Chapter 11
Coupling Functions in Neuroscience
Tomislav Stankovski
Abstract Neural interactions play one of the central roles in the brain mediating various processes and functions. They are particularly important for the brain as a complex system that has many different functions from the same structural connectivity.
When studying such interactions coupling functions are very suitable, as inherently
they can reveal the underlaying functional mechanism. This chapter overviews some
recent and widely used aspects of coupling functions for studying neural interactions. Coupling functions are discussed in connection to two different levels of brain
interactions—that of neuron interactions and brainwave cross-frequency interactions.
Aspects relevant to this from both, theory and methods, are presented. Although the
discussion is based on neuroscience, there are strong implications from, and to, other
fields as well.
11.1 Introduction
Many systems in nature are found to interact, between each other or with the environment. The interaction can cause gradual or sudden changes in their qualitative
dynamics, leading to their grouping, self-organizing, clustering, mutual coordinated
synchronization, even to some extremes when their very existence is suppressed [20,
37, 55, 74, 75, 84]. An important class of such dynamical systems are oscillators,
which also often interact resulting in a quite intricate dynamics.
On the quest to untangle and better understand interactions, one could study
several complementary aspects [14]. One is structural connectivity, where physical
actual connection is studied. Often this is not directly observable, or it exist but it is not
active and dynamic all the time. Further on, one could study functional connectivity
i.e. if a functional dependence (like correlation, coherence or mutual information)
T. Stankovski (B)
Faculty of Medicine, Ss. Cyril and Methodius University in Skopje, Skopje, North Macedonia
e-mail: t.stankovski@ukim.edu.mk
Department of Physics, Lancaster University, Lancaster, UK
© Springer Nature Switzerland AG 2021
A. Stefanovska and P. V. E. McClintock (eds.), Physics of Biological
Oscillators, Understanding Complex Systems,
https://doi.org/10.1007/978-3-030-59805-1_11
175
Coupling Functions in Neuroscience
Tomislav Stankovski
Abstract Neural interactions play one of the central roles in the brain mediating various processes and functions. They are particularly important for the brain as a complex system that has many different functions from the same structural connectivity.
When studying such interactions coupling functions are very suitable, as inherently
they can reveal the underlaying functional mechanism. This chapter overviews some
recent and widely used aspects of coupling functions for studying neural interactions. Coupling functions are discussed in connection to two different levels of brain
interactions—that of neuron interactions and brainwave cross-frequency interactions.
Aspects relevant to this from both, theory and methods, are presented. Although the
discussion is based on neuroscience, there are strong implications from, and to, other
fields as well.
11.1 Introduction
Many systems in nature are found to interact, between each other or with the environment. The interaction can cause gradual or sudden changes in their qualitative
dynamics, leading to their grouping, self-organizing, clustering, mutual coordinated
synchronization, even to some extremes when their very existence is suppressed [20,
37, 55, 74, 75, 84]. An important class of such dynamical systems are oscillators,
which also often interact resulting in a quite intricate dynamics.
On the quest to untangle and better understand interactions, one could study
several complementary aspects [14]. One is structural connectivity, where physical
actual connection is studied. Often this is not directly observable, or it exist but it is not
active and dynamic all the time. Further on, one could study functional connectivity
i.e. if a functional dependence (like correlation, coherence or mutual information)
T. Stankovski (B)
Faculty of Medicine, Ss. Cyril and Methodius University in Skopje, Skopje, North Macedonia
e-mail: t.stankovski@ukim.edu.mk
Department of Physics, Lancaster University, Lancaster, UK
© Springer Nature Switzerland AG 2021
A. Stefanovska and P. V. E. McClintock (eds.), Physics of Biological
Oscillators, Understanding Complex Systems,
https://doi.org/10.1007/978-3-030-59805-1_11
175