Fuchs, Armin

The human brain consists of billions of neurons and these neurons pool together
in groups at different scales. On one hand, these neural entities tend to behave
as single units and on the other hand show collective macroscopic patterns of activity.
The neural units communicate with each other and process information over time.
This communication is through small electrical impulses which at the macroscopic
scale are measurable as brain waves. The electric field that is produced collectively
by macroscopic groups of neurons within the brain can be measured on the surface
of the skull via a brain imaging modality called Electroencephalography (EEG). The
brain as a neural system has variant connection topology, in which an area might not
only be connected to its adjacent neighbors homogeneously but also distant areas can
directly transfer brain activity [16]. Timing of these brain activity communications
between different neural units bring up overall emerging spatiotemporal patterns.
The dynamics of these patterns and formation of neural activities in cortical surface
is influenced by the presence of long-range connections between heterogeneous neural
units. Brain activity at large-scale is thought to be involved in the information processing
and the implementation of cognitive functions of the brain. This research
aims to determine how the spatiotemporal pattern formation phenomena in the brain
depend on its connection topology. This connection topology consists of homogeneous
connections in local cortical areas alongside the couplings between distant functional
units as heterogeneous connections. Homogeneous connectivity or synaptic weight
distribution representing the large-scale anatomy of cortex is assumed to depend on
the Euclidean distance between interacting neural units. Altering characteristics of
inhomogeneous pathways as control parameters guide the brain pattern formation
through phase transitions at critical points. In this research, linear stability analysis
is applied to a macroscopic neural field in a one-dimensional circular and a twodimensional
spherical model of the brain in order to find destabilization mechanism
and subsequently emerging patterns.

The neuronal ensembles in cortical tissue, which tend to behave as single functional units, communicate
with each other and process information over time. Neural activity fields, in form of spatially continuous
networks, can be used to model a variety of neurobiological phenomena. The connection topology of
brain tissue is such that a cortical area is not only connected to its neighbors locally, but also has global
projection to distant areas via a fiber system. Such projections not only serve to organize local dynamics
within cortical areas but timing of these processes at different sites will affect the overall emerging pattern
and contributes to the macroscopic organization and global dynamics of neural activity. The dynamics
of this neural field activity gives rise to pattern formation phenomena and self-organization. Our
macroscopic spatiotemporal pattern formation approach assumes the existence of an order parameter
dynamics and leads to phenomenological models to understand the collective phenomena even though
the microscopic dynamics is not completely known. We are investigating how the emerging patterns
depend on the space-time structure of the coupling between functional units i.e. long-range
heterogeneous pathways coupling strength (space) and the axonal time delay due to propagation with
finite speed between areas (time). We analyze the stability of the rest-state activity of a neural field as
manipulating heterogeneous two-point connections varies network connection topology in two geometries with periodic boundary conditions: a closed one-dimensional loop and a closed spherical 2-
D cortical surface.

Spatially continuous cortical surface is composed of neural ensembles interconnected with a
general connectivity embedded local homogeneous connectivity to nearest neighbors and global
heterogeneous projections to distant areas. Interconnection delay and long-range connectivity in
neural field models shows activity transfer via neural oscillation.
Destabilization mechanism of two-point connected dynamical neural system with spatially
variant connection topology as a control parameter leads to phase transition and macroscopic
coherent spatiotemporal pattern formation of neural activity. Authors are intended to generalize
this neural field dynamic to more realistic geometries such as a sphere.

The experiments in this dissertation were designed to produce a systematic characterization of the neuroelectric and neuromagnetic correlates of isochronous tone stimulation and simple rhythmic movements over a broad range of rates. The goal was to determine how the cortical representation of rhythm changes with rate, which would provide insight into known rate-dependent differences in perceptual and coordinative abilities. Fundamental transitions in the composition of the auditory and motor responses were hypothesized to occur within the parameter ranges studied here, including the attenuation of major response components and a shift from discrete transient activity at low rates to continuous steady-state activity at high rates. The auditory responses were studied in separate electroencephalography (EEG) and magnetoencephalography (MEG) experiments with stimulation rates ranging from 0.5 to 8Hz. In both studies, a transition from a transient to a continuous steady-state representation of the tone sequence occurred near 2Hz. In addition, an N1m component of the transient responses disappeared at rates near 8Hz, which may indicate the border beyond which tones are no longer distinct since the response is known to be an index of novelty in the auditory environment. Moreover, in a result important for understanding how evoked activity interacts with activity already present in the cortex, the phase of ongoing 40Hz rhythms is shown to affect the amplitude of the auditory evoked 40Hz response. Rhythmic finger movement was studied using a continuation paradigm in two EEG and MEG experiments at movement rates from 0.5 to 2.5Hz. Major findings included the disappearance of activity associated with movement planning and initiation at rates above 1Hz, suggesting a transition into a steady-state motor response in which there is less direct control of individual movements by the cortex. In addition, the neural correlates of synchronization and continuation were compared, with the results showing a similar cortical organization of metronome-paced and self-paced movements. The attenuation of major response components and the development of continuous steady-state activity within the present parameter ranges indicate rate-dependent changes in the cortical representation of simple rhythms, which are proposed here to relate to known rate-dependent behavioral differences in more complex coordinative environments.