Interplay of time-delayed feedback control and temporally correlated noise in excitable systems.

The interplay of time-delayed feedback and temporally correlated coloured noise in a single and two coupled excitable systems is studied in the framework of the FitzHugh-Nagumo (FHN) model. By using coloured noise instead of white noise, the noise correlation time is introduced as an additional time scale. We show that in a single FHN system the major time scale of oscillations is strongly influenced by the noise correlation time, which in turn affects the maxima of coherence with respect to the delay time. In two coupled FHN systems, coloured noise input to one subsystem influences coherence resonance and stochastic synchronization of both subsystems. Application of delayed feedback control to the coloured noise-driven subsystem is shown to change coherence and time scales of noise-induced oscillations in both systems, and to enhance or suppress stochastic synchronization under certain conditions.

Efficient control of transient wave forms to prevent spreading depolarizations.

In various neurological disorders spatio-temporal excitation patterns constitute examples of excitable behavior emerging from pathological pathways. During migraine, seizure, and stroke an initially localized pathological state can temporarily spread indicating a transition from non-excitable to excitable behavior. We investigate these transient wave forms in the generic FitzHugh-Nagumo (FHN) system of excitable media. Our goal is to define an efficient control minimizing the volume of invaded tissue. The general point of such a therapeutic optimization is how to apply control theory in the framework of structures in differential geometry by regarding parameter plane M of the FHN system as a differentiable manifold endowed with a metric. We suggest to equip M with a metric given by pharmacokinetic-pharmacodynamic models of drug receptor interaction.

A computational perspective on migraine aura.

The classical visual aura of migraine is characterized by a unilateral hallucination, composed of a zigzag fortification pattern followed by a trailing scotoma. This pattern usually starts in central vision, expands and spreads to the periphery, and then disappears. We review a number of historical attempts to explain the migraine aura in terms of brain events, then summarize recent theories of the pathophysiology of the aura. We describe an approach to the computational modeling of migraine aura, based on the principles of (a) cortical organization, and (b) active wave propagation in an excitable medium. We demonstrate correspondences between properties of the model system and aspects of the pathophysiology of the aura. The simulations produced by the model are in agreement with descriptions and drawings of visual aura from migraine patients. We outline several testable predictions stemming from the implementation of the model, and explain how model-based empirical research has the capacity to (a) improve recording of the phenomena of the visual aura, (b) improve understanding of the spatio-temporal dynamics of other types of aura, in particular somatosensory and dysphasic aurae, and (c) clarify the theoretical requirements for the initiation of aura in the brain.

Migraine aura dynamics after reverse retinotopic mapping of weak excitation waves in the primary visual cortex.

Akinematical model for excitable wave propagation is analyzed to describe the dynamics of a typical neurological symptom of migraine. The kinematical model equation is solved analytically for a linear dependency between front curvature and velocity. The resulting wave starts from an initial excitation and moves in the medium that represents the primary visual cortex. Due to very weak excitability the wave propagates only across a confined area and eventually disappears. This cortical excitation pattern is projected onto a visual hemifield by reverse retinotopic mapping. Weak excitability explains the confined appearance of aura symptoms in time and sensory space. The affected area in the visual field matches in growth and form the one reported by migraine sufferers. The results can be extended from visual to tactile and to other sensory symptoms. If the spatiotemporal pattern from our model can be matched in future investigations with those from introspectives, it would allow one to draw conclusions on topographic mapping of sensory input in human cortex.

Image processing techniques applied to excitation waves in the chicken retina.

Image processing techniques are described in detail that are used to gain information about the dynamics of wave propagation in excitable media. We focus on a phenomenon called spreading depression (SD) observed in the chicken retina, but the techniques described here concern a large variety of excitable systems. Despite the impressive progress both in SD research of the past 50 years and, during nearly the same period, in the theory of self-organization of wave patterns, there is still little mutual overlap. However, the increasing demands for understanding complex systems, like neuronal tissue, require such theoretical concepts. Arguments are given why the chicken retina is a nearly perfect experimental system for assessing and further developing these concepts.

Does the migraine aura reflect cortical organization?

Individuals suffering from classical migraine report an astonishing diversity of migraine auras. A frequently reported symptom is a visual hallucination known as fortification illusion (FI). Here we demonstrate that the typical zig-zag pattern of the FI can be reproduced using experimental data of orientation maps of the primary visual cortex (V1) assuming that a continuous excitation front propagates across V1. We put forward a model in which the cortical neurons within this excitation wave are activated sufficiently to contribute to conscious perception. It is shown that the discontinuous repetitive nature of the zig-zag pattern of the FI can reflect the specific layout of visual cortical orientation maps. Additionally, dynamic features of the FI are predicted based on our model.

Self-induced splitting of spiral-shaped spreading depression waves in chicken retina.

Spreading depression (SD) of electroencephalographic activity is a dynamic wave phenomenon in the central nervous system (CNS). The retina, especially the isolated chicken retina, is an excellent constituent of the CNS in which to observe the dynamic behavior of the SD wave fronts, because it changes its optical properties during a SD attack. The waves become visible as milky fronts on a black background. It is still controversial what the basic mechanistic steps of SD are, but certainly SD belongs to the self-organization phenomena occurring in neuronal tissue. In this work, spiral-shaped wave fronts are analyzed using digital video imaging techniques. We report how the inner end of the wave front, the spiral tip, breaks away repeatedly. This separation process is associated with a Z-shaped trajectory (extension approximately 1.2 mm) that is described by the tip over one spiral revolution (period 2.45+/-0.1 min). The Z-shaped trajectory does not remain fixed, but performs a complex motion across the retina with each period. This is the first time, to our knowledge, that established imaging methods have been applied to the study of the two-dimensional features of SD wave propagation and to obtaining quantitative data of their dynamics. Since these methods do not interfere with the tissue, it is possible to observe the intrinsic properties of the phenomenon without any external influence.