded, sham controlled PFO closure studies. If indeed an association is proven, chaos theory may help to explain the relationship between PFO and migraine. A tiny (downstream) change in blood flow may lead(upstream) to a migraine attack.

To apply chaotic dynamics to pain or headache, we will need a great deal of basic research. The potential exists to create drugs that may utilize chaotic dynamics. For instance, glial cells modulate much of what goes on in the CNS. Glial cells utilize a small amount of neurotransmitter to modulate a large number of neurons. Future medications that affect glial cells may be effective through chaotic dynamics.

CONCLUSION
The physical dynamics involved at the neuronal level, both intra and extracellular, are too complex to be explained via random, or even linear, dynamics. Chaotic dynamics certainly play a role, at least some of the time. It has been demonstrated that chaotic dynamics help to govern individual neurons, as well as neural systems. One fundamental principal of chaotic dynamics, unlike simple linear systems, is that a tiny change in initial conditions may lead to a profound difference later in the process. Only chaotic dynamics may explain why a tiny change in weather, stress, hormones, or sleep may result in a migraine. Chaos has been demonstrated to be involved in heart rhythms; chaotic dynamics may explain why a PFO may result, upstream, in an increase in CSD and headache. It is possible that, by utilizing and affecting chaotic controls, new therapies may be employed that utilize less drug than is currently required.

REFERENCES

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