Jirsa, Viktor K.

Spatially continuous networks with heterogeneous connections are ubiquitous in
biological systems, in part icular neural systems. To understand the mutual effects
of locally homogeneous and globally heterogeneous connectivity, the st ability of the
steady state activity of a neural field as a fun ction of its connectivity is investigated.
The variation of the connectivity is operationalized through manipulation of a heterogeneous
two-point connection embedded into the otherwise homogeneous connectivity
matrix and by variation of connectivity strength and transmission speed. A detailed
discussion of the example of the real Ginzburg-Land au equation with an embedded
two-point heterogeneous connection in addition to the homogeneous coupling due to
the diffusion term is performed. The system is reduced to a set of delay differential
equations and the stability di agrams as a function of the time delay and the local and
global coupling strengths are computed. The major finding is that the stability of
the heterogeneously connected elements with a well-defined velocity defines a lower
bound for the stabil ity of the entire system . Diffusion and velocity dispersion always
result in increased stability. Various other local architectures represented by exponentially
decaying connectivity fun ctions are also discussed. The analysis shows that
developmental changes such as the myelination of the cortical large-scale fib er system generally result in the stabilization of steady state activity via oscillatory instabilities
independent of the local connectivity. Non-oscillatory (Turing) instabilities are shown
to be independent of any influences of time delay.

How do neuronal connectivity and the dynamics of distributed brain networks process
information during bimanual coordination? Contemporary brain theories of cognitive
function posit spatial, temporal and spatiotemporal network reorganization as mechanisms
for neural information processing. In this dissertation, rhythmic bimanual coordination is
studied as a window into neural information processing and subsequently an investigation of
underlying network reorganization processes is performed. Spatiotemporal reorganization
between effectors (limbs) is parameterized in a theoretical model via a continuously varying
cross-talk parameter that represents neural connectivity. Thereby, effector dynamics during
coordinated behavior is shown to be influenced by the cross-talk parameter and time delays
involved in signal processing. In particular, stability regimes of coordination patterns
as a function of cross-talk, movement frequency and the time delays are derived. On the
methodological front , spatiotemporal reorganization of neural masses are used to simulate
electroencephalographic data. A suitable choice of experimental control conditions is used
to derive a paradigmatic framework called Mode Level Cognitive Subtraction (MLCS) which
is demonstrated to facilitate the disambiguation between spatial and temporal components
of the reorganization processes to a quantifiable degree of certainty. In the experimental
section, MLCS is applied to electroencephalographic recordings during rhythmic bimanual
task conditions and unimanual control conditions. Finally, a classification of reorganization
processes is achieved for differing stability states of coordination: inphase (mirror) primarily
entails temporal reorganization of sensorimotor networks localized during unimanual
movement whereas spatiotemporal reorganization is involved during antiphase (parallel)
coordination.

Can a distributed anatomical and functional architecture serve as the basis for sufficiently complex perceptual phenomena? In addressing this question, the conceptual notion of dynamical system and its relation to other paradigms is considered including its definition. The principal goal is to develop a dynamical framework on which to ground the theoretical study of perception and other physical phenomena. As an entry point, the perceptual dynamics of auditory streaming are modeled using a neurally inspired dynamical model of auditory processing. Traditional approaches view streaming as a competition of streams, realized within a tonotopically organized neural network. In contrast, streaming can be viewed as a dynamic integration process involving locations (information convergence zones) other than the sensory specific neural subsystems. This process finds its realization in the synchronization of neural ensembles. Consequently, the model employs two interacting dynamical systems. The first system responds to incoming acoustic stimuli and transforms them into a spatiotemporal neural field dynamics. The second system is a classification system coupled to the neural field and evolves to a stationary state in the absence of input. The states of the classification system at any time t are identified with a single perceptual stream or multiple streams. Several results in human perception are modeled including temporal coherence and fission boundaries (van Noorden, 1975), and crossing of motions (Bregman, 1990). The model predicts phenomena such as the existence of two streams with the same pitch. So far, this has not been explained by the traditional stream competition models. A psychophysical study provides proof of existence of this phenomenon. Using set theoretical expressions on fMRI data, evidence was found showing that the percept of auditory streaming involves regions (convergence zones) other than just the primary auditory areas. This is a necessary condition for the existence of the network architecture proposed in the auditory streaming model. Networks specific and common to both amplitude and frequency streaming were identified. This lends support to models of perception conceived as interacting neural subnetworks acting as functional differentiation areas and information convergence zones for the classification of the perceptual world as suggested by the introductory question.

Perception and behavior are mediated by a widely distributed network of brain areas. Our main concern is, how do the components of the network interact in order to give us a variety of complex coordinated behavior? We first define the nodes of the network, termed functional units, as a strongly coupled ensemble of non-identical neurons and demonstrate that the dynamics of such an ensemble may be approximated by a low dimensional set of equations. The dynamics is studied in two different contexts, sensorimotor coordination and multisensory integration. First, we treat movement coupled to the environment as a driven functional unit. Our central hypothesis is that this coupling must be minimally parametric. We demonstrate the experimental validity of this hypothesis and propose a theoretical model that explains the results of our experiment. A second example of the dynamics of functional units is evident in the domain of multisensory integration. We employ a novel rhythmic multisensory paradigm designed to capture the temporal features of multisensory integration parametrically. The relevant parameters of our experiment are the inter-onset interval between pairs of rhythmically presented stimuli and the frequency of presentation. We partition the two dimensional parameter space using subjects perception of the stimulus sequence. The general features of the partitioning are modality independent suggesting that these features depend on the coupling between the unisensory subsystems. We develop a model with coupled functional units and suggest a candidate coupling scheme. In subsequent chapters we probe the neural correlates of multisensory integration using fMRI and EEG. The results of our fMRI experiment demonstrate that multisensory integration is mediated by a network consisting of primary sensory areas, inferior parietal lobule, prefrontal areas and the posterior midbrain. Different percepts lead to the recruitment of different areas and their disengagement for other percepts. In analyzing the EEG data, we first develop a mathematical framework that allows us to differentiate between sources activated for both unisensory and multisensory stimulation from those sources activated only for multisensory stimulation. Using this methodology we show that the influences of multisensory processing may be seen at an early (40--60 ms) stage of sensory processing.