ABSTRACT
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.
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.
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. 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.
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. 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.
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. 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.
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.
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