30
B. Pietras and A. Daffertshofer
interacting neural oscillators. By focusing on the corresponding phase dynamics, it
is possible to analyze synchronization properties of the network.
As revealed by a plethora of experimental studies relying on both invasive and noninvasive neuroimaging techniques, information processing in the brain is intrinsically
linked to synchronization phenomena of oscillatory dynamics [37, 55]. Non-invasive
EEG and MEG studies typically depict distributed cortical activity as of large-scale
brain networks. Although M/EEG recordings have high temporal resolution, they
reflect activity on rather coarse spatial scales given that signals to be perceivable
require synchronous neuronal currents of a large number of neurons, commonly of
the order of 10
4 to 10
5 cells. The resulting time series of the recordings are duly and
extensively analyzed for their extracted phase and amplitude dynamics. Emerging
synchronization patterns in the data are then assigned to particular brain functions
corresponding to the underlying hypothesis or the behavioral observations. Research
on the phase dynamics of cortical oscillatory activity is rather recent compared to
amplitude modulations in the M/EEG. However, there are several reports indicating
that the phase dynamics play a crucial role for information processing and intercortical communication [22, 64, 74, 75, 82, 84].
Phase synchronization also plays an integral part in defining functional connectivity structures of the brain. The technological advance of modern brain imaging
methods has led to elucidate the interplay of structural and functional brain connectivity. The structure of anatomical connections between brain areas is widely believed
to facilitate temporal synchronization of neural activity, and can lead to spatial patterns of functional connectivity [9, 15, 24, 48]. Yet, the extent to which structure
shapes function is still unclear [36, 44]. To unveil functional brain connectivity and
communication pathways [10, 33, 54], it is crucial to identify functional modules
consisting of remote but synchronized neuronal populations. This can be achieved
by analyzing the phase dynamics of the different brain areas.
While extensive data analysis may establish important synchronization properties
across the human brain, a comprehensive understanding of the underlying neural
mechanisms also requires theoretical models that can be validated and tested against
experimental data. Often, heuristic phase models are used as guidelines for inferring
neural network dynamics from data. But without a proper derivation of these heuristic
models, the results may become questionable. Phase reduction [32, 35, 45, 46, 51,
60, 67, 77] provides a powerful tool to derive phase models from biophysiologically
realistic models and to link parameters from the more complex with those from the
simpler model in order to identify the key factors for a particular behavioral paradigm.
Unfortunately, there is not “the” phase reduction, but one has to choose from a
variety of techniques – a recent review can be found in [67]. Even worse, different
phase reductions can lead to qualitatively different phase models, that is, reduced
phase models may predict different network behavior. For an accurate derivation of
a phase model, reduction techniques have to be tailored to the targeted macroscopic
observable and the parameter regime under study. Only then one can exploit the full
strengths of the reduced phase model. Finally, a word of caution is in order. Phase
reduction is strictly valid only for a number of necessary assumptions. Therefore,
B. Pietras and A. Daffertshofer
interacting neural oscillators. By focusing on the corresponding phase dynamics, it
is possible to analyze synchronization properties of the network.
As revealed by a plethora of experimental studies relying on both invasive and noninvasive neuroimaging techniques, information processing in the brain is intrinsically
linked to synchronization phenomena of oscillatory dynamics [37, 55]. Non-invasive
EEG and MEG studies typically depict distributed cortical activity as of large-scale
brain networks. Although M/EEG recordings have high temporal resolution, they
reflect activity on rather coarse spatial scales given that signals to be perceivable
require synchronous neuronal currents of a large number of neurons, commonly of
the order of 10
4 to 10
5 cells. The resulting time series of the recordings are duly and
extensively analyzed for their extracted phase and amplitude dynamics. Emerging
synchronization patterns in the data are then assigned to particular brain functions
corresponding to the underlying hypothesis or the behavioral observations. Research
on the phase dynamics of cortical oscillatory activity is rather recent compared to
amplitude modulations in the M/EEG. However, there are several reports indicating
that the phase dynamics play a crucial role for information processing and intercortical communication [22, 64, 74, 75, 82, 84].
Phase synchronization also plays an integral part in defining functional connectivity structures of the brain. The technological advance of modern brain imaging
methods has led to elucidate the interplay of structural and functional brain connectivity. The structure of anatomical connections between brain areas is widely believed
to facilitate temporal synchronization of neural activity, and can lead to spatial patterns of functional connectivity [9, 15, 24, 48]. Yet, the extent to which structure
shapes function is still unclear [36, 44]. To unveil functional brain connectivity and
communication pathways [10, 33, 54], it is crucial to identify functional modules
consisting of remote but synchronized neuronal populations. This can be achieved
by analyzing the phase dynamics of the different brain areas.
While extensive data analysis may establish important synchronization properties
across the human brain, a comprehensive understanding of the underlying neural
mechanisms also requires theoretical models that can be validated and tested against
experimental data. Often, heuristic phase models are used as guidelines for inferring
neural network dynamics from data. But without a proper derivation of these heuristic
models, the results may become questionable. Phase reduction [32, 35, 45, 46, 51,
60, 67, 77] provides a powerful tool to derive phase models from biophysiologically
realistic models and to link parameters from the more complex with those from the
simpler model in order to identify the key factors for a particular behavioral paradigm.
Unfortunately, there is not “the” phase reduction, but one has to choose from a
variety of techniques – a recent review can be found in [67]. Even worse, different
phase reductions can lead to qualitatively different phase models, that is, reduced
phase models may predict different network behavior. For an accurate derivation of
a phase model, reduction techniques have to be tailored to the targeted macroscopic
observable and the parameter regime under study. Only then one can exploit the full
strengths of the reduced phase model. Finally, a word of caution is in order. Phase
reduction is strictly valid only for a number of necessary assumptions. Therefore,