The problem of mental causation is a conceptual issue in the philosophy of mind. That problem, in short, is how to account for the common sense idea that intentional thoughts or intentional mental states
are causes of intentional actions. The problem divides into several
distinct sub-problems, including the problem of causal exclusion, the
problem of anomalism, and the problem of externalism. However, the
sub-problem which has attracted most attention in the philosophical
literature is arguably the exclusion problem.
Description
The basic problem of mental causation is an intuitive one: on the face of it, it seems that mental events
cause physical events (and vice versa), but how can mental events have
any causal effect on physical events? Suppose that a person, John,
orders dessert after dinner. It seems that at least one cause for such a
physical, behavioral event is that John desired to have dessert and
believed that by ordering dessert he would be able to soon have dessert.
But, how can such mental events as beliefs and desires cause John's
mouth to move in such a way that he orders dessert?
Sub-problems of mental causation
Exclusion problem
What follows is a summary of the causal exclusion problem
in its simplest form, and it is merely one of several possible
formulations.
To the extent that we do not have to go
outside human physiology in order to trace the causal antecedents of any
bodily movement, intentional action can be fully causally explained by
the existence of these physiological antecedents alone.
No mention of mental states need enter into the explanation. This
troubles philosophers because intuitively it seems that mental states
are crucial in causing a person to act (for example, their beliefs and
desires). But, given that physiological facts are sufficient to account
for action, mental states appear to be superfluous; they are at risk of
being causally and explanatorily irrelevant with respect to human action
(Yoo 2006, p.§3b.iii).
Many philosophers consider this apparent irrelevance to be a
highly counter-intuitive and undesirable position to take. It
ultimately leads to epiphenomenalism—the
view that mental events or states are causally irrelevant, they are
merely after effects that play no role in any causal chains whatsoever. Thomas Huxley
famously noted that epiphenomenalism treats mental states like the
steam coming off a train: it plays no causal role in the train's moving
forward, it is merely an "emergent property" of the actual causation
occurring in the engine (Walter 2003, p.§2).
Problem of anomalism
Another problem with mental causation is that mental events
seem anomalous in the sense that there are no scientific laws that
mental states can figure into without having exceptions. There are no
"strict" laws, and mental events must factor into strict laws in order
to fit respectably into the causal order described by current science
[see (Davidson 1970)].
In short, one response has been to deny that psychological laws involving mental states require strict, exceptionless laws. Jerry Fodor argues that non-basic (or "special") sciences do not in fact require strict laws (Fodor 1980). In current practice, special sciences (for example, biology and chemistry) have ceteris paribus
laws (or laws with "all else being equal" clauses), according to which
there are exceptions. However, only in the basic sciences (physics) are
there strict, exceptionless laws. Thus, although mental states are
anomalous, they can still figure into scientifically respectable laws of
psychology.
Problem of externalism
In the latter half of the twentieth century externalism about meanings
became espoused by many philosophers. Externalism is roughly the view
that certain parts of an individual's environment play a crucial role in
the meaning of at least some of an individual's words [see (Putnam 1975) and (Burge 1979)]. A thesis about meaning affects the mind insofar as our thoughts are about
things in the world. A common view in the philosophy of mind is that at
least certain mental states have intentional content in this sense. For
example, one's belief that water is wet has the semantic content of water is wet.
The thought is about water and the fact that it is wet. But, if
externalism is true—if some of the contents of one's thoughts are
constituted at least in part by factors external to one's mind—then
there is yet another difficulty in explaining how mental states can
cause physical states.
Some have claimed that while the mental and the physical
are quite different things, they can nonetheless causally interact with
one another, a view going back to Descartes [(Descartes & 1642/1986), especially meditations II & VI]. This view is known as interactionist dualism.
The major problem that interactionist dualism faces is that of
explicating a satisfactory notion of causation according to which
non-spatial events, such as mental events, can causally interact with
physical events. According to the current mainstream scientific
world-view, the physical realm is causally closed,
in that causal relationships only hold among physical events in the
physical realm. Given these types of considerations, some argue that it
is appropriate to say that the main assumptions in interactionist
dualism generate the problem of mental causation rather than solve it
(see (Yoo 2006, p.§1a).
The other major option is to assert that mental events are either (at least contingently) identical to physical events, or supervene on physical events. Views that fall under this general heading are called physicalism or materialism. But, such views require a particular theory to explain how mental events are physical in nature. One such theory is behaviorism. Behaviorists, in general, argue that mental events are merely dispositions to behave in certain ways. Another theory is the identity theory, according to which mental events are (either type- or token-) identical to physical events. A more recent view, known as functionalism,
claims that mental events are individuated (or constituted by) the
causal role they play. As such, mental events would fit directly into
the causal realm, as they are simply certain causal (or functional)
roles.
Idealist solutions
Popper's three-world formulation
Related to dualism above, a more general and somewhat differently posed approach to mental causation is provided by Karl Popper's three worlds. Popper split the world into three categories:
The mental or psychological world, the world of our
feelings of pain and of pleasure, of our thoughts, of our decisions, of
our perceptions and our observations; in other words, the world of
mental or psychological states or processes, or of subjective
experiences.
The world of products of the human mind, including art, science, and religion.
World 3 includes physical theory as a particular case. But
World 3 is a creation of the human imagination, and such acts of
imagination are a part of World 2. Accordingly, one could argue that the
physical notion of causality is a child of the imagination, and
although causation has its successes in describing World 1, it may not
apply to World 2 or World 3. The subjective aspects of theories
contained in World 3 are not readily framed within the third-person
perspective of science used to explain World 1.
From this perspective, it is hubris to suppose that the
methods successful in describing World 1, in particular to suppose the
notions of cause and effect, invented
by World 2 in its creation of the theory of World 3 used to explain
World 1, have direct application to Worlds 2 and 3 themselves, and
control mental agency.
Psychological nativism
A still different approach to mental causation is based
upon the philosophies of Kant, Chomsky and Pinker. These philosophers
stress the impact of built-in aspects of mind, studied in the field of psychological nativism.
Immanuel Kant (1724–1804) pointed out that we all shape our experience of things through the filter of our mind, a view sometimes called epistemological solipsism. The mind shapes that experience, and among other things, Kant believed the concepts of space and time were programmed into the human brain, as was the notion of cause and effect. We never have direct experience of things, the noumenal world, and what we do experience is the phenomenal
world as conveyed by our senses, this conveyance processed by the
machinery of the mind and nervous system. Kant focused upon this
processing. Kant believed in a priori knowledge arrived at independent of experience, so-called synthetica priori
knowledge. In particular, he thought that by introspection some aspects
of the filtering mechanisms of the mind/brain/nervous system could be
discovered. The following observations summarize Kant's views upon the subject-object problem, called Kant's Copernican revolution:
"It has hitherto
been assumed that our cognition must conform to the objects; but all
attempts to ascertain anything about these objects a priori, by
means of conceptions, and thus to extend the range of our knowledge,
have been rendered abortive by this assumption. Let us then make the
experiment whether we may not be more successful in metaphysics, if we
assume that the objects must conform to our cognition. This appears, at
all events, to accord better with the possibility of our gaining the end
we have in view, that is to say, of arriving at the cognition of
objects a priori, of determining something with respect to these
objects, before they are given to us. We here propose to do just what
Copernicus did in attempting to explain the celestial movements. When he
found that he could make no progress by assuming that all the heavenly
bodies revolved round the spectator, he reversed the process, and tried
the experiment of assuming that the spectator revolved, while the stars
remained at rest. We may make the same experiment with regard to the
intuition of objects."
—Immanuel Kant, English translation by John Meiklejohn of The Critique of Pure Reason (1. edition 1781, April 23, 1787 Immanuel Kant, Preface to the 2. edition)
Although Kant has posed the issue of built-in aspects of
mind, the particulars that depend upon the science of his day have
become outmoded. A more recent approach to these limitations is proposed
by Noam Chomsky and Steven Pinker. Like Kant, Noam Chomsky
raised the issue of the mind's inherent programming. Chomsky selected
as a particular example the acquiring of language by children. Of course, language is indispensable in the formulation and communication of our perceptions of the objective world:
"People do not
think in English or Chinese or Apache; they think in a language of
thought. This language of thought probably looks a bit like all these
languages;...But compared with any given language, mentalese must be
richer in some ways and simpler in others."
—Steven Pinker, The Language Instinct, p. 72
Chomsky marshaled evidence that a child's rapid mastery of
the complexity of language indicated an innate ability programmed into
the development of the human mind from birth that could not be explained
by the "blank slate"
view of the infant mind. Rather, the mind has a built-in propensity to
process symbolic representations. The origins of this ability were
sought by Steven Pinker in a Darwinian struggle that established the survival value of the ability to communicate. According to Pinker, Charles Darwin
himself "concluded that language ability is 'an instinctive tendency to
acquire an art', a design that is not peculiar to humans but seen in
other species such as song-learning birds." This observation is strongly
supported by research on crows.
This work can be taken to suggest that although a physical
theory is an intermediary between our observations and our notions of
connections between them, it is an elaborate mental construction that is
a meld of the way the mind works and objective observations. Although a
physical theory is used to determine connections about objective
events, the specific form of the theoretical construct is a product of
subjective activities, and this particular form may well involve the
workings of the brain. Perhaps some aspects of the universe's operation
can be expressed in terms of mental constructs, but this process is
analogous with the expression of a computer algorithm in terms of assembly language instructions peculiar to a particular computer, a translation by a compiler of the general statement of an algorithm into specific tiny steps that particular computer can handle.
From this standpoint, as with the philosophy of Kant, the
first-person active actions of mental causation may involve innate
workings of the brain itself.
Simulation of neural oscillations at 10 Hz. Upper panel shows spiking of individual neurons (with each dot representing an individual action potential within the population of neurons), and the lower panel the local field potential
reflecting their summed activity. Figure illustrates how synchronized
patterns of action potentials may result in macroscopic oscillations
that can be measured outside the scalp. When these neural oscillation
patterns of synchronization break down, a reduction of signal intensity
occurs.Autocorrelations
and spike raster plots of two single-units recorded from the secondary
somatosensory cortex of a monkey. The top neuron is oscillating
spontaneously at approximately 30 Hz. The bottom neuron is not
oscillating.
Neural oscillations, or brainwaves, are rhythmic or repetitive patterns of neural activity in the central nervous system. Neural tissue can generate oscillatory activity in many ways, driven either by mechanisms within individual neurons or by interactions between neurons. In individual neurons, oscillations can appear either as oscillations in membrane potential or as rhythmic patterns of action potentials, which then produce oscillatory activation of post-synaptic neurons. At the level of neural ensembles, synchronized activity of large numbers of neurons can give rise to macroscopic oscillations, which can be observed in an electroencephalogram.
Oscillatory activity in groups of neurons generally arises from
feedback connections between the neurons that result in the
synchronization of their firing patterns. The interaction between
neurons can give rise to oscillations at a different frequency than the
firing frequency of individual neurons. A well-known example of
macroscopic neural oscillations is alpha activity.
Neural oscillations in humans were observed by researchers as early as 1924 (by Hans Berger).
More than 50 years later, intrinsic oscillatory behavior was
encountered in vertebrate neurons, but its functional role is still not
fully understood. The possible roles of neural oscillations include feature binding, information transfer mechanisms and the generation of rhythmic motor output. Over the last decades more insight has been gained, especially with advances in brain imaging. A major area of research in neuroscience
involves determining how oscillations are generated and what their
roles are. Oscillatory activity in the brain is widely observed at
different levels of organization
and is thought to play a key role in processing neural information.
Numerous experimental studies support a functional role of neural
oscillations; a unified interpretation, however, is still lacking.
History
Richard Caton discovered electrical activity in the cerebral hemispheres of rabbits and monkeys and presented his findings in 1875. Adolf Beck
published in 1890 his observations of spontaneous electrical activity
of the brain of rabbits and dogs that included rhythmic oscillations
altered by light, detected with electrodes directly placed on the
surface of the brain. Before Hans Berger, Vladimir Vladimirovich Pravdich-Neminsky published the first animal EEG and the evoked potential of a dog.
Overview
Neural oscillations are observed throughout the central nervous system at all levels, and include spike trains, local field potentials and large-scale oscillations which can be measured by electroencephalography (EEG). In general, oscillations can be characterized by their frequency, amplitude and phase. These signal properties can be extracted from neural recordings using time-frequency analysis. In large-scale oscillations, amplitude changes are considered to result from changes in synchronization within a neural ensemble,
also referred to as local synchronization. In addition to local
synchronization, oscillatory activity of distant neural structures
(single neurons or neural ensembles) can synchronize. Neural
oscillations and synchronization have been linked to many cognitive
functions such as information transfer, perception, motor control and
memory.
The opposite of neuron synchronization is neural isolation,
which is when electrical activity of neurons is not temporally
synchronized. This is when the likelihood of the neuron to reach its threshold potential
for the signal to propagate to the next neuron decreases. This
phenomenon is typically observed as the spectral intensity decreases
from the summation of these neurons firing, which can be utilized to
differentiate cognitive function or neural isolation. However, new
non-linear methods have been used that couple temporal and spectral
entropic relationships simultaneously to characterize how neurons are
isolated, (the signal's inability to propagate to adjacent neurons), an
indicator of impairment (e.g., hypoxia).
Neural oscillations have been most widely studied in neural
activity generated by large groups of neurons. Large-scale activity can
be measured by techniques such as EEG. In general, EEG signals have a
broad spectral content similar to pink noise, but also reveal oscillatory activity in specific frequency bands. The first discovered and best-known frequency band is alpha activity (8–12 Hz) that can be detected from the occipital lobe during relaxed wakefulness and which increases when the eyes are closed. Other frequency bands are: delta (1–4Hz), theta (4–8Hz), beta (13–30Hz), low gamma (30–70Hz), and high gamma (70–150Hz)
frequency bands. Faster rhythms such as gamma activity have been linked
to cognitive processing. Indeed, EEG signals change dramatically during
sleep. In fact, different sleep stages are commonly characterized by
their spectral content. Consequently, neural oscillations have been linked to cognitive states, such as awareness and consciousness.
Although neural oscillations in human brain activity are
mostly investigated using EEG recordings, they are also observed using
more invasive recording techniques such as single-unit recordings. Neurons can generate rhythmic patterns of action potentials or spikes. Some types of neurons have the tendency to fire at particular frequencies, either as resonators or as intrinsic oscillators. Bursting is another form of rhythmic spiking. Spiking patterns are considered fundamental for information coding in the brain. Oscillatory activity can also be observed in the form of subthreshold membrane potential oscillations (i.e. in the absence of action potentials). If numerous neurons spike in synchrony, they can give rise to oscillations in local field potentials. Quantitative models can estimate the strength of neural oscillations in recorded data.
Neural oscillations are commonly studied within a mathematical framework and belong to the field of neurodynamics, an area of research in the cognitive sciences that places a strong focus on the dynamic character of neural activity in describing brain function. It considers the brain a dynamical system and uses differential equations
to describe how neural activity evolves over time. In particular, it
aims to relate dynamic patterns of brain activity to cognitive functions
such as perception and memory. In very abstract form, neural
oscillations can be analyzed analytically. When studied in a more physiologically realistic setting, oscillatory activity is generally studied using computer simulations of a computational model.
The functions of neural oscillations are wide-ranging and
vary for different types of oscillatory activity. Examples are the
generation of rhythmic activity such as a heartbeat and the neural binding
of sensory features in perception, such as the shape and color of an
object. Neural oscillations also play an important role in many neurological disorders, such as excessive synchronization during seizure activity in epilepsy, or tremor in patients with Parkinson's disease. Oscillatory activity can also be used to control external devices such as a brain–computer interface.
Oscillatory activity is observed throughout the central nervous system
at all levels of organization. Three different levels have been widely
recognized: the micro-scale (activity of a single neuron), the
meso-scale (activity of a local group of neurons) and the macro-scale
(activity of different brain regions).
Tonic firing pattern of single neuron showing rhythmic spiking activity
Microscopic
Neurons generate action potentials
resulting from changes in the electric membrane potential. Neurons can
generate multiple action potentials in sequence forming so-called spike
trains. These spike trains are the basis for neural coding and information transfer in the brain. Spike trains can form all kinds of patterns, such as rhythmic spiking and bursting, and often display oscillatory activity. Oscillatory activity in single neurons can also be observed in sub-threshold fluctuations
in membrane potential. These rhythmic changes in membrane potential do
not reach the critical threshold and therefore do not result in an
action potential. They can result from postsynaptic potentials from
synchronous inputs or from intrinsic properties of neurons.
Neuronal spiking can be classified by its activity pattern.
The excitability of neurons can be subdivided in Class I and II. Class I
neurons can generate action potentials with arbitrarily low frequency
depending on the input strength, whereas Class II neurons generate
action potentials in a certain frequency band, which is relatively
insensitive to changes in input strength. Class II neurons are also more prone to display sub-threshold oscillations in membrane potential.
Mesoscopic
A group of neurons can also generate oscillatory activity. Through synaptic interactions, the firing patterns
of different neurons may become synchronized and the rhythmic changes
in electric potential caused by their action potentials may accumulate (constructive interference).
That is, synchronized firing patterns result in synchronized input into
other cortical areas, which gives rise to large-amplitude oscillations
of the local field potential. These large-scale oscillations can also be measured outside the scalp using electroencephalography (EEG) and magnetoencephalography
(MEG). The electric potentials generated by single neurons are far too
small to be picked up outside the scalp, and EEG or MEG activity always
reflects the summation of the synchronous activity of thousands or
millions of neurons that have similar spatial orientation.
Neurons in a neural ensemble
rarely all fire at exactly the same moment, i.e. fully synchronized.
Instead, the probability of firing is rhythmically modulated such that
neurons are more likely to fire at the same time, which gives rise to
oscillations in their mean activity. (See figure at top of page.) As
such, the frequency of large-scale
oscillations does not need to match the firing pattern of individual
neurons. Isolated cortical neurons fire regularly under certain
conditions, but in the intact brain, cortical cells are bombarded by
highly fluctuating synaptic inputs and typically fire seemingly at
random. However, if the probability of a large group of neurons firing
is rhythmically modulated at a common frequency, they will generate
oscillations in the mean field. (See also figure at top of page.)
Neural ensembles can generate oscillatory activity endogenously through local interactions between excitatory and inhibitory neurons. In particular, inhibitory interneurons
play an important role in producing neural ensemble synchrony by
generating a narrow window for effective excitation and rhythmically
modulating the firing rate of excitatory neurons.
Macroscopic
Neural oscillation can also arise from interactions between different brain areas coupled through the structural connectome. Time delays play an important role here. Because all brain areas are bidirectionally coupled, these connections between brain areas form feedback loops. Positive feedback
loops tend to cause oscillatory activity where frequency is inversely
related to the delay time. An example of such a feedback loop is the
connections between the thalamus and cortex – the thalamocortical radiations. This thalamocortical network is able to generate oscillatory activity known as recurrent thalamo-cortical resonance. The thalamocortical network plays an important role in the generation of alpha activity. In a whole-brain network model with realistic anatomical connectivity
and propagation delays between brain areas, oscillations in the beta frequency range
emerge from the partial synchronisation of subsets of brain areas
oscillating in the gamma-band (generated at the mesoscopic level).
Scientists have identified some intrinsic neuronal properties that play an important role in generating membrane potential oscillations. In particular, voltage-gated ion channels
are critical in the generation of action potentials. The dynamics of
these ion channels have been captured in the well-established Hodgkin–Huxley model that describes how action potentials are initiated and propagated by means of a set of differential equations. Using bifurcation analysis,
different oscillatory varieties of these neuronal models can be
determined, allowing for the classification of types of neuronal
responses. The oscillatory dynamics of neuronal spiking as identified in
the Hodgkin–Huxley model closely agree with empirical findings.
In addition to periodic spiking, subthreshold membrane potential oscillations, i.e. resonance
behavior that does not result in action potentials, may also contribute
to oscillatory activity by facilitating synchronous activity of
neighboring neurons.
Like pacemaker neurons in central pattern generators, subtypes of cortical cells fire bursts of spikes (brief clusters of spikes) rhythmically at preferred frequencies. Bursting neurons have the potential to serve as pacemakers for
synchronous network oscillations, and bursts of spikes may underlie or
enhance neuronal resonance. Many of these neurons can be considered intrinsic oscillators, namely,
neurons that generate their oscillations intrinsically, as their
oscillation frequencies can be modified by local applications of
glutamate in-vivo.
Apart from intrinsic properties of neurons, biological neural network properties are also an important source of oscillatory activity. Neurons communicate
with one another via synapses and affect the timing of spike trains in
the post-synaptic neurons. Depending on the properties of the
connection, such as the coupling strength, time delay and whether
coupling is excitatory or inhibitory, the spike trains of the interacting neurons may become synchronized. Neurons are locally connected, forming small clusters that are called neural ensembles.
Certain network structures promote oscillatory activity at specific
frequencies. For example, neuronal activity generated by two populations
of interconnected inhibitory and excitatory cells can show spontaneous oscillations that are described by the Wilson-Cowan model.
If a group of neurons engages in synchronized oscillatory
activity, the neural ensemble can be mathematically represented as a
single oscillator. Different neural ensembles are coupled through long-range connections
and form a network of weakly coupled oscillators at the next spatial
scale. Weakly coupled oscillators can generate a range of dynamics
including oscillatory activity. Long-range connections between different brain structures, such as the thalamus and the cortex (see thalamocortical oscillation), involve time-delays due to the finite conduction velocity of axons. Because most connections are reciprocal, they form feed-back loops that support oscillatory activity. Oscillations recorded from multiple cortical areas can become synchronized to form large-scale brain networks, whose dynamics and functional connectivity can be studied by means of spectral analysis and Granger causality measures. Coherent activity of large-scale brain activity may form dynamic links
between brain areas required for the integration of distributed
information.
Microglia–the major immune cells of the brain–have
been shown to play an important role in shaping network connectivity,
and thus, influencing neuronal network oscillations both ex vivo and in vivo.
In addition to fast direct synaptic interactions between neurons forming a network, oscillatory activity is regulated by neuromodulators
on a much slower time scale. That is, the concentration levels of
certain neurotransmitters are known to regulate the amount of
oscillatory activity. For instance, GABA concentration has been shown to be positively correlated with frequency of oscillations in induced stimuli. A number of nuclei in the brainstem have diffuse projections throughout the brain influencing concentration levels of neurotransmitters such as norepinephrine, acetylcholine and serotonin. These neurotransmitter systems affect the physiological state, e.g., wakefulness or arousal, and have a pronounced effect on amplitude of different brain waves, such as alpha activity.
Oscillations can often be described and analyzed using mathematics. Mathematicians have identified several dynamical mechanisms that generate rhythmicity. Among the most important are harmonic (linear) oscillators, limit cycle oscillators, and delayed-feedback oscillators. Harmonic oscillations appear very frequently in nature—examples are sound waves, the motion of a pendulum, and vibrations of every sort. They generally arise when a physical system is perturbed by a small degree from a minimum-energy state, and are well understood mathematically.
Noise-driven harmonic oscillators realistically simulate
alpha rhythm in the waking EEG as well as slow waves and spindles in the
sleep EEG. Successful EEG analysis
algorithms were based on such models. Several other EEG components are
better described by limit-cycle or delayed-feedback oscillations.
Limit-cycle oscillations arise from physical systems that show large deviations from equilibrium,
whereas delayed-feedback oscillations arise when components of a system
affect each other after significant time delays. Limit-cycle
oscillations can be complex but there are powerful mathematical tools
for analyzing them; the mathematics of delayed-feedback oscillations is
primitive in comparison. Linear oscillators and limit-cycle oscillators
qualitatively differ in terms of how they respond to fluctuations in
input. In a linear oscillator, the frequency is more or less constant
but the amplitude can vary greatly. In a limit-cycle oscillator, the
amplitude tends to be more or less constant but the frequency can vary
greatly. A heartbeat
is an example of a limit-cycle oscillation in that the frequency of
beats varies widely, while each individual beat continues to pump about
the same amount of blood.
Computational models
adopt a variety of abstractions in order to describe complex
oscillatory dynamics observed in brain activity. Many models are used in
the field, each defined at a different level of abstraction and trying
to model different aspects of neural systems. They range from models of
the short-term behaviour of individual neurons, through models of how
the dynamics of neural circuitry
arise from interactions between individual neurons, to models of how
behaviour can arise from abstract neural modules that represent complete
subsystems.
Simulation of a Hindmarsh–Rose neuron showing typical bursting behavior: a fast rhythm generated by individual spikes and a slower rhythm generated by the bursts.
A model of a biological neuron is a mathematical
description of the properties of nerve cells, or neurons, that is
designed to accurately describe and predict its biological processes.
One of the most successful neuron models is the Hodgkin–Huxley model,
for which Hodgkin and Huxley won the 1963 Nobel Prize in physiology or medicine. The model is based on data from the squid giant axon
and consists of nonlinear differential equations that approximate the
electrical characteristics of a neuron, including the generation and
propagation of action potentials.
The model is so successful at describing these characteristics that
variations of its "conductance-based" formulation continue to be
utilized in neuron models over half a century later.
The Hodgkin–Huxley model is too complicated to understand
using classical mathematical techniques, so researchers often turn to
simplifications such as the FitzHugh–Nagumo model and the Hindmarsh–Rose model, or highly idealized neuron models such as the leaky integrate-and-fire neuron, originally developed by Lapique in 1907. Such models only capture salient membrane dynamics such as spiking or bursting at the cost of biophysical detail, but are more computationally efficient, enabling simulations of larger biological neural networks.
A neural network model describes a population of
physically interconnected neurons or a group of disparate neurons whose
inputs or signalling targets define a recognizable circuit. These
models aim to describe how the dynamics of neural circuitry arise from
interactions between individual neurons. Local interactions between
neurons can result in the synchronization of spiking activity and form
the basis of oscillatory activity. In particular, models of interacting pyramidal cells and inhibitory interneurons have been shown to generate brain rhythms such as gamma activity. Similarly, it was shown that simulations of neural networks with a
phenomenological model for neuronal response failures can predict
spontaneous broadband neural oscillations.
Simulation of a neural mass model showing network spiking during the onset of a seizure. As the gain A is increased the network starts to oscillate at 3Hz.
Neural field models are another important tool in studying
neural oscillations and are a mathematical framework describing
evolution of variables such as mean firing rate in space and time. In
modeling the activity of large numbers of neurons, the central idea is
to take the density of neurons to the continuum limit, resulting in spatially continuous neural networks.
Instead of modelling individual neurons, this approach approximates a
group of neurons by its average properties and interactions. It is based
on the mean field approach, an area of statistical physics
that deals with large-scale systems. Models based on these principles
have been used to provide mathematical descriptions of neural
oscillations and EEG rhythms. They have for instance been used to
investigate visual hallucinations.
The Kuramoto model of coupled phase oscillators is one of the most abstract and fundamental models used to investigate
neural oscillations and synchronization. It captures the activity of a
local system (e.g., a single neuron or neural ensemble) by its circular phase alone and hence ignores the amplitude of oscillations (amplitude is constant). Interactions amongst these oscillators are introduced by a simple algebraic form (such as a sine function) and collectively generate a dynamical pattern at the global scale.
The Kuramoto model is widely used to study oscillatory
brain activity, and several extensions have been proposed that increase
its neurobiological plausibility, for instance by incorporating
topological properties of local cortical connectivity. In particular, it describes how the activity of a group of interacting
neurons can become synchronized and generate large-scale oscillations.
Simulations using the Kuramoto model with realistic
long-range cortical connectivity and time-delayed interactions reveal
the emergence of slow patterned fluctuations that reproduce
resting-state BOLD functional maps, which can be measured using fMRI.
Activity patterns
Both single neurons and groups of neurons can generate
oscillatory activity spontaneously. In addition, they may show
oscillatory responses to perceptual input or motor output. Some types of
neurons will fire rhythmically in the absence of any synaptic input.
Likewise, brain-wide activity reveals oscillatory activity while
subjects do not engage in any activity, so-called resting-state activity.
These ongoing rhythms can change in different ways in response to
perceptual input or motor output. Oscillatory activity may respond by
increases or decreases in frequency and amplitude or show a temporary
interruption, which is referred to as phase resetting. In addition,
external activity may not interact with ongoing activity at all,
resulting in an additive response.
Oscillatory responses
The frequency of ongoing oscillatory activity is increased between t1 and t2.
The amplitude of ongoing oscillatory activity is increased between t1 and t2.
The phase of ongoing oscillatory activity is reset at t1.
Activity is linearly added to ongoing oscillatory activity between t1 and t2.
Ongoing activity
Spontaneous activity is brain
activity in the absence of an explicit task, such as sensory input or
motor output, and hence also referred to as resting-state activity. It
is opposed to induced activity, i.e. brain activity that is induced by
sensory stimuli or motor responses.
The term ongoing brain activity is used in electroencephalography and magnetoencephalography for those signal components that are not associated with the processing of a stimulus or the occurrence of specific other events, such as moving a body part, i.e. events that do not form evoked potentials/evoked fields, or induced activity.
Spontaneous activity is usually considered to be noise
if one is interested in stimulus processing; however, spontaneous
activity is considered to play a crucial role during brain development,
such as in network formation and synaptogenesis. Spontaneous activity
may be informative regarding the current mental state of the person
(e.g. wakefulness, alertness) and is often used in sleep research.
Certain types of oscillatory activity, such as alpha waves,
are part of spontaneous activity. Statistical analysis of power
fluctuations of alpha activity reveals a bimodal distribution, i.e. a
high- and low-amplitude mode, and hence shows that resting-state
activity does not just reflect a noise process.
In case of fMRI, spontaneous fluctuations in the blood-oxygen-level dependent (BOLD) signal reveal correlation patterns that are linked to resting state networks, such as the default network. The temporal evolution of resting state networks is correlated with
fluctuations of oscillatory EEG activity in different frequency bands.
Ongoing brain activity may also have an important role in
perception, as it may interact with activity related to incoming
stimuli. Indeed, EEG
studies suggest that visual perception is dependent on both the phase
and amplitude of cortical oscillations. For instance, the amplitude and
phase of alpha activity at the moment of visual stimulation predicts
whether a weak stimulus will be perceived by the subject.
Frequency response
In response to input, a neuron or neuronal ensemble may change the frequency at which it oscillates, thus changing the rate
at which it spikes. Often, a neuron's firing rate depends on the summed
activity it receives. Frequency changes are also commonly observed in central pattern generators and directly relate to the speed of motor activities, such as step frequency in walking. However, changes in relative oscillation frequency between different brain areas is not so common because the frequency of oscillatory activity is often related to the time delays between brain areas.
Amplitude response
Next to evoked activity, neural activity related to
stimulus processing may result in induced activity. Induced activity
refers to modulation in ongoing brain activity induced by processing of
stimuli or movement preparation. Hence, they reflect an indirect
response in contrast to evoked responses. A well-studied type of induced
activity is amplitude change in oscillatory activity. For instance, gamma activity often increases during increased mental activity such as during object representation. Because induced responses may have different phases across measurements
and therefore would cancel out during averaging, they can only be
obtained using time-frequency analysis.
Induced activity generally reflects the activity of numerous neurons:
amplitude changes in oscillatory activity are thought to arise from the
synchronization of neural activity, for instance by synchronization of
spike timing or membrane potential fluctuations of individual neurons.
Increases in oscillatory activity are therefore often referred to as
event-related synchronization, while decreases are referred to as
event-related desynchronization (ERD).
Phase resetting
Phase resetting occurs when input to a neuron or neuronal ensemble resets the phase of ongoing oscillations. It is very common in single neurons where spike timing is adjusted to
neuronal input (a neuron may spike at a fixed delay in response to
periodic input, which is referred to as phase locking)
and may also occur in neuronal ensembles when the phases of their
neurons are adjusted simultaneously. Phase resetting is fundamental for
the synchronization of different neurons or different brain regions because the timing of spikes can become phase locked to the activity of other neurons.
Phase resetting also permits the study of evoked activity, a term used in electroencephalography and magnetoencephalography for responses in brain activity that are directly related to stimulus-related activity. Evoked potentials and event-related potentials
are obtained from an electroencephalogram by stimulus-locked averaging,
i.e. averaging different trials at fixed latencies around the
presentation of a stimulus. As a consequence, those signal components
that are the same in each single measurement are conserved and all
others, i.e. ongoing or spontaneous activity, are averaged out. That is,
event-related potentials only reflect oscillations in brain activity
that are phase-locked
to the stimulus or event. Evoked activity is often considered to be
independent from ongoing brain activity, although this is an ongoing
debate.
Asymmetric amplitude modulation
It has recently been proposed that even if phases are not aligned across trials, induced activity may still cause event-related potentials
because ongoing brain oscillations may not be symmetric and thus
amplitude modulations may result in a baseline shift that does not
average out. This model implies that slow event-related responses, such as
asymmetric alpha activity, could result from asymmetric brain
oscillation amplitude modulations, such as an asymmetry of the
intracellular currents that propagate forward and backward down the
dendrites. Under this assumption, asymmetries in the dendritic current would cause
asymmetries in oscillatory activity measured by EEG and MEG, since
dendritic currents in pyramidal cells are generally thought to generate
EEG and MEG signals that can be measured at the scalp.
Cross-frequency coupling
Cross-frequency coupling (CFC) describes the coupling
(statistical correlation) between a slow wave and a fast wave. There are
many kinds, generally written as A-B coupling, meaning the A of a slow
wave is coupled with the B of a fast wave. For example, phase–amplitude
coupling is where the phase of a slow wave is coupled with the amplitude
of a fast wave.
The theta-gamma code is a coupling
between theta wave and gamma wave in the hippocampal network. During a
theta wave, 4 to 8 non-overlapping neuron ensembles are activated in
sequence. This has been hypothesized to form a neural code representing
multiple items in a temporal frame.
Function
Since neural synchronization has been linked to many cognitive functions, a theory of how it contributes to cognition is fundamental for explaining the neurophysiological basis of brain activity. According to Latvian professor Igor Val Danilov, the evolutionary basis
of brainwave entrainment to external oscillations is one plausible
solution to how the brain develops awareness and cognition. A mother-fetus neurocognitive model
provides neurophysiological insights into how cognition begins through
fetal neural entrainment to the natural oscillations (coined Natural
Neurostimulation) produced by the mother's body. This position argues
that neural synchronization of fetal neural networks to the rhythm of
the mother's heart is an evolutionary mechanism. This inherited process
for the mother-fetus nervous system synchronization during gestation
ensures fetal neural growth and the onset of cognitive functions.
According to the prevailing view in cognitive science, the
manifestation of cognitive functions is associated with the temporal
coordination of high-frequency neural oscillations across different
brain regions. Considering the propagation of high-frequency waves in
tissues is limited by local circuits (which can only provide local
coordination), the theory of Natural Neurostimulation explains why high-frequency
oscillations from anatomically non-connected nervous system zones become
synchronized. First of all, based on a review of numerous neuroscience studies, Prof.
Vinck and colleagues highlighted four hypotheses on a mechanism of
temporal coordination:
(4) Linear signal transmission (coherence-through-communication).
Among them, the idea of brainwave interactions for network oscillatory synchronization is the most influential.
Then, the theory of Natural Neurostimulation extended
these insights. Prof. Igor Val Danilov argues that, in temporal
coordination, low-frequency heart oscillations harmonize high-frequency
brain oscillations across the nervous system due to the law of
interference. Indeed, the essential principle of neural oscillations is that neurons
are both generators and recipients of electromagnetic fields. According
to physical laws, neural oscillations exhibit dual behavior in brain
networks: they are influenced by spiking inputs and, in turn, affect the
timing of spike outputs. Neurons may alter their oscillatory activity by interacting with
external electromagnetic fields. Moreover, in physics, when incoherent
waves are superimposed, the intensity of the resulting wave is equal to
the sum of the powers of the superimposed waves. The energy of the
resulting oscillations of each point of the medium is similar to the sum
of the energies of its oscillations due to all incoherent waves. So,
interference occurs when two oscillations combine: low-frequency
oscillations modulate the high ones and propagate them at the distance
of their own propagation. In neuroscience, this wave interference, where
the phase of the underlying slow rhythm modulates the power of faster
oscillations, is often called nested oscillations. Due to the
low-frequency waves' ability to propagate over long distances in human
tissues, heartbeats-nested high-frequency brain oscillations from
anatomically non-connected nervous system zones become synchronized.
That is, interference between heart oscillations and high-frequency
brain oscillations is crucial for temporal coordination, integrated
neuronal processing, and cognition.During pregnancy, the mother's heart oscillations synchronize neuronal
activity across both organisms, which coexist in the same ecological
context, i.e., auditory stimuli from the mother's environment. The fetal
environment includes both physicochemical interactions with the
mother's body and sounds from the mother's environment that can reach
the fetus's auditory system. In this manner, physical interactions between the mother and fetus
stimulate the fetal sentience. Due to neural synchrony, particular
reactions of the mature nervous system become a template for the naive
organism in the early stages of perception development, and
subsequently, cognition. This theory argues that the maternal
electromagnetic field, complex acoustic wave, and the mother's ecology
are fundamental factors in the proper development of the child's nervous
system. The fetal nervous system learns to react in the same way as the
mother's nervous system responds to stimuli. The coupling of the two
nervous systems in perceiving environmental stimuli contributes to the
initiation of cognition and the development of emotions by associating
affective cues with stimuli that activate neural pathways for simple
reflexes.
Neural synchronization can be modulated by task constraints, such as attention, and is thought to play a role in feature binding, neuronal communication, and motor coordination. Neuronal oscillations became a hot topic in neuroscience in the 1990s when the studies of the visual system of the brain by Gray, Singer and others appeared to support the neural binding hypothesis. According to this idea, synchronous oscillations in neuronal ensembles
bind neurons representing different features of an object. For example,
when a person looks at a tree, visual cortex neurons representing the
tree trunk and those representing the branches of the same tree would
oscillate in synchrony to form a single representation of the tree. This
phenomenon is best seen in local field potentials which reflect the synchronous activity of local groups of neurons, but has also been shown in EEG and MEG
recordings providing increasing evidence for a close relation between
synchronous oscillatory activity and a variety of cognitive functions
such as perceptual grouping and attentional top-down control.
Cells in the sinoatrial node, located in the right atrium of the heart, spontaneously depolarize
approximately 100 times per minute. Although all of the heart's cells
have the ability to generate action potentials that trigger cardiac
contraction, the sinoatrial node normally initiates it, simply because
it generates impulses slightly faster than the other areas. Hence, these
cells generate the normal sinus rhythm and are called pacemaker cells as they directly control the heart rate.
In the absence of extrinsic neural and hormonal control, cells in the
SA node will rhythmically discharge. The sinoatrial node is richly
innervated by the autonomic nervous system, which up or down regulates the spontaneous firing frequency of the pacemaker cells.
Synchronized firing of neurons also forms the basis of
periodic motor commands for rhythmic movements. These rhythmic outputs
are produced by a group of interacting neurons that form a network,
called a central pattern generator.
Central pattern generators are neuronal circuits that—when
activated—can produce rhythmic motor patterns in the absence of sensory
or descending inputs that carry specific timing information. Examples
are walking, breathing, and swimming, Most evidence for central pattern generators comes from lower animals, such as the lamprey, but there is also evidence for spinal central pattern generators in humans.
Neuronal spiking is generally considered the basis for
information transfer in the brain. For such a transfer, information
needs to be coded in a spiking pattern. Different types of coding
schemes have been proposed, such as rate coding and temporal coding.
Neural oscillations could create periodic time windows in which input
spikes have larger effect on neurons, thereby providing a mechanism for
decoding temporal codes.
Single-cell intrinsic oscillators serve as valuable tools
for decoding temporally-encoded sensory information. This information is
encoded through inter-spike intervals, and intrinsic oscillators can
act as 'temporal rulers' for precisely measuring these intervals. One
notable mechanism for achieving this is the neuronal phase-locked loop
(NPLL). In this mechanism, cortical oscillators undergo modulation
influenced by the firing rates of thalamocortical 'phase detectors,'
which, in turn, gauge the disparity between the cortical and sensory
periodicity.
Synchronization of neuronal firing may serve as a means to group
spatially segregated neurons that respond to the same stimulus in order
to bind these responses for further joint processing, i.e. to exploit
temporal synchrony to encode relations. Purely theoretical formulations
of the binding-by-synchrony hypothesis were proposed first, but subsequently extensive experimental evidence has been reported
supporting the potential role of synchrony as a relational code.
The functional role of synchronized oscillatory activity
in the brain was mainly established in experiments performed on awake
kittens with multiple electrodes implanted in the visual cortex. These
experiments showed that groups of spatially segregated neurons engage in
synchronous oscillatory activity when activated by visual stimuli. The
frequency of these oscillations was in the range of 40Hz
and differed from the periodic activation induced by the grating,
suggesting that the oscillations and their synchronization were due to
internal neuronal interactions. Similar findings were shown in parallel by the group of Eckhorn,
providing further evidence for the functional role of neural
synchronization in feature binding. Since then, numerous studies have replicated these findings and
extended them to different modalities such as EEG, providing extensive
evidence of the functional role of gamma oscillations in visual perception.
Gilles Laurent and colleagues showed that oscillatory
synchronization has an important functional role in odor perception.
Perceiving different odors leads to different subsets of neurons firing
on different sets of oscillatory cycles. These oscillations can be disrupted by GABA blocker picrotoxin, and the disruption of the oscillatory synchronization leads to
impairment of behavioral discrimination of chemically similar odorants
in bees, and to more similar responses across odors in downstream β-lobe neurons. Recent follow-up of this work has shown that oscillations create periodic integration windows for Kenyon cells in the insect mushroom body, such that incoming spikes from the antennal lobe are more effective in activating Kenyon cells only at specific phases of the oscillatory cycle.
Neural oscillations are also thought be involved in the sense of time and in somatosensory perception. However, recent findings argue against a clock-like function of cortical gamma oscillations.
Oscillations have been commonly reported in the motor system. Pfurtscheller and colleagues found a reduction in alpha (8–12Hz) and beta (13–30Hz) oscillations in EEG activity when subjects made a movement. Using intra-cortical recordings, similar changes in oscillatory
activity were found in the motor cortex when the monkeys performed motor
acts that required significant attention. In addition, oscillations at spinal level become synchronised to beta
oscillations in the motor cortex during constant muscle activation, as
determined by cortico-muscular coherence. Likewise, muscle activity of different muscles reveals inter-muscular coherence at multiple distinct frequencies reflecting the underlying neural circuitry involved in motor coordination.
Recently it was found that cortical oscillations propagate as travelling waves across the surface of the motor cortex along dominant spatial axes characteristic of the local circuitry of the motor cortex. It has been proposed that motor commands in the form of travelling
waves can be spatially filtered by the descending fibres to selectively
control muscle force. Simulations have shown that ongoing wave activity in cortex can elicit
steady muscle force with physiological levels of EEG-EMG coherence.
Oscillatory rhythms at 10Hz have been recorded in a brain area called the inferior olive, which is associated with the cerebellum. These oscillations are also observed in motor output of physiological tremor and when performing slow finger movements. These findings may indicate that the human brain controls continuous
movements intermittently. In support, it was shown that these movement
discontinuities are directly correlated to oscillatory activity in a
cerebello-thalamo-cortical loop, which may represent a neural mechanism
for the intermittent motor control.
Neural oscillations, in particular theta
activity, are extensively linked to memory function. Theta rhythms are
very strong in rodent hippocampi and entorhinal cortex during learning
and memory retrieval, and they are believed to be vital to the induction
of long-term potentiation, a potential cellular mechanism for learning and memory. Coupling between theta and gamma activity is thought to be vital for memory functions, including episodic memory. Tight coordination of single-neuron spikes with local theta
oscillations is linked to successful memory formation in humans, as more
stereotyped spiking predicts better memory.
Sleep is a naturally recurring state characterized by reduced or absent consciousness and proceeds in cycles of rapid eye movement (REM) and non-rapid eye movement (NREM) sleep. Sleep stages are characterized by spectral content of EEG:
for instance, stage N1 refers to the transition of the brain from alpha
waves (common in the awake state) to theta waves, whereas stage N3
(deep or slow-wave sleep) is characterized by the presence of delta
waves. The normal order of sleep stages is N1 → N2 → N3, consistently found in the first half of the night. After several cycles of sleep stages N1 → N2 → N3, where N1 does not
always recur after N3, a further sleep phase can be associated with the
rapid eye movement (REM) stage (appeared after N1 → N2 → N3),
characterized by high-frequency, low-amplitude EEG activity. The REM
sleep stages are more often observed in the second half of the night.
Development
Neural oscillations may play a role in neural development. For example, retinal waves are thought to have properties that define early connectivity of circuits and synapses between cells in the retina.
Pathology
Handwriting of a person affected by Parkinson's disease showing rhythmic tremor activity in the strokesGeneralized 3 Hz spike and wave discharges reflecting seizure activity
Specific types of neural oscillations may also appear in pathological situations, such as Parkinson's disease or epilepsy.
These pathological oscillations often consist of an aberrant version of
a normal oscillation. For example, one of the best known types is the spike and wave
oscillation, which is typical of generalized or absence epileptic
seizures, and which resembles normal sleep spindle oscillations.
A tremor is an involuntary, somewhat rhythmic, muscle
contraction and relaxation involving to-and-fro movements of one or more
body parts. It is the most common of all involuntary movements and can
affect the hands, arms, eyes, face, head, vocal cords, trunk, and legs.
Most tremors occur in the hands. In some people, tremor is a symptom of
another neurological disorder. Many different forms of tremor have been
identified, such as essential tremor or Parkinsonian
tremor. It is argued that tremors are likely to be multifactorial in
origin, with contributions from neural oscillations in the central
nervous systems, but also from peripheral mechanisms such as reflex loop
resonances.
Epilepsy is a common chronic neurological disorder characterized by seizures. These seizures are transient signs and/or symptoms of abnormal, excessive or hypersynchronous neuronal activity in the brain.
In thalamocortical dysrhythmia (TCD), normal thalamocortical resonance
is disrupted. The thalamic loss of input allows the frequency of the
thalamo-cortical column to slow into the theta or delta band as
identified by MEG and EEG by machine learning. TCD can be treated with neurosurgical methods like thalamotomy.
Applications
Clinical endpoints
Neural oscillations are sensitive to several drugs influencing brain activity; accordingly, biomarkers based on neural oscillations are emerging as secondary endpoints
in clinical trials and in quantifying effects in pre-clinical studies.
These biomarkers are often named "EEG biomarkers" or "Neurophysiological
Biomarkers" and are quantified using quantitative electroencephalography (qEEG). EEG biomarkers can be extracted from the EEG using the open-source Neurophysiological Biomarker Toolbox.
Neural oscillation has been applied as a control signal in various brain–computer interfaces (BCIs). For example, a non-invasive BCI can be created by placing electrodes
on the scalp and then measuring the weak electric signals. Although
individual neuron activities cannot be recorded through non-invasive BCI
because the skull damps and blurs the electromagnetic signals,
oscillatory activity can still be reliably detected. The BCI was
introduced by Vidal in 1973 as challenge of using EEG signals to control objects outside human body.
After the BCI challenge, in 1988, alpha rhythm was used in a brain rhythm based BCI for control of a physical object, a robot. Alpha rhythm based BCI was the first BCI for control of a robot. In particular, some forms of BCI allow users to control a device by
measuring the amplitude of oscillatory activity in specific frequency
bands, including mu and beta rhythms.
