178
T. Stankovski
death or network clustering. Moreover, depending on the known form of the coupling function and the detected quantitative inputs, one can even predict transitions
to synchronization. Decomposition of a coupling function provides a description of
the functional contributions from each separate subsystem within the coupling relationship. Hence, by describing the mechanisms, coupling functions reveal more than
just investigating correlations and statistical effects.
11.2 Suitability of Coupling Functions for Neuroscience
The human brain is an intriguing organ, considered to be one of the most complex
systems in the universe. The adult human brain is estimated to contain 86 ± 8 billion
neurons, with a roughly equal number (85 ± 10 billion) of non-neuronal cells [3].
Out of these neurons, 16 billion (19%) are located in the cerebral cortex, and 69
billion (80%) are in the cerebellum. One of the main features of the brain is how
the neurons are connected, and when and how they are active in order to process
information and to produce various functionalities.
In neuroscience, the brain connectivity is classified in three different types of
connectivity. That is, the brain connectivity refers to a pattern of links (“structural, or
anatomical, connectivity”), of statistical dependencies (“functional connectivity”) or
of causal model interactions (“effective connectivity”) between distinct units within
a nervous system [14, 25, 60]. In terms of graph theory of the brain, the units correspond to nodes, while the connectivity links to edges [23]. The connectivity pattern
between the units is formed by structural links such as synapses or fiber pathways, or
it represents statistical or causal relationships measured as cross-correlations, coherence, information flow or the all-important coupling function. In this way, therefore,
the brain connectivity is crucial to understand how neurons and neural networks
process information.
The units can correspond to individual neurons, neuronal populations, or anatomically segregated brain regions. Taking aside the anatomically structural brain regions,
the other two—the neurons and their populations—are of particular interest from a
system neuroscience point of view. Moreover, for certain conditions these systems
may operate in the oscillatory regime for some time. When having an oscillatory
nature their dynamics and connectivity can be modeled as coupled oscillators (see
for example Fig. 11.1). In this constellation, a coupling function with its functional
form can be very suitable effective connectivity measure through which much can
be learned about the mechanisms and functionality of the brain.
As the two connectivity units, the neurons and the neuronal populations, are of
particular interest to the focus of coupling functions and oscillatory dynamics, bellow
they will be discussed separately in light of the utility of coupling functions.
T. Stankovski
death or network clustering. Moreover, depending on the known form of the coupling function and the detected quantitative inputs, one can even predict transitions
to synchronization. Decomposition of a coupling function provides a description of
the functional contributions from each separate subsystem within the coupling relationship. Hence, by describing the mechanisms, coupling functions reveal more than
just investigating correlations and statistical effects.
11.2 Suitability of Coupling Functions for Neuroscience
The human brain is an intriguing organ, considered to be one of the most complex
systems in the universe. The adult human brain is estimated to contain 86 ± 8 billion
neurons, with a roughly equal number (85 ± 10 billion) of non-neuronal cells [3].
Out of these neurons, 16 billion (19%) are located in the cerebral cortex, and 69
billion (80%) are in the cerebellum. One of the main features of the brain is how
the neurons are connected, and when and how they are active in order to process
information and to produce various functionalities.
In neuroscience, the brain connectivity is classified in three different types of
connectivity. That is, the brain connectivity refers to a pattern of links (“structural, or
anatomical, connectivity”), of statistical dependencies (“functional connectivity”) or
of causal model interactions (“effective connectivity”) between distinct units within
a nervous system [14, 25, 60]. In terms of graph theory of the brain, the units correspond to nodes, while the connectivity links to edges [23]. The connectivity pattern
between the units is formed by structural links such as synapses or fiber pathways, or
it represents statistical or causal relationships measured as cross-correlations, coherence, information flow or the all-important coupling function. In this way, therefore,
the brain connectivity is crucial to understand how neurons and neural networks
process information.
The units can correspond to individual neurons, neuronal populations, or anatomically segregated brain regions. Taking aside the anatomically structural brain regions,
the other two—the neurons and their populations—are of particular interest from a
system neuroscience point of view. Moreover, for certain conditions these systems
may operate in the oscillatory regime for some time. When having an oscillatory
nature their dynamics and connectivity can be modeled as coupled oscillators (see
for example Fig. 11.1). In this constellation, a coupling function with its functional
form can be very suitable effective connectivity measure through which much can
be learned about the mechanisms and functionality of the brain.
As the two connectivity units, the neurons and the neuronal populations, are of
particular interest to the focus of coupling functions and oscillatory dynamics, bellow
they will be discussed separately in light of the utility of coupling functions.